qos-aware energy and jitter-efﬁcient downlink predictive … · 2019-05-09 · switched...

1536-1233 (c) 2017 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TMC.2017.2771353, IEEETransactions on Mobile Computing

1

QoS-Aware Energy and Jitter-Efficient DownlinkPredictive Scheduler for Heterogeneous Traffic LTE

NetworksKarim Hammad, Member, IEEE, Abdallah Moubayed, Member, IEEE,

Serguei Primak, Member, IEEE, and Abdallah Shami, Senior Member, IEEE

Abstract—Energy-efficient c ommunications h ave b ecome one of the fundamental aspects for today’s cutting-edge wireless technologies. This is due to its valuable impact, from both the user’s and the network operator’s perspectives, on the environment. In this paper, we augment our earlier study for the user equipment’s (UE) energy efficiency ( EE) i n t he long-term evolution (LTE) downlink by looking at real-time heterogeneous traffic QoS requirements. In particular, we utilize the previously proposed cloud radio access network (C-RAN) and ray tracing (RT)-based scheduling model to optimize both of the EE and the packet delay jitter for real-time applications with fixed packet delay budget subject to other traffic t ypes requirements. Using the utility-based scheduling approach, we formulate the resource allocation problem as a weighted sum binary integer programming (BIP) problem. Due to the inherent complexity of the problem formulation which hinders finding i ts solution directly, four heuristic algorithms are proposed to solve the optimization problem. Numerical simulations are conducted on three different traffic types each belonging to one of the popular QoS classes; best-effort class, rate and delay-constrained classes. The obtained results demonstrate a substantial improvement in the system’s performance achieved by our proposed schemes compared to other existing schemes.

Index Terms—Energy efficiency, delay jitter, QoS, C-RAN,resource allocation.

I. INTRODUCTION

The staggering leap that occurred in the wireless tech-nologies field has resulted in a tremendous expansion forthe wireless market. Two big industries have remarkably andsimultaneously emerged as a result of that expansion, that are,multimedia services and smart cell phones.

As one can remember, the multimedia services started withthe first deployment of the 2G system namely the globalsystem for mobile communications (GSM) system in thebeginning of the 90’s of the last century by just sendingtext, small images and short voice messages. Getting downthe wireless communications standards road, a today’s LTE(i.e., 4G) smart cell phone is simply capable of replacingany other electronic device such as laptop computers, GPSdevices, and cameras. More specifically, with the aid of thesuper fast data transfer rates (i.e., ultimately 300 Mbit/s indownlink, and 75 Mbit/s in uplink for the 20 MHz channel[1]), the LTE smart cell phone has enabled a wide spectrumof multimedia services which range from VoIP, web-browsing,e-mail and social networking to data demanding services such

as: Netflix and YouTube streaming, and interactive onlinegaming. Furthermore, it is envisioned that in the fast ap-proaching new wireless technology, known as the 5G [2]–[4], the wireless network will become a massive integratedenvironment of diversified devices and data services. Thatambitious concept is known as the Internet of things (IoT) [5],[6]. The IoT network will be seamlessly connecting the smartcell phone with the physical world (e.g., intelligent trafficand transportation systems, smart grids, smart homes, healthmonitoring systems, media, environmental monitoring systemsand emergency services) for creating better opportunities basedon the user’s location and mindset in terms of economicbenefits, security, medical care and green environment. As aresult of all these advancements that occurred and those whichare expected to come in the near future, the new wireless era(i.e., delivered by the 5G and IoT technologies) is evidentlygoing to have an even bigger effect on people’s daily life.

A. Research Problem

Despite all of the promising capabilities that the current 4Gsystem is delivering or even those coming in the future 5Gsystem, one major problem which occupies the attention ofboth the mobile users and operators, and hence, the researchand industrial communities is the Energy Efficiency (EE).The problem is getting even more exigent with the rocketingprogression of the wireless standards and data hungry multi-media services. From the user’s viewpoint, the EE problem isperceived as the insistent need of having today’s smart cellphones with longer battery lifetime than what the current bat-tery technology is delivering while maintaining the increasingprocessing power needs [7]. Nevertheless, from the operator’sperspective, all carriers seek to reduce the high operationalexpenditure (OPEX) coming from the electricity consumptionbills and to meet the new governments’ regulations: forconserving the environment’s natural resources, and decreasingthe carbon footprint.

In this work, we tackle the EE problem from the UE’s sidein the downlink. Our previous work in [8] has invesitgated theEE improvement while considering the effective bandwidthrequirements [9]. However, in this work, we provide a dualinsight on both the system’s EE and delay jitter performance(for real-time services) while concurrently considering realbehavior of different traffic types with different QoS require-ments. In particular, for real-time and jitter-sensitive traffic, our

R1, C3



2

framework targets to simultaneously improve the UE’s EE andthe packet delay jitter performance while meeting strict packetdelay or rate constraints. This is in contrast to the majority ofthe published works which target improving the EE while onlymeeting certain delay or rate constraints and disregarding thedelay jitter (i.e., fundamental QoS metric for most real-timeapplications). On the other hand, for non real-time traffics,the objective is to improve the UE’s EE subject to throughputrequirements and the fair distribution of the cell throughputamong multiple users, with less strict packet delay constraints.

B. Related Work

The problem of improving the EE has become a fundametalaspect of modern wireless access networks, and hence, hasbeen heavily studied in the literature [10]. One of the mostpopular metrics used to define the EE is the bits-per-joulemetric. Bits-per-joule is defined as the number of informationbits transmitted (or received) per each unit joule consumed.Thus, based on that definition, improving the EE is achieved bytwo regimes. The first is equivelant to increasing the numberof transmitted (or received) bits (i.e., throughput) per eachjoule consumed by the transceiver circuit, while the secondis conversely equivelant to decreasing the amount of energyconsumed for the same amount of information transmitted(or received) by the transceiver circuit. Despite the fact thatthe two regimes seem to be bilateral, they are found to beused distinctly under two major classifications of the resourceallocations problems, namely rate and margin adaption (RAand MA) [11]. The RA problem corresponds to the firstregime, whereas the MA problem corresponds to the second.Although both of the RA and MA regimes appear to increasethe bits-per-joule metric, the MA is generally considered to becrucial for energy-efficient scheduling especially for battery-limited hand-held devices [12]. Based on our research prob-lem highlighted in the previous section, we strictly considerthroughout the following survey the MA regime from the UEside only in the downlink.

The application of the MA regime in the downlink iscommonly known as a time-based power-management ap-proach [13]. More specifically, the UE’s EE in decoding thereceived data packets dictates scheduling the UE to turn onits receiver circuits in the minimum possible transmissiontime intervals (TTIs) (i.e., equivalent to the minimum possibleenergy consumption) to receive the same amount of data bits.The most popular power-management approach is the onecurrently implemented in LTE networks and is known as thediscontinuous reception (DRX) mechanism [14]. It should benoted that the application of the MA regime for optimizingthe UE’s EE in the downlink is found to be less studied inliterature compared to that in the uplink (e.g., [15], [16]). Thiscan be attributed to the common belief that the uplink powerconsumption dominates the UE’s battery power consumptionbudget [17] because of the RF power requirements, especiallyat poor channel conditions and long distance transmission.However, according to the experimental results reported in[18], the UE’s power consumed by the receiver’s basebandand RF circuits for decoding the received data in the downlink

occupies at least 40% of the total power consumption budget.As a result, we directed our efforts in our previous work [8]as well as in this work for studying the EE problem in thedownlink from the UE side by designing suitable MA-basedscheduling schemes. It is also worth mentioning that the majorcomplexity of addressing the EE problem is generally dueto other associated conflicting constraints from one side andthe limited availability of spectral resources from the otherside. That intricate and manifold picture could be explainedas seeking an energy-efficient operation for the UE whilefulfilling some stringent QoS levels (e.g., rate, delay and delayjitter) and some degrees of fairness among different users (ordifferent traffic classes) with a scarce spectral resources overtime and frequency-varying channels.

Unlike most of the published works mentioned above (in-cluding our recent work in [8]), this work uniquely studiesthe delay jitter metric as an objective besides the EE inLTE networks. The importance of the jitter stems from itsconsiderable effect on the quality-of-experience (QoE) forreal-time services, and from being known as a measure ofthe network congestion level before leading to packet losses[19]. It is worth mentioning that tackling the jitter as anobjective, rather than a constraint, was found to be essentialin specific applications as addressed in [20], [21]. The authorsin [20] designed a jitter-free packet scheduler to improve thecontrol performance in a mobile gait rehabilitation system.Such kind of wireless-networked health monitoring applica-tions is expected to be heavily supported in the future IoT-based cellular networks. In [21], the authors proposed a jitterreduction algorithm for video traffic in wireless optical inte-grated networks. Furthermore, the author in [22] has rigorouslystudied various practical aspects for implementing packet-switched communication systems with minimal jitter for real-time streaming of data. From another side, some early attempts[23], [24] have put extensive efforts to control the end-to-end packet delay jitter levels in multi-hop packet switchednetworks. The key idea of the proposed schemes was to keepthe delay experienced by any packet at each of the network’sintermediate nodes between pre-determined minimum andmaximum thresholds. That objective was achieved either bychanging the serving priority or capacity for each traffic flow.Another popular approach was noted to deal with the delay jit-ter problem, after bypassing the traffic source and the networkrouting charactersitics, by only compensating it at the receiverside. The approach is known as jitter buffer mechanism [25].Moreover, relatively recent attempt in [26] has addressed thedelay jitter problem within heterogeneous traffic environments.The authors proposed a scheduling algorithm targeting theIPTV traffic over IEEE 802.11 based wireless mesh networks(WMNs). The proposed scheduler implemented a prioritizationscheme in the medium access control (MAC) layer whichdynamically increases the reserved rate, at each network node,for the IPTV traffic while sacrificing lower priority traffictypes.

C. Motivation, Scope and ContributionIt could be concluded from the previous highlighted re-

searches that none of the published works in the context of

R1, C1



3

energy-efficient radio resource allocation for battery-limiteddevices in the OFDMA system has considered the packet delayjitter as a target QoS metric for real-time traffic flows. Thejitter (i.e., originating from the routing latencies) was rathertackled on the network layer. However, without loss of gen-erality, considering the case of direct downlink transmissionwithin a single cell of today’s advanced LTE cellular networks,the delay jitter problem is potentially emanating from thescheduling and queuing latencies in the MAC layer. Thoselatencies are the result of the network congestion level andthe wireless channel capacity limitation in time and frequency.Therefore, in this work we focus on that specific case indealing with the delay jitter problem as it was noted to be aless studied subject in the literature. The paper, thus, proposesan energy and jitter efficient predictive scheduler for battery-limited devices in downlink LTE systems while satisfyingother heterogeneous traffic QoS requirements.

We consider the LTE downlink with frame structure type1 (i.e., frequency devision duplexing (FDD) oriented) [27].In our framework, the proposed scheduler deals with threedifferent metric functions each of which characterizes a dis-tinct QoS class. The metric functions used are for best-effort,rate-constrained and delay-constrained traffic types. That is themost common classification used for provisioning the QoS ofwireless networks [28]–[30]. Each QoS class is representedby a single unique traffic type. The scheduler deals fairly withthe heterogeneous QoS classes using the utility-based schedul-ing methodology [29]. In addition to the traditional metricfunctions of each of the three aforementioned QoS classes,a new metric function (for the delay-constrained class) isproposed to address the delay jitter QoS metric simultaneouslywith the delay requirment. The proposed optimization problemhas a dynamic objective function which changes based onthe target traffic type (i.e., QoS class). In particular, whenallocating resources to jitter-sensitive traffic, the objectivefunction incorporates two objectives which are the EE andthe delay jitter performance. For all other jitter-insensitivetraffics, the EE is the only objective targeted by the scheduler.The constraints (i.e., delay and rate) are also dependent onthe traffic type. The resource allocation problem is solvedtwice with respect to the scheduling time granularity. Thescheduler first solves the optimization problem by utilizingthe channel and buffer states’ information (CSI and BSI,respectively) within a single LTE frame horizon (i.e., 10 msecof duration) similar to most traditional schedulers, and showsthe EE versus delay jitter trade-off. Then in another higherpredictive level, the scheduler utilizes our previously proposedC-RAN based ray tracing predictive scheduling model [8]to solve the optimization problem in longer time horizon(i.e., multiple LTE frames). Since we do not consider anytraffic prediction method, the short-term knowledge of the BSIessentially limits the performance of our proposed predictivescheduler despite the available future CSI (i.e., provided byour previous predictive model [8]). To overcome that problem,we further propose a sliding window mechanism to ensure anefficient operation for our predictive scheduler targeting betterEE and delay jitter performance compared to traditional shortrange schedulers.

