MICHAEL MCGARRY
1009 Caxton Lane
Brunswick, OH 44212
(480) 206-0814
November 29, 2009
Search Committee
Department of Electrical and Computer Engineering
University of Texas, El Paso
El Paso, TX
Dear Search Committee,
I am writing in regard to the position of Assistant Professor of Electrical and Computer
Engineering (CompEng) advertised at Academic Keys. My current academic
appointment, as an Assistant Professor, is with the Electrical and Computer Engineering
department at the University of Akron in Ohio. My desire is to return to the Southwest and
I feel El Paso would be a perfect fit for me.
My research is in the field of computer networks. Specifically, I have made contributions
to two areas: 1) Ethernet Passive Optical Networks (EPONs), and 2) bandwidth
forecasting. My research in EPONs began during my graduate study at Arizona State
University while my research in bandwidth forecasting began last year at the University of
Akron. My most notable research accomplishments are: 1) the IEEE Communications
Society 2009 Best Tutorial Paper Award, and 2) several highly cited articles. My research
interests most closely align with Prof. Virgilio Gonzalez. I look forward to the possibility of
collaborating with him. Please see my CV and research statement for more details.
At the University of Akron, I am currently teaching a two-course track in computer
architecture. Starting in Spring 2010, I am introducing a course in computer networks. My
teaching evaluations were 3.8/4 for Fall 2008 and 3.86/4 for Spring 2009; both scores are
much higher than the average for the College of Engineering at the University of Akron.
My teaching competencies are within digital design, computer architecture, computer
networking, and software engineering. Please see my teaching statement for more
details.
I have several years of industrial experience in telecommunications. Most recently I was a
Senior Staff Scientist at ADTRAN (http://www.adtran.com), a networking equipment
company. At ADTRAN, I led an effort to conduct physical and simulation experiments to
characterize the performance of Ethernet access equipment. As a result of this
experience, I bring valuable industrial insight into the classroom that students appreciate.
I look forward to hearing from you soon. My list of references is contained in my
accompanying CV. Please feel free to contact them for information about my abilities.
Also, please feel free to call me at +1-480-206-0814 to obtain any further information
about me.
Sincerely,
Michael McGarry
Michael McGarry 1009 Caxton Lane
Brunswick, OH 44212
(480) 206-0814
Education
Arizona State University, Tempe, AZ. PhD in Electrical Engineering (August 2007)
Arizona State University, Tempe, AZ. MS in Electrical Engineering (December 2004)
Polytechnic University, Brooklyn, NY. BS in Computer Engineering (May 1997) Award 2009 IEEE Communications Society Best Tutorial Paper Award
Book Chapter M. P. McGarry, and M. Reisslein “Multi-channel Ethernet Passive Optical Networks” Broadband Access Networks: Technologies and Deployments, Springer, ISBN: 9780387921303 Journal Publications (Citation data obtained from Google Scholar)
J. R. Ferguson, M. Reisslein, and M. P. McGarry
“Online Excess Bandwidth Distribution for Ethernet Passive Optical Networks”, OSA Journal of
Optical Networking, vol. 8, no. 4, Apr. 2009 (JCR Impact Factor = 0.941)
M. P. McGarry, M. Reisslein, and M. Maier
“Ethernet Passive Optical Network Architectures and Dynamic Bandwidth Allocation Algorithms“,
IEEE Communications Surveys and Tutorials, Third Quarter 2008 (cited 7 times)
Won the IEEE Communications Society Best Tutorial Paper Award 2009
M. P. McGarry, M. Reisslein, C. Colbourn , M. Maier, F. Aurzada, and M. Scheutzow
“Just-in-Time Scheduling for Multichannel EPONs“, IEEE/OSA Journal of Lightwave
Technology, vol. 26, no. 10, May 2008 (JCR Impact Factor = 2.736, cited 7 times)
M. P. McGarry, M. Reisslein, M. Maier, and A. Keha
“Bandwidth Management for WDM EPONs”, OSA Journal of Optical Networking,
vol. 5, no. 9, Sept. 2006 (JCR Impact Factor = 0.941, cited 9 times)
M. P. McGarry, M. Maier, and M. Reisslein
“WDM Ethernet Passive Optical Networks“, IEEE Communications Magazine,
vol. 44, no. 2, Feb. 2006 (JCR Impact Factor = 2.799, cited 38 times)
M. P. McGarry, M. Maier, and M. Reisslein
“Ethernet PONs: A Survey of Dynamic Bandwidth Allocation (DBA) Algorithms“, IEEE
Communications Magazine, vol. 42, no. 8, Aug. 2004 (JCR Impact Factor = 2.799, cited 94 times)
M. McGarry, p. 2
Conference Publications
M. P. McGarry, and R. Haddad
“A New Approach to Video Bandwidth Prediction”, Proceedings of the
IEEE International Conference on Ultra Modern Telecommunications (ICUMT ’09), St. Petersburg,
Russia, October 12-14, 2009
J. R. Ferguson, M. P. McGarry, and M. Reisslein
“When Are Online and Offline Excess Bandwidth Distribution Useful in EPONs?”, Proceedings of the
ICST Third International Conference on Access Networks (AccessNets ’08), Las Vegas, NV, October
15-17, 2008
M. P. McGarry, M. Reisslein, C. Colbourn, and M. Maier
“Just-in-Time Online Scheduling for WDM EPONs“, Proceedings of the IEEE International
Conference on Communications (ICC ‘07), Glasgow, Scotland, June 24-27, 2007
M. P. McGarry, M. Reisslein and V. R. Syrotiuk
“Access Control in Heterogeneous Multichannel Wireless Networks“, Proceedings of the ICST First
International Conference on Integrated Internet Ad hoc and Sensor Networks (Intersense ‘06), Nice,
France, May 29-31, 2006 Academic Experience
University of Akron (August 2008-Present) Assistant Professor • Received a 3.8/4 teaching evaluation for Fall 2008 and 3.86/4 for Spring 2009. • Established a networking research laboratory. • Directing one doctoral dissertation and three masters theses. Arizona State University (August 2007-August 2008) Adjunct Professor • Research advisor to graduate students engaged in communication networking research. • Led an Ethernet Passive Optical Network bandwidth management research program. • Master’s Thesis Committee member for Amit Aneja (graduated 8/2007) and Jason Ferguson
(graduated 12/2008).
Arizona State University (January 2004-December 2006) Teaching Associate • Held lectures for digital design course (EEE120: Digital Design Fundamentals). • Helped professor develop course material for a graduate level course on Hardware Description
Languages (EEE 517: Hardware Description Languages). • Graded assignments for HDL course (EEE 517). • Responsible for assisting students with their digital design laboratory experiments (EEE 120). • Responsible for grading digital design laboratory experiments (EEE 120). • Responsible for providing digital design tutoring service to students (EEE 120).
Industrial Experience
ADTRAN (July 2007-July 2008) Sr. Staff Scientist • Analyzed network equipment performance via analytical and simulation methods. • Published internal documents to educate systems engineers on the topic of congestion management
techniques for packet switching devices. • Led an effort to analyze the performance of an Ethernet access multiplexer. • Analyzed several congestion management mechanisms via simulation experiments.
M. McGarry, p. 3 PMC-Sierra (April 1999-May 2003)
Software Design Engineer • Part of a team that developed an ATM Adaptation Layer 1 Segmentation and Reassembly (AAL1
SAR) device called the AAL1gator-32. • Part of a team that developed a SONET/SDH OC-48 channelizer device capable of transporting
ATM cells and variable length packets called the S/UNI-MACH48. • Part of a team that designed an Ethernet over SONET/SDH device called the ARROW-24xFE.
TimePlex/Cabletron (May 1998-April 1999) Software Engineer
• Part of a team that developed a Digital Subscriber Line Access Multiplexer (DSLAM).
Yurie Systems (Lucent Technologies) (August 1997-May 1998) Software Engineer
• Part of a team that developed an ATM access multiplexer that carried ATM cells and Frame Relay frames over satellite, PDH and SONET/SDH links.
Research Interests
• Optimization of medium access control (MAC) protocols
• Bandwidth forecasting
• Benchmarking fairness
• Quality of Service (QoS) guarantees
Teaching Competencies
• Communication Networks (including Network Performance Analysis)
• Digital Design (including Hardware Description Languages)
• Computer Architecture
• Software Engineering
Service
Technical Program Committee (TPC) member for:
IEEE International Conference on Communications (ICC) 2010
IEEE Globecom 2010
Peer-reviewer for:
IEEE/OSA Journal of Lightwave Technology
IEEE/ OSA Journal of Optical Communications and Networking
IEEE Transactions on Networking
U Akron ECE Dept. Graduate Policy Committee (GPC) member References
Dr. Martin Reisslein Assoc. Prof. (ASU) email: [email protected] phone: (480) 965-8593
Dr. Charles Colbourn Prof. (ASU) email: [email protected] phone: (480) 727-6631
Dr. Ahmet Keha Assistant Prof. (ASU) email: [email protected] phone: (480) 965-4055
Michael McGarry 1009 Caxton Lane
Brunswick, OH 44212
(480) 206-0814
Statement of Research Interests
Improving channel utilization for Ethernet Passive Optical Networks
Ethernet passive optical networks (EPONs) can potentially suffer very poor channel utilization. This poor
channel utilization results from the type of Dynamic Bandwidth Allocation (DBA) algorithm used as well
as the distance distribution of Optical Network Units (ONUs) from the Optical Line Terminal (OLT).
The goal of this research is to increase understanding of what leads to poor channel utilization and develop
techniques to improve or maximize it.
I have developed two technologies that maximize channel utilization through transmission grant
scheduling. The first is a transmission-grant scheduling framework called Online Just-in-Time (Online JIT)
scheduling and the second is a scheduling policy called Shortest Propagation Delay (SPD) first scheduling.
I have proven that SPD can minimize the granting cycle length, which in turn maximizes channel
utilization. Through a wide set of experiments I have displayed under which conditions SPD can provide
dramatic increases in channel utilization.
I have also made a recommendation to practitioners that EPONs be designed for high channel utilization by
increasing OLT to ONU distance diversity.
This research area is continuing with an exploration of ways to provide fair access to EPON bandwidth
capacity while maximizing channel utilization. I am currently seeking sponsorship for this area of research.
Bandwidth forecasting
A core competency for emerging intelligent network protocols is the ability to predict the future bandwidth
requirements of traffic flows. With this predictive ability, intelligent network protocols will be empowered
to more efficiently manage bandwidth resources throughout the network. This more efficient bandwidth
management will lead to significant improvements for all network performance measures.
Previous efforts toward bandwidth forecasting have followed traditional time series forecasting approaches
using a multitude of existing forecast models.
My strategy for solving the bandwidth forecasting problem differs significantly from others in that I am
pursuing unconventional approaches. These unconventional forecasting approaches exploit the unique
characteristics of packet-switched networks.
I have shared some of the details of this research area with Dr. Victor Frost, a program director at NSF, and
he has indicated that this is an area of interest to the NeTS program at the NSF. A grant proposal requesting
NSF sponsorship for this research area is under preparation.
Michael McGarry 1009 Caxton Lane
Brunswick, OH 44212
(480) 206-0814
Statement of Teaching Philosophy and Interests
Teaching Philosophy
Teaching is the act of knowledge dissemination. To effectively disseminate knowledge, one must be able to
clearly organize and segment knowledge. Therefore, the best teachers can clearly organize and segment
knowledge.
When preparing learning experiences for my students, I try my best to organize and segment the knowledge
they need to obtain. In further support of effective knowledge dissemination, I introduce concepts (i.e.,
segments of knowledge) one at a time and pause in the class to have students immediately utilize this new
knowledge by means of in-class problem solving exercises.
It is also important for a teacher to inspire students to be interested in the material being covered in the
classroom. To inspire students requires a little showmanship. I try my best to make my lectures highly
interactive with many opportunities for student participation as well as a number of demonstrations that
help to illustrate the concepts being introduced.
Finally, I consider homework a teaching tool, not an assessment tool. Therefore, homework is required and
will be graded but will only constitute a small portion of any course grade.
Teaching Interests
I have a very strong background in digital design, computer architecture, computer networking, and
software engineering.
At the University of Akron, I am currently teaching a two-course sequence in computer architecture.
“Computer Organization and Design: The Hardware/Software Interface” by Patterson and Hennessy is the
textbook used for the first course and “Computer Architecture: A Quantitative Approach” by Hennessy and
Patterson is the textbook used for the second course. In the first course, we begin by learning how to
convert software represented in a high level language such as C into MIPS assembly language instructions.
We learn how both instructions and data (e.g., characters, integers, and floating point numbers) are
represented as sequences of bits that are stored in memory. We continue with an exploration of data path
and control path designs for a CPU. Finally, we end the course with a discussion of computer performance
analysis techniques and hierarchical memory design. In the second course, we learn techniques to exploit
instruction level parallelism in CPU design as well as some advanced memory system optimizations.
I could teach courses in digital design from basic introductory courses through a graduate level course that
studies hardware description languages in detail. I would use “Digital Design: Principles and Practices” by
Wakerly and “Contemporary Logic Design” by Katz as the course textbooks for a two semester
undergraduate course sequence on digital design. I would use “The Verilog Hardware Description
Language” by Thomas and Moore as a course textbook for a graduate course on digital design.
In computer networking, I could teach a senior undergraduate level course in communication networks that
would cover the OSI layering model and discuss in detail some example protocols from each layer of the
OSI model. A top down approach would be the most effective. I would use “Computer Networking: A Top-
Down Approach” by Kurose and Ross as the course textbook. I could teach two graduate level courses on
advanced communication networks. In the first course, the performance analysis of computer networks
using probability theory, queueing theory and simulation experiment analysis would be covered. In the
second course, the design of communication network protocols through the use of optimization theory
would be covered. I would use “Data Networks” by Bertsekas and Gallager, “Introduction to Operations
Research” by Hillier and Lieberman, and “Discrete Event System Simulation” by Carlson, Banks, Nelson,
and Nicol for these two graduate level courses. In addition, I could teach a plethora of special topics
courses in communication networks (e.g., Multimedia Networking, Packet Switching Architectures).
1204 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Just-in-Time Scheduling for Multichannel EPONsMichael P. McGarry, Member, IEEE, Martin Reisslein, Senior Member, IEEE, Charles J. Colbourn,
Martin Maier, Member, IEEE, Frank Aurzada, and Michael Scheutzow
Abstract—We investigate optical network unit (ONU) grantscheduling techniques for multichannel Ethernet passive opticalnetworks (EPONs), such as wavelength division multiplexed(WDM) EPONs. We take a scheduling theoretic approach tosolving the grant scheduling problem. We introduce a two-layerstructure of the scheduling problem and investigate techniquesto be used at both layers. We present an extensive ONU grantscheduling simulation study that provides: 1) insight into thenature of the ONU grant scheduling problem and 2) indicationof which scheduling techniques are best for certain conditions.We find that the choice of scheduling framework has typicallythe largest impact on average queueing delay and achievablechannel utilization. An offline scheduling framework is not workconserving and consequently wastes channel resources whilewaiting for all ONU REPORT messages before making accessdecisions. An online scheduling framework, although work con-serving, does not provide the best performance since schedulingdecisions are made with the information contained in a singleONU REPORT. We propose a novel online just-in-time (JIT)scheduling framework that is work conserving while increasingscheduling control by allowing the channel availability to drive thescheduling process. In online JIT, multiple ONU REPORTs can beconsidered together when making scheduling decisions, resultingin lower average queueing delay under certain conditions and amore effective service differentiation of ONUs.
Index Terms—Dynamic bandwidth allocation (DBA), Ethernetpassive optical network (EPON), media access control (MAC),scheduling, space division multiplexing (SDM), wavelength divi-sion multiplexing (WDM).
I. INTRODUCTION
CURRENT Ethernet passive optical network (EPON)standards dictate a single channel used for downstream
transmission and a single channel used for upstream trans-mission. The need for more passive optical network (PON)bandwidth capacity will drive up the utilization of multipleupstream and downstream channels. In an effort to providemore bandwidth capacity we can increase the bit-rate as well
Manuscript received June 26, 2007; revised December 14, 2007. This workwas supported in part by the DFG Research Center MATHEON “Mathematics forkey technologies” in Berlin. A preliminary overview of this work has appearedin Proceedings of IEEE International Conference on Communications (ICC),Glasgow, U.K., pp. 2174–2179, June 2007.
M. P. McGarry and M. Reisslein are with the Department of ElectricalEngineering, Arizona State University, Tempe, AZ 85287-5706 USA (e-mail:michael.mcgarry; [email protected]).
C. J. Colbourn is with the Department of Computer Science and Engi-neering, Arizona State University, Tempe, AZ 85287-8809 USA (e-mail:[email protected]).
M. Maier is with the Institut National de la Recherche Scientifique, Montreal,QC H5A 1K6, Canada (e-mail: [email protected]).
F. Aurzada and M. Scheutzow are with the Institute of Mathematics, Tech-nical University Berlin, 10623 Berlin, Germany (e-mail: [email protected]; [email protected]).
Digital Object Identifier 10.1109/JLT.2008.919366
as utilize multiple upstream and downstream channels. Thetransition from increased bit-rate to utilizing multiple channelsfor an increase in bandwidth capacity will be a function of cost.At some point the transition to multiple transmission channelsto increase bandwidth capacity will occur.
Besides an increase in bandwidth capacity there are addi-tional benefits provided by utilizing multiple upstream anddownstream channels. With multiple channels, several opticalnetwork units (ONUs) can transmit concurrently to the opticalline terminal (OLT) thereby lowering the average queueingdelay [1] experienced by the Ethernet frames queued at theONUs. Multiple channels provide a method for dynamic band-width allocation (DBA) algorithms to reserve certain channelsfor certain traffic classes [2]. The discovery and registrationprocess can be kept on a single channel which would allowtransmissions on the other channels to be uninterrupted. Fi-nally, selected channels can be used to provide all-optical OLTbypassing services [3].
Wavelength division multiplexed (WDM)-based multiplechannel PONs were first proposed in the mid-1990s [4]. Re-cently, WDM PON architectures have regained interest as theenabling technologies have become mature [5]–[10]. Spacedivision multiplexing (SDM) is another approach to channelseparation, whereby each fiber strand carries a unique channelor channels. SDM can be combined with WDM for an evenlarger number of channels and service separation.
Dynamic bandwidth allocation (DBA) in multichannelEPONs can be viewed as consisting of grant sizing and grantscheduling. Grant sizing techniques have been examined in[11]–[13]. In this paper, we suppose that the grants are sizedaccording to some existing technique and focus on the grantscheduling portion of the DBA problem for multichannelEPONs. We frame our investigation in the context of sched-uling theory [14]. We model the grant scheduling problem usingstandard scheduling theory notation. We discover solution tech-niques for this model that result in a set of possible schedulingpolicies for producing a schedule given a set of ONU grants.More specifically, we partition the scheduling problem into:1) a scheduling framework and 2) a scheduling policy operatingwithin the adopted scheduling framework. Online scheduling,where the optical line terminal (OLT) schedules grants as soonas a REPORT message is received from an ONU, and offlinescheduling where the OLT waits for REPORT messages fromall ONUs before scheduling grants are the extreme ends of acontinuum of possible scheduling frameworks. The choice ofscheduling framework, as we will explain, depends on the levelof control that is required by the scheduler. A hybrid betweenthe two extremes provides generally the best performance.
This paper is organized as follows. In Section II we review re-lated work on DBA for multichannel EPONs. In Section III wemodel the multichannel EPON ONU grant scheduling problem
0733-8724/$25.00 © 2008 IEEE
MCGARRY et al.: JUST-IN-TIME SCHEDULING FOR MULTICHANNEL EPONS 1205
using standard scheduling theory notation. We then use thismodel to find good scheduling policies and discuss schedulingframeworks. In Section IV we discuss our online just-in-time(JIT) scheduling framework and how some scheduling policiescan be adapted to be used within this framework. In Section Vwe present the results of our simulation study that analyzesthe differences between the different scheduling techniques. Weconclude in Section VI.
II. RELATED WORK
We now discuss the related work on dynamic bandwidth al-location (DBA) for multichannel or WDM EPONs.
A. WDM Variants of IPACT
In [15], Kwong et al. propose a multiple upstream wave-length version of IPACT [12], called WDM IPACT-ST, wherebyST refers to single polling table. This algorithm keeps trackof the wavelength available time of all upstream wavelengths.Upon receiving a REPORT from an ONU, the OLT schedulesthe ONU’s next transmission grant on the next available wave-length. This algorithm assumes each ONU supports all wave-lengths. This scheme is similar to the WDM IPACT we proposedin [16]. In [16] we supported differing ONU WDM architecturesby selecting the next available supported wavelength for sched-uling whereas WDM IPACT-ST does not allow for this flexi-bility. In [17], Clarke et al. propose SIPACT, another WDM ex-tension of IPACT, that is similar to the WDM IPACT in [16].
B. Dynamic Bandwidth Allocation Schemes in Hybrid
TDM/WDM Passive Optical Networks
Dhaini et al. [18] investigate WDM-PONs and dynamicwavelength and bandwidth allocation (DWBA) algorithmsfor two fundamental WDM-PON architectures they label A1and A2. In A1, the ONUs are placed into wavelength sets andcontain a fixed transmitter at the selected wavelength. In A2,the ONUs have tunable transmitters capable of transmissionon several wavelengths. In both A1 and A2, the OLT has anarray of fixed receivers for upstream reception. Dhaini et al.
proceed to investigate the problem of dynamically allocatingbandwidth in both time and wavelength. Their first approach,Static Wavelength Dynamic Time (SWDT), relies on archi-tecture A1. SWDT statically assigns a wavelength channel toall grants from each ONU, this wavelength is the wavelengthsupported by the fixed transmitter at that ONU. Time is thenmanaged using an existing single channel DBA.
Dhaini et al. then propose three variants of a dynamic wave-length and time bandwidth allocation. The first (DWBA-1)schedules ONUs after all REPORT messages have been re-ceived for a cycle. Further, DWBA-1 incorporates “fair” distri-bution of excess bandwidth. The second (DWBA-2) schedulesunderloaded ONUs upon receipt of their REPORT message andoverloaded ONUs after receiving all ONU REPORT messages.When limiting grant sizes and distributing excess from ONUsnot fully utilizing their guaranteed minimums, all REPORTsmust be received in a cycle in order to know the excess fromthat cycle. Therefore, it makes sense to have overloaded ONUswait until this information is available in order to properly sizetheir grant. Finally, the third (DWBA-3) schedules all ONUsupon receipt of their REPORT message. Since the OLT needs
to grant excess bandwidth, the authors create two grants in thisapproach. As soon as the ONU REPORT is received, one grantsthe guaranteed minimum; and after all REPORTs have beenreceived, another grants the excess assigned to that ONU. Thereare two problems with that approach: 1) each overloaded ONUreceives two grants which decreases efficiency due to moreguard times, and 2) the split between the two grants will mostlikely not occur on frame boundaries causing one frame to beunnecessarily delayed till the next cycle. Therefore, DWBA-2is more efficient.
C. Quality of Service in TDM/WDM Ethernet Passive
Optical Networks
In [2], Dhaini et al. propose two approaches for providingQoS on a TDM/WDM EPON: 1) QoS-DBA-1, which uses theOLT scheduler (DWBA-2) of [19] with a Modified DeficientWeighted Round Robin (M-DWRR) intra-ONU scheduler, and2) QoS-DBA-2 and QoS-DBA-3, which segregate constant bit-rate expedited forwarding (EF) traffic [20] from assured for-warding (AF) [21] and/or best effort (BE) traffic by wavelength.Some wavelengths are allocated for EF traffic, and some are al-located for AF and BE traffic. In QoS-DBA-2, this segregationis strict where as in QoS-DBA-3 the unused capacity on the EFwavelengths can be utilized by AF and BE traffic.
D. Summary
The various WDM IPACT variants [15]–[17] do not considerthe problem of grant scheduling. They simply apply a first-fittime and wavelength assignment. In [18], Dhaini et al. explorethe problem of grant scheduling but only in the context of excessbandwidth distribution. In this paper we examine grant sched-uling in a more general context and propose a new schedulingframework that is more efficient than either online or offlinescheduling.
III. GRANT SCHEDULING
The multichannel EPON scheduling problem can be formu-lated using the scheduling theory notation defined in [14]. The-oretical analysis of all the scheduling models discussed in thissection can be found in [14]. Scheduling theory is concernedwith scheduling a set of jobs with specific processing times tobe executed on a set of machines as efficiently as possible withrespect to an optimization criterion. We can view each ONUas representing a job, its grant size as defining its processingtime, and the channels used for transmission on the EPON asrepresenting the machines. In scheduling notation, a schedulingproblem is defined by a triple , where describes themachine environment (e.g., single machine, parallel machines,etc.), describes the processing characteristics and constraints,and describes the objective to be minimized.
For the formulation of the multichannel EPON grant sched-uling problem in the scheduling theory notation, we letdenote identical parallel machines (channels) that define ourmachine environment. Our only processing characteristic orconstraint is which refers to machine (channel) eligibilityconstraints. Specifically, is the set of machines (channels)that job (ONU) can be executed (transmitted) on. Letdenote the time at which the transmission for ONU is com-plete. With this notation we define the scheduling problem with
1206 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Fig. 1. Illustration of constituent delays of a scheduling cycle.
the objective to minimize the unweighted sum of the comple-tion times as . The processing constraint isrequired because each ONU has, in general, its own subsetof supported channels. If all ONUs supported transmissionon all wavelengths, we could remove the machine eligibilityconstraint to obtain .
Our performance objective in designing a scheduler for aWDM EPON is to lower the queueing delays experienced byframes in transit across the EPON and to increase the achiev-able resource (i.e., channel) utilization. To see how these perfor-mance objectives relate to the objectives from scheduling theorywe first explore in detail the component delays in a schedulingcycle. We start by defining cycle length, which we also referto as the GTG or GATE-to-GATE delay, as the time betweenback-to-back grants to an ONU. The component delays of ascheduling cycle are visualized in Fig. 1. GTR is the GATE-to-REPORT delay (since we append the REPORT at the end of thetransmission window, GTR is equal to the transmission time ofthe grant), and RTG is the REPORT-to-GATE delay, that in-cludes the propagation delay from ONU to OLT. Using GTRand RTG we express the cycle length as GTG GTR RTG.
The STG is the Schedule-to-GATE delay which is the timebetween the OLT scheduling an ONU’s next grant to the time thegrant starts being received at the OLT. The STG includes a prop-agation delay from OLT to ONU, a GATE message transmissiontime and propagation delay from ONU to OLT. The STG alongwith the grant time represents the completion time of an ONU’stransmission from the point in time it is scheduled, i.e.,STG GTR. Since, the grant time (or size) is not determinedby the scheduler, the scheduler can only work to minimize thevariable portion of completion time, i.e., the STG. Minimizing
minimizes STG. The RTS is the REPORT-to-Schedule delayand is the delay from the OLT receiving a REPORT from anONU to when the scheduling of the ONUs’ REPORT is com-pleted by the OLT. (The RTS includes the computation time forthe schedule, which we neglect in our simulations in Section V.)Thus, REPORT-to-GATE RTG delay is composed of the RTSand STG delays, i.e., RTG RTS STG.
