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8/3/2019 Performances Comparison of Two Buffer Less Contention Resolution Schemes in Optical Burst Switching Networks 2

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102Journal of Optical Communications

31 (2010) 2

Summary

In this paper, we evaluate two bufferless contentionresolution schemes for optical burst switching (OBS)networks. Three performances evaluating models have

been proposed and been compared. Several results anddiscussions are useful for the design of OBS test-bed.

1 Introduction

Optical burst switching (OBS) is a novel paradigm,which has the switching granularity between the opti-cal circuit switching and the optical packet switching [1].An OBS network is consist of edge routers, core routersand WDM links. Edge routers create optical bursts and burst control packet (BCP). Under single-direction re-

source reservation protocols, a burst and its correspond-ing BCP use out-of-band model to come into the OBScore switching network [2]. If a wavelength resource hasbeen satisfied, a burst can full-optically passing throughthe core routers, otherwise, it will be blocked

Recent research on contention resolution schemes main-ly focus on burst dropping (BD) [3], buffering and burstsegmentation (BS) [3-4]. BD is a simple realized buffer-less scheme but it may cause large data loss. Bufferingscheme will cause noise and routers structure complexi-ty. BS is an effective bufferless scheme for its high net-

work resource utilization. In this paper, we give three an-alytical models to evaluate the performance of BD andBS in contention under different network scenarios, andgive the comparative results of them.

2 BD and BS schemes

In OBS core routers, when several bursts come from input data channels attempt to be outputted by one out-put data channel, contention will occurs. Based on BDscheme, when a contention occurs, the core router will

drop the entire contending burst to resolve the conten-tion. But based on BS scheme, the core router will droponly the overlapping part of contending bursts and willcontinue transmitting the remainder part of the contend-

ing bursts. In the next section, we will give three analyti-cal models to evaluate the performance of an OBS block-ing system.

3 Contention evaluating models

3.1 M/M/k/kmodel

When an OBS network applies JET protocol to imple-ment resource reservation, the blocking system in corerouters can be applied with M/M/k/k queuing model [2].

If gives a specified output-port, the bursts arriving proc-ess is Poisson with rate , and the bursts length obeyexponential distributed with average value /1 , then,the packet loss probability could be expressed as ErlangB equation [2]:

( )

=

=

k

j

jk

Erlang jAkAAkP0

!/!/).( (1)

where /=A is the traffic load. (1) also could be ex-pressed as an iterative format:

( ) (

+=

=

AnPAnAnPAAnP

AP

ErlangErlangErlang

Erlang

),1(),1(),(

1),0(

= kn ,...,2,1

(2)

3.2 M/G/ model

According to BS scheme, when a contention occurs, corerouters only drop the part of burst. Such blocking sys-tem can be applied M/G/ queuing model to evaluate asshown in the follow [5]:

ALEAkPBSInf /][),( = (3)

where E[L] is the average packet loss probability, whichcan be written as follows:

)!(][

1 jk

eAjLE

Ajk

j +=

+

= (4)

J. Opt. Commun. 31 (2010), 102-104

Performances Comparison of Two Bufferless Contention ResolutionSchemes in Optical Burst Switching Networks

Rui Hou

Address of author:

South-Central University for Nationalities

College of Computer Science

Wuhan, Hubei, 430073, P. R. China

Email: [email protected]

Received 20 October 2009; accepted 5 January 2010


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31 (2010) 2

on the same, we can write the iterative expression of (4)

as follows:

( )

==

=

,...,...2,1),1(),(

),0(

knnAnAPAnP

eAP

BSInfBSInf

A

BSInf

(5)

3.3 OBS/BS model

When the number of the input data channel is differentfrom the output data channel, the bursts arriving processwill obey an On-Off model, such blocking system willbe analyzed by the OBS/BS model [6]. In this model, the

packet loss probability can be written as follows [6]:][/][/ XEKXEP BSOBS

+= . (6)

In (6), Xis the output wavelengths occupied random var-iable for bursts, which obey the binomial distribution

with parameter ),( MA

, where

A can be expressed asfollows:

)/( +=

A . (7)

Given a specified time, the bursts being transmitted prob-

ability for each input wavelength is

A , on the while, the

idle probability is A1 . Thus, we can get the followingequations:

jM

jM

Kj

AAj

MKjKXE

+=

+

= )1()(][

1

(8)

MAXE

=][ (9)

where )(XE has been called as planning load [7].

4 Analytical resultsIn this section, we give the comparison of the threecontention models in core routers. Here, we use ][XEas the traffic load for the kkMM /// model and the

//GM model.

Figures 1 and 2 gives the packet loss probability ver-sus the normalized traffic load per channel. In Figure 1,

the number of input wavelength and output wavelengthis 21 and 18, respectively, and wavelength conversionis available. In Figure 2, the number of input and out-put wavelength is 9 and 7, respectively, and wavelengthconversion is unavailable in this case. Here Erlang de-notes the kkMM /// model and BSInf denotes the

//GM model. From this graph we could observethat in the two cases the packet loss probability become

large with the increasing traffic load. The benefits of BSscheme over BD scheme also been presented and proved.Under the same load condition the packet loss probabil-ity got by OBS/BS is lower than it is got by //GM model, in some cases the difference could reach severalquantity degree.

Figure 3 gives the packet loss probability versus thenumber of output channels. In this case, we set the numberof input channel is 50, and the normalized traffic load is0.8. From the graph we could observer that, packet lossprobability will decrease with the increasing number of

output channels. We also could observe that, the decre-ment range of packet loss probability got by OBS/BS islarger than that got by kkMM /// and //GM ,particularly under the condition that the number of inputchannels and output channels are almost the same.

Fig. 1: Packet loss probability versus normalized traffic load per chan-nel with the wavelength conversion

Fig. 2: Packet loss probability versus normalized traffic load per chan-nel without the wavelength conversion

Fig. 3: Packet loss probability versus different number of output chan-nels


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5 Conclusion

In this paper, the performances of two bufferless conten-tion resolution schemes have been analyzed. Three ana-lytical models have been compared and discussed. Fromthe results we could observe that BS scheme has the ben-efit over BD scheme on the data loss reducing in conten-tion resolutions for OBS networks.

6 Acknowledgement

This work has been supported by the National NaturalScience Foundation of China under grant of 60841001.

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