The contributions of this work are summarized as follows:• We propose an optimal packet scheduling framework for

improving the UE’s EE and the delay jitter performancefor real-time traffic flows in presence of heterogeneoustraffic requirements for the downlink of LTE networks.The resource allocation problem is formulated as a mutli-objective integer linear programming (i.e., binary integerprogramming (BIP)) problem.

• To ensure the ability of our proposed scheduler in sup-porting different QoS requirements, the proposed frame-work utilizes the popular utility-based scheduling ap-proach to simultaneously deal with different traffic typeswhich belong to best-effort, rate-constrained and delay-constrained QoS classes.

• We propose a two stage paradigm for improving thepacket delay jitter. In the first stage, a newly proposedmetric function that keeps monitoring the jitter perfor-mance (besides the delay) is used for jitter-sensitiveconnections. In particular, the conventional delay metricfunction is altered by the delay jitter resulting in acomposite delay/jitter prioritization scheme. In the secondstage, two jitter-efficient resource allocation mechanismsare proposed for minimizing the packet delay jitter.

• We propose two different heuristic versions of our packetscheduler based on the scheduling granularity. The firstversion tackles the EE/delay jitter problem within thecommonly employed time horizon of single LTE frame.The second version provisions further potential in improv-ing the EE and delay jitter performances by utilizing ourpreviously proposed cloud-based predictive schedulingmodel. For better referencing throughout the paper, wedenote the first and second versions by short range version(SRV) and predictive version (PRV), respectively.

• To enable the PRV version of our proposed scheduler,a window-based mechanism is proposed to alleviate theshort-term BSI/long-term CSI imbalance problem.

• To address the complexity of the optimal scheduler, atotal of four heuristic algorithms are proposed based onthe designed jitter control mechanisms for each versionof our proposed scheduler.

The rest of this paper is organized as follows. Section IIpresents the system model, design objectives, and the proposedutility-based energy and jitter efficient packet scheduler. Atwofold definition for the packet delay jitter and a summaryof the paper’s notations are provided in Section III. Theformulation of the resource allocation problem describingour proposed scheduler is thoroughly studied in Section IV.Section V introduces various low complexity heuristic solu-tions for solving the formulation of Section IV. Numericalvalidation of our proposed schemes compared to other existingschemes is provided in Section VI. Finally, Section VIIconcludes the paper.

II. SYSTEM MODEL

As shown in Fig. 1, we focus on a single cell of downlinkmultiuser LTE system that is based on the evolving cloud radioaccess network (C-RAN) [31]. The studied model of Fig. 1



4

illustrates the structure of the proposed downlink schedulingsystem. It is close to our earlier model proposed in [8].However, it is more detailed in dealing with heterogeneoustraffics’ QoS requirements. In [8], the model provisionedthe QoS requirements of each UE connection by ultimatelymeeting its effective bandwidth [9]. In this work, the employedmodel in Fig. 1 distinctly provisions the QoS requirementsof each UE connection (i.e., bearer) type based on its targetmetrics (e.g., rate, delay, jitter and average throughput). This isdone using the real-time QoS hypervisor which is responsiblefor monitoring the QoS level of each UE connection in a strictand timely manner. Based on the attained QoS levels and theQoS class metrics, the packet scheduler is configured using ascheduler controller. The controller is used to set the appropri-ate resource allocation algorithm, metric function parametersand the solution space (i.e., scheduling time granularity) of thepacket scheduler. The detailed structure of the packet scheduleris explained later in Fig. 2.

As will be shown later in Section V, despite having theutility-based approach as the main prioritization scheme be-tween different QoS connections, the proposed packet sched-uler implements different resource allocation algorithms forreal-time connections (e.g., VoIP) than that used for nonreal-time connections (e.g., video streaming and FTP). Thedifference is due to designing jitter-efficient resource alloca-tion algorithms for real-time (i.e., jitter-sensitive) applicationswhich directly tackle the packet delay jitter requirement. Thisis unlike most of the published works which loosely assumeacceptable jitter performance by just meeting certain level forthe average packet delay. As mentioned before, the selection ofthe appropriate resource allocation algorithm is the controller’sfirst function. The second function for the controller is toconfigure the priority weighting factors or even the metricfunction itself (as will be shown later in the case of VoIP). Thisis done for different QoS classes either in a dynamic manneror based on the operator’s revenue policy. Last but not least,the scheduler’s controller can potentially enhance the system’sperformance, in terms of EE and jitter, by dynamically expand-ing the scheduler’s time granularity. The expansion is basedon the UE’s future CSI and how far the UE’s connection isfrom meeting the target QoS levels. The CSI for each UE ispredicted using a single processing thread from the pool ofshared ray tracing (RT) engines available in the cloud. TheRT engine is capable of accurately pre-estimating the UE’spropagation characteristics by just knowing the geometricaland morphological description of the propagation environment[32] and the UE’s geographical location.

As illustrated in Fig. 1, we assume that the eNB is locatedat the center of the cell and communicates with K UEs.As conventionally known in LTE, the total cell bandwidthis equally divided into N OFDMA resource blocks (RBs)each with a bandwidth of 180 KHz. Considering the LTE’sfrequency division duplexing (FDD) frame structure, eachsingle frame consists of 10 subframes (TTIs) with a 1 msecduration for each. According to the LTE standard [27], theeNB generally schedules the downlink transmissions for eachUE over the physical downlink shared channel (PDSCH)during one TTI at a time. However, in our framework we

eNB

UE1

UE2 UE3

UEk

. . .

Packet

scheduler

UE1 UE2 UEk

Virtual BBUs pool

Packet

scheduler

(Fig. 2)

Real-time QoS

hypervisorController

Pool of channel ray

tracing processorsUE localization

Fronthaul optical

distribution network

PHY/MAC GPP GPPPHY/MAC

Optical

circuit

switch

Wireless network cloud

Downlink scheduling

system

Fig. 1: System model

assume that the normal setting of the eNB’s packet scheduleris capable of scheduling downlink transmissions for the wholeframe at a time. This is supported by the fact that the standardperiodic channel state reporting mechanism [27] for the UEover the physical uplink control channel (PUCCH) - or thephysical uplink shared channel (PUSCH) - can span up to 160msec intervals which is much greater than the frame duration.

A. Utility-Based Scheduling

The eNB is assumed to send Hk connections for each of theK UEs located within the cell coverage area. For the sake ofstudying the practical scheduling problem in a heterogeneoustraffic network, each of the UE’s connections is assumed tobelong to one of three QoS classes. The classes which arewidely adopted are: average throughput, rate-constrained anddelay-constrained. Those classes are used to characterize theQoS requirements for best-effort (i.e., NGBR), rate and delaysensitive (i.e., GBR) traffic types, respectively. Unlike theprevious works, in our framework we further add the delayjitter for the delay-sensitive QoS class as a QoS metric whichis optimized simultaneously with the EE while provisioningthe delay metric. As will be elaborated in Sections IV andV, the delay jitter optimization takes place in two stages. Inthe first stage, the conventional delay metric function [29] isadjusted by the jitter metric as follows

Xhk (m) = αk(h)−

Dhk(m)

Dmax −∆th

k (m)

∆tmax , ∀k ∈ K, h ∈ D∗ (1)

where Xhk (m) is the metric function for connection index h of

UE k at TTI m, αk(h) is a weighting factor designated forthe QoS class characterizing the connection h of UE k suchthat 0 ≤ αk(h) ≤ 1, Dh

k(m) is the average packet delay for



5

VoIP

Buffer

FTP Buffer

Video Buffer

FTP Buffer

VoIP Buffer

UE-1

UE-2

UE-3

………..

FTP Buffer

Video Buffer

UE-K

Metric function

calculator

X11

X12

X21

X31

X32

XK1

XK2

Utility Based Inter-class

Prioritization Policy

with Intra-class Fairness

Proposed QoS-Aware

Energy/Jitter Efficient

Packet Scheduler

single packet

at a time

Fig. 2: Proposed utility-based energy/jitter efficient packetscheduler

connection h of UE k experienced up to TTI m, Dmax is thepacket delay budget for delay-constrained connections, ∆th

k (m)is the attained average packet delay jitter for connection h ofUE k until TTI m, ∆tmax is a predefined threshold for thepacket delay jitter, and D∗ is the set of indexes for delay/jittersensitive connections among the K UEs. The second stage ofoptimizing the delay jitter resides in the jitter-efficient resourceallocation algorithms that will be discussed in Section V.

For the other two classes of traffic (i.e., best-effort and rate-constrained), we utilize the metric functions defined in [29] asfollows

Xhk (m) =

Shk(m)

maxh

{Sh

k(m)} − αk(h), ∀k ∈ K, h ∈ E∗ (2)

Xhk (m) =

Shk(m)

Smax − αk(h), ∀k ∈ K, h ∈ R∗ (3)

where Shk(m) is the average achieved throughput for connection

h of UE k until TTI m, maxh

{Sh

k(m)}

is the maximumachieved average throughput among the best-effort connec-tions up to TTI m, E∗ is the set of indexes for the best-effortconnections among the K UEs, Smax is the maximum requireddata rate for the rate-constrained connections, and R∗ is theindexes set of the rate-constrained connections for the K UEs.

The above metric functions provide a quantitative measurefor the QoS perceived by the corresponding UE’s traffic con-nection. In other words, the greater the metric function value,the higher the QoS level attained by the UE’s connection.The metric functions are then used to build a utility-basedinter-class prioritization platform with intra-class fairness forour proposed energy and jitter efficient packet scheduler. Thiscould be illustrated with the aid of Fig. 2. It shows the detailedstructure of our proposed packet scheduler (i.e., initially pre-sented in Fig. 1). The metric function calculator determines the

metric function value for each UE connection as of equations(1), (2) and (3). All UEs’ connections (i.e., correspondingto all traffic classes) associated with their calculated metricfunctions are then placed in the same priority pool. Trafficconnections are then prioritized out of the pool based ontheir calculated utility functions irrespective of which UEsthey belong to. Thus, the utility-based prioritization policy iscapable of dealing simultaneously with the heterogeneous QoSrequirements, highlighted above, for all UEs based on a unifiedscale for all traffic types. In particular, the utility approachprovides our proposed packet scheduler with a composite inter-user and intra-class prioritization policy. The utility functionvalue for each UE connection reflects the degree of satisfactionfor its correponding QoS metric. Hence, the higher the utilityfunction value for a certain UE connection the lower thepriority given (momentarily) to scheduling its packets. Inaddition, the intra-class fairness is coming from the fact thatall connections which belong to the same QoS class havethe same threshold(s) for the target QoS metric(s). In otherwords, all connections belonging to the same QoS class areweighted equally. However, the three defined QoS classes areweighted differently in the utility function, as shown below,based on the standard QoS class identifier (QCI) prioritization[27] produced by the European Telecommunications StandardsInstitute (ETSI). More specifically, by selecting the VoIP, videostreaming and FTP traffics to represent the delay-constrained,rate-constrained and best-effort QoS classes, respectively, VoIPtraffic takes the highest priority followed by the video stream-ing and the FTP traffic comes at the end.

The reason behind selecting the widely deployed utility-based prioritization policy in our framework pertains to itsdynamic ability of continuously changing the priority betweendifferent traffic classes based on the network state (i.e., UEs’CSI, BSI and fairness) to maximize the social welfare ofthe system (i.e., summation of utility functions for all UEs’connections) [33]. This is in contrast to other strict prioritytechniques reported in literature (e.g., differentiated service-based scheduling [34] and QCI-based scheduling [35]). Theutility function used to prioritize UEs’ connections is ex-pressed as follows [29]

Uhk

(Xh

k (m))= 1− e−βh Xh

k (m), ∀k ∈ K, h ∈ Hk (4)

where Uhk

(Xh

k (m))

is the utility function for connection hof UE k, and βh is the inter-class prioritization parameter.Generally speaking, βh is left to be designed by the networkoperator based on either revenue or standard perspectives.However, for comparison purposes later in Section VI, inour work we stick to the βh values assumed in [29] (whichfollow the standard ETSI QCI prioritization) for the VoIP,video streaming and FTP traffic types as follows

βh =

4 , h ∈ D∗

3 , h ∈ R∗

2.5 , h ∈ E∗(5)

It can be seen in (4) that larger values for βh imply highersensitivity of the utility function (i.e., steeper slope) to thevariation of Xh

k (m) across different UEs connections, andhence, higher priority.