We introduce a layered approach to scheduling (see Fig. 2).We refer to the first layer as the scheduling framework, and thesecond layer as the scheduling policy. The scheduling frame-work is a logistical framework that determines when the OLTmakes scheduling decisions, whereas the scheduling policy is amethod for the OLT to produce the schedule. The OLT can pro-duce a schedule with partial information about the ONU trans-
Fig. 2. Layered approach to scheduling.
missions to be scheduled or after waiting to receive all of the in-formation about the ONUs transmissions to be scheduled. Oncethe OLT has a set of ONU transmissions to schedule, the OLTuses a scheduling policy to create the schedule. The schedulingframework impacts the RTS delay by determining at what timeafter a REPORT message is received an ONU’s next grant isscheduled. On the other hand, the scheduling policy impacts theSTG delay by determining when an ONU grant is actually trans-mitted on a channel.
In Section III-A, we discuss scheduling frameworks in moredetail, and in Section III-B we discuss scheduling policies formultichannel EPONs.
A. Scheduling Frameworks
As mentioned above, the scheduling framework determineswhen the OLT produces a schedule. If the OLT produces aschedule as soon as any ONU REPORT is received withoutwaiting for REPORT messages from other ONUs, this isreferred to as an online scheduling framework. However, ifthe OLT were to wait for the REPORT messages from all theONUs to be received before making scheduling decisions,this is referred to as an offline scheduling framework. Thescheduling framework can be viewed as a continuum betweenthe extremes of online and offline scheduling as illustrated inFig. 3. On the online scheduling end of the continuum, theOLT only considers a single ONU REPORT in a schedulingdecision. On the offline scheduling end of the continuum, theOLT considers all ONU REPORTs in a scheduling decision.Any scheduling framework that lies between online and offlineis some form of an online scheduling framework because notall of the ONU REPORTs have been received. We will howeverreserve the term online scheduling framework to indicate thecase where the OLT considers only one ONU REPORT at atime. In Section III-A1 we will explore offline scheduling in
MCGARRY et al.: JUST-IN-TIME SCHEDULING FOR MULTICHANNEL EPONS 1207
Fig. 3. Scheduling framework continuum (� : number of ONUs).
the context of multichannel EPONs, and in Section III-A2 wewill explore online scheduling in the context of multichannelEPONs. We will see that both schemes have very differentchannel utilization characteristics.
1) Offline Scheduling: In an offline scheduling framework,scheduling decisions are made with full knowledge of all thejobs to be scheduled including their processing times for aparticular scheduling cycle. Specifically for a multichannelEPON, an offline scheduling framework schedules ONUgrants for transmission when the OLT has received the currentMPCP REPORT messages from all ONUs. This allows theOLT to take the current bandwidth requirements of all ONUsinto consideration in the grant sizing and scheduling, i.e., thescheduling pool contains all ONUs. The scheduling policy isexecuted after the OLT receives the end of the last ONU’s gatedtransmission window. The RTS delay for the last ONU will benegligible; however the RTS may not be negligible for the otherONUs. This RTS delay introduces further queueing delays inthe ONUs because it introduces additional delay in the cyclelength GTG for an ONU. Waiting for all ONU REPORTmessages to be received results in wasted channel capacity. Thewasted capacity increases as the number of channels increases.
2) Online Scheduling: In an online scheduling framework,an ONU is scheduled for upstream transmission as soon asthe OLT receives the REPORT message from the ONU, i.e.,the scheduling pool contains one ONU. This is the schedulingframework that is at the far end of the online side of the sched-uling framework continuum depicted in Fig. 3. This approachavoids wasted channel capacity by not keeping any channelsidle while there is an ONU REPORT message for the OLT toact on.
B. Scheduling Policies
We now use our scheduling model developed in the begin-ning of Section III to find the best scheduling policies for a mul-tichannel EPON that supports an evolutionary migration fromsingle-channel EPONs to multichannel EPONs. The OLT usesthese scheduling policies once a set of ONU grants to be sched-uled has been determined by the scheduling framework.
1) Next Available Supported Channel: A simple schedulingpolicy for a multichannel EPON considers one ONU at a timeand schedules the upstream transmission for that ONU on thewavelength channel that is available the earliest among the chan-nels supported by that ONU. We refer to this scheduling policyas the next available supported channel (NASC) policy. NASCis our variation on an algorithm proposed by Graham [22] nearly
40 years ago called the List algorithm for identical parallel ma-chines. This algorithm schedules jobs one by one and assignsthem to the next available machine.
2) Parallel Machine Models and Solutions: We refer to [23]for a detailed exploration of scheduling policies for our parallelmachine environment scheduling model. Least flexible job first(LFJ) with shortest processing time (SPT) first dispatching rulewas shown to be a good heuristic for this model.
3) Unrelated Machine Models and Solutions: Another pos-sible approach to modeling the multichannel EPON grant sched-uling problem is to loosen our original parallel machine environ-ment model by recognizing that can be viewed asa special case of , where refers to an unrelated ma-chine environment where each machine executes a job at a dif-ferent speed. For machines that are in , we set the executiontime to the processing time or grant length; for machines not in
, we set the execution time to infinity. In [23] we pointed outthat a weighted bipartite matching formulation can optimallysolve .
4) Summary: Using our parallel machine model, the resultsfrom scheduling theory indicate a few dispatching rules that canprovide good scheduling policies. A dispatching rule (see [14,Secs. 14.1 and 14.2]) is a defined method of ordering jobs fordispatch in first fit fashion on available machines. Some exam-ples of general dispatching rules are: Least Flexible Job (LFJ)first, Shortest Processing Time (SPT) first, and Largest Pro-cessing Time (LPT) first. The best scheduling policies for ourmultichannel EPON grant scheduling model are the dispatchingrules discussed in Section III-B2; LFJ for machine eligibility re-strictions, SPT for minimizing the sum of the completion times,and LPT for minimizing the maximum completion time. Otherpotential dispatching rules for the multichannel EPON grantscheduling problem are: Largest Number of Frames (LNF) first,Earliest Arriving Frame (EAF) first, and Earliest Average Ar-rival (EAA) first. LNF favors ONUs with more queued Eth-ernet frames, EAF favors ONUs that have the earliest arrivinghead-of-line (HOL) Ethernet frame, and EAA favors ONUs thathave the earliest average Ethernet frame arrival time.
Dispatching rules can be used alone or grouped togetherto form composite dispatching rules. For multichannel EPONgrant scheduling, LFJ can be combined with some of the otherdispatching rules to create a composite dispatching rule thatcan provide better performance. The second dispatching rule isused to break ties from the first dispatching rule. Rather thanusing the second dispatching rule for tie breaking in the firstdispatching rule, a weight can be set for each dispatching rulein the composite.
1208 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Fig. 4. Online JIT on the Scheduling Framework Continuum (� : Number of ONUs,� : Number of Channels).
The weighted bipartite matching (WBM) formulation that isproven optimal for minimizing the sum of the completion timesfor the unrelated machine environment scheduling model oper-ates differently from the dispatching rules. Unlike the dispatchrules, the WBM scheduling policy results in a direct assign-ment of each ONU grant to a specific channel and time (po-sition). There is no need to apply NASC for the scheduling. Theoutput from the WBM scheduling policy fully characterizes theschedule. This is in contrast to the dispatching rules that specifythe order in which the ONU grants are scheduled for first fitchannel assignment according to NASC.
IV. ONLINE JIT SCHEDULING
We now present a new scheduling framework that is ahybrid between offline and online scheduling discussed inSections III-A1 and A2 respectively. We call this new sched-uling framework online just-in-time (JIT) scheduling. Thename indicates that scheduling is performed in just in timefashion. In our online JIT scheduling framework, ONUs areadded to a scheduling pool as their MPCP REPORT messagesare received by the OLT. When a wavelength becomes avail-able, the ONUs in the pool are scheduled together accordingto the selected scheduling policy across all wavelengths. TheONUs that are scheduled so that their transmissions would startshortly (i.e., close to the one-way propagation delay from OLTto the ONU into the future) after the time they are scheduled areclassified as “imminent”; the current schedule for these ONUsis considered firm. The OLT transmits GATE messages to theseONUs to inform them of their granted transmission window.The remaining ONUs are classified as “tentative” and canremain in the scheduling pool for the next scheduling round.Alternatively, all ONUs (i.e., both imminent and tentative) canalways be firmly scheduled. We refer to the case where allONUs are firmly scheduled as online JIT and the case wherethe tentative ONUs participate in future scheduling rounds asonline JIT Tentative.
The online JIT scheduling framework gives the OLT moreopportunity to make better scheduling decisions than standardonline scheduling. ONUs are scheduled at the moment rightbefore they potentially begin transmitting. To facilitate this onan EPON, we need to ensure the GATE message is transmittedby the OLT at least the one-way OLT-to-ONU propagationdelay before we intend the ONU to begin transmission. In otherwords, the GATE message must be transmitted soon enoughto accommodate the OLT-ONU-OLT round trip time (RTT)before we want to begin receiving the ONU’s transmission atthe OLT. Using the largest RTT in the EPON for this timingof the GATE message transmissions ensures that any ONU
receives the GATE message in time. Since we desire the ONUto transmit as soon as the next wavelength becomes free, weneed to schedule the ONUs in the pool at least an RTT beforethe next wavelength free time. Fig. 4 illustrates where theonline JIT scheduling framework lies on the scheduling frame-work continuum. The online JIT scheduling framework can liesomewhere from the online scheduling framework up to a pointjust short of the offline scheduling framework. Let us considerthe bounds of where the online JIT scheduling framework canlie with respect to the number of considered ONU REPORTs.
To obtain the lower bound, consider an EPON with very lowtraffic load, i.e., very few ONUs have traffic and those ONUswith traffic have small queue occupancies. In such a low trafficscenario, there are always free upstream channels. When theOLT receives an ONU REPORT, the OLT makes immediately ascheduling decision based on this one REPORT, i.e., the lowerbound is 1 ONU REPORT.
To obtain the upper bound, consider a high traffic load sce-nario where all ONUs report high queue occupancies re-sulting in grants that are larger than one RTT. In this high trafficscenario, the scheduling pool at the OLT contains all ONUs, ex-cept those that are currently transmitting (and will send theirREPORTs at the end of their transmissions). That is, withONUs in an EPON with upstream channels, there areONUs in the scheduling pool, which is the upper bound onthe number of REPORTs considered for online JIT scheduling.Thus, the online JIT scheduling framework can get very closeto emulating an offline scheduling framework, especially with asmall number of channels.
If the OLT has , ONUs inthe scheduling pool, then wavelengths are idle for one RTTto permit for the REPORTs to reach the OLT and the cor-responding grants to propagate to the ONUs. Hence, with theoffline scheduling framework, for which , the up-stream channels are not utilized for one RTT to allow for all
REPORTs to be received by the OLT and the GRANTs topropagate to the ONUs. Thus, the offline scheduling frameworkutilizes the channels less efficiently than the online and onlineJIT scheduling frameworks. On the other hand, both the on-line and online JIT scheduling frameworks are fully work-con-serving, i.e., they do not let any upstream channel go unusedwhile there is data to transmit. Importantly, note that the onlineJIT scheduling framework does not introduce any inefficienciescompared to the online scheduling framework, as further con-firmed in Section IV-C. The only added complexity with theonline JIT scheduling framework is keeping track of and sched-uling the REPORTs in the scheduling pool, which can rangefrom one to REPORTs, whereas only one REPORT isconsidered at a time in the online scheduling framework.
MCGARRY et al.: JUST-IN-TIME SCHEDULING FOR MULTICHANNEL EPONS 1209
When using the online JIT Tentative scheduling framework,an ONU may participate in several scheduling rounds as “tenta-tive” before it becomes firmly scheduled. It is possible that cer-tain ONUs that are unfavorable to a particular scheduling policycan continuously be preempted by those that are more favorable.To prevent these ONUs from being starved of medium access,an aging mechanism is incorporated to keep these “less favor-able” ONUs (or jobs) from being starved by the scheduler. Astraightforward method to implement starvation prevention isto set a threshold at which an ONU is immediately scheduledon the next available wavelength regardless of the schedulingpolicy. This ensures that no ONU waits indefinitely for mediumaccess. This threshold can be based on the number of partici-pated scheduling rounds to adapt to changing cycle times.
A. Dispatching Rules for Online JIT
Dispatching rules or composite dispatching rules can be
used without any modification within the online JIT scheduling
framework. The dispatching rules result in an ordering of the
ONUs in the scheduling pool. This ordering is used in conjunc-
tion with NASC to schedule an ONU grant at a specific time
on a specific channel.
B. Weighted Bipartite Matching Adapted for Online JIT
The standard weighted bipartite matching (WBM) schedulingformulation [14] for minimizing the sum of the completiontimes needs to be modified to support an online schedulingframework. In any online scheduling framework, not all ma-chines are immediately available for scheduling (i.e., theymay still be processing jobs). We introduce this in the WBMformulation by setting an additive cost to a matching that isdifferent for each machine. This additive cost is related to whenthe wavelength becomes available. We refer to this cost as ,the availability cost of wavelength for ONU . Let bethe RTT delay for ONU be the time the REPORTmessage from ONU is received at the OLT, be the timewhen wavelength is free, and be the time when ONU
is ready to transmit. Given ,then . is the Euclidean distancebetween wavelength free time and ONU ready to transmit time.A weight can be used to control how much this availability costaffects the solution, we will use to represent this weight.
The following is the Integer Program that represents theWBM where is the scheduling position, is the grantprocessing time for ONU on channel (either ONU granttime for supported channel , or for nonsupported channel), is the availability cost for channel , are binary
variables representing whether or not position on machine(channel) is selected for job (ONU) , is the number ofmachines (channels), and is the number of jobs (ONUs):
(1)
subject to
(2)
(3)
The first constraint forces an ONU to be assigned to only onescheduling position. The second constraint forces each sched-uling position to be assigned to no more than one ONU. If asingle ONU supplies traffic from multiple classes, each trafficclass is treated as a separate job in the WBM formulation.
C. Stability Analysis
In this section we formally analyze the stability character-istics of the online JIT scheduling framework. Stability in thecontext of EPONs has so far been primarily examined for grantsizing techniques employing prediction of traffic newly arrivingbetween sending a REPORT and the start of the correspondingupstream transmission, e.g., see [24]–[27]. These analyses con-sider the prediction control loop and examine controllability andstability of the grant sizing for rapid fluctuations in the trafficloads; whereby the grant size prediction is considered stablewhen ONUs receive a fair bandwidth share. The scheduling ofthe grants and the resulting utilization of the upstream trans-mission channels are not explicitly considered in the existingstudies. Our stability analysis is fundamentally different fromthe existing analyses in that we examine whether the generatedlong-term traffic load can be accommodated on the upstreamtransmission channels. We consider grant sizing without predic-tion in our analysis. We remark that the online JIT schedulingframework could be used in conjunction with grant sizing tech-niques employing prediction; the analysis of such a combinedsystem is left for future work.
Recall that we consider a multichannel EPON with ONUsand channels. Let if ONU supports channel , and
if ONU does not support channel , forand . Let denote the long-run average packet(Ethernet frame) generation rate at ONU (in packets/second),and let denote the average packet length (in bits). Further, let
denote the transmission bit-rate of an upstream channel (inbits per second). We define the relative loads for
.We begin the analysis by considering the upstream transmis-
sions on a given upstream channel. We define the upstream
transmission of an ONU to consist of the upstream transmissionof Ethernet frames and the MPCP REPORT. Consider an arbi-trary upstream transmission of a given ONU. Let be a randomvariable denoting the transmission time of the payload data (Eth-ernet frames) in the upstream transmission. Let be a randomvariable denoting the “proportional” overhead in the upstreamtransmission in terms of transmission time (i.e., number of over-head bits divided by channel transmission bit-rate ). The pro-portional overhead accounts for the preamble of eight bytesfor each Ethernet frame in the upstream transmission and theinterpacket gap of 12 bytes between successive Ethernet framesin the upstream transmission. Note that is given by a con-stant times the payload transmission time, i.e.,(whereby , with denoting the fixed overhead perEthernet frame and denoting the mean of the considered Eth-ernet frame lengths). Let be a constant denoting the “fixed”overhead in the upstream transmission, i.e., the MPCP Report,plus the guard time between successive upstream transmissions.
1210 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
The utilization of the upstream channel during the consideredupstream transmission is then
(1)
To examine the maximum achievable utilization, we initiallyconsider two ONUs that transmit upstream on a given upstreamchannel. (We incorporate the impact due to the possibly re-stricted set of wavelengths supported by an ONU shortly.) Withgated service and sufficiently high loads, the upstream trans-mission of an ONU is typically sufficiently long to mask theround-trip propagation REPORT-to-GATE delay for the otherONU. (For shorter upstream transmissions, we can considermore ONUs to mask the round-trip propagation delay.) Then,for any combination of scheduling framework and schedulingpolicy that ensures that there is exactly a guard time betweensuccessive upstream transmissions, the utilization on the con-sidered upstream channel is equal to the given in (1). Themaximum achievable utilization arises when the transmissiongrants become very large such that and is givenby
(2)
We now turn to the constraints imposed by the transmissioncapabilities of the individual ONUs onthe upstream channels . We immediately ob-serve that an ONU with a single transmitter can only transmiton one channel at a time. Hence, the ONU must not generatemore traffic load than it can transmit, i.e., we have to requirethat , or equivalently that , for all
.We claim that if the EPON upstream transmission system
is stable, then there are long-run average relative transmissionrates such that
for all (3)
and
for all (4)
This can be seen as follows. Note that the relative transmissionrates are obtained by normalizing long-run average transmis-sion rates (in bits/second) of ONU on channel , by thechannel bit-rate , i.e., . For any ONU , the rel-ative transmission rates over all channels that ONU supportsadd up to ; thus, (3) follows. On the other hand, in the longrun, one cannot send more over channel than permitted by themaximum utilization of the channel transmission bit-rate,which is (4).
If (3) and (4) hold, then one can construct a static periodictransmission strategy, similar to a time division multiplexing(TDM) transmission, that is indeed stable. To see this, note that(3) and (4) imply that we know how much traffic ONU can sendon channel in the long run without causing stability problems.
Namely, this is exactly . So, we allocatefraction of time of channel to ONU . This can be done in aperiodic fashion resembling a TDM strategy. Then (3) ensures
that this strategy accommodates all traffic load generated at eachONU and (4) guarantees that one does not send more on anychannel in the long run than permitted by the maximum achiev-able utilization of the channels’s transmission bit-rate, i.e., wesee that this periodic transmission strategy is stable.
Any grant sizing mechanism that bases grants on actualqueue occupancies (to avoid allocation of excess bandwidththat would then go unused), in combination with any workconserving scheduling framework and policy that ensures theminimum spacing between upstream transmissions (so thatthere is no unnecessary unused time on the upstream channels)achieves the same stability limit as the periodic transmissionstrategy. In particular, gated service grant sizing in conjunctionwith both the online and online JIT scheduling frameworkswith any scheduling policy spacing upstream transmissions ona channel by no more than the guard time are stable if and onlyif (3) and (4) hold. We remark that when all ONUs support allchannels, i.e., when for all , then (3) and (4) hold
if and only if .
We briefly remark regarding a formal analysis of the delay
performance of online JIT that online JIT scheduling always
makes scheduling decisions no earlier than online scheduling.
Hence, online JIT can make better scheduling decisions. How-
ever, it is relatively easy to find examples where online JIT and
online scheduling behave in exactly the same way. In general, it
can therefore only be proven that online JIT never makes worse
scheduling decisions than online scheduling, which is straight-
forward to verify. (Note that the converse is not true, because
online scheduling makes decisions with less information and
hence it cannot mimic online JIT.)
V. SIMULATION EXPERIMENTS
In this section we study different scheduling techniques that
can be used for grant scheduling in multichannel EPONs by
means of simulations. We developed a multichannel EPON sim-
ulation engine using the CSIM [28] simulation library. Each
wavelength supports Gbps transmission bit-rate, and the
reported load corresponds to the payload data rate .
Following common packet size models, 60% of the packets have
64 bytes, 4% have 300 bytes, 11% have 580 bytes, and 25% have
1518 bytes. The simulations were conducted using self-similar
traffic sources [29] with a Hurst parameter of 0.75. The RTTs
were uniformly distributed over s s , which corre-
sponds to distances of 2–15 km.
In our simulations we use the gated grant sizing technique
which grants each ONU its full bandwidth request. The gated
sizing technique has been demonstrated to achieve small delays
in EPONs [30]. By fixing the grant sizing technique, we are
comparing the scheduling aspects of the multichannel EPON.
A. Offline Scheduling Versus Online Scheduling
We refer the reader to our simulation study presented in [23]
for a comparison of offline versus online scheduling. Our re-
sults showed that an online scheduling framework significantly
outperformed the offline scheduling framework regardless of
scheduling policy with respect to average queueing delay. The
better scheduling decisions made by the scheduling policies
MCGARRY et al.: JUST-IN-TIME SCHEDULING FOR MULTICHANNEL EPONS 1211
used with the offline scheduling framework were not enough
to overcome the RTS delay that dominated the cycle length.
Therefore, the average queueing delay values were significantly
higher with the offline scheduling framework. We provide fur-
ther results for the comparison of offline and online scheduling
in Section V-C.
B. Online Scheduling Versus Online JIT Scheduling
We want to study the impact of the type of scheduler and the
ONU multichannel diversity. To vary the ONU multichannel di-
versity, we simulated an EPON with ONUs and created
three sets of ONU WDM configurations: WDM Mix 1, WDM
Mix 2, and WDM Mix 3. WDM Mix 1 contains 16 ONUs that
support all wavelengths, 8 that support half of the wavelengths,
and 8 that support the other half. WDM Mix 1 provides ONU
multichannel diversity without any single channel ONUs. By
not having any single channel ONUs, the scheduling process
has increased flexibility in wavelength assignment. WDM Mix
2 contains 16 ONUs that support all wavelengths, 6 that support
half of the wavelengths, 6 that support the other half of the wave-
lengths, and 4 that only support one wavelength. WDM Mix 2
provides ONU multichannel diversity with some single channel
ONUs. Finally, WDM Mix 3 provides less multichannel diver-
sity with 8 ONUs that support all wavelengths and 24 ONUs
that support only one wavelength. Of the three ONU WDM con-
figurations, WDM Mix 3 is the most restrictive with respect to
wavelength assignment.
In the experiments for WDM Mix 1 and WDM Mix 2, all
ONUs generate the same traffic load. For the WDM Mix 3 ex-
periments, each of the eight ONUs supporting all channels gen-
erates nine times the traffic load of each of the 24 ONUs sup-
porting one channel; this load distribution gives a theoretical
stability limit of 4 Gbps for the WDM Mix 3 scenario.
We varied the scheduler for each of the ONU WDM config-
urations. Two dispatching rule-based schedulers from our par-
allel machine scheduling model (see Section III-B2): LFJ-SPT
and LFJ-LNF, and two weighted bipartite matching (WBM)-
based schedulers with weight from our unrelated ma-
chine model (see Section III-B3): WBM and WBM-LNF. These
schedulers are all compared to an online scheduler: NASC that
provides the baseline for performance.
Figs. 5, 7, and 8 show the average queueing delay plotted
against load for WDM Mix 1 with total wavelengths,
WDM Mix 2 with total wavelengths, and WDM Mix 3
with total wavelengths, respectively.
For WDM Mix 1, plots a) and b) in Fig. 5 show up to a 10%
decrease in average queueing delay at low and moderate loads
provided by the WBM-based schedulers. The plotted confidence
intervals indicate that the difference appears to be statistically
significant. The confidence intervals were obtained through the
CSIM batch means method with batches sized to minimize cor-
relations, and individual batch means representing the average
queueing delays of the Ethernet frames occurring in a given
batch. The lower average queueing delay achieved by the WBM-
based schedulers is due to more efficient wavelength scheduling
decisions made by the scheduler. The WBM-based schedulers
Fig. 5. Average queueing delay for WDM Mix 1, eight wavelength EPON.The WBM-based schedulers can provide lower queueing delays at lower loads.However, schedulers that incorporate the LNF dispatching rule provide lowerqueueing delays at higher loads. (a) Low load. (b) High load. (c) Very high load.
evaluate the costs of all possible wavelength assignments and
select the lowest cost matching, i.e., the wavelength for which
the availability time most closely matches the time when
the ONU is ready . From plots of the wavelength uti-
lization of each of the eight wavelengths for each of the sched-
uling schemes, which are not included due to space constraints,
we observed that all compared scheduling strategies achieved
equally good load balancing. The WBM-based schedulers are
simply making more efficient wavelength assignment decisions
that are resulting in shorter cycle lengths. Fig. 6 shows the cycle
length for the WBM-based schedulers compared to NASC.
At higher loads a different pattern emerges, we observe from
plot b) in Fig. 5 that at high loads the schedulers that use LNF
1212 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Fig. 6. Average cycle length for WDM Mix 1, eight wavelength EPON. Thetwo WBM-based schedulers, whose curves fall on top of each other in the figure,provide lower cycle lengths due to better wavelength assignment.
(i.e., LFJ-LNF or WBM-LNF) provide a small improvement
over the other schedulers. Plot c) in the same figure confirms this
by zooming in on the higher loads. Again, the plotted confidence
intervals appear to indicate a statistically significant difference.
This indicates that at high loads the wavelength assignment has
limited impact on average queueing delay. However, preferring
ONUs with a larger number of queued frames can lower the av-
erage queueing delay. This is largely due to a frame sampling
effect: ONUs with more frames have a larger impact on the av-
erage queueing delay measure than ONUs with fewer frames.
For WDM Mix 2, with less wavelength assignment flexibility
due to the single wavelength ONUs, we observe from Fig. 7
a smaller decrease in average queueing delay provided by the
WBM-based schedulers. The plots a) and b) in Fig. 7 indicate
about a 3% decrease in average queueing delay. The plotted
confidence intervals indicate that the difference is not statisti-
cally significant. At high loads, shown in plot b) and zoomed
in plot c), we see the same pattern as seen for WDM Mix 1: at
high loads the wavelength assignment has no impact on average
queueing delay, but time ordering does have an impact due to a
frame sampling effect.
For WDM Mix 3, with its limited ONU multichannel diver-
sity and restrictive wavelength assignment capabilities, there is
no measurable difference with respect to average queueing de-
lays between the schedulers as observed from Fig. 8.