6

B. Energy-Efficient Scheduling

The energy-efficient operation for the UE in the downlink,as originally defined in [14], dictates optimizing the operationtime for the UE’s receiver circuits subject to the packet delayconstraint. In essence, the packet scheduler must find theminimum possible number of TTIs, within a certain intervalof time, for the UE to receive the required amount of datathat maintains stable buffer queue length and the averagepacket delay within a predefined threshold. During the restof the scheduling interval’s TTIs, the UE is switched to thesleep (or idle) mode during which the UE only listens to thedowlink channel (i.e., primary sychronization signal (PSS) orsecondary sychronization signal (SSS) [1]) ocassionally forsynchronization purposes. According to the LTE UE’s powerconsumption model developed by Jensen et al. in [18], theUE receiver circuits (i.e., RF and baseband) consume constantpower during the wake-up mode that is approximately fourtimes the amount in the idle mode. Based on Jensen’s modeland our insights in [8], the critical energy (i.e., only theconstant component dominating the total budget) consumedby the LTE UE’s receiver circuit in the downlink every singleTTI can be expressed as follows

Ek = Ts

midle Pidle︸︷︷︸idle state

+ midle (Pon +Prx)︸︷︷︸wake−up state

J (6)

where Ts is the TTI duration in seconds, midle is a logicvariable that determines the UE’s operation state, Pidle is theidle state power consumption (i.e., equal to 0.5 w [18]), Ponis the active state power consumption (i.e., equal to 1.53 w[18]), and Prx is the base power consumed by the receiverchain during the active state (i.e., equal to 0.42 w [18]).

According to the previous discussion, a simplified formula-tion for the energy-efficient scheduling of K UEs (each havingsingle connection) during M TTIs interval is expressed asfollows

Objective : MinΓk(m,n),n∈N,Hk∈K=1

K

∑k=1

mo+M

∑m=mo

Wk Ek,wake−up Γk(m,n)

(7a)Subject to:

Dk(m)Γk(m,n)≤ Dmaxk , ∀k, m, n (7b)

K

∑k=1

Γk(m,n)≤ 1, ∀m, n (7c)

Γk(m,n) ∈ {0,1} , ∀k, m, n (7d)

where Wk is an energy optimization weighting factor for UEk, Ek,wake−up is the UE’s receiver circuit wake-up energyconsumption (i.e., Ts(Pon+Prx)), Γk(m,n) is a binary decisionvariable which determines the allocation decision of the RBwith index n at TTI m to UE k, Dk(m) is the packet delayattained by UE k if scheduled for transmission at TTI m (overany of the available N RBs), and Dmax

k is the packet delaythreshold for the traffic class of UE k connection.

The QoS constraint in (7b) ensures that the packet delay foreach UE does not violate the predetermined threshold. On the

other hand, the constraint in (7c) avoids allocating single RB tomore than one user during a specific TTI. The weighting factorWk in the objective function of (7a) could be dynamicallyadjusted. For instance, this can be based on either the UE’sremaining battery capacity or a specific EE fairness criteria,especially in situations when the network is highly congested.The binary constraint (7d) ensures only binary values for theproblem’s decision variables.

III. DELAY JITTER DEFINITION AND NOTATIONS

Before formulating the complete scheduling problem, whichintegrates the utility-based and energy-efficient schedulingmechanisms (explained in Sections II-A and II-B, respectively)and the delay jitter optimization, we first present in the follow-ing paragraph the definition and notation for the packet delayjitter. Furthermore, for better referencing, Table I includes thenotation meaning for all symbols used in the paper.

TABLE I: List of symbols

Symbol MeaningN Number of RBs per TTIK Number of UEsM Number of TTIs within the scheduling intervalHk Number of active traffic connections for UE kAh

k(mo) Number of packets waiting in the queue for buffer h ofUE k up to TTI mo

Bhk(m,n) Number of physical data bits that could be delivered by

RB n during TTI m for connection h of UE kωh

k(mo) Buffer length (in bits) for connection h of UE k at thescheduling interval starting with TTI mo

Xhk (m) Metric function for connection h of UE k at TTI m

αk(h) Weighting factor of the QoS class characterizing theconnection h of UE k

Dhk(m) Average packet delay for connection h of UE k to TTI m

Dak,h(m) Delay of packet a of connection h of UE k if scheduled

during TTI mDmax Packet delay budget for delay-constrained connections∆th

k (m) Average delay jitter for connection h of UE k to TTI m∆th

k (a−1,a|m) Delay jitter for packet a with its predecessor a− 1 forconnection h of UE k if scheduled at TTI m

∆tmax Delay jitter thresholdSh

k(m) Average throughput for connection h of UE k to TTI m

maxh

{Sh

k(m)}

Maximum achieved average throughput among the best-effort connections until TTI m

Smax Maximum required bit rate for the rate-constrained con-nections

Smin Minimum required bit rate for the rate-constrained con-nections

D∗ Set of indexes for delay/jitter sensitive connectionsE∗ Set of indexes for best-effort connectionsR∗ Set of indexes for rate-constrained connectionsUh

k

(Xh

k (m))

Utility function for connection h of UE kβh Inter-class prioritization parameterWk Energy optimization weighting factor for UE kEk,wake−up LTE UE’s receiver wake-up energy consumptionΨa

k,h(m,n) Binary decision variable which denotes the allocation de-cision for RB n during TTI m for packet a of connectionh of UE k

Φk(m) Binary decision variable which denotes the consumptionof Ek,wake−up if UE k is scheduled during TTI m

tAk,h(a) Arrival time of packet a to the buffer of connection h

belonging to UE kτA

k (a−1,a) Interarrival time between packets indexed a and a−1τD

k (a−1,a) Interdeparture time between packets indexed a and a−1



7

Considering the downlink connection h (essentially VoIPtraffic) of UE k, the packet delay jitter of a specific packetindexed a is the difference between its experienced queuingdelay and the queuing delay of the preceding packet, in thequeue, indexed a−1, i.e. [23],

∆thk (a−1,a) = Da

k,h−Da−1k,h (8)

Assuming that the arrival times of packets a and a−1 are equalto tA

k,h(a) and tAk,h(a−1), respectively, and similarly tD

k,h(a) andtDk,h(a−1) for the departure times, (8) could be re-written as

follows

∆tk(a−1,a) = τDk (a−1,a) − τ

Ak (a−1,a) (9)

where τDk (a−1,a) and τA

k (a−1,a) are the interdeparture andinterarrival times between two consecutive packets indexeda−1 and a, respectively. Thus, according to (9), minimizingthe delay jitter for packet a is equivalent to keeping itsinterdeparture time as close as possible to its interarrival timewith respect to the preceding packet a−1. However, utilizing(9) for a stream of packets leads to minimizing the averagedelay jitter across a whole stream of packets. That idea islater employed in one the of proposed heuristic schedulingalgorithms presented in Section V for optimizing the VoIPjitter performance.

IV. PROBLEM FORMULATION

In this section, the optimal resource allocation problemfor the heterogeneous traffic environment is formulated. Theproblem formulation provisions the QoS requirements for thethree traffic classes highlighted in Section II-A. The problem’sglobal objective for all traffic types is to optimize the UE’sEE, according to the methodology explained in Section II-B,subject to their corresponding constraints. However, and unlikeprevious works, the delay jitter is defined as an additionalobjective for the VoIP traffic (i.e., delay and jitter sensitive).In other words, the scheduling problem is a weighted sumoptimization problem of both the EE and delay jitter, subjectto fixed packet delay budget, only for the VoIP traffic connec-tions. On the other hand, single objective optimization in termsof the EE is the case for the video and FTP connections. Theresource allocation for video connections is constrained by theminimum acceptable rate, whereas, best-effort allocations areconsidered for the FTP. Furthermore, the inter-user and intra-class fairness are attained using the utility-based approach asdiscussed in Section II-A. To simplify the introduction of theproblem we first introduce the problem’s individual constraintsas follows.

To set a strict requirement for scheduling all packets waitingin the various queues of all UEs and utilize all the availableRBs, the following constraint has to be met

Ahk(mo)

∑a=1

mo+M−1

∑m=mo

N

∑n=1

Bhk(m,n)Ψa

k,h(m,n) ≥ ωhk(mo) , ∀k,h (10)

where mo is the first TTI of the currently observed schedulingtime interval, Ah

k(mo) is the total number of packets waitingin the queue for buffer h of UE k up to TTI mo, M isthe scheduler’s time granularity (conventionally single frame)

measured in TTIs, Bhk(m,n) is the number of physical data

bits that could be delivered by the RB n during TTI m forconnection h of UE k based on its effective SNR and thecorresponding configured MCS, Ψa

k,h(m,n) is a binary decisionvariable which indicates the scheduler’s allocation decision forRB n during TTI m for packet indexed a of connection h ofUE k, and ωh

k(mo) is the total length (in bits) for connectionh traffic buffer of UE k at the beginning of the currentscheduling interval (i.e., mo). To provide delay guarantees forVoIP connections, all packet assignments have to meet thepre-determined packet delay budget as follows

Dak,h(m)Ψa

k,h(m,n)≤ Dmax , ∀k,h ∈ D∗, a,m,n (11)

where Dak,h(m) is the UE k experienced delay for packet a of

connection h if scheduled over any of the RBs available duringTTI m. Similarly for the rate-constrained connections, thefollowing constraint ensures meeting the minimum requireddata rate to support video connections.

mo+M−1

∑m=mo

N

∑n=1

Bhk(m,n)Ψa

k,h(m,n) ≥ SminTsM, ∀k,h ∈ R∗ (12)

where Smin is the minimum required bit rate for rate-sensitiveconnections, and Ts is the TTI duration in seconds. To maintaina first-come-first-serve (FCFS) discipline of the proposedpacket scheduler for each single UE queue, the followingconstraint allows earlier departure times for earlier packetarrivals compared to those of later arrived packets.(

Dak,h(m)+ tA

k,h(a))

Ψak,h(m,n)≤(

Da+1k,h (m)+ tA

k,h(a+1))

Ψa+1k,h (m,n), ∀k,h, a,m

(13)

where tAk,h(a) is the arrival time of packet a to the buffer of

connection h belonging to UE k. Last but not least, the intra-cell interference constraint which allows unique RB allocationto only single UE within a single TTI is defined as follows

K

∑k=1

Ψak,h(m,n) ≤ 1 , ∀h,a,m,n (14)

All of these constraints are then combined together in a singleoptimal formulation for the proposed packet scheduler asfollows

MinΨa

k,h(m,n),Φk(m)

Z1 =K∑

k=1

Hk∑

h=1

mo+M−1∑

m=mowk Ek,wake−up Φk(m) +

K∑

k=1∑

h∈D∗1

1− e−βh

(αk(h)−

Dhk (mo)

Dmax −∆thk (mo)∆tmax

)︸︷︷︸

Uhk (Xh

k (mo))|h∈D∗

×

Ahk(mo)

∑a=1

mo+M−1∑

m=mo

N∑

n=1∆th

k (a−1,a|m)Ψak,h(m,n)

)(15a)

R1, C3



8

Subject to

(10),(11),(12),(13), and (14) (15b)

Ψak,h(m,n)−Φk(m)≤ 0 , ∀k,h,a,m,n (15c)

Ψak,h(m,n),Φk(m) ∈ {0,1} , ∀k,h,a,m,n (15d)

where Hk is the number of traffic connections for UE k,∆th

k (a− 1,a|m) is the delay jitter for the packet indexed awith its predecessor indexed a−1 for connection h of UE k ifscheduled at TTI m, and Φk(m) is another binary decisionvariable which adds Ek,wake−up to the energy consumptionbudget of UE k if any of the N available RBs during TTI m isallocated to any of the packets belonging to its connections.

The above formulation described in (15) is an NP-hardweighted sum BIP optimization problem. The NP-hardnesswas previously proved in [20] for jitter-free resource allocationproblems. For the composite objective function of (15a), theterm before the summation operator is the EE objective,whereas, the term after the summation constitutes the delayjitter objective for the delay (and jitter) sensitive VoIP connec-tions. The delay jitter optimization is weighted by the inverseof the proposed delay and jitter sensitive utility function asdescribed in (1) and (4). Therefore, the utility function iscalculated for all VoIP connections (across all UEs) up tothe beginning of the scheduling observation time interval (i.e.,m = {mo,mo +M− 1}) to set the jitter optimization priorityfor each UE connection. Finally, one additional constraint isdefined in (15c) (i.e., if-then constraint) which combine thetwo binary decision variables Ψa

k,h(m,n) and Φk(m) to ensurethat the objective function (15a) is penalized by Ek,wake−upeach TTI for each UE if at least one RB is allocated to anyof its connections.

It is obvious that the formulation described in (15) has asort of ideality which questions its feasibility. This is dueto the strict requirement addressed by the constraint (10) inscheduling all packets waiting in all queues for all UEs. Inpractice, the system’s limited spectral resources as well asthe time and frequency varying CSI restrain the schedulerfrom ideally guaranteeing the allocation of resources enoughto serve 100% of the total traffic load for all users. Eventhough network operators implement call admission controlpolicies to maintain stable operation for the network andsecure certain QoS levels, the total traffic load is still beingserved in a queue according to the adopted scheduling policiesdue to the aforementioned practical limitations. Therefore,the constraint (10) makes the formulation presented in (15)practically unfeasible.

To fix the practicality issue associated with the formulationin (15), we adopt the well known penalty method [36] torelax the constraint in (10). The relaxation implies partialsatisfaction of the constraint in (10) for each UE connectionbased on a certain weighting mechanism. More precisely, thelarger the weight designated to a connection the higher the par-tial satisfaction is achieved relative to other smaller weightedconnections. The weighting mechanism utilized follows theutility approach discussed in Section II-A. As a result, theformulation presented in (15) can be rewritten as follows

MinΨa

k,h(m,n),Φk(m)

Z2 = Z1 +

(K∑

k=1

Hk∑

h=1

1Uh

k (Xhk (mo))

×

Ahk(mo)

∑a=1

mo+M−1∑

m=mo

N∑

n=1ωh

k(mo)−Bhk(m,n)Ψa

k,h(m,n)

) (16a)

Subject to

Ahk(mo)

∑a=1

mo+M−1

∑m=mo

N

∑n=1

Bhk(m,n)Ψa

k,h(m,n) ≤ ωhk(mo) , ∀k,h (16b)

(11),(12),(13),(14),(15c), and (15d) (16c)

It could be seen that the new objective function in (16a)is equal to the former objective function in (15a) added tothe penalty term. As explained in the previous paragraph,the added penalty term to the objective function provides aweighted partial satisfaction for the constraint in (10) afterrelaxing it as shown in (16b). The rest of the constraints informulation (15) remain unchanged.

Despite the fact that the formulation in (16) solves the fea-sibility limitation of the formulation in (15), formulation (16)is still intractable to find its solution using direct techniques.In particular, optimizing the second objective (i.e., delay jitter)in Z1 (i.e., depicted in (15a)) incurs dramatically large degreesof freedom and recursive dependency on the scale of singleVoIP queue size as well as the total number of active VoIPconnections (i.e., size of the indexes set D∗) across the KUEs. This problem is commonly referred to as a discretetime stochastic control process [16]. Some techniques (e.g.,Markov decision process [37]) were known to solve such kindof problems. However, the solution was found to be heavilydependent on the problem dimensionality. In our case, theproblem dimensionality is a function of K, Hk, M, N andAh

k(mo). As a result, the solution of the optimization problem in(16) is practically unreachable. Therefore, we propose differentheuristic algorithms in the next section to efficiently find asub-optimal solution for the problem in (16).

V. HEURISTIC SOLUTIONS

In this section, we propose four computationally-efficientheuristic schemes to facilitate finding a sub-optimal solutionfor the intricate optimization problem proposed in (16). Thefirst two algorithms which correspond to the first version,labeled as SRV, of our proposed scheduler are designed tosolve (16) for short range scheduling within a single frametime horizon (i.e., M = 10 TTIs). The other two algorithmsbelong to the predictive version of our proposed scheduler,labeled as PRV, and solve (16) within longer time horizonthat is multiples of single frame (i.e., M = 10y TTIs,where y={2,3,4, ...}).

As will be elaborated in the following discussions, all of theproposed algorithms are based on the well known recursivegreedy strategy. More specifically, the basic idea for all of thedesigned algorithms is that only single packet for single UEconnection is scheduled at a time in an iterative fashion. AUE packet is selected among various packets waiting in other

R1, C5

R1, C3R1, C4

R1, C5



9

UEs’ queues based on the utility-based prioritization policyexplained in Section II-A. The algorithms keep iterating overthe head packets of all UEs’ queues until at least one of twostopping conditions becomes valid. That is, either all of theNM available RBs within the M scheduling epoch becomesallocated or all UEs buffers are empty. Just as all heuristics,that iterative mechanism provides an acceptable alternative tothe optimal solution of (16) which, otherwise, uniquely andconcurrently finds the optimal allocations for all packets thatcould possibly be scheduled.

A. SRV-Based schedulers

In this part, we introduce two heuristic algorithms represent-ing the short range version (SRV) of our proposed schedulerto solve the optimization problem in (16) within a singleframe time horizon (i.e., M = 10). This version is intendedto compare the performance of our proposed scheduler withother existing schedulers which typically work within the samehorizon. The scheduler allocates the available resources of thewhole LTE frame at once at the beginning of the frame. Forevery scheduled frame, it considers packets that only arrivedto the UE buffer in preceding frames. In other words, eachpacket arrives to a UE connection buffer within a specificframe gets stored in the scheduler’s list of buffered packets tillthe end of the same arriving frame. At the end of its arrivingframe, each packet becomes relocated from the buffered listto the scheduling list to depart its buffer queue in any ofthe following frames. The details of the proposed allocationalgorithms are provided in Tables II and III.

Considering the first algorithm illustrated in Table II, itworks as follows. The algorithm starts, in line 2, by initializingan empty RB allocation matrix R of size N×M. As explainedabove, the algorithm goes through iterations. In each iteration(lines 3-36) the algorithm sequentially allocates the requiredresources for scheduling the head-of-line (HOL) packet foreach UE connection, one at a time. The prioritization (asrequired in the function Z1 and the penalty term in Z2) forHOL packets is done in lines 4 and 5 by calculating the utilityfunction for each UE buffer (i.e., updated each iteration) andsorting them in ascending order, respectively. The FOR loop inline 6 resembles the HOL packet scheduling loop for all UEsconnection. In line 8, the algorithm then finds the feasibleRB allocations indexes in frequency and time (i.e., N∗ andM∗) from the matrix R which meet the FCFS constraint in(13) and the exclusivity constraint in (14). The RB indexesare then updated, in line 9, after dropping those which violatethe current packet delay threshold (i.e., Dmax

k,h ) as required byconstraint (11). The RB indexes of line 9 are then sorted inline 10 according to the energy-efficient scheduling strategyproposed in [8] (i.e., RBs with higher capacity have higherallocation priority than lower capacity ones) to meet the firstobjective of the function Z1. In line 11, the algorithm identifiesthe packet type to set the corresponding resource allocationapproach. If the currently observed packet belongs to VoIPconnection, then the scheduler will re-arrange the RBs of line10 to optimize the packet delay jitter in addition to the EE,otherwise (i.e., video or FTP packets) the scheduler finds the

RB allocations (in lines 31-32) based on their arrangementin line 10 while provisioning the constraint in (12) onlyin case of video packets. In case of VoIP type packet, thealgorithm’s key strategy is optimizing the average packetdelay jitter for the whole VoIP connection (in addition tothe EE), which makes the algorithm perceived as connectionoriented (CO) in terms of jitter optimization, hence, namedSRV-CO. The optimization of the connection’s average jitteris achieved by selecting the RB allocations which results ina minimum absolute difference between the means of thepreviously scheduled packets’ interarrival and interdeparturetimes, including the current packet, as highlighted in (9). To

TABLE II: SRV-CO algorithm

1: Require: K, Hk , M, N2: Initialize emtpy RB allocations matrix R , iter = 13: while (isempty(R ) AND Ah

k 6= 0, ∀k,h) do4: Calculate Uh

k

(Xh

k (iter))∀k , h

5: [Idk, Idh] = Sort(Uhk

(Xh

k (iter)),′ ascend′)

6: for i = 1 toK∑

k=1Hk do

7: Set k = Idk(i), h = Idh(i)8: Find N∗, M∗to satisfy FCFS9: Update N∗, M∗based on Dmax

k,h10: SortEE(N∗)11: if hk ∈ D∗ then12: Calculate

∣∣∣τAk,h(a−1,a)

∣∣∣ , ∣∣∣τDk,h(a−1,a))

∣∣∣ , ∀a ∈ A∗k,h13: if length(A∗k,h) == 0 then14: Find Ψa

k,h(m,n), a = HOLk,h, n ∈ N∗, m ∈M∗

15: Update R ,A∗k,h16: else if length(A∗k,h) == 1 then17: Calculate

∣∣∣∆thk (A

∗k,h,a |m)

∣∣∣ , ∀n ∈ N∗, m ∈M∗, a = HOLk,h

18: Sort (N∗,∣∣∣∆th

k (A∗k,h,a |m)

∣∣∣ ,′ ascend′)19: Update M∗20: Find Ψa


21: Update R ,A∗k,h22: else23: Calculate

∣∣∣τAk,h(A∗k,h

∣∣∣last

,a)∣∣∣ , a = HOLk,h

24: Calculate∣∣∣τD

k,h(A∗k,h∣∣∣last

,a |m)∣∣∣ , a = HOLk,h, m ∈M∗

25: SortJITTER1(N∗)26: Update M∗27: Find Ψa


28: Update R ,A∗k,h29: end if30: else31: Find Ψa


32: Update R ,A∗k,h33: end if34: end for35: Set iter = iter+136: end while

reach this objective, the interarrival and interdeparture timesfor the past scheduled packets of the current observed UEconnection (i.e., A∗k,h) are first calculated (line 12). Three casesexist for the past scheduled packet interarrival and interdepar-ture times. The first case (lines 13-15) occurs at the beginningof the connection where no history of scheduled packets isavailable. Consequently, the algorithm only considers the EEwhen allocating resources using the RBs arrangement of line10. After allocating the resources that fit the current packetsize, the allocation matrix R and the scheduled packets historylist A∗k,h are updated accordingly. The second case (lines 16-21) is when only one past packet exists in A∗k,h. The jitter of

R2, C2

R2, C2

R2, C2

R2, C2



10

the current packet, in this case, is optimized only with respectto the delay of the single packet stored in A∗k,h by calculatingthe jitter (as in line 17) that would be experienced at eachRB allocation addressed by the sets N∗ and M∗. The RBs inN∗ are then re-sorted (in line 18) in ascending order basedon the calculated jitter values. The algorithm then searchesfor the required resources in the sorted RBs list, as in lines14-15, and updates R and A∗k,h. The third and final case forscheduling a VoIP packet is addressed in lines 22-28. This caseis clearly the dominating case in which the UE connection hasmore than one packet in the scheduling history list A∗k,h. Thejitter optimization in this case is uniquely attained by selectingthe RBs which result in the least absolute difference betweenthe average interarrival and interdeparture times of the packetsin A∗k,h after adding the new corresponding packet departuretime. For this, in line 23, the algorithm updates the interarrivalcalculations of line 12 by the current packet interarrival time.Following in line 24, the possible interdeparture times forthe current packet over all of the available RB allocationsaddressed by N∗ and M∗ are calculated. For each value ofthe calculated interdeparture times, the absolute differencebetween the means of the interdeparture and interarrival times(after accounting for the current packet) is evaluated. Accord-ingly, the RBs in N∗ are re-sorted in ascending order of theinterarrival/interdeparture deviation. Both of the sorting func-tion and inter interarrival/interdeparture deviation calculationsare conducted by the function SortJITTER1 in line 25. Afterupdating the TTI indexes order in M∗, the algorithm finds thesufficient allocations to schedule the VoIP packet and updatesR and the corresponding UE connection scheduled packetshistory list A∗k,h. Thus, lines 18 and 25 are both responsiblefor meeting the second objective of the function Z1. Thealgorithm continues in the same fashion, for the head packetsof all UEs connections, inside the WHILE loop of line 3 untileither no empty allocations are existing in the matrix R or nobuffered packets are spotted in any of the UEs’ queues. Thisiterative mechanism resembles the relaxed constraint in (16b)and the added penalty term to Z2. It should be noted that thelogical function isempty in line 3 searches for any empty RBallocations inside the matrix R . Thus, it gives logic ”1” if atleast one empty allocation is found available in matrix R .