In summary, with increased ONU multichannel diversity and
wavelength assignment flexibility, the WBM-based schedulers
are able to provide lower average queueing delays. At high
loads, the schedulers that favor ONUs with the largest number
of frames provide lower average queueing delays, because of
a frame sampling effect. Therefore, the online JIT scheduling
framework has some utility in lowering the average queueing
delay. However, its utility is much larger than this, as will be
discovered in the next section.
C. Differentiated ONU Treatment Using Online JIT Scheduling
In this set of simulation experiments we explore how the on-
line JIT scheduling framework can be used to provide differen-
tiated treatment to ONUs without using an offline scheduling
Fig. 7. Average queueing delay for WDM Mix 2, eight wavelength EPON.With less wavelength assignment flexibility as compared to WDM Mix 1, thereduction in average queueing delays achieved by the WBM-based schedulersis less pronounced. (a) Low Load. (b) High load. (c) Very high load.
mechanism. Avoiding use of an offline scheduling framework
improves channel utilization and consequently lowers queueing
delays. We have simulated the same EPON system described
above for WDM Mix 1, WDM Mix 2, and WDM Mix 3. We
now use a scheduler that always schedules two preferred ONUs,
which support all wavelengths, ahead of any of the other 30
ONUs. The other 30 ONUs are scheduled with the LFJ-LNF
dispatching rule.
Figs. 9–11 show plots of the average queueing delay experi-
enced by all ONUs (labeled “Avg ONU”) and the 2 preferred
ONUs (labeled “Pref ONU”) for the online JIT scheduling
framework, the online JIT Tentative scheduling framework
MCGARRY et al.: JUST-IN-TIME SCHEDULING FOR MULTICHANNEL EPONS 1213
Fig. 8. Average queueing delay for WDM Mix 3, four wavelength EPON. Withvery limited wavelength assignment flexibility, the WBM-based schedulers donot provide a reduction in average queueing delay. (a) Low Load. (b) High load.
with a starvation threshold set to 32 scheduling rounds, and the
Offline scheduling framework.
Examining first the performance for the online JIT scheduling
frameworks, we observe that they are able to provide differential
treatment without using an offline scheduling framework. At
high loads, the difference in average queueing delay becomes
quite significant. For example, Fig. 10 shows that at a load of
6.8 Gbps, the preferred ONUs experience an average queueing
delay of approximately 500 s as opposed to approx. 1.6 ms
for all ONUs. Comparing the figures for the different WDM
Mixes, we see that as we move from WDM Mix 1 to WDM
Mix 2, i.e., as we increase the number of single channel ONUs
from zero to four, the average queueing delay increases but the
queueing delay experienced by the two preferred ONUs stays
the same. In Fig. 11 we see that when we increase the single
channel ONUs to 75% of all ONUs and limit the EPON to four
wavelengths, the average queueing delay increases significantly.
However, the queueing delay experienced by the two preferred
ONUs is significantly lower than the delay for the other ONUs.
At a load of 3.8 Gbps, the delay for the preferred ONUs is nearly
eight times smaller than the average queueing delay.
Comparing the online JIT scheduling framework with the on-
line JIT Tentative scheduling framework, we observe a slight
reduction in the average delay for the preferred ONUs with the
online JIT Tentative scheduling framework as compared to the
online JIT scheduling framework.
Fig. 9. Queueing delay for average ONUs versus the two ONUs given preferen-tial scheduling (WDM Mix 1). Average ONUs are scheduled using the LFJ-LNFdispatching rule. The online JIT scheduling framework is able to provide signif-icant differential treatment through scheduling. The oOffline scheduling frame-work does not provide differential treatment through scheduling. (a) Online JITscheduling framework. (b) Offline scheduling framework.
We summarize the main observations from comparing the
online JIT scheduling framework with the offline scheduling
framework as follows. First, we observe that the achievable
maximum channel utilization (stability limit) is lower for of-
fline scheduling as compared to online scheduling. Fig. 11, for
instance, indicates that for offline scheduling of WDM Mix 3
the average ONU delays shoot up to very large values for loads
around 3 Gbps, whereas we observe a similar jump in ONU
delays for online scheduling at a load of 3.75 Gbps. The lower
stability limit with offline scheduling is due to the nonwork
conserving nature of offline scheduling, which forces the OLT
to wait for all REPORT messages before making scheduling
decisions. This waiting imposes idle times on the upstream
channels which are avoided by the work conserving online
scheduling frameworks, including online JIT and online JIT
Tentative.
Second, we observe that the queueing delays are much larger
for offline scheduling than online JIT scheduling. For a 6 Gbps
load for WDM Mix 1, for instance, we observe from Fig. 9
average queueing delays around 20 ms for offline scheduling
compared to less than 0.4 ms with online JIT. The larger delays
with offline scheduling are mainly due to the increased RTS de-
lays that increase the cycle lengths and subsequently increase
the queueing delays.
1214 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Fig. 10. Queueing delay for all ONUs versus the two ONUs given preferentialscheduling (WDM Mix 2). Although the delay for the average ONU increasesbecause of the single channel ONUs, the delay for the two preferred ONUsremains the same as with WDM Mix 1. (a) Online JIT scheduling framework.(b) Offline scheduling framework.
Finally, turning to the differentiated ONU treatment, we
observe from Figs. 9–11 that in contrast to online JIT, offline
scheduling provides very little differentiation between the av-
erage ONUs and the preferred ONUs. This is mainly due to the
fact that offline scheduling forces a relatively large RTS delay
upon all ONUs, as illustrated by the delay components provided
for WDM Mix 1 in Table I. In fact, for moderate to high loads,
the RTS delay is the largest of the three delay components,
which add up to the cycle length GTG RTS STG GTR.
In addition, the grant times, i.e., GTR delays, are relatively
large compared to the STG delays, leaving little flexibility
for differentiation due to reordering of the sequence of the
upstream transmissions. In contrast, we observe from Table I
that the RTS delays are relatively small for online JIT. At
the same time, the STG delays are relatively large, compared
to both RTS and GTR delays, providing significantly more
flexibility in influencing the relative treatment of the ONUs
through scheduling of the upstream transmissions.
In summary, the online JIT scheduling framework has the po-
tential of reducing the average queueing delay experienced by
all ONUs. However, its strongest utility appears to be for sched-
ulers that provide differential treatment to ONUs. The OLT can
benefit from an increased level of scheduling control without
waiting for all ONU REPORT messages. Practical implemen-
tations may fine tune exactly when schedules are produced. It
Fig. 11. Queueing delay for all ONUs versus the two ONUs given preferen-tial scheduling (WDM Mix 3). The online JIT scheduling framework is able toprovide very significant differential treatment. (a) Online JIT scheduling frame-work. (b) Offline scheduling framework.
TABLE IAVERAGE REPORT-TO-SCHEDULE (RTS) DELAY, SCHEDULE-TO-GATE (STG)
DELAY, AND GRANT TIME (GTR) IN MICROSECONDS FOR WDM MIX 1WITH ONLINE JIT AND OFFLINE SCHEDULING FRAMEWORKS
may be advantageous to purposefully leave a channel idle while
waiting for more ONU REPORT messages to arrive at the OLT
in an effort to gain a higher level of control.
VI. CONCLUSION
We have proposed: 1) a two-layer structure of scheduling
in multichannel EPONs consisting of a scheduling frame-
work layer and a scheduling policy layer, as well as 2) online
just-in-time (JIT) scheduling, a novel work conserving sched-
uling framework. In the online JIT scheduling framework,
channel availability, rather than ONU REPORT messages,
drives the scheduling process. When a channel becomes avail-
able, the OLT makes an access decision with the information
MCGARRY et al.: JUST-IN-TIME SCHEDULING FOR MULTICHANNEL EPONS 1215
(i.e., REPORT messages) that has accumulated since the last
channel became available. This gives the online JIT scheduling
framework the ability to make better scheduling decisions
as compared to an online scheduling framework that only
considers one ONU REPORT message. Further, the online JIT
scheduling framework is still work conserving and therefore
is more efficient than the nonwork conserving offline sched-
uling framework where the OLT waits for all ONU REPORT
messages to make access decisions.
In our simulation study, we found that with increased ONU
multichannel diversity and wavelength assignment flexibility,
the WBM-based scheduling policies used in the online JIT
scheduling framework are able to provide lower average
queueing delays. We also found that at high loads, the sched-
ulers that favor ONUs with the largest number of frames
provide lower average queueing delays, because of a frame
sampling effect. Therefore, the online JIT scheduling frame-
work has some utility in lowering the average queueing delay.
However, it has stronger utility for use with schedulers that may
provide differential treatment to ONUs. The OLT can benefit
from an increased level of scheduling control, i.e., considering
a larger scheduling pool, to differentiate ONU service. The
only trade-off is the slightly increased complexity of online
JIT, which requires the OLT to simultaneously consider and
schedule up to close to as many ONU REPORTS as there are
ONUs on the EPON; whereas, only one ONU REPORT at a
time is considered and scheduled with online scheduling.
Future research could study how grant sizing techniques are
affected by this new online JIT scheduling framework, and the
impact of schedule generation time on performance.
REFERENCES
[1] M. Marsan and D. Roffinella, “Multichannel local area network proto-cols,” IEEE J. Sel. Areas Commun., vol. 1, no. 5, pp. 885–897, Nov.1983.
[2] A. Dhaini, C. Assi, and A. Shami, “Quality of Service in TDM/WDMethernet passive optical networks (EPONs),” in Proc. IEEE ISCC, Jun.2006, pp. 616–621.
[3] M. Maier, M. Herzog, and M. Reisslein, “STARGATE: The next evo-lutionary step toward unleashing the potential of WDM EPONs,” IEEE
Commun. Mag., vol. 45, no. 5, pp. 50–56, May 2007.[4] N. Frigo, P. Iannone, P. Magill, T. Darcie, M. Downs, B. Desai, U.
Koren, T. Koch, C. Dragone, H. Presby, and G. Bodeep, “A wave-length-division multiplexed passive optical network with cost-sharedcomponents,” IEEE Photon. Technol. Lett., vol. 6, no. 11, pp.1365–1367, Nov. 1994.
[5] F. An, K. Kim, D. Gutierrez, S. Yam, E. Hu, K. Shrikhande, and L.Kazovsky, “SUCCESS: A next-generation hybrid WDM/TDM opticalaccess network architecture,” J. Lightw. Technol., vol. 22, no. 11, pp.2557–2569, Nov. 2004.
[6] Y. Hsueh, W. Shaw, L. Kazovsky, A. Agata, and S. Yamamoto, “Suc-cess PON demonstrator: Experimental exploration of next-generationoptical access networks,” IEEE Commun. Mag., vol. 43, no. 8, pp.S26–S33, Aug. 2005.
[7] F. An, D. Gutierrez, K. Kim, J. Lee, and L. Kazovsky, “SUCCESS-HPON: A next generation optical access architecture for smooth mi-gration from TDM-PON to WDM-PON,” IEEE Commun. Mag., vol.43, no. 11, pp. S40–S47, Nov. 2005.
[8] Y. Hsueh, M. Rogge, S. Yamamoto, and L. Kazovsky, “A highly flex-ible and efficient passive optical network employing dynamic wave-length allocation,” J. Lightw. Technol., vol. 23, no. 1, pp. 277–286, Jan.2005.
[9] C. Bock, J. Prat, and S. Walker, “Hybrid WDM/TDM PON usingthe AWG FSR and featuring centralized ligth generation and dy-namic bandwidth allocation,” J. Lightw. Technol., vol. 23, no. 12, pp.3981–3988, Dec. 2005.
[10] M. McGarry, M. Maier, and M. Reisslein, “WDM ethernet passive op-tical networks,” IEEE Commun. Mag., vol. 44, no. 2, pp. S18–S25, Feb.2006.
[11] C. Assi, Y. Ye, S. Dixit, and M. Ali, “Dynamic bandwidth allocation forquality-of-service over ethernet PONs,” IEEE J. Sel. Areas Commun.,vol. 21, no. 9, pp. 1467–1477, Nov. 2003.
[12] G. Kramer, B. Mukherjee, and G. Pesavento, “IPACT: A dynamic pro-tocol for an ethernet PON (EPON),” IEEE Commun. Mag., vol. 40, no.2, pp. 74–80, Feb. 2002.
[13] G. Kramer, B. Mukherjee, S. Dixt, Y. Y., and R. Hirth, “Supportingdifferentiated classes of service in Ethernet passive optical networks,”J. Opt. Networking, vol. 1, no. 8, pp. 280–298, Aug. 2002.
[14] M. Pinedo, Scheduling: Theory, Algorithms, and Systems, 2nd ed.Englewood Cliffs, NJ: Prentice-Hall, 2002.
[15] K. Kwong, D. Harle, and I. Andonovic, “Dynamic bandwidth alloca-tion algorithm for differentiated services over WDM EPONs,” in Proc.
9th Int. Conf. Communications Systems, Sep. 2004, pp. 116–120.[16] M. McGarry, “An evolutionary wavelength division multiplexing up-
grade for Ethernet passive optical networks,” Master’s thesis, ArizonaState Univ., Tempe, 2004.
[17] F. Clarke, S. Sarkar, and B. Mukherjee, “Simultaneous and interleavedpolling: An upstream protocol for WDM-PON,” in Proc. Optical Fiber
Communication Conf., Mar. 2006, p. 3.[18] A. Dhaini, C. Assi, M. Maier, and A. Shami, “Dynamic wavelength
and bandwidth allocation in hybrid TDM/WDM EPON networks,” J.
Lightw. Technol., vol. 25, no. 1, pp. 277–286, Jan. 2007.[19] A. Dhaini, C. Assi, and A. Shami, “Dynamic bandwidth allocation
schemes in hybrid TDM/WDM passive optical networks,” in Proc.
IEEE CCNC, Jan. 2006, vol. 1, pp. 30–34.[20] V. Jacobson, K. Nichols, and K. Poduri, An expedited forwarding PHB
Jun. 1999 [Online]. Available: http://www.ietf.org/rfc/rfc2598.txt,RFC 2598 (Proposed Standard) obsoleted by RFC 3246.
[21] J. Heinanen, F. Baker, W. Weiss, and J. Wroclawski, Assured for-warding PHB group June 1999 [Online]. Available: http://www.ietf.org/rfc/rfc2597.txt, RFC 2597 (Proposed Standard) updated by RFC3260.
[22] R. Graham, “Bounds for certain multiprocessing anomalies,” Bell Syst.
Tech. J. , vol. 45, pp. 1563–1581, 1966.[23] M. McGarry, M. Reisslein, M. Maier, and A. Keha, “Bandwidth man-
agement for WDM EPONs,” OSA J. Opt. Networking, vol. 5, no. 9, pp.637–654, Sep. 2006.
[24] H.-J. Byun, J.-M. Nho, and J.-T. Lim, “Dynamic bandwidth allocationalgorithm in ethernet passive optical networks,” Electron. Lett., vol. 39,no. 13, pp. 1001–1002, Jun. 2003.
[25] J. M. Joo and Y. J. Ban, “Dynamic bandwidth allocation algorithm fornext generation access network,” in Proc. OFC, Mar. 2006.
[26] S. Yin, Y. Luo, N. Ansari, and T. Wang, “Bandwidth allocation overEPONs: A controllability perspective,” in Proc. IEEE Globecom, Nov.2006.
[27] S. Yin, Y. Luo, N. Ansari, and T. Wang, “Stability of predictor-baseddynamic bandwidth allocation over EPONs,” IEEE Commun. Lett., vol.11, no. 6, pp. 549–551, Jun. 2007.
[28] Csim (Mesquite Software) [Online]. Available: http://www.mesquite.com
[29] K. Park and W. Willinger, Self-Similar Network Traffic and Perfor-
mance Evaluation. Hoboken, NJ: Wiley-Interscience, 2000.[30] G. Kramer, Ethernet Passive Optical Networks. New York: McGraw-
Hill, 2005.
Michael P. McGarry (M’98) received the B.S.degree in computer engineering from PolytechnicUniversity, Brooklyn, NY, in 1997, and the M.S.and Ph.D. degrees in electrical engineering fromArizona State University, Tempe, in 2004 and 2007,respectively.
He is currently a Senior Staff Scientist at Adtranand an Adjunct Professor at Arizona State University,Tempe. From 1997 through 2003 he was employedin industry by companies including PMC-Sierra andYurie Systems (now Lucent Technologies). His re-
search interests include congestion control and the optimization of MAC proto-cols for both optical access and mobile ad hoc networks.
1216 JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 26, NO. 10, MAY 15, 2008
Martin Reisslein (A’96–S’97–M’98–SM’03)received the Dipl.-Ing. (FH) degree from the Fach-hochschule Dieburg, Dieburg, Germany, in 1994,and the M.S.E. degree from the University of Penn-sylvania, Philadelphia, in 1996, both in electricalengineering, and the Ph.D. degree in systems engi-neering from the University of Pennsylvania in 1998.
He is currently an Associate Professor in the De-partment of Electrical Engineering at Arizona StateUniversity (ASU), Tempe. From July 1998 throughOctober 2000 he was a Scientist with the German Na-
tional Research Center for Information Technology (GMD FOKUS), Berlin andLecturer at the Technical University Berlin. From October 2000 through August2005 he was an Assistant Professor at ASU.
Dr. Reisslein served as Editor-in-Chief of the IEEE COMMUNICATIONS
SURVEYS AND TUTORIALS from January 2003 through February 2007.
Charles J. Colbourn received the M.Math. degreein 1978 from the University of Waterloo, Waterloo,ON, Canada, and the Ph.D. degree in 1980 from theUniversity of Toronto, Toronto, ON, both in computerscience.
He has held academic positions at the University ofSaskatchewan, the University of Waterloo, the Uni-versity of Vermont, and is currently a Professor ofComputer Science and Engineering at Arizona StateUniversity, Tempe. He is the author of The Combina-
torics of Network Reliability (Oxford) and Triple Sys-
tems (Oxford). He is Editor-in-Chief of the Journal of Combinatorial Designs
and serves on the editorial boards of Networks; Discrete Mathematics; Journal
of Combinatorial Theory (A); Designs, Codes and Cryptography; and others.He edited the standard reference work The CRC Handbook of Combinatorial
Designs. He is the author of more than 250 refereed journal papers focussing oncombinatorial designs and graphs with applications in networking, computing,and communications.
Dr. Colbourn was awarded the Euler Medal for Lifetime Research Achieve-ment by the Institute for Combinatorics and its Applications in 2004.
Martin Maier (M’03) received the M.Sc. andPh.D. degrees (both with distinctions) in electricalengineering from the Technical University Berlin,Berlin, Germany, in 1998 and 2003, respectively.
He is currently an Associate Professor withthe Institut National de la Recherche Scientifique(INRS), Montreal, QC, Canada. In summer 2003,he was a Postdoctoral Fellow at the MassachusettsInstitute of Technology (MIT), Cambridge. He wasa Visiting Professor at Stanford University, Stanford,CA, from October 2006 through March 2007. His
recent research activities aim at providing insights into technologies, protocols,and algorithms shaping the future of optical networks and their seamlessintegration with next-generation wireless networks. He is the author of thebooks Metropolitan Area WDM Networks—An AWG Based Approach (Kluwer,2003) and Optical Switching Network (Cambridge University Press, 2008).
Frank Aurzada studied mathematics at theFriedrich-Schiller University, Jena, Germany andthe University of York, York, U.K. He received theDipl.-Math. and Ph.D. degrees in mathematics fromFriedrich-Schiller University in 2003 and 2006,respectively.
After completing his Ph.D., he joined the DFGResearch Center Matheon at Technical UniversityBerlin. His research interests lie in the queueingtheoretic analysis of telecommunication networks,coding theory, and limit theorems in probability
theory. He is currently a Postdoctoral Researcher at the Technical UniversityBerlin, Berlin, Germany.
Michael Scheutzow received the Diploma inmathematics from the Johann-Wolfgang-GoetheUniversity, Frankfurt/Main, Germany, in 1979, thePh.D. degree in mathematics (magna cum laude)from the University of Kaiserslautern, Kaiser-slautern, Germany, in 1983, and the Habilitation inmathematics from the University of Kaiserslauternin 1988.
He is currently a Professor in the Departmentof Mathematics, Technical University (TU) Berlin,Berlin, Germany. From 1988 through 1990 he was
Project Leader with Tecmath GmbH, Kaiserslautern. Since 1990, he has beena Professor of stochastics in the Department of Mathematics, TU Berlin. From1997 through 1999 he was Associate Chair of the department. He has visitedthe University of Carbondale, Rutgers University, the University of Rochester,Warwick University, and the MSRI at UC Berkeley.
IEEE Communications Surveys & Tutorials • 3rd Quarter 200846
ver the past decade, the telecommunications infra-structure has transitioned from a copper-based plantto a fiber-based plant. The transition began with the
wide area networks (WANs) that provide connectivity betweencities and progressed through the metropolitan area networks(MANs) that provide connectivity between service providerlocations within a metropolitan area. At the same time, localarea networks (LANs) that interconnect nodes within an indi-vidual location have seen average bit rates migrate from 10Mb/s to 1 Gb/s over copper cabling. Although significantbandwidth improvements occurred in the service provider net-works (i.e., WANs and MANs), as well as at the subscriberpremises (i.e., LANs), the link between the private customernetworks and the public service provider networks did notexperience the same level of progress. This so-called accessnetwork that provides the link between the private and publicnetworks still relies on an aging copper infrastructure. ThexDSL and cable modem technology developments mademarginal improvements in bandwidth capacity but failed toopen the bottleneck that exists in access networks.
A fiber infrastructure is required in the access networks toprovide higher bit rates, as well as more flexibility. From theservice provider perspective, access network links have differ-ent revenue dynamics than links in the WAN and MAN.Whereas WAN and MAN links carry the bit streams of manyrevenue generating customers, access network links carry a
single or only a few revenue generating bit streams. For thisreason, access networks are very sensitive to cost. Cost issuesare slowing the deployment of a new physical plant in theaccess networks.
Deploying a passive optical network (PON) between ser-vice providers and customer premises can provide a cost effi-cient and flexible infrastructure that will provide the requiredbandwidth to customers for many years to come. PONs are anetwork in which a shared fiber medium is created using apassive optical splitter/combiner in the physical plant. Sharingthe fiber medium means reduced cost in the physical fiberdeployment, and using passive components in the physicalplant means reduced recurring costs by not maintainingremote facilities with power. These reduced costs make PONsan attractive choice for access networks, which are inherentlycost sensitive.
At a top level, PONs are classified by the used link-layerprotocol. Whereas an asynchronous transfer mode (ATM)PON (APON) uses ATM, an Ethernet PON (EPON) usesEthernet, and a gigabit PON (GPON) uses the GPON encap-sulation method (GEM) in addition to ATM cells to supportEthernet. The International Telecommunication Union (ITU)has generated standards for APONs: G.983 broadband PON(BPON), as well as GPONs: G.984 gigabit-capable PON(GPON). The IEEE has generated a standard for EPONs:IEEE 802.3ah Ethernet in the first mile. Given the fact that
O
S U R V E Y S
I E EE
COMMUNICAT IONS
MICHAEL P. MCGARRY, UNIVERSITY OF AKRONMARTIN REISSLEIN, ARIZONA STATE UNIVERSITY
MARTIN MAIER, INSTITUT NATIONAL DE LA RECHERCHE SCIENTIFIQUE (INRS)
ABSTRACT
We compile and classify the research work conducted for Ethernet passive optical
networks. We examine PON architectures and dynamic bandwidth allocation algo-
rithms. Our classifications provide meaningful and insightful presentations of the
prior work on EPONs. The main branches of our classification of DBA are: grant
sizing, grant scheduling, and optical network unit queue scheduling. We further
examine the topics of QoS support, as well as fair bandwidth allocation. The presen-
tation allows those interested in advancing EPON research to quickly understand
what already was investigated and what requires further investigation. We summarize
results where possible and explicitly point to future avenues of research.
ETHERNET PASSIVE OPTICAL NETWORKARCHITECTURES AND DYNAMIC BANDWIDTH
ALLOCATION ALGORITHMS
3RD QUARTER 2008, VOLUME 10, NO. 3
www.comsoc.org/pubs/surveys
1553-877X
IEEE Communications Surveys & Tutorials • 3rd Quarter 2008 47
90 percent of data traffic originates and terminates in Ether-net frames, using an EPON can reduce the adaptationrequired to move data between the LAN and the access net-work. Furthermore, ATM creates inefficiencies in data trans-port as a result of its fixed data unit that requires most datapackets to be segmented and reassembled at the end points ofthe network. This segmentation and reassembly results inhigher processing delays, as well as reduced efficiency of errorrecovery techniques. For these reasons, EPONs appear to bemore promising than APONs for data dominated networks.GPONs, on the other hand, by using GEM instead of ATM,avoid the inefficiency of segmentation and reassembly.
In this article, we review and classify the existing researchon EPONs. The focus is on EPON architectures and dynamicbandwidth allocation (DBA) for EPONs, and our classifica-tions provide insight into areas that are open for furtherinvestigation. For a survey on EPON security issues, which arenot covered in this article, see [1]. This article provides a com-prehensive and up-to-date EPON research survey as of spring2007. The status and the main directions of this research as ofearly 2004 were presented in [2]. The EPON research areahas been very active over the last few years, resulting in a dra-matically expanded and more intricate body of EPONresearch. Therefore, a fundamentally new classification andsurvey of this area is required and provided in this article.
We review the standard PON architecture and two alterna-tive architectures that were proposed. We review and classifyall of the research done on the problem of DBA for EPONs.We classify this work in a meaningful way that providesinsight to researchers currently working on EPONs and thoseconsidering working on EPONs. We discuss medium accesscontrol (MAC) protocols for the two alternative PON archi-tectures. Finally, we conclude the article with a discussion ofavenues of further investigation.
PON ARCHITECTURE
A PON generally has a physical tree topology, where oneoptical line terminal (OLT) residing at the central office ofthe service provider connects to several optical network units(ONUs) in the field. The OLT is connected to the ONUs witha feeder fiber that is subsequently split using a 1 : N optical
splitter/combiner to enable the ONUs to share the opticalfiber. This is illustrated in Fig. 1. The transmission directionfrom OLT to ONU is referred to as downstream and operatesas a broadcast medium. The transmission direction from theONUs to the OLT is referred to as upstream. The upstreamsignals propagate from ONU to OLT but are not reflectedback to each ONU; therefore, the PON is not a broadcastmedium in the upstream direction. The EPON is a multi-point-to-point [3] medium, where the ONUs cannot detecteach other’s transmission because the upstream optical signalis not received by the ONUs. However, ONUs share the samefiber; hence, their transmissions can collide, and contentionresolution must be performed.
To avoid collisions in the upstream direction, time divisionmultiplexing (TDM) or wavelength division multiplexing(WDM) can be used [4]. WDM provides a large amount ofbandwidth to each user, but requires that each ONU use aunique wavelength, which presents inventory challenges forservice providers that must stock many different ONU types.TDM allows all ONUs to share a single wavelength, thus,reducing the number of transceivers at the OLT and allowingfor a single ONU type. First generation PONs use wave-lengths to separate the upstream and downstream channelsbut use TDM to avoid upstream transmission collisionsbetween ONUs. Due to the topology of the PON, MAC pro-tocols that rely on connectivity between all nodes cannot beutilized. A PON allows for connectivity from the OLT to allONUs in the downstream and from each ONU to the OLT inthe upstream (i.e., only the OLT has connectivity to allnodes). This connectivity pattern dictates the use of a central-ized MAC protocol residing at the OLT. This leads to apolling-based MAC, where the OLT polls ONUs and grantsthem access to the shared PON medium.
BROADCAST PON
An alternative PON architecture proposed in [5, 6] requiresreflection of the upstream signal back to the ONUs, as illus-trated in Fig. 2. Splitter 1 splits the upstream signal back tothe ONUs, and splitter 2 splits the downstream signal as inthe standard PON architecture. This creates a broadcast net-work that enables a decentralized medium access control pro-tocol (e.g., carrier sense multiple access with collision
■ Figure 1. Network architecture of a PON with one optical line terminal (OLT) and N = 5 opti-cal network units (ONUs), each with a different round-trip time (RTT).
(Single subcriber)
RTT=6
RTT=10
RTT=4
RTT=18
RTT=6
RTT: Round Trip Time
1:N splitterOLT ONU3
ONU1 (Multiple subcribers)
ONU2
ONU4 (Multiple subcribers)
ONU5 (Single subcriber)
(Single subcriber)
IEEE Communications Surveys & Tutorials • 3rd Quarter 200848
detection [CSMA/CD]) to be employed. Unfortunately, thereare economic downsides to this approach. The ONUs becomemore expensive because they must:• Contain higher power lasers to overcome the loss
incurred by splitting their upstream signals to reflectback to other ONUs.
• Contain an extra receiver for the upstream wavelength.• Have more intelligence to participate in the medium
access arbitration.• Have an extra fiber for the reflected upstream signal.
Further, the large bandwidth-propagation delay product ofthe optical access network limits the feasibility of this type ofarchitecture.
TWO-STAGE PON
A two-stage PON architecture [7] can enable a PON toaccommodate a higher number of ONUs compared to a sin-gle-stage PON. Two-stage PONs help to increase the reach ofthe PON. In the first stage, some ONUs act as sub-OLTs forother ONUs, as illustrated in Fig. 3. These sub-OLTs regener-ate the optical signal in the upstream and downstream, as wellas aggregate the traffic of their child ONUs. This allows a sin-gle OLT in a central office to potentially reach a larger num-
ber of ONUs because the sub-OLTs actas optical switches, mitigating opticalpower budget concerns that arise whenincreasing the number of ONUs.
DYNAMIC BANDWIDTH
ALLOCATION
DBA generally is defined as the processof providing statistical multiplexing amongONUs. To understand the importance ofstatistical multiplexing in PONs, note thatthe data traffic on the individual links inthe access network is quite bursty. This isin contrast to metropolitan or wide areanetworks where the bandwidth require-ments are relatively smooth due to theaggregation of many traffic sources. In anaccess network, each link represents a sin-gle or small set of subscribers with verybursty traffic due to a small number ofbursty sources (e.g., Web data and packe-tized video). Because of this bursty traffic,the bandwidth requirements vary widelywith time. Therefore, the static allocation
of bandwidth to the individual subscribers (or sets of sub-scribers) in a PON is typically inefficient [8]. Statistical multi-plexing that adapts to instantaneous bandwidth requirements istypically more efficient. The DBA that operates at the OLT isresponsible for providing statistical multiplexing.
The OLT requires instantaneous bandwidth requirementinformation from each ONU to make access decisions. Havingthis precise information is not possible due to the non-zeropropagation delays on a PON, typically up to 100 Jsec, whichis significantly larger than the transmission time of the maxi-mum size Ethernet frame: 12.3 Jsec. The ONUs must reporttheir instantaneous queue sizes in a control frame and propa-gate this through the PON to the OLT.
A PON is a remote scheduling system [9] that suffers thefollowing problems:• Significant queue switchover overhead [9] (in the case of
PONs, this is due to the guard times between ONUtransmissions). Guard times between ONU transmissionsare required to enable the previously transmitting ONUto power off its laser to prevent spurious transmissionwhile the next ONU transmits; the next ONU to poweron its laser in preparation for transmission; and the OLTto adjust its receiver to account for power-level differ-ences in transmissions from different ONUs due to their
■ Figure 2. Broadcast PON Architecture: Downstream OLT to ONUs transmissionsare copied by splitter ”d” to all ONUs, while each upstream ONU to OLT transmissionis reflected by splitter ”ru” back to all ONUs, thus creating a broadcast network forboth upstream and downstream transmissions. The dashed lines represent the extrafibers used to carry the reflected upstream signal back to the ONUs.
(Single subscriber)OLT ONU3
(Single subscriber)ONU5
(Single subscriber)ONU2
(Multiple subscribers)ONU1
d
ru
(Multiple subscribers)ONU4
■ Figure 3. Two-Stage PON Architecture: Certain ONUs act as sub-OLTs that regenerate the opti-cal signal for ONUs in a second stage, thereby allowing for an increase in the total number ofserved ONUs.
OLT1:N splitter
ONU4 (Single subscriber)
ONU7 (Single subscriber)ONU6 (Single subscriber)
ONU5 (Single subscriber)
ONU3 (Single subscriber)
ONU1
sub-OLT1
(Multiple subscribers)
1:N splitter
sub-OLT2
1:N splitter
ONU2 (Multiplesubscribers)
IEEE Communications Surveys & Tutorials • 3rd Quarter 2008 49
different distances from the OLT. The queue switchoveroverhead should be mitigated by using a cyclic PONscheduler that issues one grant to an ONU per cycle.
• Large control plane propagation delay as a result of dis-tances between OLT and ONUs. Interleaved polling isused to mitigate the large propagation delays on PONs[3]. With interleaved polling, the next ONU to be polledis issued a message giving transmission access while theprevious ONU is still transmitting. This message, referredto as a grant, contains the start time of the transmissionwindow, as well as the length (duration) of the transmis-sion window. Figure 4 illustrates the difference betweenpolling with and without interleaving.
• Limited control plane bandwidth, which is mitigated byshort control plane messages.
A cyclic interleaved polling MAC called interleaved polling withadaptive cycle time (IPACT) [3] mitigates all of these issues.
The process of DBA consists of two parallel but potentiallyoverlapping problems: grant sizing and grant scheduling (orinter-ONU scheduling). Grant sizing determines the size of agrant, that is, the length of the transmission window assignedto an ONU for a given grant cycle. Grant scheduling deter-mines the order of ONU grants for a given cycle. Althoughthe focus of this section is on DBA for EPONs, most of theresults extend to other PONs as well. Specifically, the resultsthat are not tied to the MultiPoint Control Protocol (MPCP)or Ethernet frame can be extended beyond EPONs to BPONsand GPONs.
Figure 5 shows our taxonomy for dynamic bandwidth allo-cation. We use this taxonomy as a framework for discussing
■ Figure 4. With interleaved polling, the OLT can issue the grants on the downstream wavelengthchannel ⁄d such that successive upstream transmissions on channel ⁄u are separated in time by onlya guard time interval compared to a round trip time with standard polling.
TX OLT
6400 bytes data+ 64 bytes RPT
5120+RPT
λdRX λu
TX ONU1
λuRX λd
6400 bytes data+RPT
6400
TX ONU2
λuRX λd
5120 Standard polling
5120+RPT
TX OLT
6400 bytes data+ 64 bytes RPT
5120+RPT
λdRX λu
TX ONU1
λuRX λd
6400 bytes data+RPT
6400
TX ONU2
λuRX λd
5120 Interleaved polling
5120+RPT
■ Figure 5. Dynamic bandwidth allocation taxonomy.
Queue (intra-ONU)scheduling [25,32,33,34]
Grant (inter-ONU)scheduling [12,25,27,28]
DBA
Grant sizing
Fixed[3]
Dynamic
Gated[3]
Limited[3]
Excessdistribution(see fig. 8)
Exhaustive[17,18,19,20]
IEEE Communications Surveys & Tutorials • 3rd Quarter 200850
the research on dynamic bandwidth allocation for EPONs. Wediscuss the MPCP defined in the IEEE 802.3ah standard. Thisprotocol defines the control plane used in EPONs to coordi-nate medium access. We discuss two fundamentally differentproblem-solving approaches to DBA; we call these approach-es DBA frameworks. We discuss the research work done forthe problem of grant sizing. We discuss the research on grantscheduling. We discuss intra-ONU scheduling, that is, arbi-trating the different queues in a given ONU. We discuss thetopic of quality of service (QoS), and we also discuss the issueof fairness, which is touched on later. All of these sectionsassume the standard PON architecture of Fig. 1. Discussionsof protocols for broadcast and two-stage PON architecturesare deferred to later.
MULTIPOINT CONTROL PROTOCOL
To facilitate the discovery and registration of ONUs, as wellas medium access control, the IEEE 802.3ah task forcedesigned the MPCP. The MPCP consists of five messages.REGISTER REQ, REGISTER, and REGISTER ACK areused for the discovery and registration of new ONUs.REPORT and GATE are used for facilitating centralizedmedium access control. The REPORT message is used toreport the instantaneous queue occupancies at an ONU to theOLT. This REPORT message also can contain queue occu-pancies at certain threshold levels as opposed to only the fulloccupancy. This threshold queue reporting allows the OLTflexibility in determining the size of a granted transmissionwindow. The GATE message is used by the OLT to grantnon-overlapping transmission windows to the ONUs.
■ Figure 6. MPCP operation: Two-way messaging assignment of time slots for upstream transmission between ONU and OLT.
Grantedtransmissionwindow
Dataplane
REPORT msg
GATE msg
Subscriber data
DBA
OLT ONU
Controlplane
algorithm
Intra-ONUscheduler
■ Figure 7. In interleaved polling with stop, the OLT waits to receive the REPORT message fromthe last ONU in a cycle before polling the first ONU in the next cycle. This allows the OLT tomake DBA decisions based on the REPORTs from all ONUs. As a result, a walk time of at leastan RTT is incurred between grant cycles.
twalk
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IEEE Communications Surveys & Tutorials • 3rd Quarter 2008 51
Figure 6 illustrates the infrastructure for facilitating DBA.REPORT messages flow upstream to report queue occupan-cies, and GATE messages flow downstream to grant upstreamtransmission windows. Upon receiving queue occupancy infor-mation by means of REPORT messages, the OLT — using aDBA algorithm — makes MAC decisions for the next cycleand communicates these decisions to the ONUs throughGATE messages.
DBA FRAMEWORKS
With interleaved polling, the DBA granting cycles of theindividual ONUs are interleaved, and the OLT typicallymakes grant decisions based on individual ONU REPORTmessages. That is, the OLT typically does not wait untilREPORT messages are received from all ONUs before mak-ing grant decisions. This prohibits the OLT from makingDBA decisions that consider the bandwidth requirements ofall ONUs. As a result, it is very difficult for the OLT tomake fair access decisions. An alternative approach is theso-called interleaved polling with stop (Fig. 7) in which theOLT stops and waits between granting cycles for all ONUREPORT messages to be received before making DBA deci-sions. This affords the OLT the opportunity to provide a fairdistribution of bandwidth. The trade-off is that interleavedpolling with stop decreases the bandwidth utilization by forc-ing an idle period, twalk, of the one-way propagation delayfrom the last polled ONU to the OLT plus the one-waypropagation delay from the OLT to the first polled ONU, asillustrated in Fig. 7, that is, the walk time is typically equalto the average round trip time (RTT). Depending on thelength of the granting cycle, this walk time can become a sig-nificant portion of the available bandwidth. For example,with a cycle length of 1.5 msec and an RTT on the order of50 Jsec, at least 3.33 percent of the available bandwidth iswasted on the walk time. For a 750 Jsec cycle time, the walktimes would consume 6.66 percent of the available band-width.
Interleaved polling and interleaved polling with stop alsocan be compared by their problem-solving approach to DBA.Interleaved polling without stop requires an online problem-solving approach to DBA, that is, the OLT makes DBA deci-sions with incomplete knowledge of the bandwidthrequirements of all the ONUs. Whereas, interleaved pollingwith stop allows for an offline problem-solving approach toDBA, that is, the OLT makes DBA decisions with full knowl-edge of the bandwidth requirements of all the ONUs. Werefer to these DBA problem-solving approaches as the onlineand offline DBA frameworks, respectively.
GRANT SIZING
Grant sizing can be divided into four major categories:• Gated• Limited• Limited with excess distribution• Exhaustive using queue size prediction
Let Gi be the grant size for the current cycle for ONU i, Ri
the queue size reported in the most recently receivedREPORT message from ONU i, Gi
max the limit on the maxi-mum grant size for ONU i, Ei the share of the excess band-width in a cycle allocated to ONU i, and Pi the predictedqueued traffic between the time of the REPORT transmissionfrom ONU to OLT and the end of the granted transmissionwindow to ONU i for the next cycle. The general equation forgrant sizing would then be: Gi = f(Ri, Gi
max) + Ei + Pi. Wenow discuss different techniques used for this general functionf(·) and for determining Ei and Pi.
Fixed — In the fixed grant-sizing scheme, the grant size isfixed for an ONU every cycle. The function for Gi is simply Gi
= Gimax. Simulation results [3] have shown that the fixed
grant-sizing severely underperforms the dynamic grant-sizingtechniques described below. An analysis in [8] confirms thesimulation results.
Gated — In the gated grant-sizing technique, the grant sizefor an ONU is simply the queue size reported by that ONU,the function for Gi is Gi = Ri. This scheme provides low aver-age delay but does not provide adequate control to ensure fairaccess between ONUs. In-depth delay analyses of the gatedscheme can be found in [10] and [11].
Limited — In the limited grant-sizing technique [3], the grantsize is set to the reported queue size up to a maximum grantsize for that ONU. The function for Gi for the limited schemeis Gi = min(Ri, Gi
max). This grant-sizing scheme prevents anyONU from monopolizing the shared link. Simulation results[3] have shown that there is no average packet delay differ-ence between gated and limited grant sizing. However, limitedgrant sizing can assist in providing fair access between ONUsby limiting the size of the grant to Gi
max and thereby prevent-ing an ONU from monopolizing the link. Let tcycle be thelength of a grant cycle and tguard be the guard time betweengrants. Under high traffic load, tcycle
max = xi(Gimax + tguard) (i.e.,
the maximum grant cycle length is defined by the maximumgrant sizes). A large maximum grant cycle results in largerdelays, whereas a short maximum grant cycle reduces thechannel utilization due to increased guard times [12].
The limited scheme suffers from two detriments. First, thequeue is underserved if Gi
max < Ri. Second, i bandwidth is
■ Figure 8. Excess distribution taxonomy.
Excessdivision
Demanddriven excess
[13]
Equitableexcess[14]
Weightedexcess[15]
Excessallocation
Uncontrolledexcess[14]
Controlledexcess
[7,15]
Iterativeexcess[15]
Excessdistribution
IEEE Communications Surveys & Tutorials • 3rd Quarter 200852
wasted if the request is not fully satisfied, and the end of thegrant does not accommodate the next Ethernet frame. In thebest case, this head-of-line (HOL) Ethernet frame that doesnot fit into the remainder of the grant is only 64 bytes, whichresults in up to 63 bytes of wasted grant. The worst case is ifthe HOL packet is the maximum length 1518 bytes. Thisresults in up to 1517 bytes of wasted grant.
Limited with Excess Distribution — Limited with excessdistribution [13] augments the limited grant-sizing scheme toimprove statistical multiplexing while still preventing ONUsfrom monopolizing the link. In general, ONUs are partitionedinto two groups: underloaded ONUs and overloaded ONUs.Underloaded ONUs are those whose REPORTed queue sizeis less than or equal to the maximum grant size, that is, Ri HGi
max. Overloaded ONUs are those whose REPORTed queuesize is larger than their maximum grant size, that is, Ri >Gi
max. In the excess distribution schemes, the overloadedONUs share the unused or excess bandwidth left over fromunderloaded ONUs. The grant for an overloaded ONU thenbecomes G i = G i
max + E i. The total excess bandwidth isdefined i to be the sum of the differences between the maxi-mum grant size and the REPORTed queue size of all theunderloaded ONUs. Let Etotal be the total excess bandwidthfor a cycle, U the set of underloaded ONUs, O the set of over-loaded ONUs, and Ei the excess assigned to overloaded ONUi. The total excess is calculated as Etotal = xicu (Gi
max – Ri).The computation of the total excess bandwidth requires theOLT to wait for all ONU REPORT messages, that is, requiresthe use of interleaved polling with stop or the offline DBAframework. A hybrid DBA framework that allows underload-ed ONUs to be granted before the stop and overloadedONUs to be granted after the stop [13] can help to mitigatethe inefficiencies of the offline DBA framework. After it iscomputed, the Etotal is divided between all the overloadedONUs.
Excess distribution can be divided into excess division andexcess allocation. Excess division divides Etotal among theoverloaded ONUs and excess allocation can, if used efficient-ly, redistribute excess credits that are unused by some over-loaded ONUs. Figure 8 shows the taxonomy of excessdistribution schemes (including excess division and allocation).
One approach to excess division (referred to as DBA1 in[13]) divides the excess according to demand, that is, DBA1divides the excess according to relative request size followingthe formula:
We refer to this approach as demand-driven excess (DDE)division. Because each ONU’s share of the excess is complete-ly determined by its request size, the larger the ONU requestsize relative to the other ONUs, the more excess bandwidth it
receives. This provides statistical multiplexing but is not nec-essarily fair. The fair excess [14] or equitable excess (EE) divi-sion method divides Etotal equally among the overloadedONUs. Let M be the total number of overloaded ONUs, EEdivides the excess according to the formula:
This approach gives all ONUs an equal piece of the totalexcess, implying fairness. The weighted excess (WE) divisionmethod [15] uses ONU priority weights to divide the excessbandwidth. The total excess is divided among overloadedONUs according to their weights:
This method allows the ONUs to have differing priorities withrespect to their fair share of the excess bandwidth.
After the excess is divided among the overloaded ONUs —according to DDE, EE, or WE — it is possible for the size ofthe grant to be larger than the request, that is, Gi + Ei > Ri,which results in wasted bandwidth. The excess division can beaugmented by an excess allocation algorithm that sizes thegrant so that it does not exceed the request, as well as redis-tributes unused excess credits.
The uncontrolled excess (UE) allocation method [14]assigns overloaded ONUs their share of the excess withoutregard to their request size. Therefore, bandwidth is wasted assome overloaded ONUs receive grants that are larger thantheir requests. The controlled excess (CE) allocation method[7, 15] provides better utilization by avoiding wasted band-width under certain conditions. Specifically, if the total excessdemand from the overloaded ONUs Edemand = xjcO (Rj –Gj
max) is less than the total excess Etotal, then each ONU isgranted its full request Ri. This avoids wasted bandwidth forthe situation when the total request does not exceed the maxi-mum grant cycle size xi Gi
max.The iterative excess (IE) allocation method [15] follows an
iterative grant sizing approach to maximize the number of sat-isfied overloaded ONUs. To avoid sizing a grant larger thanthe request, the grant size for each ONU is determined as:
(1)
Initially, all of the overloaded ONUs are in a list. Ei iscomputed for each overloaded ONU according to one of theexcess division methods. One by one an overloaded ONU’sgrant size is computed according to the above formula. If an
GR R G E
G E R G Ei
i i i i
i i i i i
=H +
+ > +
Ä
ÅÈ
Ç
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max
max max
if
if ÈÈ.
Ei =wi
jcOw jL· Etotal.
Ei =1
M· Etotal.
Ei =Ri
x jcO Rj·Etotal
■ Figure 9. Illustration of queue waiting times.
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IEEE Communications Surveys & Tutorials • 3rd Quarter 2008 53
ONU is satisfied (i.e., Ri H Gimax + Ei), it is issued a grant and
removed from the list. Unsatisfied ONUs remain in the listand participate in future iterations. After an iteration throughthe list, Etotal is recomputed by removing the excess used bythe satisfied ONUs. This allows the excess bandwidth unusedby those satisfied ONUs to be made available to the unsatis-fied overloaded ONUs. Ei is recomputed for the overloadedONUs that remain in the list, and another iteration takesplace. The iterations continue until there are no satisfiedONUs. On this final iteration, the unsatisfied ONUs simplyare allocated their fair share of the total remaining excess(i.e., Ei). The iterative grant-sizing approach mitigates wastedbandwidth by not over-assigning bandwidth to ONUs andmaximizes the number of satisfied ONUs to lower the amountof unused slot remainder. Further, it provides a more efficientdistribution of the excess bandwidth.
Exhaustive Service System Using Queue Size Prediction— Queue size prediction is concerned with estimating thetraffic that is generated during the period between theREPORT message transmission by the ONU and the begin-ning of the gated transmission window. Let trgs denote thistime between the REPORT transmission at the ONU and thestart of the next grant for that ONU. A service system thataccommodates the traffic included in trgs is referred to as apartially gated service system [16]. Alternatively, additionallythe traffic generated during the granted transmission windowcould be predicted. Let trge denote the time between theREPORT transmission by the ONU and the end of the nextgrant at that ONU. This results in an exhaustive service sys-tem [16]. Figure 9 illustrates these time periods. Let Qi be theactual amount of traffic that queued up during trgs or trge. Thegoal of queue size prediction is to get Pi as close to Qi as pos-sible. For constant bit rate (CBR) traffic, which has a constantand therefore predictable rate of traffic generation, this israther simple. Multiplying the constant rate of the CBR trafficin bits/sec by trge [13, 17] is a sufficient predictor for CBRtraffic. For bursty variable bit rate (VBR) traffic, the queuesize prediction is more challenging.
Elementary schemes for queue size prediction for burstysources are [3]: constant credit and linear credit. In the con-stant credit scheme, the OLT adds some constant credit to thegrant size. Let † be this credit, then Pi = †. In the linearcredit scheme, the credit adapts to the size of the request. Let\ be the fraction of the request used as the credit, that is, Pi =\Ri. The idea is that the request size gives some indication asto how much traffic will arrive in the waiting period, that is,trgs or trge.
Using control theory [18] to drive the gap between predict-ed and actual queued traffic to zero, an ONU reports the dif-ference between the grant, Gi, and the actual data queued atthe start of the granted transmission window. Let Gi
prev be thegranted transmission window size, Ri
prev be the data queued atthe time of the report, and Qi
prev be the data queued duringtrgs, all for the previous grant cycle. Let ‘i be the differencereported by the ONU, that is, ‘i = Gi
prev – (Riprev + Qi
prev).Let ̃ be a control gain parameter, then: Gi = Gi
prev – ̃‘i.Control theoretic approaches are used for modifying the
control gain parameter to stabilize ‘i. Simulation results [18]show that this scheme has almost an order of magnitude lowerpacket delay compared to IPACT with gated grant sizing. Thisdifference is attributed to much better queue size prediction.The results provide limited insight because they did notexplicitly show that this control theoretic approach drove ‘i
closer to zero than gated grant sizing.A simple one step back linear predictor [19] can be used
for prediction, that is, predictions are based on the actual data
received during the previous waiting period. Let tnprev be the
time of the previous cycle; the formula used for prediction is,
This formula is identical to the linear credit scheme with
Simulation results show that a one step back linear predictorprovides lower packet delay for expedited forwarding trafficcompared to fixed bandwidth allocation and limited band-width allocation.
A higher order linear predictor [20] for predicting trafficduring the waiting period at an ONU also could be used. Thislinear predictor has its weights updated by means of the LeastMean Square (LMS) algorithm (see Section 3.5 in [21]). Thelinear predictor attempts to predict Qi using informationabout a number, L, of previous Qi values. Because it wasshown in [22] that prediction of self-similar traffic is best per-formed using short-term correlation rather than long-termcorrelation, simulations were conducted using L = 4. Analternative approach could use this value as a starting point ofa search to find the optimal value of L. Mathematical analysisproves that an increase in the accuracy of the predictor leadsto a decrease in average delay.
In the simulation results presented in [20], the higher orderlinear traffic prediction scheme is compared against fixedgrant sizing, limited grant sizing, and limited grant sizing withexcess distribution. In limited grant sizing with excess distribu-tion, the underloaded ONUs are scheduled immediately uponreceipt of the REPORT, whereas overloaded ONUs arescheduled after REPORTs are received from all ONUs. Theresults show a reduction of average packet delay, as well asloss probability. However, it is unclear how much of the dif-ference is attributable to traffic prediction and how much tothe difference in scheduling, either waiting for all REPORTsor immediately scheduling each ONU.
Summary — The gated grant-sizing technique is the simplest,adapts to changing traffic demands, and eliminates wasted por-tions of a grant. However, it does not provide partially gatedor exhaustive service, and it cannot prevent ONUs frommonopolizing the upstream channel. This lack of control limitsthe ability to provide fair access and quality of service guaran-tees. The limited grant-sizing scheme can place limits on anONU’s access to the medium but can be inefficient in utilizingthe upstream capacity. Further, the limited and any other non-gated grant-sizing scheme open up the possibility of a wastedportion of a grant due to lack of frame segmentation in Ether-net. When using a fixed-size protocol data unit (PDU), such asfor a BPON, this is not a problem. Employing excess distribu-tion can improve the efficiency of the limited scheme by allow-ing overloaded ONUs to take advantage of the bandwidth notused by underloaded ONUs in a granting cycle.
Queue size prediction can lower queuing delays by attempt-ing to predict the precise instantaneous traffic demands of anONU to allow for an exhaustive service discipline. The risk isin reduced throughput due to wasted portions of a grant thatresult from imprecise prediction. The bursty nature of datatraffic in the access network makes precise prediction difficult.A slight over prediction will reduce throughput but decreasedelay by at least accommodating all of the queued Ethernet
\ =t
t
rgs
cycleprev
.
Pt
tRi i= ·rgs
cycleprev
.
IEEE Communications Surveys & Tutorials • 3rd Quarter 200854
frames. Investigating non-linear neuro-computational methodsfor the queue size prediction problem potentially is an areafor further research.
GRANT SCHEDULING (INTER-ONU SCHEDULING)
Medium access control for an EPON contains two schedulingproblems. The first is concerned with scheduling grants toeach ONU, namely, inter-ONU scheduling. The second isconcerned with scheduling the individual queues of Ethernetframes at the ONU for transmission within the granted trans-mission window, that is, intra-ONU scheduling. This divisionof the scheduling often is referred to as hierarchical schedul-ing [9, 23, 24]. We discuss inter-ONU or grant scheduling inthis section and defer discussion of intra-ONU scheduling tothe next section.