As explained in the previous paragraph, the SRV-CO al-gorithm provisions the VoIP connection’s whole history ofscheduled packets in minimizing its overall average delayjitter. In contrast, the second algorithm, described in Table III,optimizes the delay jitter of each single packet (i.e., packetoriented (PO)) only with respect to the delay of its precedingpacket, hence, named as SRV-PO. As a consequence, the SRV-PO algorithm in Table III follows the general approach of theSRV-CO algorithm except for the jitter optimization part. Morespecifically, for the VoIP packet case (lines 12-21), only twocases exist for allocating resources to the observed packet.The first case (lines 12-14) is similar to that of the SRV-CO algorithm (lines 13-15 in Table II) which correspondsto the beginning of the connection where no history forscheduled packets is recorded. The second case (lines 15-20)encompasses the system’s dominating state where at least onepacket has been scheduled. In this case, as in lines 17-21 in

TABLE III: SRV-PO algorithm

1: Require: K, Hk , M, N2: Initialize emtpy RB allocations matrix R , iter = 13: while (isempty(R ) AND Ah


k

(Xh

k (iter))∀k , h


(Xh


6: for i = 1 toK∑

k=1Hk do


k,h10: SortEE(N∗)11: if hk ∈ D∗ then12: if length(A∗k,h) == 0 then13: Find Ψa



∣∣∣∆thk (A∗k,h

∣∣∣last

,a |m)∣∣∣ , ∀n ∈ N∗, m ∈ M∗, a =

HOLk,h17: SortJITTER2(N∗)18: Update M∗19: Find Ψa




24: Update R ,A∗k,h25: end if26: end for27: Set iter = iter+128: end while

Table II, the available RBs addressed by the sets N∗ and M∗

are re-sorted by the function SortJITTER2 which only takes thedelay of the last scheduled packet (i.e., A∗k,h

∣∣∣last

) into account.

Based on the noted difference between the computationalrequirements of the proposed SRV-based schedulers explainedabove, it could be deduced that the SRV-PO algorithm isless complex than that of the SRV-CO. This pertains to thepackets’ history-based heavy computational requirement forthe SRV-CO. This could be further confirmed by evaluating thecomplexity for both algorithms using the standard O notation.For the SRV-CO algorithm in Table II, the complexity of theutility calculations and sorting in lines 4 and 5 is equal to

O(

K∑

k=1Hk

)and O

(K∑

k=1Hk.log

(K∑

k=1Hk

)), respectively. The

searching operation in lines 8 and 9 costs O(NM). As ofline 5, the complexity for the sorting operation in line 10is O(NMlog(NM)) in the worst case scenario. For the IF-statement spanning lines 11-33, the worst case for the com-plexity corresponds to the VoIP type packet when A∗k,h has arecord of scheduled packets (line 12 and lines 23-28). Theworst complexity for the interarrival and interdeparture timecalculation in line 12 is at the end of the VoIP connectiontime interval and is equal to O(25T tot

k,h ), where T totk,h is the total

duration for the VoIP connection h of UE k. The value 25T totk,h

is equivalent to the average number of VoIP packets generatedduring the connection’s total time interval. The calculation isbased on the ON-OFF traffic model [38] with a single packetgenerated every 20 msec within the ON spurts each witha mean duration of 3 sec. Finally, complexities of O(NM),NMO(25T tot

k,h )+O(NMlog(NM)) and O(NM) are spent in lines24, 25 and 27, respectively. Hence, the asymptotic upperlimit for the complexity of a single iteration of the SRV-CO

R2, C2

R2, C2



11

Frame i Frame i+1 Frame i+2 Frame i+3 Frame i+4

Packet(s) arriving

during frame i

A(i)

Packet(s) arriving

during frame i+1

A(i+1)

Packet(s) arriving

during frame i+2

A(i+2)

Packet(s) arriving

during frame i+3

A(i+3)

Packet(s) arriving

during frame i+4

A(i+4)

Buffered packet(s)

before frame i

A(i-1)

A(i-1) packet(s) scheduling window

A(i) packet(s) scheduling window

A(i+1) packet(s) scheduling window

A(i+2) packet(s) scheduling window

A(i+3) packet(s)

scheduling window

Total scheduling time horizon (i.e., scheduler’s granularity)

A(i+4)

packet(s)

are moved

for the

following

scheduling

horizon

Fig. 3: Sliding window predictive scheduling mechanism

algorithm is approximately in the order of O(25T totk,h ). Similar

inspection for the complexity of the SRV-PO algorithm, inTable III, leads to O(NM)+O(NMlog(NM)). The previouscomplexity results strictly confirm a substantial complexityreduction for the SRV-PO algorithm compared to the SRV-COalgorithm as 25T tot

k,h >> NM.It is compelling to highlight at this point that both the SRV-

CO and SRV-PO algorithms achieve the delay jitter optimiza-tion in two stages. The first stage encompasses the delay/jitterprioritization for VoIP connections (in line 4 of Tables II andIII), with respect to video and FTP connections, with theaid of the proposed metric function in (1). The second stageis the jitter-efficient resource allocation approaches explainedpreviously for both algorithms.

B. PRV-Based schedulers

In contrast to the SRV-based algorithms presented above,the proposed PRV-based algorithms in this section investigatea different approach to reconcile the EE/delay jitter trade-off(as will be quantitatively illustrated in Section VI) resultingfrom the short-term scheduling and knowledge of the channel.Conversely, the PRV-based algorithms utilize the long-termknowledge about the UEs’ CSI provided by the cloud-basedray tracing channel prediction system shown in Fig. 1, and asinitially proposed in our recent study in [8]. This draws a newpicture for the system of having a short-term demand (i.e.,packets arriving to the UEs’ buffers every frame), and long-term information about the system’s frequency resources (i.e.,provided by the pool of ray tracing processors available in thecloud). In other words, the CSI is known for multiple futureframes, whereas the BSI is only available every single frame(i.e., no traffic prediction is employed) upon the generation ofnew packet(s). Generally speaking, the PRV-based algorithmshave similar structure to their SRV counterparts in terms ofoptimizing the EE and the delay jitter, however, tailored tothe new aforementioned picture. In particular, after havingall the new arriving packets for each UE connection settledin their corresponding buffer until the end of the arrivingframe (i.e., frame during which the packet is generated), thePRV-based scheduler utilizes the RT future CSI knowledge inscheduling the buffered packets across multiple future framesusing a sliding window mechanism as depicted in Fig. 3.The picture of Fig. 3 shows an example of the proposed

scheduling mechanism for the PRV-based scheduler with fiveframes of scheduling granularity. The scheduler’s granularity,or the total scheduling window size, is practically determinedby the RT engine computing power (i.e., beyond the scopeof this paper). As will be seen in the following discussion,the PRV scheduler with its new extended scheduling timegranularity might appear as a generalization for the singleframe granularity SRV scheduler in optimizing the EE anddelay jitter, however, with different execution procedure.

TABLE IV: PRV-CO algorithm

1: Require: K, Hk , M, N2: Initialize iter = 13: for j = jo to jo + M

10 −1 do4: Initialize emtpy RB allocations matrixR while neglecting

those allocated in the previous iteration window5: Find Ah

k ∀k,h for the window of frames j and j+16: while (isempty(R ) AND Ah


k

(Xh

k (iter))∀k , h


(Xh


9: for i = 1 toK∑

k=1Hk do


k,h13: SortEE(N∗)14: if hk ∈ D∗ then15: Calculate

∣∣∣τAk,h(a−1,a)

∣∣∣ , ∣∣∣τDk,h(a−1,a))

∣∣∣ , ∀a ∈ A∗k,h16: if length(A∗k,h) == 0 then17: Find Ψa


18: Update R ,A∗k,h19: else if length(A∗k,h) == 1 then20: Calculate

∣∣∣∆thk (A

∗k,h,a |m)

∣∣∣ , ∀n ∈ N∗, m ∈ M∗, a =

HOLk,h

21: Sort (N∗,∣∣∣∆th

k (A∗k,h,a |m)

∣∣∣ ,′ ascend′)22: Update M∗23: Find Ψa



∣∣∣τAk,h(A∗k,h

∣∣∣last

,a)∣∣∣ , a = HOLk,h

27: Calculate∣∣∣τD

k,h(A∗k,h∣∣∣last

,a |m)∣∣∣ , a = HOLk,h, m ∈M∗

28: SortJITTER1(N∗)29: Update M∗30: Find Ψa




35: Update R ,A∗k,h36: end if37: end for38: Set iter = iter+139: end while40: end for

Considering a total of five frames (i.e., M= 50 TTIs)for the scheduling time horizon as shown in Fig 3, eachof the buffered packets inside a single UE buffer can betheoretically scheduled in any frame following its arrivingframe (i.e., causal time scheduling) within the schedulinghorizon. However, to avoid having the scheduler bottle-necked,we limit the scheduling time horizon for each of the bufferedpackets to a smaller window of only two frames, for instance,following its arriving frame. The two frames window, then,slides in time with a one frame overlap for subsequent framesarriving packets. The motivation behind employing the sliding



12

window mechanism in scheduling packets could be explainedas follows. For instance, having one of the buffered packets(i.e., for single UE buffer) scheduled in the last frame ofthe scheduling time horizon will lead to having most (if notall) of the subsequent buffered packets potentially staying inthe buffer for the following horizon, resulting in a buffer-overflow. The overflow problem is even more severe in case ofdemanding traffic types (e.g., video and FTP). In addition tothe buffer-overflow problem, which causes packet losses, mostof the frequency resources in the beginning of the schedulingtime horizon are potentially wasted. Therefore, the trade-offbetween better exploiting more information about the CSI infuture frames - for reaching objectives (i.e., optimizing theEE and delay jitter for VoIP, and EE for video and FTP)and satisfying constraints (i.e., delay for VoIP and throughputfor video and FTP) - and the spectral inefficiency and highqueuing delays has to be carefully provisioned by settingproper sizes for the scheduling time horizon and the smallersliding window.

TABLE V: PRV-PO algorithm

1: Require: K, Hk , M, N2: Initialize iter = 13: for j = jo to jo + M

10 −1 do4: Initialize emtpy RB allocations matrixR while neglecting

those allocated in the previous iteration window5: Find Ah

k ∀k,h for the window of frames j and j+16: while (isempty(R ) AND Ah


k

(Xh

k (iter))∀k , h


(Xh


9: for i = 1 toK∑

k=1Hk do


k,h13: SortEE(N∗)14: if hk ∈ D∗ then15: if length(A∗k,h) == 0 then16: Find Ψa



∣∣∣∆thk (A∗k,h

∣∣∣last

,a |m)∣∣∣ , ∀n ∈ N∗, m ∈ M∗, a =

HOLk,h20: SortJITTER2(N∗)21: Update M∗22: Find Ψa




27: Update R ,A∗k,h28: end if29: end for30: Set iter = iter+131: end while32: end for

Similar to the SRV-based schedulers, and based on theprevious discussion, the heuristic algorithms for both of theconnection and packet oriented versions of the proposed PRVscheduler are illustrated in Tables IV and V, respectively. Themain structure is similar to that of the SRV-based algorithmsexcept for the sliding window loop in line 3. In each iterationof the loop, for both of the PRV-CO and PRV-PO algorithms,the algorithm slides the scheduling window as explained inthe previous paragraph. In particular, the algorithm creates the

empty allocation matrix R (in line 4) for the frames of theobserved window while excluding those allocated within theoverlapped frame with the preceding iteration window withinthe same scheduling time horizon. The sliding window size isassumed to be two frames for both algorithms. The potentialpackets for each UE buffer that could be scheduled within thecurrently observed window are then determined in line 5 basedon their arrival times. The WHILE loop then keeps iterating toschedule the packets found in line 5, for the current window,the same way as the SRV-based algorithms. The algorithmcontinues in the same fashion for the subsequent windowswithin the current scheduling time horizon until the loop ofline 3 terminates. Finally, due to the fact the PRV algorithmshave similar structures to those of the SRV, the computationalcomplexities calculated in the previous subsection for the SRVapply to the PRV, however, with larger contribution of M incase of the PRV compared to the SRV (i.e., SRV-PO is simplerthan PRV-PO by a factor of M).