Since grant scheduling works at the inter-ONU level and iscoupled with the process of grant sizing, it is performed at theOLT. Typically, to change the scheduling order from roundrobin, the OLT must wait for all REPORTed queue sizesfrom the ONUs and then determine the grant order. Thisrequires the use of interleaved polling with stop or the offlineDBA framework, as illustrated in Fig. 7.
ONU transmissions ordered longest queue first (LQF) [12,25] or earliest packet first (EPF) [12] have been examined.LQF allows ONUs with the largest grant size to transmit first.This is the same as largest processing time (LPT) first schedul-ing in standard scheduling theory notation [26]. EPF allowsONUs with the earliest arriving HOL Ethernet frame totransmit first. To avoid the walk time between cycles when theOLT waits for all ONUs to REPORT before making anyscheduling decisions, the scheduling can leave out the last orlast few ONUs when scheduling. Simulation results [25, 27]using Poisson traffic show that both LQF and EPF providelower average delay at medium loads compared to a roundrobin scheduler. At low and high loads, the average delay wasthe same as a round robin scheduler.
Implementing the limited with excess distribution grant siz-ing technique requires special consideration with respect togrant scheduling. To accumulate and distribute the totalexcess bandwidth, the OLT must wait to receive REPORTmessages from all ONUs before issuing grants for the nextcycle. This means a walk time, twalk, is wasted between cycles.To mitigate this, lightly loaded ONUs can be scheduled imme-diately upon receiving their REPORT messages because theywill not receive any excess [13]. However, as the traffic loadincreases to the point where all ONUs become overloaded,twalk still is wasted between cycles. To avoid wasting twalk inbetween cycles, an overloaded ONU can be scheduled imme-diately if there is no underloaded ONU available for schedul-ing when the channel becomes available [28].
Summary — Examining the performance of these existingscheduling schemes for self-similar traffic is an important
topic for future research. Another avenue for future researchis to employ scheduling theory to find a better scheduler.
ONU QUEUE SCHEDULING (INTRA-ONU SCHEDULING)
Intra-ONU scheduling is concerned with scheduling the multi-ple queues of Ethernet frames at an ONU, for transmissionwithin the ONU’s granted transmission window. If the numberof queues in an ONU is relatively small, this intra-ONUscheduling can be performed at the OLT. However, as thenumber of queues increases, scheduling is typically made hier-archical [9] with the inter-ONU scheduling at the root of thehierarchy in the OLT and one level of branches. The ONUcontains the branch (i.e., intra-ONU) schedulers.
Low complexity is a key design goal for intra-ONU sched-ulers so that the cost of the ONUs is kept at a minimum.There are typically two classes of scheduling that service mul-tiple queues of differing priority:• Strict priority (SP) scheduling, which can be unfair• Weighted fair queuing (WFQ) schedulingSP scheduling creates unfairness when starving lower prioritytraffic due to unrestricted preemption. The ideal schedulershould allow statistical multiplexing, but guarantee a minimalportion of the available bandwidth to each priority queue (i.e.,provide link sharing). Generalized processor sharing (GPS)[29] achieves these goals for the fluid traffic model, wherepackets are infinitesimally small. Unfortunately, in practicalsystems with finite-size packets, the ideal GPS link sharing isnot directly applicable because a packet must monopolize theserver (i.e., transmission link) while in service. WFQ [30] is apacket approximation of GPS whose deviation from the idealcase is bounded by the maximum packet size. WFQ calculatesthe start time of a packet under the ideal GPS system andbased on this start time, computes the finish time under idealGPS. Then, packets are transmitted in the order of the calcu-lated finish time. The calculations of the ideal GPS times canbe computationally intensive for ONUs. A few schemes wereproposed to simplify these calculations at the expense ofapproximation accuracy to the ideal GPS.
Start-time fair queuing (SFQ) [31] is one simplified versionof WFQ. In SFQ, the calculation of server virtual time that isused to calculate the start time of a packet is reduced to thestart time of the packet currently in service, greatly reducingthe computational complexity. In contrast to WFQ, SFQ sortspackets by start time rather than finish time. An intra-ONUframe scheduler that employs a modified start-time fair queu-ing (M-SFQ) algorithm [32, 33] can be used as a low complex-ity alternative to SFQ. M-SFQ further simplifies thescheduling by calculating the start time only for the HOLpackets.
Simulation results comparing M-SFQ to strict priorityscheduling indicate that M-SFQ provides the same averagedelay for the expedited forwarding class (delay sensitive traf-fic), higher average delay for assured services class 1 (high-
■ Figure 10. Quality of service taxonomy.
Differentiatedservice
[13,23,35,36,37]
Bandwidthguarantees
[38,39]
Delayguarantees
[40]
Delay jitterguarantees
[17,41]
Admissioncontrol
[44,45,46]
Quality of service
IEEE Communications Surveys & Tutorials • 3rd Quarter 2008 55
speed video), and lower average delay for assured servicesclass 2 (low-speed pre-recorded video). Further, the averagedelay for class 2 is lower than for class 1, which seems unde-sirable, but is not commented on in the simulation study. Onecan conclude that M-SFQ provides improved delay andthroughput for assured services class 2 at the expense of worseperformance of assured services class 1. It is not clear howthis displays the strengths of M-SFQ over strict priorityscheduling. M-SFQ achieves better inter-class isolation [33]but also treats class 2 traffic better than class 1 traffic, whichis undesirable.
An additional shortcoming of M-SFQ is that it tends tostarve best-effort traffic to provide better QoS to the assuredservices and expedited forwarding classes [34]. A modifiedversion of deficit weighted round robin (M-DWRR) was pro-posed and examined in [34] to address this shortcoming. M-DWRR maintains a credit deficit counter for each class andconsiders only the HOL packets, ensuring low computationalcomplexity. In a first scheduling pass, M-DWRR offers band-width to each class queue according to the class weight (whichis reflected in the deficit credit counter). The bandwidth thatis not required by the individual queues is redistributed in asecond scheduling pass, which has some resemblance to theexcess distribution mentioned earlier, but is conducted inter-nally by the ONU. Simulation results indicate that M-DWRRensures fairness according to the chosen weights for the dif-ferent service classes, including best-effort traffic. Also, over-all throughput with M-DWRR is about 10 percent higher thanwith M-SFQ due to eliminating best-effort traffic starvation.
A non-work-conserving scheduling discipline, called priori-ty with insertion scheduling (PIS) [25], that transmits real-time packets when their delay-bound will be exceeded is yetanother ONU queue scheduling approach. PIS allows non-real-time traffic to gain access to the medium, as long as thereal-time traffic can be delayed without detriment.
Summary — To keep ONU costs low, the complexity of theONUs should be kept low. Therefore, the ideal intra-ONUscheduler provides quality of service guarantees through linksharing with low complexity. Alternatively, the intra-ONUscheduling can be performed at the OLT. This can result inpotential scalability problems as the number of queuesincreases [9]. However, allowing the OLT to perform theONU queue scheduling reduces ONU complexity concerns.
QUALITY OF SERVICE
EPONs are intended not only to carry best-effort data traffic,they also are expected to carry packetized voice and videothat have strict bandwidth and delay requirements, as well asdelay jitter sensitivity. We present in Fig. 10 the taxonomy fororganizing the research work on quality of service guaranteesfor EPONs.
Differentiated Service — The simplest way to facilitate QoSis to provide differentiation of traffic and different service toeach differentiated traffic class. The ONUs classify and sepa-rately buffer ingress traffic and can perform strict priorityscheduling between the classes when deciding which frames tosend during a gated transmission window. The use of strictpriority scheduling is required for compliance with 802.1dbridging [23]. Standard strict priority scheduling results in aphenomenon referred to as the light load penalty [13, 23].The individual queue sizes are REPORTed at the end of agrant. During the period trge, more high-priority traffic canarrive at the ONU, which can preempt the lower-priority traf-fic that was accounted for in the REPORT. If the grant sizing
predicts this higher priority traffic, newly arriving during trge,then the grant will accommodate this traffic; otherwise, it willunfairly preempt the lower priority traffic that was accountedfor in the REPORT. This problem occurs at low loads whenthe grants are typically small and are more likely used up bythe newly arriving high-priority traffic. To alleviate this prob-lem, a two-stage buffering scheme [23] should be used at theONU. The two-stage buffering moves the frames that wereaccounted for in the REPORT scheduled into a single sec-ond-stage queue that is emptied first during the next grant.This scheme effectively enforces a strict priority schedulingperformed at REPORT time, as opposed to the time of thegrant, which will have a queue occupancy that is potentiallydifferent than that REPORTed. Simulation results [13, 23]demonstrate the existence of the light-load penalty and indi-cate that the two-stage buffering eliminates the light-loadpenalty at the expense of higher delay of high-priority traffic.
Strict priority scheduling can be extended to the PON level[35]. A DBA algorithm that uses a fixed-cycle length anddivides this cycle between three priority classes on a strict pri-ority basis is one approach. The OLT would send a separategrant for each priority class [13, 35].
A two-layer DBA (TLBA) scheme [36] for differentiatedservices also could be used. In the first layer, the OLT decidesthe cycle partitioning between the classes of service (class-layer allocation), and in the second layer, the partition foreach class is further divided for each ONU (ONU-layer allo-cation). Within a class, all ONUs share the bandwidth accord-ing to a max-min fairness policy. To keep any class frommonopolizing the available bandwidth in a frame, a per-classbandwidth threshold is enforced. The bandwidth thresholdguarantees a minimum bandwidth for a class under heavyload. Any remaining bandwidth from classes that request lessthan their threshold is divided among classes that requestmore than their threshold. The division of that remainingbandwidth is handled through weights that are assigned toeach class. For ONU buffer management, weighted randomearly detection (RED) can be used. Simulation results [36]indicate that TLBA can divide the bandwidth as set throughclass weights when under heavy load. This allows for band-width guarantees for each class. The results also show thatunder lower loads, TLBA allows for effective utilization of themedium.
Class-of-service oriented packet scheduling (COPS) [37] isanother method to provide differentiated services. COPS reg-ulates the traffic of each ONU, as well as each class-of-service(CoS) using two sets of credit pools, one per ONU and oneper CoS. Granting begins with the highest CoS and ends withthe lowest CoS. In the first round of granting, each ONU withtraffic for the current CoS is granted up to the number ofcredits stored for that ONU, as well as that CoS. To mitigatethe unused slot remainder for those grants that cannot befully satisfied, a threshold queue-reporting scheme is used. Atthe end of the first round, the unused credits are pooledtogether and in the second round, these unused credits aredistributed to the CoS-ONU pairs that were not fully satisfied.Simulation results [37] show that COPS can provide loweraverage and maximum delay for all but the highest CoS ascompared to IPACT with limited grant sizing (IPACT-LS).The highest CoS experiences slightly higher average delayunder COPS as compared to IPACT-LS.
All of the above schemes suggest differentiating traffic atthe ONU into classes, separately reporting queue sizes ofeach class, and allowing the OLT to provide individual grantsto each class. The schemes differ in how they determine thegrant sizes for each class. It is also apparent that two-stagebuffering is required to keep higher priority traffic arriving
IEEE Communications Surveys & Tutorials • 3rd Quarter 200856
during trge from preempting the lower priority traffic that wasaccounted for in the REPORT.
Bandwidth Guarantees — A DBA algorithm for EPONscalled Bandwidth Guaranteed Polling (BGP) [38] can be usedfor providing bandwidth guarantees. The BGP algorithm actsas a compromise between fixed TDM and statistical multiplex-ing. In BGP, ONUs are divided into two disjoint sets:• Bandwidth guaranteed ONUs• Non-bandwidth guaranteed ONUsThe algorithm maintains two polling tables.
The first polling table divides a fixed length polling cycleinto a number of bandwidth units. The required bandwidth ofan ONU, as dictated by a service level agreement (SLA) witha service provider, determines the number of bandwidth unitsallocated in the polling table to that ONU. A bandwidth-guar-anteed ONU with more than one entry in the polling tablehas these entries spreading through the table rather thanappearing contiguously. This lowers the average queuing delaybecause these ONUs are polled more frequently. However,the increased polling frequency results in more grants percycle and hence, more guard times between grants, and thuslower channel utilization. Further, fragmenting the grants canpotentially lead to lower grant utilization because Ethernetframes cannot be fragmented to be transmitted across grantboundaries. Therefore, a frame that is too large to fit in theremainder of a bandwidth unit must wait for the next band-width unit, and a portion of the current bandwidth unit iswasted. Lower grant utilization further reduces the channelutilization. BGP employs a method to mitigate the grant uti-lization problem by allowing an ONU to communicate itsactual use of a bandwidth unit to an OLT. If the unused por-tion of the bandwidth unit is sufficiently large, this portion isgranted to a non-bandwidth guaranteed ONU. Otherwise, thenext bandwidth-guaranteed ONU is polled. However, thisapproach is severely limited by the propagation delays (i.e.,walk times) required for message exchange on an EPON.
In BGP, unused bandwidth units in the first polling tableare given to non-bandwidth-guaranteed ONUs in their orderof appearance in the second polling table. The second pollingtable, is constructed differently than the first. Entries in thesecond polling table are created as non-bandwidth-guaranteedONUs request grants. This is in contrast to the first pollingtable, which represents a division of time on the upstreamchannel of the EPON. Simulation results presented in [38]show that, as one expects, ONUs with more entries in thepolling table have lower queuing delay than those with fewerentries, and IPACT lies somewhere in the middle.
BGP can be augmented to include admission control fornew bandwidth-guaranteed ONUs [39]. This admission con-trol uses standard parameter-based admission control. Thereare two parameters that describe the resource requirements ofONUs:• Bandwidth requirement (peak rate)• Delay bound requirementUsing these parameters, the admission control determineswhether the ONU is accepted as a bandwidth-guaranteed(BG) ONU or as a best-effort (non-BG) ONU.
Delay Guarantees — A DBA algorithm called Dual DEB-GPS Scheduler [40] potentially can help provide delay guaran-tees. This DBA uses deterministic effective bandwidth (DEB),to determine the scheduling weights used in a generalizedprocessor sharing (GPS) scheduler. The scheduling is per-formed in two layers, hence the name Dual. The first layerperforms class-level multiplexing at the OLT. The secondlayer performs source level multiplexing at the ONU.
Traffic arriving at the ONU is regulated by a leaky bucketmechanism. This leaky bucket enforces a traffic profile char-acterized by: burst size P, peak rate {, and average rate J.These leaky bucket parameters are used to determine theDEB for a source. This DEB is directly used as a weight todetermine the portion of the upstream bandwidth assigned tothis traffic source. The DEB guarantees a particular delaybound. Let U be the desired delay bound, and Beff (U) be theeffective bandwidth to guarantee the delay bound. Then,
(2)
The OLT divides each bandwidth cycle according to theBeff (U) weights; the remaining bandwidth in a cycle is dividedequally among all best-effort sources (i.e., those that do notrequire any delay bounds). The OLT generates the grants perONU based on the weights and the information about whichsources belong to each ONU. The ONU is then responsiblefor performing the intra-ONU scheduling that determineshow the different sources fill the granted transmission win-dow. DEB attempts to guarantee delay bounds by guarantee-ing a certain bandwidth (i.e., Beff).
Simulation results are presented [40] with ONUs havingtwo QoS-aware traffic sources (QoS1 and QoS2) and twobest-effort sources (BE1 and BE2). QoS1 has a delay boundof 1 msec and jitter bound of 0.2 msec. QoS2 has a delaybound of 2 msec and jitter bound of 0.4 msec. According tothe presented results, QoS1 traffic experiences roughly a 2 to2.5-millisecond delay at a load of 0.7 and higher (bound is 1millisecond). QoS2 traffic experiences roughly a 3-milliseconddelay at a load of 0.7 and higher (bound is 2 milliseconds).From the presented results, it seems Dual DEB-GPS provideslow delay and jitter for traffic sources that require QoS butdoes not provide a guaranteed delay bound at higher loads.
Delay Jitter Guarantees — A scheme called the Hybrid SlotSize/Rate algorithm (HSSR) [41] can stabilize packet delayvariation in EPONs for jitter-sensitive high-priority traffic.HSSR not only uses a fixed cycle length but also fixes theposition of jitter-sensitive high-priority traffic grants (fixed tothe beginning of the frame). The lower priority traffic fromONUs occupies the remainder of the frame. HSSR causesmore than one grant per cycle to an ONU, which reduces effi-ciency due to extra guard times. However, the reduced effi-ciency allows for guaranteeing packet-delay variation boundsfor certain traffic. A portion of the fixed grant cycle is parti-tioned for jitter-sensitive traffic. Quasi non-intrusive rangingkeeps the ranging and registration process of new ONUs fromdisturbing high-priority traffic. The ranging and registrationresponses from new ONUs are scheduled to occur during thebest-effort portion of the fixed frame. The fixed frame is largeenough to provide ample time for this process.
Simulation results show that HSSR offers lower averagedelay and packet-delay variation than the conventionalscheme (i.e., no fixed position of high-priority traffic). Fur-ther, the packet-delay variation for HSSR is due solely toqueuing delay and not from the scheduling by the DBA.
The Hybrid Granting Protocol (HGP) [17] can ensure QoSthrough minimizing jitter and guaranteeing bandwidth. It is ahybrid of two approaches to sizing grants, one uses the
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IEEE Communications Surveys & Tutorials • 3rd Quarter 2008 57
REPORT message to size the grant; the other uses a queueprediction mechanism to size the grant to accommodate allqueued traffic at the point the grant begins (i.e., accommo-dates traffic in trgs). The first approach is used for assured for-warding (AF) [42] and best-effort (BE) services, whereas thelatter approach is used for expedited-forwarding (EF) [43]services that are assumed to have a constant bit rate andtherefore can be estimated easily.
A scheduling cycle is then divided into two subcycles: EFsubcycle and AF/BE subcycle. The EF subcycle carries the EFservices for each ONU and the AF/BE subcycle carries theAF and BE services for each ONU. Hence, every schedulingcycle there are two grants for each ONU. REPORTing of theAF and BE queues in an ONU is delayed until the end of theEF grant for that ONU. This allows the OLT to obtain moreup-to-date queue occupancy for the ONU because the DBAcomputation is performed after the EF subcycle.
By fixing the scheduling cycle size and fixing the positionof the EF grant to each ONU, HGP can guarantee bandwidthto EF traffic and minimize the jitter experienced by the EFtraffic. This QoS comes at the expense of more guard timesper cycle because of the separate grant to each ONU for itsEF traffic. To mitigate this inefficiency, a grant for AF/BEtraffic is not sent if there is no pending traffic, eliminating theneed for a guard time for the AF/BE grant.
HGP and HSSR [41] share the same frame structure anddivision. The novelty of HGP is the way in which theREPORTs are generated. Simulation results [17] show thatHGP provides lower queuing delay at higher loads as com-pared to a regular EPON scheduler. At lower loads, the regu-lar EPON scheduler provides lower queuing delay, which isattributed to the increased number of guard times per cyclewith HGP.
Admission Control — As reviewed, a variety of inter- andintra-ONU scheduling solutions exist to provide QoS inEPON networks. These solutions should be effective not onlyin supporting QoS but also must be designed carefully to pro-tect the requirements of already admitted traffic, as specifiedin the associated SLAs. Toward this end, admission controlmay become necessary to both support and protect the QoSrequirements in EPON networks.
Research on admission control for EPON began only veryrecently [44, 45]. An admission control framework togetherwith an appropriate DBA algorithm that is capable of sup-porting and protecting QoS of real-time traffic while guaran-teeing a minimum bandwidth for best-effort traffic wasintroduced and studied in [46]. The examined admission con-trol algorithm determines whether or not to admit a new real-time traffic stream based on its requirements and theutilization of the upstream wavelength channel. To achievethis, each polling cycle is divided into two subcycles. In thefirst subcycle, each ONU is assigned a guaranteed minimumbandwidth to support the respective QoS requirements of itsstreams. The second subcycle is used by the OLT to dynami-cally assign transmission windows to best-effort traffic of allONUs. The proposed admission control proceeds in twosteps. First, by using its assigned guaranteed bandwidth, eachONU performs local rate-based admission control accordingto the bandwidth requirements of newly arriving flows andcurrent bandwidth availability. Second, flows that could not belocally admitted are reported to the OLT, which in turn triesto admit them in the second subcycle, provided sufficientunused bandwidth is available.
The performance of the proposed admission control wasstudied by means of simulation using a strict priority and adeficit-weighted round-robin based intra-ONU scheduling
algorithm for real-time voice and video streams, as well asbest-effort data traffic. The obtained results show that theconsidered admission control is able to satisfy the QoSrequirements in terms of delay bound and throughput.
Summary — Differentiated services require differentiatedqueuing and reporting and different grant sizing and schedul-ing treatment for each class at the OLT. As the number ofqueues increases, scalability becomes an issue and a hierarchi-cal approach should be followed. Grant reservations arerequired for providing bandwidth guarantees. A fixed andproperly-sized cycle length with fixed position of delay and jit-ter-sensitive traffic can provide delay and jitter guarantees.More research must be conducted in the area of providingbandwidth, delay, and jitter guarantees on an EPON.
FAIRNESS
EPONs carry traffic from a diverse group of non-cooperativesubscribers. This non-cooperation requires fairness mecha-nisms to ensure that all nodes receive their “fair” share of thenetwork resources. Fairness is most effectively tackled by thegrant-sizing process and requires the use of the offline DBAframework. The limited and limited with excess distributiongrant-sizing schemes offer a method to provide fairness on anEPON. We now discuss other approaches to fairness.
A sibling fair scheduler [9], in the case of EPONs, is ascheduler that ensures fairness for queues within an ONU. Acousin fair scheduler [9] can guarantee fairness among allleaves (i.e., queues) regardless of grouping. An EPONrequires a scheduler that is fair among all queues and there-fore requires a cousin fair scheduler. Fair Queuing with Ser-vice Envelopes (FQSE) [9] is a hierarchical schedulingalgorithm that is cousin fair.
A service envelope (SE) is a grant to a node in the schedul-ing hierarchy. A service envelope for a leaf node is a piece-wise linear function of how satisfied a node is, wherebysatisfaction is measured in terms of a satisfiability parameter(SP). The SP begins at 0 when the SE is at its minimum guar-anteed bandwidth and increases linearly until the request iscompletely satisfied. The slope of the linear increase is deter-mined by the weight of the node.
The SE of non-leaf nodes is calculated as an approxima-tion of the sum of the SEs of all their children. The approxi-mation is necessary to keep the number of knee points in thepiecewise linear function from exceeding a prescribed maxi-mum. Limiting the number of knee points is necessary to keepthe request message that conveys the piecewise linear functionwithin a fixed length.
A deficit round robin approach within an ONU can beused to allow queues to contend for the cumulative slotremainder. This guarantees that there is only one slot remain-der per ONU as opposed to a slot remainder for each queue.As a result, unused slot remainders are reduced. Simulationand mathematical analysis [9] show that FQSE is capable ofmaking bandwidth guarantees, as well as providing fairnessbetween all queues regardless of which ONU they reside in(i.e., cousin fairness).
For open access EPONs, in which multiple service pro-viders share a single EPON, fairness must be maintainedamong service providers, as well as subscribers. Dual servicelevel agreements (Dual-SLAs) [47] can be used to manage thefairness for both subscribers and service providers. A Dual-SLA manages two sets of SLAs, one for the subscribers andone for the service providers. One of the sets of SLAs isselected as the primary. The primary SLA set is given priorityover the secondary.
IEEE Communications Surveys & Tutorials • 3rd Quarter 200858
MAC PROTOCOLS FOR
ALTERNATIVE PON ARCHITECTURES
MAC PROTOCOLS FOR A BROADCAST PON
Full-utilization local-loop request contention multiple access(FULL-RCMA) [5] is an extension of RCMA that allows fortransmission interleaving to tolerate the walk times on anEPON and provides a bounded cycle time for support of CBRtraffic. RCMA is a hybrid between a token-passing and con-tention MAC protocol. A cycle of time is divided into a con-tention-based request period and a token-passing data period.During the request period, ONUs contend through requestmessages to be added to the token-passing list for the upcom-ing data period. One of the ONUs is designated the masterand generates the token-passing list for the upcoming dataperiod. ONUs, according to the order determined by the mas-ter, pick up the token to gain access to the medium for theirtransmission. If ONUs remain backlogged after receiving theirtransmission window, they set a “more data” bit to signify thatthey automatically should be added to the token-passing listfor the next cycle. This helps to reduce the probability ofrequest collisions. ONUs that are added to the token-passinglist through request contention are given priority over ONUsthat are added through setting the “more data” bit in the pre-vious cycle. This allows new ONUs to gain prompt access tothe network. Performance analysis shows that FULL-RCMAcan provide higher upstream link utilization compared toIPACT or RCMA. However, a comparison of average packetdelay between the schemes is not available.
For the MAC protocol proposed in [6], cycles are dividedinto a control period and a data period separated by a waitingtime that is used to collect all control messages and to pro-duce a schedule. The control period is divided using fixedtime division multiple access (TDMA), one slot for eachONU. The ONUs independently compute the same transmis-sion schedule given the control information, and the dataperiod is divided between the ONUs according to this sched-ule. Because the control messages and data messages are sep-arated, there are 2 · N guard intervals per scheduling cycle asopposed to N guard intervals for a typical EPON, in which thecontrol information is appended to the end of the data trans-missions. This increased number of guard intervals degradesthe channel utilization.
MAC PROTOCOLS FOR TWO-STAGE PONS
A DBA scheme for a two-stage PON called EPON DynamicScheduling Algorithm (EDSA-2) [7] takes advantage of somepredictability of the aggregated traffic from the sub-OLTs.Because sub-OLTs aggregate traffic from several burstysources, the sub-OLT traffic tends to be less bursty and hence,more predictable. Specifically, EDSA-2 predicts the traffic dur-ing trgs by assuming short-term rate stationarity from the aggre-gated ONUs. Differentiated services are provided by having aset of class queues for the local sub-OLT traffic, as well as aseparate set of class queues for the aggregated ONU traffic.The aggregate ONU class queues are given priority over thecorresponding class queues for the local sub-OLT traffic.
Simulation results that compare EDSA-2 to a QoS DBAthat performs no traffic prediction (EDSA-1) show thatEDSA-2 provides lower average packet delay for all classes oftraffic from both standard ONUs and the sub-OLT ONUs.The lower delays for the sub-OLT traffic can be explained bythe accommodation of traffic received during the grantingperiod (i.e., trgs) through traffic prediction. However, it is notclear why the standard ONUs would experience lower delays.
CONCLUSION
In this article, we summarized and classified the existingresearch on EPONs. We introduced a meaningful frameworkthat allows those interested in advancing EPON research toquickly understand the state-of-the-art and to identify areasrequiring further study. We outlined the standard physicalPON architecture, as well as two alternative architectures,broadcast PON and two-stage PON. We also examined andprovided a meaningful taxonomy for dynamic bandwidth allo-cation. Using this taxonomy, we presented the existing workon dynamic bandwidth allocation. The major branches of thetaxonomy are• Grant sizing• Grant scheduling• Queue schedulingWe also surveyed the existing approaches for supporting qual-ity of service and fairness. Finally, we presented a discussionof protocols for the alternative physical PON architectures.We conclude by outlining areas that we believe are in urgentneed of further research.
The problem of ONU grant sizing has received significantattention from the research community, but there are stillimportant open questions. Providing an exhaustive service dis-cipline for EPONs can lower queuing delays by up to a cycletime. However, due to the nature of EPONs as a remotescheduling system, an exhaustive service discipline is not pos-sible without queue-size prediction. Prediction of queuedCBR traffic is straightforward as a result of its constant rate.VBR traffic, on the other hand, is difficult to predict. Withthe proliferation of VBR video through IPTV services, itwould be worthwhile to explore schemes to predict its short-term bandwidth requirements. These schemes can be used forqueue-size prediction to help lower the queuing delay for thisdelay-sensitive traffic. Data traffic is typically delay insensitive,so there is less of a need to reduce the queuing delays for thistype of traffic.
The problem of distributing excess bandwidth has beenexplored in the context of the offline DBA framework (i.e.,interleaved polling with stop). It would be of value to explorethe possibility of providing fair excess bandwidth distributionin the online DBA framework (i.e., a purely interleaved grant-ing system).
The topic of ONU grant scheduling has received someattention from the research community. However, we feelthis topic can be explored further to uncover the best grantscheduler for an EPON. The topic of ONU grant schedulinganchored in scheduling theory has been studied extensivelyin [48, 49] within the context of multiple-channel EPONs.Similar exposition should be extended to single-channelEPONs.
With respect to providing QoS on EPONs, providing dif-ferentiated services has received significant attention from theresearch community. However, providing bandwidth, delay,and delay variation (i.e., jitter) guarantees requires furtherstudy. Providing guaranteed service across an EPON will becritical because the access network is required to be an inte-grated services network carrying packetized voice and videoalong with data traffic. The voice and video services willrequire some level of bandwidth, delay, and jitter guaranteesfor successful operation.
Emerging from the work on single-channel EPONs,researchers are beginning to extend the DBA problem toEPONs that employ more than one upstream and/or down-stream channel [14, 50, 51, 52]. DBA for multi-wavelengthEPONs represents a broad area for future research.
IEEE Communications Surveys & Tutorials • 3rd Quarter 2008 59
REFERENCES[1] M. Hajduczenia et al., “On EPON Security Issues,” IEEE Com-
mun. Surveys and Tutorials, vol. 9, no. 1, 1st Quarter 2007,pp. 68–83.
[2] M. McGarry, M. Maier, and M. Reisslein, “Ethernet PONs: ASurvey of Dynamic Bandwidth Allocation (DBA) Algorithms,”IEEE Commun. Mag., vol. 42, no. 8, Aug. 2004, pp. S8–S15.
[3] G. Kramer, B. Mukherjee, and G. Pesavento, “IPACT: A Dynam-ic Protocol for an Ethernet PON (EPON),” IEEE Commun. Mag.,vol. 40, no. 2, Feb. 2002, pp. 74–80.
[4] G. Kramer, B. Mukherjee, and G. Pesavento, “Ethernet PON(ePON): Design and Analysis of an Optical Access Network,”Photonic Network Commun., vol. 3, no. 3, July 2001, pp.307–19.
[5] C. Foh et al., “FULL-RCMA: A High Utilization EPON,” IEEE
JSAC, vol. 22, no. 8, Oct. 2004, pp. 1514–24.[6] S. Sherif et al., “A Novel Decentralized Ethernet-Based PON
Access Architecture for Provisioning Differentiated QoS,”IEEE/OSA J. Lightwave Tech., vol. 22, no. 11, Nov. 2004, pp.2483–97.
[7] A. Shami et al., “QoS Control Schemes for Two-Stage EthernetPassive Optical Access Networks,” IEEE JSAC, vol. 23, no. 8,Aug. 2005, pp. 1467–78.
[8] T. Holmberg, “Analysis of EPONs under the Static PriorityScheduling Scheme with Fixed Transmission Times,” Proc. IEEE
Conf. Next Generation Internet Design and Engineering (NGI),Apr. 2006, pp. 192–99.
[9] G. Kramer et al., “Fair Queuing with Service Envelopes (FQSE):A Cousin-Fair Hierarchical Scheduler For Subscriber Access Net-works,” IEEE JSAC, vol. 22, no. 8, Oct. 2004, pp. 1497–1513.
[10] S. Bhatia, D. Garbuzov, and R. Bartos, “Analysis of the GatedIPACT Scheme for EPONs,” Proc. IEEE ICC, June 2006, pp.2693–98.
[11] F. Aurzada et al., “Delay Analysis of Ethernet Passive OpticalNetworks with Gated Service,” Arizona State University Techni-cal Report, Mar. 2007.
[12] J. Zheng and H. Mouftah, “Media Access Control for EthernetPassive Optical Networks: An Overview,” IEEE Commun. Mag.,vol. 43, no. 2, Feb. 2005, pp. 145–50.
[13] C. Assi et al., “Dynamic Bandwidth Allocation for Quality-of-Service over Ethernet PONs,” IEEE JSAC, vol. 21, no. 9, Nov.2003, pp. 1467–77.
[14] A. Dhaini et al., “Dynamic Wavelength and Bandwidth Alloca-tion in Hybrid TDM/WDM EPON Networks,” IEEE/OSA J. Light-
wave Tech., vol. 25, no. 1, Jan. 2007, pp. 277–86.[15] X. Bai, A. Shami, and C. Assi, “On the Fairness of Dynamic
Bandwidth Allocation Schemes in Ethernet Passive Optical Net-works,” Computer Commun., vol. 29, no. 11, July 2006, pp.2123–35.
[16] D. Bertsekas and R. Gallager, Data Networks, 2nd Ed., Pren-tice Hall, 1991.
[17] A. Shami et al., “Jitter Performance in Ethernet Passive Opti-cal Networks,” IEEE/OSA J. Lightwave Tech., vol. 23, no. 4,Apr. 2005, pp. 1745–53.
[18] H.-J. Byun, J.-M. Nho, and J.-T. Lim, “Dynamic BandwidthAllocation Algorithm in Ethernet Passive Optical Networks,”Electronics Letters, vol. 39, no. 13, June 2003, pp. 1001–2.
[19] Y. Luo and N. Ansari, “Bandwidth Allocation for MultiserviceAccess on EPONs,” IEEE Commun. Mag., vol. 43, no. 2, Feb.2005, pp. S16–S21.
[20] Y. Luo and N. Ansari, “Limited Sharing with Traffic Predictionfor Dynamic Bandwidth Allocation and QoS Provisioning overEthernet Passive Optical Networks,” OSA J. Opt. Net., vol. 4,no. 9, Sept. 2005, pp. 561–72.
[21] S. Haykin, Neural Networks: A Comprehensive Foundation,
2nd Ed., Prentice Hall, 1999.[22] S. Ostring and H. Sirisena, “The Influence of Long-Range
Dependence on Traffic Prediction,” Proc. IEEE Int’l. Conf. Com-
munications (ICC), vol. 4, June 2001, pp. 1000–1005.[23] G. Kramer et al., “Supporting Differentiated Classes of Service
in Ethernet Passive Optical Networks,” OSA J. Opt. Net., vol. 1,no. 8, Aug. 2002, pp. 280–98.
[24] Y. Zhu, M. Ma, and T. Cheng, “Hierarchical Scheduling toSupport Differentiated Services in Ethernet Passive Optical Net-
works,” Computer Networks, vol. 50, no. 3, Feb. 2006, pp.350–66.
[25] M. Ma, L. Liu, and T. H. Cheng, “Adaptive Scheduling for Dif-ferentiated Services in the Ethernet Passive Optical Networks,”Proc. 9th Int’l. Conf. Commun. Systems, Sept. 2004, pp.102–6.
[26] M. Pinedo, Scheduling: Theory, Algorithms, and Systems, 2nd
Ed., Prentice Hall, 2002.[27] J. Zheng and H. Mouftah, “Adaptive Scheduling Algorithms
for Ethernet Passive Optical Networks,” IEE Proc. Commun.,vol. 152, no. 5, Oct. 2005, pp. 643–47.
[28] J. Zheng, “Efficient Bandwidth Allocation Algorithm for Eth-ernet Passive Optical Networks,” IEE Proc. Commun., vol. 153,no. 3, June 2006, pp. 464–68.
[29] A. Parekh and R. Gallager, “A Generalized Processor SharingApproach to Flow Control in Integrated Services Networks: TheSingle-Node Case,” IEEE/ACM Trans. Net., vol. 1, no. 3, June1993, pp. 344–57.
[30] A. Demers, S. Keshav, and S. Shenker, “Analysis and Simula-tion of a Fair Queuing Algorithm,” Internetworking: Research
and Experience, vol. 1, no. 1, Sept. 1990, pp. 3–26.[31] P. Goyal, H. M. Vin, and H. Cheng, “Start-Time Fair Queuing:
A Scheduling Algorithm for Integrated Services Packet Switch-ing Networks,” IEEE/ACM Trans. Net., vol. 5, no. 5, Oct. 1997,pp. 690–704.
[32] N. Ghani et al., “Quality of Service in Ethernet Passive OpticalNetworks,” Proc. 2004 IEEE/Sarnoff Symp. Advances in Wired
and Wireless Commun., Apr. 2004, pp. 161–65.[33] N. Ghani et al., “Intra-ONU Bandwidth Scheduling in Ethernet
Passive Optical Networks,” IEEE Commun. Letters, vol. 8, no.11, Nov. 2004, pp. 683–85.
[34] A. Dhaini et al., “Adaptive Fairness through Intra-ONUScheduling for Ethernet Passive Optical Networks,” Proc. IEEE
Int. Conf. Commun. (ICC), June 2006, pp. 2687–92.[35] S.-I. Choi and J.-D. Huh, “Dynamic Bandwidth Allocation
Algorithm for Multimedia Services over Ethernet PONs,” ETRI
Journal, vol. 24, no. 6, Dec. 2002, pp. 465–68.[36] J. Xie, S. Jiang, and Y. Jiang, “A Dynamic Bandwidth Alloca-
tion Scheme for Differentiated Services in EPONs,” IEEE Com-
mun. Mag., vol. 42, no. 8, Aug. 2004, pp. S32–S39.[37] H. Naser and H. Mouftah, “A Joint-ONU Interval-Based
Dynamic Scheduling Algorithm for Ethernet Passive OpticalNetworks,” IEEE/ACM Trans. Net., vol. 14, no. 4, Aug. 2006,pp. 889–99.
[38] M. Ma, Y. Zhu, and T. Cheng, “A Bandwidth GuaranteedPolling MAC Protocol for Ethernet Passive Optical Networks,”Proc. IEEE INFOCOM, vol. 1, Mar. 2003, San Francisco, pp.22–31.
[39] M. Ma, Y. Zhu, and T. Cheng, “A Systematic Scheme for Mul-tiple Access in Ethernet Passive Optical Access Networks,”IEEE/OSA J. Lightwave Technology, vol. 23, no. 11, Nov. 2005,pp. 3671–82.
[40] L. Zhang et al., “Dual DEB-GPS Scheduler for Delay-ConstraintApplications in Ethernet Passive Optical Networks,” IEICE
Trans. Commun., vol. E86-B, no. 5, May 2003, pp. 1575–84.[41] F. An et al., “A New Dynamic Bandwidth Allocation Protocol
with Quality of Service in Ethernet-Based Passive Optical Net-works,” Proc. IASTED Int’l. Conf. Wireless and Optical Commu-
nications (WOC 2003), vol. 3, July 2003, pp. 165–69.[42] J. Heinanen et al., “Assured Forwarding PHB Group,” RFC
2597 (Proposed Standard), June 1999, updated by RFC 3260;http://www.ietf.org/rfc/rfc2597.txt
[43] V. Jacobson, K. Nichols, and K. Poduri, “An Expedited For-warding PHB,” RFC 2598 (Proposed Standard), June 1999,obsoleted by RFC 3246; http://www.ietf.org/rfc/rfc2598.txt
[44] A. Dhaini et al., “Admission Control in Ethernet Passive Opti-cal Networks (EPONs),” Proc. IEEE Int’l. Conf. Communications
(ICC), Glasgow, Scotland, June 2007.[45] A. Dhaini et al., “Per-Stream QoS and Admission Control in
Ethernet Passive Optical Networks (EPONs),” IEEE/OSA J. Light-
wave Tech., vol. 25, no. 7, July 2007, pp. 1659–69.[46] C. Assi, M. Maier, and A. Shami, “Toward Quality-of-Service
Protection in Ethernet Passive Optical Networks: Challengesand Solutions,” IEEE Network, vol. 21, no. 5, Sept.–Oct. 2007.
[47] A. Banerjee, G. Kramer, and B. Mukherjee, “Fair Sharing
IEEE Communications Surveys & Tutorials • 3rd Quarter 200860
Using Dual Service-Level Agreements to Achieve Open Accessin a Passive Optical Network,” IEEE JSAC, vol. 24, no. 8, Aug.2006, pp. 32–44.
[48] M. McGarry et al., “Bandwidth Management for WDMEPONs,” OSA J. Opt. Net., vol. 5, no. 9, Sept. 2006, pp.637–54.
[49] M. McGarry et al., “Just-in-Time Online Scheduling for WDMEPONs,” Proc. IEEE ICC 2007, June 2007.
[50] K. Kwong, D. Harle, and I. Andonovic, “Dynamic BandwidthAllocation Algorithm for Differentiated Services over WDMEPONs,” Proc. 9th IEEE Int’l. Conf. Commun. Systems (ICCS),Sept. 2004, pp. 116–20.
[51] M. McGarry, M. Maier, and M. Reisslein, “WDM Ethernet Pas-sive Optical Networks,” IEEE Commun. Mag., vol. 44, no. 2,Feb. 2006, pp. S18–S25.
[52] A. Dhaini, C. Assi, and A. Shami, “Quality of Service inTDM/WDM Ethernet Passive Optical Networks (EPONs),” Proc.
IEEE ISCC 2006, June 2006, pp. 616–21.
BIOGRAPHIESMICHAEL MCGARRY ([email protected]) received his BS inComputer Engineering from Polytechnic University, Brooklyn, NYin 1997. He received his M.S. and Ph.D. in Electrical Engineeringfrom Arizona State University, Tempe, AZ in 2004 and 2007respectively. He is an Assistant Professor at the University ofAkron, Akron, OH. From 2007 through 2008 he was a Senior StaffScientist at ADTRAN and an Adjunct Professor at Arizona State
University. From 1997 through 2003 he was employed in industryby companies including PMC-Sierra and Yurie Systems (now partof Alcatel-Lucent). His research interests include congestion con-trol and the optimization of MAC protocols for both opticalaccess and mobile ad hoc networks.
MARTIN REISSLEIN ([email protected]) received his Ph.D. in systemsengineering from the University of Pennsylvania, Philadelphia, in1998. He is an associate professor in the Department of ElectricalEngineering at Arizona State University, Tempe. From July 1998through October 2000 he was a scientist with the GermanNational Research Center for Information Technology (GMDFOKUS), Berlin, and lecturer at the Technical University Berlin. Hemaintains an extensive library of video traces for network perfor-mance evaluation, including frame size traces of MPEG-4 andH.264 encoded video, at http://trace.eas.asu.edu.
MARTIN MAIER ([email protected]) received his M.Sc. and Ph.D.degrees (both with distinction) in electrical engineering from theTechnical University Berlin, Berlin, Germany, in 1998 and 2003,respectively. In the summer of 2003, he was a Postdoctoral Fellowat the Massachusetts Institute of Technology (MIT), Cambridge.He is an associate professor with the Institut National de laRecherche Scientifique (INRS), Montreal, Canada. His recentresearch activities aim at providing insights into technologies,protocols, and algorithms shaping the future of optical networksand their seamless integration with next-generation wireless net-works. He was a visiting professor at Stanford University, Califor-nia, October 2006 through March 2007.
1
Shortest Propagation Delay (SPD) First Scheduling
for EPONs with Heterogeneous Propagation DelaysMichael P. McGarry, Martin Reisslein, Frank Aurzada, and Michael Scheutzow
Abstract—Due to the geographic distribution of its subscribers,Ethernet Passive Optical Networks (EPONs) have typicallyvarying propagation delays between the Optical Network Units(ONUs) and the Optical Line Terminal (OLT). In this paper, weconsider EPONs with an offline scheduling framework, whichenables Quality-of-Service mechanisms by collecting bandwidthrequests from all ONUs before the OLT makes dynamic band-width allocations for transmissions on the shared ONUs-to-OLT upstream channel. We propose and evaluate the ShortestPropagation Delay (SPD) first scheduling policy which sequencesthe ONUs’ upstream transmissions in increasing order of theONUs’ propagation delays, i.e., the upstream transmission ofthe ONU with the smallest propagation delay is scheduled first.We formally analyze the competitiveness of SPD first schedulingand find that it achieves very close to optimal performance.We characterize the stability limit for Gated and Limited grantsizing in conjunction with SPD grant scheduling. We evaluatethe cycle length and packet delay with SPD scheduling throughprobabilistic analysis and simulations and find significant reduc-tions in packet delay with SPD first scheduling in EPONs withheterogeneous propagation delays, especially when Limited grantsizing is employed.
Index Terms—Ethernet Passive Optical Network, Grantscheduling, Packet delay, Propagation delay.
I. INTRODUCTION
Passive Optical Networks (PONs) have emerged as an
attractive technology for high-speed access networks [1]–[4].
In particular, the combination of PON technologies with the
ubiquitous Ethernet networking technologies has made Ether-
net PON (EPON) a promising access network choice [5]–[14].
In Ethernet Passive Optical Networks (EPONs), an Optical
Network Unit (ONU) provides high-speed network access to
an individual subscriber or a group of subscribers. Several
ONUs connect to a single Optical Line Terminal (OLT),
typically in the form of a tree topology rooted at the OLT.
Due to the geographic distribution of the served subscribers,
the individual ONUs have typically different distances, and
thus different propagation delays from the OLT. With the
emergence of long reach and next-generation PONs [15]–
[19] covering larger geographic areas with spans of 100 km
or higher (i.e., one-way ONU-to-OLT propagation delays of
M. McGarry is with the Dept. of Electrical and Computer Eng., Universityof Akron, Akron, OH 44325, Email: [email protected], Phone: (330)972-7168, Fax: (330) 972-6487.
M. Reisslein is with the School of Electrical, Computer, and EnergyEngineering, Arizona State University, Tempe, AZ 85287-5706, Email:[email protected], Phone: (480) 965-8593, Fax: (480) 965-8325.
F. Aurzada and M. Scheutzow are with the Institute of Mathematics,Technical University Berlin, Berlin, Germany, Email: {aurzada, ms}@tu-berlin.de.
0.5 ms or higher), the disparities of the propagation delays are
likely becoming more pronounced.
EPONs avoid collisions on the shared upstream (ONUs-to-
OLT) channel through a polling based medium access control
protocol. The ONUs signal their bandwidth demands with
REPORT messages to the OLT, while the OLT dynamically
allocates bandwidth and schedules the upstream transmis-
sions so as to avoid collisions. The OLT signals the ONUs
with GATE messages their upstream transmission windows
(grants). A key challenge for efficient sharing of the upstream
channel is the masking of the round trip propagation delay
between OLT and ONUs. One of the first approaches for
masking the propagation delays has been the Interleaved
Polling with Adaptive Cycle Time (IPACT) approach [9], [20]
which interleaves the REPORT-GATE cycles of the individual
ONUs so that they can mask each others propagation delays.
The basic IPACT approach implements the online scheduling
framework in that the OLT considers a single ONU REPORT
when making bandwidth allocation and scheduling decisions.
Quality of Service (QoS) control generally requires that the
OLT considers and trades off requests from several ONUs
when making bandwidth allocation and scheduling decisions.
With the offline scheduling framework [21], which is referred
to as interleaved polling with stop in [14], [22], the OLT
collects REPORTs from all ONUs before making bandwidth
allocation and scheduling decisions. The offline scheduling
framework thus enables the wide variety of QoS mechanisms,
see for instance, [23]–[28], which consider jointly all RE-
PORTs in their bandwidth allocation and scheduling decisions.
On the downside, the offline scheduling framework imposes
an idle period on the upstream channel between cycles due to
the OLT schedule computation time, and transmission time of
the first GATE message and the round trip propagation delay
to the first scheduled ONU of a new cycle, as described in
more detail in Section III-B. Further idle periods are possible
if an upstream transmission is not long enough to mask the
propagation delay to the next ONU in the schedule.
A few studies have pursued strategies that combine online
scheduling and offline scheduling. For instance, the stud-
ies [29]–[32] schedule ONUs with small bandwidth requests
immediately (i.e., in online fashion), while ONUs with large
bandwidth requests are only scheduled after REPORTs from
all ONUs have been collected (i.e., in offline fashion) and more
informed decisions are possible. When the ONU propagation
delays are fairly homogeneous, scheduling small bandwidth
request (which have a small impact on the QoS and fairness
properties of the schedule) right away can indeed be a good
strategy to mask propagation delays for the larger requests,
2
which require more careful informed decisions. However,
when the propagation delays of the ONUs are vastly different
then scheduling a small grant for a far-away ONU can result
in large idle times. Thus, for EPONs with heterogeneous
propagation delays, the scheduling decisions need to take the
propagation delays into consideration.
In this paper, we examine, to the best of our knowledge, for
the first time the problem of efficiently masking heterogeneous
propagation delays in EPONs with offline scheduling. We
propose and evaluate the Shortest Propagation Delay (SPD)
first scheduling policy. The SPD first policy strives to mask
the long round trip propagation delays to far-away ONUs
by first scheduling the upstream transmissions of near-by
ONUs. We prove that the SPD first policy minimizes the
cycle length to within a small time period (number of ONUs
times transmission delay of GATE message) of an optimal
scheduling policy. We characterize the cycle length and packet
delay of SPD first scheduling for Gated grant sizing in low
load and high load regimes through probabilistic analysis and
derive stability limits for Limited grant sizing [9]. We conduct
extensive simulations to verify our analysis and to broadly
assess the reductions in cycle length and packet delay as well
as the increase in channel utilization achieved with SPD first
scheduling.
Importantly, by including a sufficient number of close-
by ONUs with small propagation an EPON using SPD first
scheduling can be engineered to allow for offline scheduling
with a very small imposed idle time between scheduling
cycles. Further, SPD first scheduling is very simple in that
a given set of served ONUs needs to be sorted only once in
increasing propagation delays.
This article is organized as follows. In Section II we
provide background on scheduling in EPONs and review
related work. In Section III we formally model the grant
scheduling problem with heterogeneous propagation delays
and characterize the competitiveness of SPD first scheduling.
We also derive approximations of the mean cycle length and
packet delay. In Section IV we present numerical results from
our analytical cycle length and delay evaluation and provide
extensive simulation results for SPD first scheduling. Finally,
in Section V we summarize our findings.
II. BACKGROUND AND RELATED WORK
In this section we briefly provide background on the dy-
namic bandwidth allocation in EPONs and review related
research on scheduling in EPONs. The dynamic bandwidth
allocation (DBA) in EPONs can be divided into: 1) the
sizing of the upstream transmission windows (grants), and
2) the scheduling of the grants on the upstream wavelength
channel [11]. Widely used grant sizing methods are Gated
grant sizing, where the OLT sets the grant size equal to the
ONU request and Limited grant sizing, where the OLT sets
the grant size equal to the ONU request up to a maximum
grant size; if request exceeds the maximum grant size, then
the maximum grant size is allocated [9], [20].
As noted in the Introduction, the basic online scheduling
framework considers and schedules one ONU request at a
time, whereas the offline scheduling framework collects re-
ports from all ONUs before making scheduling decisions. A
few studies have examined a just-in-time scheduling frame-
work, where ONU requests are collected and scheduling
decisions are made when the channel is about to become
idle [21], [33], [34]. In [35] the ONUs are split into two groups
whereby each group is scheduled in offline fashion and the
cycles of the two groups are interleaved to mask the idle time
in between cycles. We also note that a few studies have sought
to improve on the REPORT-GATE traffic signaling through
traffic prediction, see e.g., [36]–[38]. In this first study on grant
scheduling in EPONs with heterogeneous propagation delays
we focus on the offline scheduling framework as efficient
offline scheduling in EPONs with heterogeneous propagation
delays can serve as a basis for future studies combining QoS
mechanisms, such as [23]–[28], with efficient scheduling for
heterogeneous propagation delays. We leave the study of grant
scheduling for heterogeneous propagation delays in EPONs
with just-in-time scheduling, a combination of online and
offline scheduling, or traffic prediction for future research.
Primarily for the offline scheduling framework, where all
ONU requests are considered in scheduling decisions, but also
for the approaches combining online and offline scheduling
and for the just-in-time approaches, where a subset of the
ONUs are considered, a wide variety of specific scheduling
policies have been examined. A number of studies have
examined scheduling policies that provide prescribed QoS
differentiation or fairness properties, e.g., [23]–[32]. We focus
in this first study on heterogeneous propagation delays on min-
imizing the average packet delay; considering heterogeneous
propagation delays in conjunction with QoS differentiation
and fairness mechanisms are important directions for future
research. Existing scheduling policies for minimizing the
average packet delay include:
• Earliest Arrival First (EAF) scheduling [14], [39] which
orders ONUs by the arrival time of the head of line
packet.
• Shortest Processing Time (SPT) first scheduling [21], [33]
which orders ONUs by their grant size.
• Largest Processing Time (LPT) first scheduling [14],
[25] which orders ONUs by their grant size (descending
order).
• Largest Number of Frames (LNF) first scheduling [21]
which orders ONUs by the number of frames queued
(descending order).
A recent comparison found that LNF provided slightly smaller
or the same average queueing delays [21] than the other
policies and we consider therefore LNF as a benchmark in
our performance evaluation in Section IV.
We also note that efforts to mask propagation and other
system delays (such as laser tuning times) have been examined
for medium access control and scheduling in WDM star
networks, e.g., [40], [41]. These WDM star networks provide
all-to-all connectivity and are thus fundamentally different
from the EPON tree network, where only the OLT can reach
all ONUs.