VI. NUMERICAL RESULTS

In this section, the performance of the two versions (i.e.,SRV and PRV) for our proposed scheduler with their connec-tion (CO) and packet (PO) oriented set-ups is evaluated. Sincethe EE is one major objective for our proposed scheduler, theevaluation is conducted in comparison to the energy-efficientresource allocation scheme, namely green resource allocation(GRA), proposed in [13]. However, the GRA scheme was notdesigned to simultaneously deal with different QoS require-ments. Therefore, and to ensure fair comparison, the GRAscheme is integrated with the utility-based scheduling schemeproposed in [29], namely fair class-based packet scheduling(FCBPS), to be able to deal with the heterogeneous trafficenvironment as our scheduler. For simplicity, the compositescheme is, thus, denoted as GRA-FCBPS. In addition to theGRA-FCBPS, the performance of our previously proposedenergy-efficient predictive scheduler (EEPS) in [8] is includedin our comparison. The investigations are carried out using adiscrete event simulator built in MATLAB to simulate the real-time behavior of the considered traffic types. As explained inSection II-A, VoIP, video streaming and FTP traffic types areconsidered in our simulations to address the delay, rate andbest-effort QoS classes, respectively. The generation methodsfor the three traffic types are similar to those adopted in [29].For video streaming, the minimum and maximum data ratesare 64 Kbps and 384 Kbps, respectively. On the other hand,for FTP traffic, the maximum data rate is 128 Kbps. Also, thepacket delay budget for the VoIP traffic is 100 msec. Withoutloss of generality, we simulate the system behavior due toan equal increase in the traffic connections requested for eachtraffic type. In particular, each UE is assumed to handle singletraffic type. However, that assumption does not violate thescheduler model depicted in Fig. 2, since the scheduler dealswith each traffic connection independently based on its utilityas explained in Section II-A.

The wireless channel for each UE is assumed to be fre-quency and time selective within each LTE frame (i.e., fastand frequency selective fading channel). Thus, the channel is



13

10 20 30 40 50 60 70 80 90 100Number of VoIP UEs

10

15

20

25

30

35

40

45

50

55

60

Ave

rage

ene

rgy

effic

ieny

per

UE

(K

bits

/J)

GRA-FCBPSProposed SRV-CO scheme ( tmax = )Proposed SRV-CO scheme ( tmax= 20 msec)Proposed SRV-PO scheme ( tmax = )Proposed SRV-PO scheme ( tmax= 20 msec)Proposed PRV-CO scheme ( tmax= 20 msec)Proposed PRV-PO scheme ( tmax= 20 msec)EEPS

Fig. 4: EE performance for VoIP UEs

10 20 30 40 50 60 70 80 90 100Number of Video UEs

100

200

300

400

500

600

700

800

Ave

rage

ene

rgy

effic

ieny

per

UE

(K

bits

/J)


Fig. 5: EE performance for Video UEs

modeled as a quasi-static block Rayleigh fading channel [39].In each TTI, 50 RBs are available for scheduling the UEs’traffic which corresponds to the 10 MHz LTE channel.

Looking at the results depicted in figures 4, 5 and 6 whichshow the EE performance for VoIP, video and FTP users,respectively, three conclusions are deduced. First, the EE has ageneral decaying trend, for all types of users, with increasingsystem load. This is understood due to the scheduler’s limitedoptimization ability in highly congested network situationsduring which the limited available resources become incapableof satisfying the increasing traffic demand. Second, the videousers have the highest achieved average EE followed byFTP then VoIP. We attribute this to the fact that the UEreceiver’s circuit consumes the same base power in the wake-up state (i.e., Pon + Prx as explained in Section II-B) everyTTI regardless of the type of traffic. Consequently, the trafficwith the highest average rate certainly achieves the highestaverage EE. In our case, the video has the highest averagerate (i.e., 224 Kbps), followed by FTP and VoIP. The thirdconclusion is regarding the relative EE performance of theproposed SRV-CO and SRV-PO schedulers compared to theGRA-FCBPS. It could be noticed that the difference is highlypronounced for VoIP users than that for video and FTP. This isbecause the proposed schedulers only optimize the EE in caseof video and FTP traffics just as the GRA-FCBPS scheduler,

10 20 30 40 50 60 70 80 90 100Number of FTP UEs

100

150

200

250

300

350

400

450

Ave

rage

ene

rgy

effic

ieny

per

UE

(K

bits

/J)


Fig. 6: EE performance for FTP UEs


0

5

10

15

20

25

Ave

rage

pac

ket d

elay

jitte

r (m

sec)


Fig. 7: Average packet delay jitter for VoIP UEs

while in case of VoIP the jitter is an additional objective toimprove the quality of experience (QoE) perceived by VoIPUEs. Hence, we note a trade-off between the EE and delayjitter performances for the VoIP traffic.

In the following discussions, we start shedding a lighton the EE/delay jitter trade-off for the VoIP traffic in the

0 5 10 15 20 25 30 35 40Jitter (msec)

0

0.05

0.1

0.15

0.2

0.25

PDF

GRA-FCBPSProposed SRV-PO scheme ( tmax= 20 msec)Proposed PRV-PO scheme( tmax= 20 msec)EEPS

Fig. 8: PDF of the delay jitter for an arbitrary VoIP UE atthe high network load case (i.e., 100 UEs)

R1, C1



14

considered heterogeneous traffic environment as originallyenvisioned by our proposed framework. To avoid the dis-continuty in discussions and confusing the reader, we firstfocus on the performance of our proposed SRV schedulersin reference to the GRA-FCBPS, and conclude by the RT-based PRV schedulers compared to both the GRA-FCBPS andEEPS schedulers. Considering the VoIP traffic users, the EEresults of Fig. 4 can be justified in conjunction with thoseobtained in Fig. 7. As shown in both figures, each of theproposed SRV-CO and SRV-PO scheduler is considered twicewith different values for the jitter threshold (i.e., ∆tmax) in(1). Two extreme cases were assumed. In the first case, thethreshold is set to the highest possible value that is equal to ∞

which corresponds to the conventional delay metric functionoriginally used by the FCBPS scheduler in [29]. The secondcase corresponds to our proposed VoIP utility in (1) having∆tmax set to an arbitrarily smaller value of 20 msec. It shouldbe noted that for both cases, as explained in the previoussection, the proposed energy and jitter efficient allocationschemes are implemented. Thus, the first case (i.e., ∆tmax =∞)implies single stage of jitter optimization, while the secondcase (i.e., ∆tmax =20 msec) corresponds to two stage jitteroptimization. For both cases, the EE performance for both ofthe SRV-CO and SRV-PO is lower than that attained by theGRA-FCBPS scheduler. This can be directly justified by theremarkable jitter improvement attained by our schedulers asillustrated in Fig. 7. Moreover, the results obtained in Fig. 8give more insight on how our proposed SRV scheme tends tostatistically bound the jitter performance and ensure meetinga fixed threshold compared to the GRA-FCBPS scheme. Inparticular, our proposed SRV scheme was able to bound thejitter at 20 msec whereas the GRA-FCBPS failed to do so.At this point, it is imperative to indicate that the EE/jittertrade-off for VoIP allocations is attributed to the fact that ourproposed jitter-efficient resource allocation algorithms (boththe connection and packet oriented) tend to statistically expandthe scheduling of resources in time to compensate for the delayjitter induced on the go. That behavior is obviously adverse tothe EE scheduling strategy, explained in Section II-B, whichtargets to minimize the number of allocated TTIs (i.e., circuitwake-up periods of reception) to each UE while receiving thesame amount of data. A minor impact for the jitter-efficientallocations of VoIP users is observed on the EE of video andFTP users as depicted in figures 5 and 6, respectively. That is,only a slight drop in the attained EE for video and FTP usersarising from the time spread VoIP allocations which mightspan TTIs initially allocated in full to video and FTP users.In other words, the same video or FTP UE might takes lessnumber of RBs during single TTI while consuming the samepower.

It can also be noticed from the results obtained in Figures 4and 7 that the double stage jitter optimization for our proposedSRV schedulers (i.e., ∆tmax =20 msec) is substantially boost-ing both of their EE and jitter performances compared to theirsingle stage optimization arrangement (i.e., ∆tmax = ∞). Thereason is that adding the delay jitter parameter to the VoIP met-ric function in (1) makes it more sensitive to changes resultingin more aggressive utility requirements (i.e., prioritization) to


10

20

30

40

50

60

70

80

90

100

Ave

rag

e p

ack

et

de

lay

(mse

c)

GRA-FCBPSProposed SRV-CO scheme ( tmax = )Proposed SRV-CO scheme ( tmax = 20 msec)Proposed SRV-PO scheme ( tmax = )Proposed SRV-PO scheme ( tmax= 20 msec)Proposed PRV-CO scheme ( tmax= 20 msec)Proposed PRV-PO scheme ( tmax= 20 msec)EEPSVoIP packet delay budget

Fig. 9: Average packet delay for VoIP UEs


-20

0

20

40

60

80

100

120

140

160

180

200

220

EE

loss

(%)

-20

0

20

40

60

80

100

120

140

160

180

200

220

Pac

ket d

elay

jitte

r im

prov

men

t (%

)

EE loss - SRV-CO ( tmax = )EE loss - SRV-CO ( tmax = 20 msec)EE loss - SRV-PO ( tmax = )EE loss - SRV-PO ( tmax = 20 msec)EE loss - PRV-CO ( tmax = 20 msec)EE loss - PRV-PO ( tmax = 20 msec)Jitter improvment - SRV-CO ( tmax = )Jitter improvment - SRV-CO ( tmax = 20 msec)Jitter improvment - SRV-PO ( tmax = )Jitter improvment - SRV-PO ( tmax = 20 msec)Jitter improvment - PRV-CO ( tmax = 20 msec)Jitter improvment - PRV-PO ( tmax = 20 msec)

Fig. 10: EE/delay jitter trade-off for VoIP UEs

VoIP users compared to video and FTP users. This can befurther illustrated by the improved delay performance obtainedin Fig. 9. Therefore, by allowing jitter-dependent VoIP utility,the proposed schedulers strike better EE/delay jitter trade-offcompared to the single stage jitter optimization (i.e., jitter-independent utility). From another perspective, the SRV-POscheme generally shows better performance (i.e., EE/delayjitter trade-off) compared to the SRV-CO. This is due to thefact that the SRV-CO algorithm is performing jitter optimiza-tion with respect to the entire delay history of scheduledpackets. Having in mind that some of the scheduled packetsmight have attained high jitter values, the jitter optimizationof subsequent packets gets consequently negatively influenced.This is a problem that does not exist in the SRV-PO algorithmwhich only provisions the last scheduled packet departuretime when optimizing the jitter for the following packet. Thiscan be seen obviously in the double stage jitter optimizationcase where the SRV-PO algorithm is clearly outperformingthe SRV-CO algorithm in terms of EE and jitter. However, inthe case of single stage jitter optimization (i.e., ∆tmax = ∞),some discrepancies are noted to be taking place. The SRV-PO scheme performs all the way better than the SRV-COscheme in terms of EE as shown in Fig. 4. Nevertheless,in terms of jitter, as observed Fig. 7, it only outperforms

R1, C1



15


0

20

40

60

80

100

120

140

160

180

200

220

240

Pe

r use

r a

vera

ge

th

rou

gh

pu

t (K

bps)

GRA-FCBPSProposed SRV-CO scheme ( tmax = )Proposed SRV-CO scheme ( tmax= 20 msec)Proposed SRV-PO scheme ( tmax = )Proposed SRV-PO scheme ( tmax= 20 msec)Proposed PRV-CO scheme ( tmax= 20 msec)Proposed PRV-PO scheme ( tmax= 20 msec)EEPSMinimum required rate

Fig. 11: Average throughput for Video UEs

at light load (i.e., 10, 20 and 30 VoIP users). At moderateload (i.e., 40, 50, 60 and 70 VoIP users) the performanceis almost equal to the SRV-CO. Then at high load (i.e., 80,90 and 100 VoIP users), SRV-CO showed even better jitterperformance than SRV-PO. The sudden jump in jitter in Fig. 7(i.e., at 80 VoIP UEs) could be seen happening in the delaydepicted in Fig. 9 at the same point. This behavior conveysan overloaded system situation during which the effect of theinter-class distinguishing parameter βh in prioritizing the VoIPtraffic becomes minor compared to the utility of the growingnumber of heavy traffic video and FTP users. Hence, a lowerpriority will be rather given most of the time to the light VoIPtraffic for the sake of heavy rates video and FTP traffics.The stable jitter performance trend illustrated in Fig. 7 forthe double stage optimization arrangement, which adds morepriority to VoIP users over others, of our proposed schedulersessentially supports the previous conclusion. To summarizeall the previous discussions about the SRV schedulers resultsobtained in figures 4 and 7, Fig. 10 shows the EE lossversus the delay jitter improvement trade-off attained by theproposed algorithms, in their jitter-dependent and independentutility arrangements, with respect to the GRA-FCBPS sched-uler performance. The fluctuations pronounced in the jitterimprovement percentage, in Fig. 10, pertains directly to therelative jitter performance between our proposed schemes andthe GRA-FCBPS scheme depicted in Fig. 7. In other words,the selected simulation step size in terms of the number of UEs(i.e., 10 UEs), produces slowly varying jitter performance incase of the GRA-FCBPS scheme except at discrete points (i.e.,40, 80, and 90 UEs) where the jitter rises remarkably. In caseof our proposed SRV-based schemes, the jitter performance isrelatively smooth (i.e., at 40, 80, 90, 100 UEs) and rises atdifferent points (i.e., 70 UEs). This relative jitter performanceexplains the fluctuations observed in Fig. 10.