3
Γ
2
stall
schedt
tR tR tRG1 G2 G3
tR
tR
tR
G1
G2
G3
tG tG tG
τ (3)
τ (3)τ (3)τ (3)
τ (2)
τ (2)
τ (1)
τ (1)
tR
tR
tstall
1
OLT
t 3
stall=0
t=0
t tgg
ONU 1
ONU 2
ONU 3
t
Fig. 1. Illustration of offline scheduling with three ONUs. The upstream channel experiences an idle (stall) period due to the scheduling computation timetsched, transmission time of first GATE message tG, and round trip propagation delay 2τ(1). There are further stall periods if the upstream transmission ofan ONU does not mask the round trip propagation delay of the next ONU.
III. PERFORMANCE ANALYSIS
A. Model Notation
We consider the EPON reporting and granting cycle with the
offline scheduling framework, which is illustrated in Fig. 1 for
N = 3 ONUs. We denote tsched for the schedule computation
time, i.e., the time duration from the instant when all REPORT
messages have been received at the OLT to the instant the
transmission of the first GATE message commences. We
denote tG for the fixed transmission time [in seconds] of
an MPCP GATE message, tg for the fixed guard time [in
seconds] required between ONU transmission windows, and
tR for the fixed transmission time of a MPCP REPORT
message. We let the constants τi, i = 1, . . . , N , denote the
one-way propagation delays [in seconds] between OLT and
ONU i (which we consider to be equal to the ONU i to OLT
propagation delay). We let τ(i), i = 1, . . . , N , denote the prop-
agation delays sorted in ascending order, i.e., τ(1) = mini τi
and τ(N) = maxi τi. For a given cycle, we let Ri be a
random variable denoting the reported queue depth (in units of
seconds of upstream transmission time) and Gi [in seconds]
be a random variable denoting the duration of the upstream
transmission window (grant) of ONU i, i = 1, . . . , N . We
suppose that Gi includes all “per-Ethernet frame” overheads,
such as Preamble and Inter Packet Gap (IPG).
For a given cycle, we define the cycle length Γ as the
time period from the instant the scheduling commences to the
instant the upstream transmissions of the cycle are completely
received. We define the upstream channel utilization η as the
ratio of the sum of upstream transmission windows to the cycle
length, i.e., η =∑N
i=1 Gi/Γ
B. Problem Overview
Generally, in order to minimize packet delays and maximize
the utilization on the EPON upstream channel, idle periods
on the upstream channel should be minimized. In turn, with
minimal idle periods, the cycle length Γ is minimized. With
the offline scheduling framework, there is an idle period
(stall time) between the instant the end of the last upstream
transmission of the preceding cycle arrives at the OLT and the
instant the beginning of the first upstream transmission of the
current cycle arrives at the OLT. Clearly, this first stall time
is minimized by sending the first GATE message to the ONU
with the shortest propagation delay, which results in
tstall1 = max(tsched + tG + 2τ(1), tg). (1)
For illustration of the problem suppose that next the GATE
messages and upstream transmissions of ONUs 2 and 3 follow,
see Fig. 1. If the first upstream transmission is too short to
mask the round-trip propagation delay to ONU 2, a stall time
tstall2 occurs between the end of the first upstream transmission
and the beginning of the reception of the second upstream
transmission. More specifically, if
tstall1 + G1 + tR + tg < tsched + 2tG + 2τ2, (2)
then a non-zero stall time tstall2 occurs. On the other hand, as
illustrated for ONU 3 in Fig. 1, if the round-trip propagation
delay is masked by a preceding upstream transmission, then
there is no stalling.
Note that in the illustration in Fig. 1, the sequence of the
GATE message transmissions is equal to the sequence of up-
stream transmissions reaching the OLT. These two sequences
do not necessarily need to be the same. In fact, one can
4
relatively easily construct examples where first sending the
GATE message to a far-away ONU, followed by sending the
GATE messages and receiving the upstream transmissions of
near-by ONUs, followed by the reception of the upstream
transmission from the far-away ONU minimizes idle periods,
and thus the cycle length. We also note that [20] briefly
mentioned that GATE messages to far-away ONUs may need
to be sent before GATE messages to near-by ONUs to achieve
close to continuous utilization of the upstream channel, but
did not analyze in any detail the scheduling of the upstream
transmission windows.
C. Solution Strategy
The scheduling of the upstream transmissions can be viewed
as a generalized version of the scheduling problem with release
times, i.e., times when a given job becomes eligible for
execution. Even for fixed known release times, the problem of
minimizing the total completion time is strongly NP-hard [42].
Our problem is more general in that the release times, i.e., the
times when upstream transmissions can at the very earliest
arrive at the OLT depend on the sequencing of the GATE
message transmissions.
To the best of our knowledge, the combined problem of
scheduling the sequence of GATE message transmissions and
upstream transmissions so as to minimize the cycle time is
mathematically intractable. Our solution strategy is to consider
two restrictions: (R1) We suppose that the GATE message
transmission time tG is equal to the REPORT message trans-
mission time tR, This is reasonable as both of these MPCP
messages are sent in minimum-length Ethernet frames. Noting
that every upstream transmission must at least contain a
REPORT to obtain the current queue depth of the ONU,
tG = tR implies that Gi ≥ tG ∀i. (R2) We initially suppose
that the sequence of the GATE message transmissions is equal
to the sequence of the upstream transmissions arriving at
the OLT. Note that even with this restriction, the problem
of scheduling the upstream transmissions is a generalized
version of the scheduling with release times in that the release
times of the jobs are not fixed, but rather depend on their
position in the schedule (i.e., the number of tG delays in
the release time varies according to the sequence of the
upstream transmissions). Given these two restrictions, we show
in Section III-D that the shortest propagation delay (SPD) first
scheduling policy minimizes the cycle time. Subsequently, in
Section III-E we relax the restriction R2 on the sequence of
the GATE messages and characterize the competitiveness of
SPD scheduling.
D. Shortest Propagation Delay (SPD) First Optimality
Theorem 1. If Gi ≥ tG ∀i and the GATE message trans-
mission sequence is equal to the sequence of the upstream
transmissions, then Shortest Propagation Delay (SPD) first
scheduling of the upstream transmissions minimizes the cycle
duration Γ.
Proof: Without loss of generality, we neglect the schedul-
ing time tsched and the guard times tg in the following
Case (A): Cycle length governed by τ2:
tG tG¡
¡¡
¡¡@@
@@@
τ1 τ1
G1
@@
@@
@@
τ2
¡¡
¡¡
¡¡
τ2
G2
Γ1,2 = 2tG + 2τ2 + G2
Case (B): Cycle length governed by τ1:
tG tG¡
¡¡
¡¡
¡¡@@
@@
@@@
τ1 τ1
G1 G2
@@@τ2 ¡
¡¡τ2
Γ1,2 = tG + 2τ1 + G1 + G2
Fig. 2. Illustration of cases for evaluation of cycle length Γ1,2.
as they are not affected by the scheduling of the upstream
transmissions.
a) Comparison of two ONUs: Consider two ONUs 1 and
2. Let Γ1,2 denote the cycle length when ONU 1 is scheduled
before ONU 2. As illustrated in Fig. 2, there are two cases for
the evaluation of Γ1,2: (A) the propagation delay τ2 governs
the cycle length, and (B) the propagation delay τ1 governs the
cycle length. Clearly, the actual cycle length Γ1,2 is obtained
as the maximum of the two cases:
Γ1,2 = max (2tG + 2τ2, tG + 2τ1 + G1) + G2. (3)
Analogously, we obtain by symmetry (which only exchanges
the roles of 1 and 2) the cycle length when ONU 2 is scheduled
first, followed by ONU 1:
Γ2,1 = max (2tG + 2τ1, tG + 2τ2 + G2) + G1. (4)
We want to show that if Gi ≥ tG then we cannot have
τ1 > τ2 and Γ1,2 < Γ2,1, (5)
i.e., it cannot be that scheduling the ONU with the longer
propagation delay (no. 1 in this case) leads to a shorter cycle
length.
We proceed to show that (5) leads to a contradiction. We
distinguish all possible cases according to where the maximum
in the definition of Γ1,2 and Γ2,1, respectively, is attained.
Case 1: 2tG + 2τ2 ≤ tG + 2τ1 + G1 and 2tG + 2τ1 ≤
tG +2τ2 +G2. In this case, we have (the first condition comes
from Γ1,2 < Γ2,1, the other two from the condition for the
case).
tG + 2τ1 + G1 + G2 < tG + 2τ2 + G2 + G1 (6)
2tG + 2τ2 ≤ tG + 2τ1 + G1 (7)
2tG + 2τ1 ≤ tG + 2τ2 + G2. (8)
Note that equation (6) is a contradiction to τ1 > τ2.
5
Case 2: 2tG + 2τ2 ≥ tG + 2τ1 + G1 and 2tG + 2τ1 ≤
tG + 2τ2 + G2. Here, we get
2tG + 2τ2 + G2 < tG + 2τ2 + G2 + G1 (9)
2tG + 2τ2 ≥ tG + 2τ1 + G1 (10)
2tG + 2τ1 ≤ tG + 2τ2 + G2. (11)
Note that (10) is a contradiction to τ1 > τ2 and tG ≤ G1.
Case 3: 2tG + 2τ2 ≤ tG + 2τ1 + G1 and 2tG + 2τ1 ≥
tG + 2τ2 + G2. Here, we get
tG + 2τ1 + G1 + G2 < 2tG + 2τ1 + G1 (12)
2tG + 2τ2 ≤ tG + 2τ1 + G1 (13)
2tG + 2τ1 ≥ tG + 2τ2 + G2. (14)
Note that (12) is a contradiction to tG ≤ G2.
Case 4: 2tG + 2τ2 ≥ tG + 2τ1 + G1 and 2tG + 2τ1 ≥
tG + 2τ2 + G2. Here, we get
2tG + 2τ2 + G2 < 2tG + 2τ1 + G1 (15)
2tG + 2τ2 ≥ tG + 2τ1 + G1 (16)
2tG + 2τ1 ≥ tG + 2τ2 + G2. (17)
Note that (16) is a contradiction to τ1 > τ2 and tG ≤ G1.
b) General case: Now, consider N ONUs with propaga-
tion delays τ1, . . . , τN , respectively. We show that it is optimal
to schedule them in SPD first manner.
Assume that they are scheduled in the natural order (first
ONU 1 with τ1, etc.). Consider ONUs i and i + 1. We have
shown above that it is better (in the sense that the overall
cycle time is shorter (at least not longer)) when scheduling
the upstream transmission of ONU i before the upstream
transmission of ONU i+1 if τi ≤ τi+1. This is not influenced
by the fact that the transmissions of ONUs i and i + 1 may
be delayed by preceding transmissions of other ONUs. In any
case, it cannot be a loss to schedule the ONU with the shortest
propagation delay first. This implies the assertion, since i was
arbitrary.
Note that an immediate corollary of Theorem 1 is that SPD
first scheduling maximizes the upstream channel utilization.
As examined in detail in the next section, the bound in
Theorem 1 shows that SPD first scheduling is very close to
optimal, since the GATE transmission time tG is typically
small compared to traffic.
E. Competitiveness of SPD Scheduling
In this section, we examine the competitiveness of SPD
first scheduling in comparison to an optimal schedule that
minimizes the cycle length. The optimal schedule may have
different sequences of GATE transmissions and upstream
transmissions, i.e., does not need to meet restriction R2. We
still require that the optimal schedule meets restriction R1
that Gi ≥ tG since the EPON polling requires that each
upstream transmission contains at least a REPORT. We first
characterize the absolute difference of the cycle length with
SPD ΓSPD compared to the minimal cycle length Γopt of an
optimal schedule. Next, we examine the competitive ratio of
SPD scheduling, i.e., the bound on the ratio of the cycle length
with SPD scheduling ΓSPD to the cycle length of an optimal
schedule Γopt.
Theorem 2. The cycle length with SPD first scheduling
exceeds the minimal cycle length by no more than (N −
1)tG, i.e.,ΓSPD ≤ Γopt + (N − 1)tG.
Proof: For SPD first scheduling, let tstarti , i = 1, . . . , N ,
denote the instant when the upstream transmission of ONU ibegins to arrive at the OLT. We define for convenience tstart0 :=0 and G0 = 0 and note that
tstarti = max(itG + 2τ(i), tstarti−1 + Gi−1 + tg). (18)
The cycle length is
ΓSPD = tstartN + GN . (19)
Now, consider a imaginary EPON where the grants to all
ONUs are communicated with one GATE message requiring
only one transmission time tG. This imaginary EPON serves
as a comparison for the optimal scheduling in the real EPON.
Let Γopt,c denote the cycle time in the imaginary EPON (the
subscript c is for “comparison strategy”). Clearly, SPD first
scheduling of the upstream transmissions is optimal in the
imaginary EPON.
We proceed to show that
ΓSPD − (N − 1)tG ≤ Γopt,c ≤ Γopt ≤ ΓSPD, (20)
where the last two inequalities are trivially satisfied. We prove
the first inequality by induction. In the imaginary EPON let
sstarti denote the instant when the upstream transmission of
ONU i begins to arrive at the OLT. Denote sstart0 := 0 and
note that
sstarti = max(tG + 2τ(i), sstart
i−1 + Gi−1 + tg),
for i = 1, . . . , N. (21)
We obtain by induction that
tstarti ≤ sstarti + (i − 1)tG. (22)
The case i = 1 is trivial. In general, we get
tstarti = max(itG + 2τ(i), tstarti−1 + Gi−1 + tg) (23)
≤ max(itG + 2τ(i),
sstarti−1 + (i − 2)tG + Gi−1 + tg) (24)
≤ max((i − 1)tG + tG + 2τ(i),
sstarti−1 + (i − 1)tG + Gi−1 + tg) (25)
= (i − 1)tG + max(tG + 2τ(i),
sstarti−1 + Gi−1 + tg) (26)
= (i − 1)tG + sstarti . (27)
The assertion follows from (22), since
ΓSPD = tstartN + GN (28)
≤ sstartN + GN + (N − 1)tG (29)
= Γopt,c + (N − 1)tG. (30)
We remark that the bound in Theorem 2 is attained for an
example scenario with τ1 = . . . = τN−1 = 0, 2τN = NtG,
6
and G1 = . . . = GN = tG. For this example, the cycle length
with optimal scheduling is Γopt = (N + 2)tG, whereas the
cycle length with SPD scheduling is ΓSPD = (2N + 1)tG.
That is, the difference ΓSPD−Γopt is exactly (N−1)tG in this
example, and thus the bound in Thm 2 cannot be improved.
Proposition 1. The competitive ratio for the cycle length with
Smallest Propagation Delay (SPD) first scheduling is
ΓSPD
Γopt≤ min
{
tG + 2maxi τi +∑
i Gi
tG + 2mini τi +∑
i Gi
,
tG + 2maxi τi +∑
i Gi
tG + maxi(2τi + Gi)
}
. (31)
Proof: First, note that the shortest possible cycle length
must satisfy
Γopt ≥ tG + 2τ(1) +
N∑
i=1
Gi (32)
since at least the first GATE needs to be transmitted and at
least the round trip propagation delay to the nearest ONU is
incurred before all the upstream transmissions (with aggregate
duration∑N
i=1 Gi) can arrive at the OLT. This bound is
attained when the ONU with the shortest propagation delay
has a very large upstream transmission.
Second, note that cycle must be long enough to accommo-
date the GATE message transmission, round-trip propagation
delay, and upstream transmission of each individual ONU i,i.e.,
Γopt ≥ tG + 2τi + Gi (33)
for each ONU i, i = 1, . . . , N . Since this holds for all i we
can take the maximum over all ONUs yielding
Γopt ≥ tG + maxi
(2τi + Gi). (34)
This bound is attained if one ONU with a large propagation
delay has a large upstream transmission and all other ONUs
have small propagation delays and upstream transmissions.
Thirdly, for the cycle time with SPD first scheduling
ΓSPD ≤ tG + 2τ(1) +
N∑
i=1
Gi +
N−1∑
i=1
δi,i+1 (35)
where we define δi,i+1 as the difference between the (i +1)th smallest and the ith smallest round trip propagation delay,
i.e., δi,i+1 = 2τ(i+1) − 2τ(i) for i = 1, . . . , N − 1. Note that∑N−1
i=1 δi,i+1 is the worst case for the stall times in between
the upstream transmissions arriving at the OLT. This worst-
case occurs if each ONU has only a REPORT message to
send upstream, i.e., Gi = tG. The δ-sum is telescoping and
we get
N−1∑
i=1
δi,i+1 = 2τ(N) − 2τ(1). (36)
Thus,
ΓSPD ≤ tG + 2τ(N) +
N−1∑
i=1
Gi. (37)
Combining (32) and (37) we get
ΓSPD
Γopt≤
tG + 2τ(N) +∑N
i=1 Gi
tG + 2τ(1) +∑N
i=1 Gi
. (38)
From (34) and (37) we get
ΓSPD
Γopt≤
tG + 2τ(N) +∑N
i=1 Gi
tG + maxi(2τi + Gi). (39)
The bounds in Proposition 1 show that the SPD first
scheduling policy has a good competitive ratio in most cases.
Indeed, the first bound is a good competitive ratio, i.e., is
close to one, if∑N
i=1 Gi is large, i.e., if there is heavy traffic.
The second bound is a good competitive ratio if τ(N) is large
compared to∑N
i=1 Gi, i.e., typically if there is light traffic.
From the derivations of the preceding bounds we obtain
the following insights into SPD first scheduling and potential
heuristics to improve on SPD first scheduling: a) If there is
heavy traffic at ONUs with short propagation delays, then send
them their GATE messages as soon as possible following the
SPD first policy. With this strategy the traffic from the ONUs
with short propagation delays can mask the GATE transmis-
sions and round trip propagations to the far-away ONUs. b)
If there is little traffic at the ONUs with short propagation
delays, then GATE messages could first be sent to the ONUs
with large propagation delays, even though their upstream
transmission windows should, of course, be scheduled after the
windows of the ONUs with short propagation delays. With this
strategy, the ONUs with short propagation delays can finish
their transmissions by the time the upstream transmissions
from the ONUs with long propagation delays arrive at the
OLT.
F. Packet Delay Analysis
In this section, we analyze the cycle length and packet delay
with SPD first scheduling for Gated grant sizing. We consider
approximations for light traffic and heavy traffic. We define
the Poissonian packet traffic load ρi, i = 1, . . . , N of ONU ias the ratio of the average traffic bit rate (including Ethernet
frames plus “per-Ethernet frame” overhead, i.e., preamble and
IPG) generated at ONU i to the upstream channel bit rate
C [bit/s]. Unlike for the analysis in the preceding sections,
we do not consider the REPORT message with transmission
time tR = tG as part of a grant Gi in this section, but rather
account for the REPORT transmission times separately from
the grant duration. We denote ρt =∑N
i=1 ρi for the total load.
Noting that with Gated grant sizing the “per-grant” overhead
(REPORT message, guard time) becomes negligible as the
grants grow very large in heavy traffic, the stability condition
(maximum throughput) with gated grant sizing is ρt < 1(which holds for arbitrary packet traffic patterns, including
self-similar traffic). We let L̄ and σL [in bit] denote the mean
and standard deviation of the packet size (plus Preamble and
IPG). We define Poi[ω] for a random variable with Poisson
distribution with parameter ω.
7
1) Low load scenario: In a low load situation with SPD
scheduling, the cycle time is determined by the last (longest
prop. delay) ONU. Namely, the cycle time in cycle n + 1satisfies
ΓLL(n + 1) = NtG + 2τ(N) +L̄
CPoi
[
ρ(N)C
L̄ΓLL(n)
]
+ tG,
(40)
where ρ(N) is the load parameter of the ONU with the
largest propagation delay τ(N). The cycle consists of N GATE
message transmission and the data packet transmissions plus
REPORT message transmission of the last ONU. The other
transmissions are masked by the long propagation delay of
the last ONU (due to the low load assumption).
Taking expectations we get
EΓLL = NtG + 2τ(N) + ρ(N)EΓLL + tG. (41)
This yields
EΓLL =(N + 1)tG + 2τ(N)
1 − ρ(N). (42)
Since we need the second moment of the cycle time for the
delay analysis, we obtain in the same way from (40):
EΓ2LL = VΓLL + (EΓLL)2 (43)
= ρ(N)L̄
CEΓLL + (EΓLL)2 (44)
= EΓLL(ρ(N)L̄
C+ EΓLL). (45)
The delay of a packet generated at ONU i consists of the
backward recurrence time of the cycle length [43, Ch. 5.5]EΓ2
LL
2EΓLL
, i.e., the time until the generated packet is included in
a REPORT, the time period from the instant the transmission
of the REPORT is complete to the instant the next upstream
transmission commences, which is itG + 2τ(i) due to the low
load assumption, and the time needed within the grant until
the considered packet commences transmission ρiEΓ2
LL
2EΓLL
:
D(i)LL =
EΓ2LL
2EΓLL
+ itG + 2τ(i) + ρi
EΓ2LL
2EΓLL
+τ(i) +L̄
C. (46)
= (1 + ρi)ρ(N)
L̄C
+ EΓLL
2+ itG
+3τ(i) +L̄
C(47)
The overall delay is then given by
DLL =1
ρt
N∑
i=1
ρ(i)D(i)LL, (48)
where ρt :=∑N
i=1 ρi and ρ(i) is the load parameter of the
ONU with the i-th smallest propagation delay.
2) Heavy load scenario: In a heavy load scenario, all ONUs
have data to send, which masks the round-trip delays between
OLT and the second to last ONUs in the SPD first schedule.
In this case, the cycle length satisfies
EΓHL = tG +2τ(1) +
N∑
i=1
ρiEΓHL +NtG +(N −1)tg, (49)
because a cycle consists of the GATE transmission plus round
trip propagation delay to the first ONU (the one with the
shortest propagation delay) and all the traffic that is sent
(which consists of the accumulated data traffic and the NREPORT messages). This gives
EΓHL =(N + 1)tG + (N − 1)tg + 2τ(1)
1 −∑N
i=1 ρi
. (50)
This scenario resembles the case of a single ONU for which
the packet delay was analyzed in [44]. Inserting τHL :=N+1
2 tG + N−12 tg + τ(1) and ρt :=
∑N
i=1 ρi in Eqn. (39)
in [44], namely
DHL = 2τHL
2 − ρt
1 − ρt
+ρt
2C(1 − ρt)
(
σ2L
L̄+ L̄
)
+L̄
C(51)
gives an approximation of the packet delay.
G. Stability of Limited grant sizing
For Limited grant sizing with SPD scheduling we evaluate
the maximum throughput (stability limit) as follows. First,
for arbitrary packet traffic, including self-similar traffic, we
calculate the maximal cycle time by tstart,max0 := 0
tstart,maxi = max(itG + 2τ(i), tstart,max
i−1 + Gmaxi−1 + tg), (52)
where Gmaxi are the given maximal grant sizes (Gmax
0 = 0).
Then,
ΓmaxSPD = tstart,max
N + GmaxN (53)
is the maximum cycle length (even in the heaviest traffic, no
cycle will be longer than this). The stability condition for SPD
is then
ρiΓmaxSPD < Gmax
i (54)
for all i. (The stability limit for Largest Propagation Delay
(LPD) first scheduling is obtained analogously by considering
the τi in decreasing order in (52).) For homogeneous ONU
loads ρ1 = ρ2 = · · · = ρN and maximum grant sizes Gmax1 =
· · · = GmaxN , the total load is ρt = Nρi, resulting in the
stability condition
ρmaxt,SPD <
NGmaxi
ΓmaxSPD
. (55)
8
0.0 sec
200.0 usec
400.0 usec
600.0 usec
800.0 usec
1.0 msec
1.2 msec
1.4 msec
1.6 msec
1.8 msec
2.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
Self−similar, simulationPoisson, simulationPoisson, analysis high loadPoisson, analysis low load
a) 50 µs max. prop. delay (i.e., up to 10 km)
200.0 usec
400.0 usec
600.0 usec
800.0 usec
1.0 msec
1.2 msec
1.4 msec
1.6 msec
1.8 msec
2.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
Self−similar, simulationPoisson, simulationPoisson, analysis high loadPoisson, analysis low load
b) 250 µs max. prop. delay (i.e., up to 50 km)
200.0 usec
400.0 usec
600.0 usec
800.0 usec
1.0 msec
1.2 msec
1.4 msec
1.6 msec
1.8 msec
2.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
Self−similar, simulationPoisson, simulationPoisson, analysis high loadPoisson, analysis low load
c) 500 µs max. prop. delay (i.e., up to 100 km)
Fig. 3. Average cycle length for SPD grant scheduling and Gated grantsizing.
IV. EXPERIMENTAL PERFORMANCE ANALYSIS
We conducted a set of simulation experiments to: 1) validate
our analytical models presented in Section III, and 2) quantify
the improvements to cycle length and packet delay achieved
by SPD grant scheduling under different operating conditions.
We use an EPON simulator that we have developed using the
CSIM discrete event simulation library [45]. We simulated an
EPON with 32 ONUs and varied the maximum propagation
delay to represent different EPON reaches.
In the absence of any diversity in propagation delay, the
impact of minimizing cycle length will be minor. In our
experiments, we use a continuous (uniform) distribution for
one-way (OLT-to-ONU) propagation delays with a minimum
value of 6.68 µs and different maximum one-way propagation
delay values. We modify this distribution slightly by forcing
0.0 sec
500.0 usec
1.0 msec
1.5 msec
2.0 msec
2.5 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
a) 50 µs max. prop. delay (i.e., up to 10 km)
0.0 sec
1.0 msec
2.0 msec
3.0 msec
4.0 msec
5.0 msec
6.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9cy
cle
leng
th (
in s
econ
ds)
load (in Gbps)
LPDLNFSPD
b) 250 µs max. prop. delay (i.e., up to 50 km)
0.0 sec
2.0 msec
4.0 msec
6.0 msec
8.0 msec
10.0 msec
12.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
c) 500 µs max. prop. delay (i.e., up to 100 km)
Fig. 4. Average cycle length with Gated grant sizing for self-similar traffic.
one ONU to have a minimum propagation delay value and
another to have a maximum propagation delay value. The
propagation delays for the other 30 ONUs are continuously
distributed over the range.
We compare SPD scheduling to Largest Number of
Frames (LNF) first scheduling which was previously demon-
strated [21] to provide low average queueing delay compared
to other scheduling policies [39]. We also present some results
for Largest Propagation Delay (LPD) first scheduling which is
the opposite of SPD to illustrate the range of possibilities for
cycle length and packet delay. The average cycle length and
average packet delay values presented in this section represent
the mean of several independent runs that were constructed
using the batch means feature in the CSIM discrete event
simulation library. The resulting statistical confidence intervals
for Poisson traffic are smaller than the point marks in the plots.