For the video and FTP users, the results reported in figures11 and 12 confirm that the improvement in the EE and delayjitter performances for VoIP users achieved by our proposedSRV schedulers does not harmfully affect the video and FTPusers in terms of the achieved throughput. However, the dropin the attained throughput for our proposed SRV schedulers,especially in case of FTP users, pertains to the jitter allocation

10 20 30 40 50 60 70 80 90 100Number of FTP UEs

0

20

40

60

80

100

120

140

Per

use

r av

erag

e th

roug

hput

(K

bps)

GRA-FCBPS

Proposed SRV-CO scheme ( tmax = )Proposed SRV-CO scheme ( tmax= 20 msec)Proposed SRV-PO scheme ( tmax = )Proposed SRV-PO scheme ( tmax= 20 msec)Proposed PRV-CO scheme ( tmax= 20 msec)Proposed PRV-PO scheme ( tmax= 20 msec)EEPSMinimum required rate

Fig. 12: Average throughput for FTP UEs


0

0.2

0.4

0.6

0.8

1

1.2

JFI o

f the

ave

rage

pac

ket d

elay


Fig. 13: JFI for VoIP UEs

strategy, as previously discussed, which might be sometimesspectrally inefficient in favor of VoIP users. In terms offairness, as expected all the results depicted in figures 13,14 and 15 show comparable satisfactory intra-class fairnessfor the VoIP, video and FTP users, respectively. Since all theimplemented schedulers are based on the utility-based strategydiscussed in Section II-A, the intra-class fairness was expected.The fairness is measured using the Jain’s fairness index (JFI)[40]. For VoIP users, the JFI is calculated in terms of theaverage packet delay experienced by each user. For video andFTP, the JFI is calculated based on the users’ average attainedthroughput. The fairness drop observed for FTP traffic (i.e.,lowest priority traffic) is due to the scarcity of the spectralresources to carry the FTP users traffic at high network load.As a result, some FTP users might starve compared to others.Hence, the fairness gets slightly affected.

When investigating the peak performance of our proposedscheduler in its predictive version (i.e., PRV) supported bythe cloud-based RT prediction (as discussed in Section II) andthe proposed sliding window mechanism (i.e., explained inthe previous section), we were able to obtain the following.First, compared to the GRA-FCBPS, our proposed PRV-basedschedulers attained a considerable improvement for both theEE and delay jitter performances in case of VoIP users asillustrated in figures 4 and 7, respectively. The improvements

R1, C6



16


0

0.2

0.4

0.6

0.8

1

1.2JF

I of t

he a

vera

ge th

roug

hput


Fig. 14: JFI for Video UEs

are due to the increased scheduling time horizon (i.e., 5frames with sliding window of 2 frames) which allows thescheduler to better exploit the channel diversity gain over timeand explore bigger solution space to solve the optimizationproblem more efficiently. As in the case of SRV schedulers,the PRV-PO algorithm showed better performance comparedto its PRV-CO counterpart, however, with wider gap. Theincreased performance gap is regarded to magnifying the jitterrelative inefficiency of the CO-based algorithm in case of thePRV scheduler. In particular, the PRV-CO has more freedomto inaccurately move its RB allocations to future frames tocompensate for the delay jitter of the observed packet basedon the whole history of scheduled packets. This intuition issupported by the relative large delay attained by the PRV-COalgorithm compared to the PRV-PO as depicted in Fig. 9. Interms of the EE/delay jitter trade-off, both algorithms shownegative values for the EE loss percentage which impliesan EE improvement, that is close to 20% as illustrated inFig. 10. However, the PRV-PO algorithm is able to maintainnearly constant jitter improvement (i.e., corresponding to theconstant performance depicted in Fig. 7) by approximately90% relative to the GRA-FCBPS, whereas 60% at most isattained by the PRV-CO algorithm. Furthermore, the perfor-mance gap discussed above, between the PRV-PO and PRV-COalgorithms, is found also in the fairness among VoIP users. Asdemonstrated in Fig. 13, the redundant jitter mechanism for thePRV-CO scheduler has obviously affected the uniformity of theaverage packet delay experienced by each VoIP user leadingto a drop in the JFI to 0.8. This drop is clearly found at lightnetwork load in which the redundancy of the CO jitter-efficientresource allocation algorithm is highly pronounced for eachof the existing VoIP users. On the opposite side, the precisejitter mechanism employed in the PRV-PO algorithm leadsto sustained fairness with JFI very close to 1 irrespective ofthe network load. Second, the proposed PRV-based schedulersachieved slightly lower EE (by 11.6% on average) comparedto the EEPS as depicted in Fig. 4. This is due to the factthat the EEPS focuses solely on the UE’s EE, unlike ourPRV schedulers which optimizes both the EE and jitter. Thiscan be directly justified by the poor jitter performance of the

10 20 30 40 50 60 70 80 90 100Number of FTP UEs

0

0.2

0.4

0.6

0.8

1

1.2

JFI o

f the

ave

rage

thro

ughp

ut


Fig. 15: JFI for FTP UEs

EEPS compared to the PRV-based schedulers as illustrated inFig. 7. Furthermore, the results depicted in Fig. 8 confirm thecapability of our proposed PRV scheme to statistically boundthe packet delay jitter and ensure meeting a strict thresholdlevel (at 20 msec) compared to the GRA-FCBPS and theEEPS. It even demonstrated narrower jitter range comparedto our proposed SRV scheme.

The performance gain for the PRV schedulers was notlimited to VoIP users. Video and FTP users were also able toacquire boosted EE and throughput performances. The resultsobtained in figures 5 and 6 demonstrate dramatic increase inthe EE for video and FTP UEs, respectively, compared tothe GRA-FCBPS. However, at high network load, FTP UEshave experienced sudden drop in their EE performance dueto their low inter-class priority compared to video UEs whichrelatively retain more resistance to the EE drop. Moreover,the EE drop for FTP connections is clearly observed in caseof the EEPS due to the remarkable increase in case of VoIPand the slight increase in case of video connections. Fromanother perspective, the proposed PRV schedulers generallyattain higher EE compared to the SRV and GRA-FCBPSschedulers. The EE results for video and FTP UEs can bedirectly justified with their corresponding throughput resultsobtained in figures 11 and 12. In Fig. 11, the video UEsexperience as significant throughput increase as that for the EEin Fig. 5. As in the case of VoIP, this improvement is attributedto the channel diversity gain over future frames utilized by thePRV schedulers. In particular, the scheduler was able to findbetter TTI(s) to receive more average packets per each videoUE while consuming the same circuit energy. As expected, thethroughput increase for video UEs is directly translated as adecay in the attained throughput by the FTP users as portrayedin Fig. 12. This dependency is due to the higher priority forvideo users which require an average rate (i.e., 224 Kbps) ap-proximately twice that required by FTP users (i.e., 128 Kbps),and the bounded cell capacity (i.e., number of RBs/TTI) evenat high spectral efficiency. Despite the throughput drop inmoderately loaded network, the PRV schedulers were ableto maintain improved throughput performance for FTP userscompared to the SRV and GRA-FCBPS schedulers at light and

R2, C3

R2, C4

R1, C1



17

high loaded network situations. The EEPS on the other handachieved slightly better throughput performance for both videoand FTP users compared to the PRV schedulers. As previouslyexplained, this is attributed to the absence of the jitter-efficientallocation scheme which was found to negatively affect boththe EE and throughput performances of video and FTP usersin the case of SRV schedulers. Meanwhile, the reduced systemcapacity for the PRV schedulers compared to the EEPS in caseof video and FTP users (i.e., 12.8% and 19.6%, respectively)is justified by increasing the capacity and QoE of VoIP usersby an average of 44.4% and 93.2% as depicted in Fig. 9 andFig. 7, respectively. Finally, the PRV schedulers were able tomaintain high JFI among video users as illustrated in Fig. 14.Meanwhile, the same high fairness is also achieved by thePRV schedulers in case of FTP users as depicted in Fig. 15,which confirms the equal throughput improvement among allusers during network congestion compared to the SRV andGRA-FCBPS schedulers.

It is obvious that the above results and discussions demon-strate the effectiveness of the proposed PO-based algorithmsover their CO counterparts in terms of performance andcomplexity. However, there are two final notes which are worthmentioning about this comparison. Firstly, the key idea of theCO-based schemes is more consistent with the framework ofthe IETF RFC 3550 standard [19] which targets the mean valueof the jitter rather than tracking it instantaneously as the casein the PO algorithms. Secondly, from the operator’s point ofview, the PO-based schemes might look more demanding interms of the signalling overhead requirement compared to theCO-based schemes. In other words, the PO algorithms mightrequire more spectral and power resources to continuouslyreport the delay of every single scheduled packet in the queueto optimize the assignment of the following packet in terms ofthe jitter. Thus, from a deployment perspective, the selectioncriteria of the suitable scheduling algorithm is left to theoperator’s choice based on its objectives and policies in lightof the obtained results.

VII. CONCLUSION

In this paper, we developed a framework for implementinga QoS-aware energy and jitter efficient scheduling method-ologies in downlink OFDMA heterogeneous traffic cellularsystems.

Firstly, we utilized our previously proposed C-RAN basedpredictive scheduling system to provide a more detailed modelin case of real-time heterogeneous traffic networks. Secondly,based on the popular utility-based inter-class prioritizationscheme, we proposed a new metric function which capturesthe packet’s delay and delay jitter QoS metrics. The functiontargeted optimal jitter performance within the packet’s deliverydelay threshold for the real-time traffic class. Thirdly, weformulated a BIP problem which optimizes the LTE UE’sreceiving EE for delay-sensitive, rate-sensitive and best-effortQoS classes concurrently. In the case of delay-sensitive class,the formulation was of a weighted sum composite structurehaving the delay jitter as a coexisting objective besides theEE and constrained by a fixed packet delay budget. For the

rate-sensitive and best-effort classes, the formulation targetedonly the EE as a single objective while setting a minimum rateconstraint for the rate-sensitive class of traffic. Fourthly, dueto the inherent intractability of the optimal formulation, fourdifferent heuristic algorithms were proposed to find a sub-optimal solution for the problem with reasonable computa-tional requirements. Two of the proposed algorithms belong tothe traditional short range schedulers which work with a singleframe time granularity (at most). The other two algorithmsbelong to the predictive scheduling class which are capable ofallocating resources in multiple future frames using the modelproposed in the first part of our work. All the proposed algo-rithms employed the jitter optimization in two stages. The firststage encompassed the proposed jitter-based utility function,whereas the second stage involved two proposed jitter-efficientresource allocation algorithms. Furthermore, a sliding windowmechanism was proposed to allow the heuristic algorithmsprofit from the future predicted CSI (i.e., provided by the poolof ray tracing engines residing in the cloud) without the needof implementing a traffic prediction mechanism.