9
1.0 msec
2.0 msec
3.0 msec
4.0 msec
5.0 msec
6.0 msec
7.0 msec
8.0 msec
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
a) 50 µs max. prop. delay (i.e., up to 10 km)
0.0 sec
2.0 msec
4.0 msec
6.0 msec
8.0 msec
10.0 msec
12.0 msec
14.0 msec
16.0 msec
18.0 msec
20.0 msec
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
b) 250 µs max. prop. delay (i.e., up to 50 km)
0.0 sec
5.0 msec
10.0 msec
15.0 msec
20.0 msec
25.0 msec
30.0 msec
35.0 msec
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
c) 500 µs max. prop. delay (i.e., up to 100 km)
Fig. 5. Average cycle length with Gated grant sizing for self-similar trafficas the load approaches the channel capacity.
A. Gated grant sizing
In this section we present our results of the experiments we
conducted using Gated grant sizing.
1) Cycle length: Figure 3 shows the average cycle length
as a function of the total load for SPD grant scheduling
by means of analysis using Eqs. (42) and (50), as well as
simulation experiments using Poisson traffic sources and self-
similar traffic sources. We observe from this figure that Eqs.
(42) and (50) provide an excellent fit to the average cycle
length measured in the simulation experiments.
Figure 4 shows the average cycle length for LPD, LNF,
and SPD grant scheduling and varying propagation delay
configurations. Figure 5 shows the same for load values
approaching the channel limit. We observe from these figures
that SPD always provides a lower average cycle length than
0.0 sec
2.0 msec
4.0 msec
6.0 msec
8.0 msec
10.0 msec
12.0 msec
14.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dela
y (in
sec
onds
)
load (in Gbps)
Self−similar, simulationPoisson, simulationPoisson, analysis high loadPoisson, analysis low load
a) 50 µs max. prop. delay (i.e., up to 10 km)
0.0 sec
2.0 msec
4.0 msec
6.0 msec
8.0 msec
10.0 msec
12.0 msec
14.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1de
lay
(in s
econ
ds)
load (in Gbps)
Self−similar, simulationPoisson, simulationPoisson, analysis high loadPoisson, analysis low load
b) 250 µs max. prop. delay (i.e., up to 50 km)
0.0 sec
2.0 msec
4.0 msec
6.0 msec
8.0 msec
10.0 msec
12.0 msec
14.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dela
y (in
sec
onds
)
load (in Gbps)
Self−similar, simulationPoisson, simulationPoisson, analysis high loadPoisson, analysis low load
c) 500 µs max. prop. delay (i.e., up to 100 km)
Fig. 6. Average packet delay for SPD grant scheduling and Gated grantsizing.
LPD or LNF. The difference increases significantly with an
increasing load and increasing maximum propagation delay.
As an example, with a 500 µsec maximum propagation delay
and load value of 0.9 the average cycle length was 2.0
milliseconds using SPD and 6.0 milliseconds using LNF.
2) Packet delay: Figure 6 shows the average packet delay
for SPD grant scheduling by means of analysis using Eqs. (48)
and (51), as well as simulation experiments using Poisson traf-
fic sources and self-similar traffic sources. The measurements
for average packet delay with the self-similar traffic sources
are, as expected, much higher despite average cycle lengths
similar to those observed with Poisson traffic sources. This is
a result of a few very long cycles, whose lengths are observed
once, that have many packets whose associated large delay is
observed once for each of these packets.
Figure 7 shows the average packet delay for LPD, LNF,
10
0.0 sec
5.0 msec
10.0 msec
15.0 msec
20.0 msec
25.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
a) 50 µs max. prop. delay (i.e., up to 10 km)
0.0 sec
5.0 msec
10.0 msec
15.0 msec
20.0 msec
25.0 msec
30.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
b) 250 µs max. prop. delay (i.e., up to 50 km)
0.0 sec
5.0 msec
10.0 msec
15.0 msec
20.0 msec
25.0 msec
30.0 msec
35.0 msec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
c) 500 µs max. prop. delay (i.e., up to 100 km)
Fig. 7. Average packet delay with Gated grant sizing for self-similar traffic.
and SPD grant scheduling and varying propagation delay
configurations for self-similar traffic. Figure 8 shows the same
for load values approaching the channel limit. We observe
from Figures 7 and 8 that SPD provides lower average packet
delay for the experiments with 250 µs and 500 µs maximum
propagation delays. The difference with LNF becomes more
pronounced at high load values. As an example, with a 500
µs maximum propagation delay and load value of 0.9 Gbps
the average packet delay was 21.3 milliseconds using SPD
and 26.5 milliseconds using LNF. At 50 µs, the difference
between LNF and SPD is rather insignificant. However, it is
worth noting that SPD clearly provides a lower average cycle
length for all load values (see Figures 4 and 5) which leads
to lower average packet delay.
15.0 msec
20.0 msec
25.0 msec
30.0 msec
35.0 msec
40.0 msec
45.0 msec
50.0 msec
55.0 msec
60.0 msec
65.0 msec
70.0 msec
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
a) 50 µs max. prop. delay (i.e., up to 10 km)
10.0 msec
20.0 msec
30.0 msec
40.0 msec
50.0 msec
60.0 msec
70.0 msec
80.0 msec
90.0 msec
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
b) 250 µs max. prop. delay (i.e., up to 50 km)
10.0 msec
20.0 msec
30.0 msec
40.0 msec
50.0 msec
60.0 msec
70.0 msec
80.0 msec
90.0 msec
100.0 msec
110.0 msec
0.9 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
c) 500 µs max. prop. delay (i.e., up to 100 km)
Fig. 8. Average packet delay with Gated grant sizing for self-similar trafficas the load approaches the channel capacity.
One-way prop. delay [µs] ΓmaxSPD
Eq. (53) [ms] ΓmaxSPD
sim. [ms]
50 (up to 10 km) 2.058 2.03250 (up to 50 km) 2.058 2.03500 (up to 100 km) 2.058 2.031000 (up to 200 km) 2.104 2.11
TABLE IMAXIMUM AVERAGE CYCLE LENGTH (IN MILLISECONDS) FOR SPD FOR
LIMITED GRANT SIZING WITH Gmaxi = 7188 BYTES,∀i FOR
SELF-SIMILAR TRAFFIC.
B. Limited grant sizing
In this section we present our results of the experiments
we conducted using Limited grant sizing with Gmaxi = 7188
bytes, ∀i.
1) Cycle length: Figure 9 shows the average cycle length
for LPD, LNF, and SPD grant scheduling for varying propa-
11
200.0 usec
400.0 usec
600.0 usec
800.0 usec
1.0 msec
1.2 msec
1.4 msec
1.6 msec
1.8 msec
2.0 msec
2.2 msec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
a) 50 µs max. prop. delay (i.e., up to 10 km)
400.0 usec
600.0 usec
800.0 usec
1.0 msec
1.2 msec
1.4 msec
1.6 msec
1.8 msec
2.0 msec
2.2 msec
2.4 msec
2.6 msec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
b) 250 µs max. prop. delay (i.e., up to 50 km)
1.0 msec
1.2 msec
1.4 msec
1.6 msec
1.8 msec
2.0 msec
2.2 msec
2.4 msec
2.6 msec
2.8 msec
3.0 msec
3.2 msec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
c) 500 µs max. prop. delay (i.e., up to 100 km)
2.0 msec
2.2 msec
2.4 msec
2.6 msec
2.8 msec
3.0 msec
3.2 msec
3.4 msec
3.6 msec
3.8 msec
4.0 msec
4.2 msec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
cycl
e le
ngth
(in
sec
onds
)
load (in Gbps)
LPDLNFSPD
d) 1000 µs max. prop. delay (i.e., up to 200 km)
Fig. 9. Average cycle length for different grant scheduling policies withLimited grant sizing for self-similar traffic.
gation delay configurations. We make two observations: 1) in
all plots SPD provides lower average cycle length for all load
One-way prop. delay [µs] ρmaxt,SPD
Eq. (55) ρmaxt,SPD
sim.
50 (up to 10 km) 0.894 0.90250 (up to 50 km) 0.894 0.90500 (up to 100 km) 0.894 0.901000 (up to 200 km) 0.874 0.87
TABLE IILOAD AT WHICH THE AVERAGE CYCLE LENGTH APPROACHES THE
MAXIMUM CYCLE LENGTH, WHICH IS EQUAL TO THE STABILITY LIMIT,FOR SPD WITH LIMITED GRANT SIZING WITH Gmax
i = 7188 BYTES,∀i
FOR SELF-SIMILAR TRAFFIC.
values, and 2) as the maximum propagation delay is increased
from 50 µs to 1000 µs, SPD is able to maintain a maximum
average cycle length around 2 milliseconds.
Exploring the second observation further, we see that the
maximum average cycle length for LNF increases from around
2 milliseconds at 50 µs to close to 3.6 milliseconds at 1000
µs. With a 1000 µsec maximum propagation delay, the load at
which the cycle length reaches its maximum is 0.87 Gbps for
SPD and approximately only 0.46 Gbps for LNF. In Table I
we compare the maximum average cycle length using Eq. (53)
with the results from our simulation experiments. The data in
this table indicates that the equation is within 1.4% of the
experimental data.
Our experimental data and Eq. (53) indicate that SPD is able
to keep the maximum cycle length near 2 milliseconds as the
maximum propagation delay is increased. Whereas, LNF is
unable to do the same. Eq. (53) illustrates that the maximum
cycle length is a function of the order of the ONUs as well
as their propagation delays. LNF constantly changes the order
of ONUs with respect to their propagation delays resulting in
the variations that can be seen in its maximum average cycle
length. Further, SPD is able to minimize the cycle length by
ordering the ONUs in increasing order of propagation delay.
LNF does not order the ONUs according to their propagation
delays and, as a result, does not minimize the cycle length.
2) Stability limit: As the load increases and the grant sizes
approach the prescribed maximum grant size Gmaxi , the cycle
length approaches the maximum cycle length. That is, the
average cycle length levels out at the maximum cycle length
plotted in Fig. 9 and tabulated for SPD in Table I. Further
increases in the load can not increase the cycle length, but
result in infinite queue build-up in the ONUs, i.e., instability.
The load value at which the average cycle length levels
out to the maximum cycle length in Fig. 9 thus represents
the stability limit, which is tabulated for SPD in Table II.
We observe from Table II that Eqn. (55) very accurately
characterizes the stability limit.
Turning to Fig. 9, we observe that the stability limit dif-
ference between LNF and SPD increases significantly as the
maximum propagation delay is increased. As an example, with
a 500 µs maximum propagation delay, the stability limit is
approximately 0.89 Gbps using SPD (the average cycle length
converges to the maximum cycle length very slowly between
a load of 0.85 and 0.89) and approximately 0.62 Gbps using
LNF.
By scheduling the grants to the close-by ONUs first, SPD
masks the long round-trip delays to the ONUs that are further
12
0.0 sec
50.0 msec
100.0 msec
150.0 msec
200.0 msec
250.0 msec
300.0 msec
350.0 msec
400.0 msec
450.0 msec
500.0 msec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
a) 50 µs max. prop. delay (i.e., up to 10 km)
0.0 sec
50.0 msec
100.0 msec
150.0 msec
200.0 msec
250.0 msec
300.0 msec
350.0 msec
400.0 msec
450.0 msec
500.0 msec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
b) 250 µs max. prop. delay (i.e., up to 50 km)
50.0 msec
100.0 msec
150.0 msec
200.0 msec
250.0 msec
300.0 msec
350.0 msec
400.0 msec
450.0 msec
500.0 msec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
c) 500 µs max. prop. delay (i.e., up to 100 km)
100.0 msec
200.0 msec
300.0 msec
400.0 msec
500.0 msec
600.0 msec
700.0 msec
800.0 msec
900.0 msec
1.0 sec
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
dela
y (in
sec
onds
)
load (in Gbps)
LPDLNFSPD
d) 1000 µs max. prop. delay (i.e., up to 200 km)
Fig. 10. Average packet delay for different grant scheduling policies withLimited grant sizing for self-similar traffic.
away. This more efficient utilization of the upstream channel
increases the stability limit substantially as the propagation
0.0 sec
100.0 msec
200.0 msec
300.0 msec
400.0 msec
500.0 msec
600.0 msec
700.0 msec
800.0 msec
900.0 msec
1.0 sec
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9load (in Gbps)
dela
y (in
sec
onds
)
LNF, 0SPD, 0LNF, 4SPD, 4LNF, 8SPD, 8LNF, 16SPD, 16
Fig. 11. Average packet delay for EPON with 4 ONUs between 50 km and100 km from OLT with varying number of close-by ONUs (i.e., 0.5 km to 5km from OLT) added.
delays become more diverse.
3) Packet delay: Figure 10 shows the average packet delay
for LPD, LNF, and SPD grant scheduling and varying prop-
agation delay configurations. We observe that SPD provides
lower average packet delay for all load values and reconfirm
the higher stability limit for SPD. It is instructive to compare
the packet delay reductions with SPD compared to LNF grant
scheduling for Gated grant sizing in Figs. 7 and 8 to the
corresponding delay reductions for Limited grant sizing in
Fig. 10. Clearly, for Limited grant sizing we observe substan-
tially larger delay reductions. With Gated grant sizing, any
reported queue size is served in one upstream transmission.
In contrast, with Limited grant sizing, a large reported queue
requires several maximum sized grants of size Gmaxi , and
thus several cycles to transmit the traffic to the OLT. The
cycle length minimizing SPD scheduling policy leads hence
to significantly more pronounced delay reductions for Limited
grant sizing than for Gated grant sizing.
C. Engineering EPONs for better channel utilization
In this final set of simulation experiments we wish to illus-
trate the utility of SPD grant scheduling in allowing close-by
ONUs to be added to an EPON without taking bandwidth from
existing ONUs. Essentially, the maximum channel utilization
is significantly improved when adding close-by ONUs and
utilizing SPD scheduling. We consider an EPON with 4 ONUs
with ONU-to-OLT propagation delays continuously distributed
between 250 µs and 500 µs (i.e., ONU-to-OLT distances of
50 km to 100 km). We then added a varying number of close-
by ONUs with ONU-to-OLT propagation delays continuously
distributed between 2.5 µs and 25 µs (i.e., ONU-to-OLT
distances of 0.5 km to 5 km).
Figure 11 shows the average packet delay for different
numbers of added close-by ONUs for both LNF and SPD. We
observe that adding close-by ONUs increases the maximum
achievable channel utilization (stability limit). The shorter
propagation delays of the close-by ONUs allow these ONUs to
be serviced while the GATE messages are propagating to the
ONUs with the larger propagation delays and their upstream
transmissions are propagating up to the OLT. With LNF
13
scheduling the ONUs are ordered by their grant size, irrespec-
tive of their propagation delays leading to poor exploitation
of this ability. SPD, on the other hand, always services the
ONUs with shorter propagation delays first allowing them
to mask the round-trip time to the ONUs with the larger
propagation delays, and thus achieving substantially higher
channel utilization than LNF.
V. CONCLUSION
In conclusion, we introduced a new EPON grant scheduling
technique called Shortest Propagation Delay (SPD) first grant
scheduling to exploit heterogenous propagation delays. We
proved that SPD minimizes granting cycle length to within
a small time period (number of ONUs times GATE message
transmission time) and maximizes channel utilization. We
analytically characterized the stability limit (maximum packet
throughput or equivalently maximum channel utilization) for
both Gated and Limited grant sizing for arbitrary traffic and
characterized the cycle length and packet delay for Gated grant
sizing for Poisson traffic. We have illustrated the utility of SPD
through a set of simulation experiments. Specifically, we found
that SPD can improve performance measures when using
Gated grant sizing as well as Limited grant sizing. The most
significant improvements came from its use with Limited grant
sizing and long reach EPONs. In those circumstances, packet
delay and channel utilization were significantly improved.
Another significant finding is the potential channel uti-
lization improvement that is possible when using SPD grant
scheduling in conjunction with certain EPON design princi-
ples. Generally, EPONs should be engineered to have prop-
agation delay diversity to promote higher channel utilization.
ONUs that are within a short range of the OLT can fill the
idle times in which the OLT waits for data from the ONUs
that are further away.
An interesting avenue for future research arises from the
convergence of fiber-based and wireless access networks, see
e.g., [46], [47], which will potentially cover large geographic
areas and thus have highly heterogeneous propagation delays.
Further, the integration of medium access control on the fiber
and wireless media may lump the propagation delay on the
fiber and the wireless medium access delay together to lead to
additional diversification of the round-trip delays experienced
by the OLT.
REFERENCES
[1] F. Effenberger, “An introduction to PON technologies,” IEEE Commu-
nications Magazine, vol. 45, no. 3, pp. S17–S25, Mar. 2007.[2] P. Green, Fiber to the Home: The New Empowerment. Wiley-
Interscience, 2005.[3] G. Keiser, FTTX Concepts and Applications. Wiley-IEEE Press, 2006.[4] C. Lam, Passive Optical Networks: Principles and Practice. Academic
Press, 2007.[5] M. De Andrade, L. Gutierrez, and S. Sallent, “A distributed scheduling
approach for Ethernet-based passive optical networks,” in Proceedings
of IEEE Conference on Local Computer Networks, Oct. 2007, pp. 205–206.
[6] C. Foh, L. Andrew, E. Wong, and M. Zukerman, “FULL-RCMA: a highutilization EPON,” IEEE Journal on Selected Areas in Communications,vol. 22, no. 8, pp. 1514–1524, Oct. 2004.
[7] M. Hajduczenia, H. J. A. da Silva, and P. P. Monteiro, “EPON versusAPON and GPON: a detailed performance comparison,” OSA Journal
of Optical Networking, vol. 5, no. 4, pp. 298–319, Apr. 2006.
[8] G. Kramer, B. Mukherjee, and G. Pesavento, “Ethernet PON (ePON):Design and Analysis of an Optical Access Network,” Photonic Network
Communications, vol. 3, no. 3, pp. 307–319, July 2001.[9] ——, “IPACT: A dynamic protocol for an Ethernet PON (EPON),” IEEE
Communications Magazine, vol. 40, no. 2, pp. 74–80, February 2002.[10] M. Ma, Y. Zhu, and T. Cheng, “A systematic scheme for multiple
access in Ethernet passive optical access networks,” IEEE/OSA Journal
of Lightwave Technology, vol. 23, no. 11, pp. 3671–3682, November2005.
[11] M. McGarry, M. Reisslein, and M. Maier, “Ethernet Passive OpticalNetwork Architectures and Dynamic Bandwidth Allocation Algorithms,”IEEE Communication Surveys and Tutorials, vol. 10, no. 3, pp. 46–60,October 2008.
[12] M. R. Radivojevic and P. S. Matavulj, “Implementation of intra-ONUscheduling for Quality of Service support in Ethernet passive opticalnetworks,” IEEE/OSA Journal of Lightwave Technology, vol. 27, no. 18,pp. 4055–4062, Sept. 2009.
[13] B. Skubic, J. Chen, J. Ahmed, L. Wosinska, and B. Mukherjee, “Acomparison of dynamic bandwidth allocation for EPON, GPON, andnext-generation TDM PON,” IEEE Communications Magazin, vol. 47,no. 3, pp. S40–S48, Mar. 2009.
[14] J. Zheng and H. Mouftah, “Media access control for Ethernet passive op-tical networks: an overview,” IEEE Communications Magazine, vol. 43,no. 2, pp. 145–150, February 2005.
[15] L. G. Kazovsky, W.-T. Shaw, D. Gutierrez, N. Cheng, and S.-W. Wong,“Next-generation optical access networks,” IEEE/OSA J. of Lightwave
Tech., vol. 25, no. 11, pp. 3428–3442, Nov. 2007.[16] J. Lazaro, J. Prat, P. Chanclou, G. T. Beleffi, A. Teixeira, I. Tomkos,
R. Soila, and V. Koratzinos, “Scalable extended reach PON,” in Proc.
OFC, Feb. 2008.[17] C. Michie, T. Kelly, I. Andonovic, and J. McGeough, “Reach extension
of passive optical networks using semiconductor optical amplifiers,” inProceedings of IEEE Int. Conf. on Transparent Opitcal Networks, June2008, pp. 194–197.
[18] H. Song, B. Kim, and B. Mukherjee, “Multi-thread polling: a dynamicbandwidth distribution scheme in long-reach PON,” IEEE Journal on
Selected Areas in Communications, vol. 27, no. 2, pp. 134–142, Feb.2009.
[19] G. Talli and P. Townsend, “Hybrid DWDM-TDM long-reach PONfor next-generation optical access,” IEEE/OSA Journal of Lightwave
Technology, vol. 24, no. 7, pp. 2827–2834, July 2006.[20] G. Kramer, B. Mukherjee, and G. Pesavento, “Interleaved polling with
adaptive cycle time (IPACT): A dynamic bandwidth distribution schemein an optical access network,” Photonic Network Communications,vol. 4, no. 1, pp. 89–107, Jan. 2002.
[21] M. McGarry, M. Reisslein, C. Colbourn, M. Maier, F. Aurzada, andM. Scheutzow, “Just-in-Time scheduling for multichannel EPONs,”IEEE/OSA Journal of Lightwave Technology, vol. 26, no. 10, pp. 1204–1216, May 2008.
[22] J. Zheng and H. Mouftah, “A survey of dynamic bandwidth allocationalgorithms for Ethernet Passive Optical Networks,” Optical Switching
and Networking, vol. 6, no. 3, pp. 151–162, July 2009.[23] A. Banerjee, G. Kramer, and B. Mukherjee, “Fair sharing using dual
service-level agreements to achieve open access in a passive opticalnetwork,” IEEE Journal on Selected Areas in Communications, Part
Supplement, vol. 24, no. 8, pp. 32–44, Aug. 2006.[24] B. Chen, J. Chen, and S. He, “Efficient and fine scheduling algorithm
for bandwidth allocation in ethernet passive optical networks,” IEEE
Journal on Selected Topics in Quantum Electronics, vol. 12, no. 4, pp.653–660, July-August 2006.
[25] M. Ma, L. Liu, and T. Cheng, “Adaptive scheduling for differentiatedservices in an Ethernet passive optical network,” OSA Journal of Optical
Networking, vol. 4, no. 10, pp. 661–67, 2005.[26] H. Naser and H. Mouftah, “A joint-ONU interval-based dynamic
scheduling algorithm for Ethernet passive optical networks,” IEEE/ACM
Transactions on Networking, vol. 14, no. 4, pp. 889–899, Aug. 2006.[27] F. Melo Pereira, N. L. S. Fonseca, and D. S. Arantes, “A fair scheduling
discipline for Ethernet passive optical networks,” Computer Networks,vol. 53, no. 11, pp. 1859–1878, July 2009.
[28] A. Shami, X. Bai, N. Ghani, C. Assi, and H. Mouftah, “QoS controlschemes for two-stage Ethernet passive optical access networks,” IEEE
Journal on Selected Areas in Communications, vol. 23, no. 8, pp. 1467–1478, Nov. 2005.
[29] C. Assi, Y. Ye, S. Dixit, and M. Ali, “Dynamic bandwidth allocationfor Quality-of-Service over Ethernet PONs,” IEEE Journal on Selected
Areas in Communications, vol. 21, no. 9, pp. 1467–1477, November2003.
14
[30] P. Choudhury and P. Saengudomlert, “Efficient queue based dynamicbandwidth allocation scheme for ethernet PONs,” in Proceedings of
IEEE Globecom, Nov. 2007, pp. 2183–2187.[31] A. Shami, X. Bai, C. Assi, and N. Ghani, “Jitter performance in Ethernet
passive optical networks,” IEEE/OSA Journal of Lightwave Technology,vol. 23, no. 4, pp. 1745–1753, Apr. 2005.
[32] J. Zheng, “Efficient bandwidth allocation algorithm for ethernet passiveoptical networks,” IEE Proceedings Communications, vol. 153, no. 3,pp. 464–468, June 2006.
[33] S. Bhatia and R. Bartos, “IPACT with smallest available report first:A new DBA algorithm for EPON,” in Proc. of IEEE International
Conference on Communications, June 2007, pp. 2168–2173.[34] A. Kamal and B. F. Blietz, “A priority mechanism for the IEEE 802.3ah
EPON,” in Proceedings of IEEE ICC, May 2005, pp. 1879–1883.[35] G. Kramer, A. Banerjee, N. Singhal, B. Mukherjee, S. Dixit, and Y. Ye,
“Fair queueing with service envelopes (FQSE): a cousin-fair hierarchicalscheduler for subscriber access networks,” IEEE Journal on Selected
Areas in Communications, vol. 22, no. 8, pp. 1497–1513, Oct. 2004.[36] Y. Luo and N. Ansari, “Bandwidth allocation for multiservice access on
EPONs,” IEEE Communications Magazine, vol. 43, no. 2, pp. S16–S21,Feb. 2005.
[37] ——, “Limited sharing with traffic prediction for dynamic bandwidthallocation and QoS provioning over EPONs,” OSA Journal of Optical
Networking, vol. 4, no. 9, pp. 561–572, 2005.[38] Y. Zhu and M. Ma, “IPACT with grant estimation (IPACT-GE) scheme
for Ethernet passive optical networks,” IEEE/OSA Journal of Lightwave
Technology, vol. 26, no. 14, pp. 2055–2063, July 2008.[39] J. Zheng and H. Mouftah, “Adaptive scheduling algorithms for ethernet
passive optical networks,” IEE Proceedings Communications, vol. 152,no. 6, pp. 643–647, October 2005.
[40] P. Sarigiannidis, G. I. Papadimitriou, and A. S. Pomportsis, “A high-throughput scheduling technique with idle timeslot elimination mecha-nism,” IEEE/OSA Journal of Lightwave Technology, vol. 24, no. 12, pp.4811–4827, Dec. 2006.
[41] V. Sivaraman and G. N. Rouskas, “HiPeR-l: A high performancereservation protocol with look-ahead for broadcast WDM networks,”in Proceedings of IEEE Infocom, 1997, pp. 1270–1277.
[42] M. Pinedo, Scheduling: Theory, Algorithms, and Systems, 3rd ed.Springer, 2008.
[43] D. P. Heyman and M. J. Sobel, Stochastic Models in Operations Re-
search: Volume 1: Stochastic Processes and Operating Characteristics.Courier Dover, 2003.
[44] F. Aurzada, M. Scheutzow, M. Herzog, M. Maier, and M. Reisslein,“Delay analysis of Ethernet passive optical networks with gated service,”OSA Journal of Optical Networking, vol. 7, no. 1, pp. 25–41, Jan. 2008.
[45] “Csim (mesquite software),” http://www.mesquite.com.[46] P. L. Tien, Y.-M. Lin, and M. C. Yuang, “A novel OFDMA-PON
architecture toward seamless broadband and wireless integration,” inProceedings of OFC, Mar. 2009, pp. OMV2–1–OMV2–3.
[47] Z. Zheng and J. Wang, “A study of network throughput gain in optical-wireless (FiWi) networks subject to peer-to-peer communications,” inProceedings of IEEE ICC, June 2009.