To evaluate the performance of our proposed schedulers,extensive numerical simulations were conducted in compar-ison with existing schedulers. The first part of the resultsdemonstrated the ability of our proposed short range sched-ulers to remarkably improve the delay jitter, for the real-time traffic, on the expense of the EE while maintaining thedelay bounds. This is in addition to maintaining comparableEE and throughput performances for rate-sensitive and best-effort traffic types. In the second part, the predictive versionsof our proposed scheduler were able to strike a dramaticimprovement for the EE/delay-jitter trade-off, compared toexisting schedulers and our short range schedulers, in case ofthe delay-sensitive traffic. Furthermore, the EE and throughputperformances were also substantially improved for the rate-sensitive and best-effort traffics. The improvements were dueto the predictive scheduler’s capability of exploiting futurechannel conditions in making better decisions compared totraditional short range schedulers. Finally, since employing theutility-based prioritization scheme, all the proposed schedulersshowed high degree of intra-class fairness for each of theconsidered traffic classes.

REFERENCES

[1] S. Stefania, I. Toufik, and M. Baker, LTE - The UMTS Long TermEvolution: From Theory to Practice. John Wiley & Sons Ltd., 2011.

[2] M. R. Palattella, M. Dohler, A. Grieco, G. Rizzo, J. Torsner, T. Engel,and L. Ladid, “Internet of things in the 5G era: Enablers, architecture,and business models,” IEEE J. Sel. Areas Commun., vol. 34, no. 3, pp.510–527, Mar. 2016.

[3] P. Demestichas, A. Georgakopoulos, K. Tsagkaris, and S. Kotrotsos,“Intelligent 5G networks: Managing 5G wireless/mobile broadband,”IEEE Veh. Technol. Mag., vol. 10, no. 3, pp. 41–50, Sept. 2015.

[4] T. Wang, G. Li, J. Ding, Q. Miao, J. Li, and Y. Wang, “5G spectrum:is China ready?” IEEE Commun. Mag., vol. 53, no. 7, pp. 58–65, July2015.

[5] S. Chen, H. Xu, D. Liu, B. Hu, and H. Wang, “A vision of IoT:Applications, Challenges, and Opportunities with China Perspective,”IEEE Internet of Things Journal, vol. 1, no. 4, pp. 349–359, Aug. 2014.

[6] J. A. Stankovic, “Research directions for the internet of things,” IEEEInternet Things J., vol. 1, no. 1, pp. 3–9, Feb. 2014.

[7] M. Altamimi, A. Abdrabou, K. Naik, and A. Nayak, “Energy costmodels of smartphones for task offloading to the cloud,” IEEE Trans.Emerg. Topics Comput., vol. 3, no. 3, pp. 384–398, Sept. 2015.

R2, C4

R1, C2

R1, C3



18

[8] K. Hammad, S. Primak, M. Kalil, and A. Shami, “QoS-aware energy-efficient downlink predictive scheduler for OFDMA-based cellular de-vices,” IEEE Trans. on Veh. Technol., vol. 66, no. 2, pp. 1468–1483,Feb. 2017.

[9] C. Courcoubetis and R. Weber, “Effective bandwidths for stationarysources,” Probability in the Engineering and Informational Sciences,vol. 9, no. 02, pp. 285–296, 1995.

[10] D. Feng, C. Jiang, G. Lim, J. Cimini, L.J., G. Feng, and G. Li, “A surveyof energy-efficient wireless communications,” IEEE Commun. SurveysTuts., vol. 15, no. 1, pp. 167–178, Feb. 2013.

[11] C. Y. Wong, R. S. Cheng, K. B. Lataief, and R. D. Murch, “MultiuserOFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel.Areas Commun., vol. 17, no. 10, pp. 1747–1758, Oct. 1999.

[12] M. Bohge, J. Gross, A. Wolisz, and M. Meyer, “Dynamic resourceallocation in OFDM systems: an overview of cross-layer optimizationprinciples and techniques,” IEEE Network, vol. 21, no. 1, pp. 53–59,Jan. 2007.

[13] F. Chu, K. Chen, and G. Fettweis, “Green resource allocation to min-imize receiving energy in OFDMA cellular systems,” IEEE Commun.Lett., vol. 16, no. 3, pp. 372–374, Mar. 2012.

[14] C. Bontu and E. Illidge, “DRX mechanism for power saving in LTE,”IEEE Commun. Mag., vol. 47, no. 6, pp. 48–55, June 2009.

[15] D. Dechene and A. Shami, “Energy-aware resource allocation strategiesfor LTE uplink with synchronous HARQ constraints,” IEEE Trans.Mobile Comput., vol. 13, no. 2, pp. 422–433, Feb. 2014.

[16] M. Kalil, A. Shami, and A. Al-Dweik, “QoS-aware power-efficientscheduler for LTE uplink,” IEEE Trans. Mobile Comput., vol. 14, no. 8,pp. 1672–1685, Aug. 2015.

[17] G. Miao, N. Himayat, G. Li, and S. Talwar, “Low-complexity energy-efficient scheduling for uplink OFDMA,” IEEE Trans. Commun., vol. 60,no. 1, pp. 112–120, Jan. 2012.

[18] A. Jensen, M. Lauridsen, P. Mogensen, T. Srensen, and P. Jensen, “LTEUE power consumption model: For system level energy and performanceoptimization,” in IEEE Veh. Technol. Conf., Sept. 2012, pp. 1–5.

[19] H. Schulzrinne, S. L. Casner, R. Frederick, and V. Jacobson, “RTP: ATransport Protocol for Real-Time Applications,” RFC 3550, Jul. 2003.

[20] Q. Leng, Y. H. Wei, S. Han, A. K. Mok, W. Zhang, and M. Tomizuka,“Improving control performance by minimizing jitter in RT-WiFi net-works,” in IEEE Real-Time Systems Symposium, Dec. 2014, pp. 63–73.

[21] A. Mukhopadhyay and G. Das, “A proposal for WLAN-EPON inte-gration that reduces video traffic jitter in presence of mixed traffic,” inIEEE International Conference on Advanced Networks and Telecommu-nications Systems, Nov. 2016, pp. 1–6.

[22] L. Ortiz, “Methods and systems for jitter minimization in streamingmedia,” Jul. 28 2009, US Patent 7,567,509. [Online]. Available:https://www.google.com/patents/US7567509

[23] D. C. Verma, H. Zhang, and D. Ferrari, “Delay jitter control for real-time communication in a packet switching network,” in Proceedings ofTRICOMM’91, pp. 35–43, Apr. 1991.

[24] C. Rosado-Sosa and I. Rubin, “Jitter compensation scheduling schemesfor the support of real-time communications,” IEEE Int.Conf. on Com-mun., vol. 2, pp. 885–890, June 1998.

[25] F. P. Zhang, O. W. W. Yang, and B. Cheng, “Performance evaluation ofjitter management algorithms,” Canadian Conference on Electrical andComputer Engineering, vol. 2, pp. 1011–1016, May 2001.

[26] B. Rong, Y. Qian, M. H. Guiagoussou, and M. Kadoch, “Improvingdelay and jitter performance in wireless mesh networks for mobile IPTVservices,” IEEE Trans. Broadcast., vol. 55, no. 3, pp. 642–651, Sept.2009.

[27] C. Cox, An Introduction to LTE. John Wiley & Sons Ltd., 2012.[28] X. Wang, G. B. Giannakis, and A. G. Marques, “A unified approach

to QoS-guaranteed scheduling for channel-adaptive wireless networks,”Proceedings of the IEEE, vol. 95, no. 12, pp. 2410–2431, Dec. 2007.

[29] B. Al-Manthari, H. Hassanein, N. Ali, and N. Nasser, “Fair class-baseddownlink scheduling with revenue considerations in next generationbroadband wireless access systems,” IEEE Trans. Mobile Comput.,vol. 8, no. 6, pp. 721–734, June 2009.

[30] R. Ruby, V. C. M. Leung, and D. G. Michelson, “Uplink scheduler forSC-FDMA-based heterogeneous traffic networks with QoS assuranceand guaranteed resource utilization,” IEEE Trans. Veh. Technol., vol. 64,no. 10, pp. 4780–4796, Oct. 2015.

[31] C. I, J. Huang, R. Duan, C. Cui, J. Jiang, and L. Li, “Recent progresson C-RAN centralization and cloudification,” IEEE Access, vol. 2, pp.1030–1039, Aug. 2014.

[32] M. F. Catedra and J. Perez, Cell Planning for Wireless Communications,1st ed. Artech House, Inc., 1999.

[33] H. Varian, Intermediate Micoreconomics: A Modern Approach, 6th ed.W.W. Norton and Company, 2003.

[34] M. Gidlund and J. C. Laneri, “Scheduling algorithms for 3GPP long-term evolution systems: From a quality of service perspective,” in IEEEInt. Symp. on Spread Spectrum Techniques and Applications, Aug. 2008,pp. 118–123.

[35] Y. Zaki, T. Weerawardane, C. Gorg, and A. Timm-Giel, “Multi-QoS-aware fair scheduling for LTE,” in IEEE Veh. Technol. Conf., May 2011,pp. 1–5.

[36] D. P. Bertsekas, Constrained Optimization and Lagrange MultiplierMethods. MA: Athena Scientific, 1996.

[37] M. J. Neely and S. Supittayapornpong, “Dynamic markov decisionpolicies for delay constrained wireless scheduling,” IEEE Trans. Autom.Control, vol. 58, no. 8, pp. 1948–1961, Aug. 2013.

[38] K. Yong-Seok, “Capacity of VoIP over HSDPA with frame bundling,”IEICE trans. on commun., vol. 89, no. 12, pp. 3450–3453, 2006.

[39] J. Proakis, Digital Communications, 4th ed. New York: McGraw-Hill,2001.

[40] R. Jain, D. Chiu, and W. Hawe, “A quantitative measure of fairnessand discrimination for resource allocation in shared computer systems,”DEC Research Report TR-301, Sept. 1984.

Karim Hammad received his B.Sc. and M.Sc.degrees in Electronics and Communications Engi-neering from the Arab Academy For Science, Tech-nology and Maritime Transport, Egypt, in 2005 and2009, respectively, and the Ph.D. degree in Electricaland Computer Engineering from the University ofWestern Ontario, Canada in 2016. His research in-terests include wireless networks cross-layer design,physical layer security and digital circuit design.

Abdallah Moubayed received his B.E degree inElectrical Engineering from Lebanese AmericanUniversity, Beirut, Lebanon in 2012 and his M.Sc.degree in Electrical Engineering from King Abdul-lah University of Science and Technology, Thuwal,Saudi Arabia in 2014. He is currently pursuing hisPh.D. (started September 2014) in Electrical andComputer Engineering at the University of WesternOntario, London, Ontario, Canada. His research in-terests include wireless communication, cross-layerdesign, resource allocation, wireless resource virtu-

alization, machine learning, data analytics, and e-learning.

Serguei L. Primak (S’94 - M’97) was born in Mozdok, USSR, in 1967. Hereceived the M.S.E.E. degree from St. Petersburg University of Telecommu-nications, St. Petersburg, Russia, in 1991 and the Ph.D. degree in electricalengineering from Ben-Gurion University of the Negev, Beer-Sheva, Israel, in1996. Currently, he is a Lecturer and Post-Doctoral Fellow at the University ofWestern Ontario, London, Ont., Canada. His current interests are in the fieldof ultrawideband radar applications, random signal generations, modeling ofwave propagation in a city, timefrequency analysis, and inverse problems ofelectromagnetics.

Abdallah Shami received his B.E. degree in Elec-trical and Computer Engineering from the LebaneseUniversity, Beirut, Lebanon in 1997, and the Ph.D.Degree in Electrical Engineering from the GraduateSchool and University Center, City University ofNew York, New York, NY in September 2002. SinceJuly 2004, he has been with Western University,Canada where he is currently a Professor in theDepartment of Electrical and Computer Engineering.His current research interests are in the area ofnetwork-based cloud computing and wireless/data

networking. Dr. Shami is currently an Associate Editor for IEEE Com-munications Survey and Tutorials, IET Communications Journal and WileyJournal of Wireless Communications and Mobile Computing. Dr. Shami haschaired key symposia for IEEE GLOBECOM, IEEE ICC, IEEE ICNC, andICCIT. Dr. Shami is a Senior Member of IEEE and the Chair of the IEEECommunications Society Technical Committee on Communications Software.

R1, C1

R1, C1

R1, C1

qos-aware energy and jitter-efﬁcient downlink predictive … · 2019-05-09 · switched...

Documents