An Adaptive Parameter Deflection Routing to Resolve Contentions in OBS Networks

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1 An Aaptive Parameter Deflection Routing to Resolve Contentions in OS etwors Keping Long, Xiaolong Yang, 2 *, Sheng Huang 2, Qianbin Chen 2, Ruyan Wang 2 Research Centre for Optical Internet an Mobile Information etwors (COIMI), University of Electronic Science an Technology of China, Chengu 60054, China 2 Chongqing Univ. of Posts an Telecomm., Chongqing , China Abstract. Currently, the contention resolution is one of research focuses for optical burst switching (OS). The paper presents a new contention resolution scheme, name as aaptive parameter-base eflection routing, which can control the eflection accoring to the time-varying traffic loa an the QoS requirements. Compare with other schemes, the simulation results show that it can improve the overall LP an the iniviual LP of each class burst, an alleviate the offset-time eficit on QoS guarantee. Keywors. Contention, Deflection Routing, Optical urst Switching, QoS. Introuction Currently, many approaches[]-[5] are propose to resolve the burst contentions for OS networs. Among them, the eflection routing is much more promising because of its lower requirements for optical components. However, the existing eflection routing algorithms[3]-[5] have some rawbacs in the control strategy an the path optimization. Motivate by the situations, the paper proposes a new contention resolution scheme, calle Aaptive Parameter Deflection Routing (APDR for short), which features largely in the aaptivity to the traffic loa an the QoS requirements. The rest of the paper is organize as follows. The aaptive parameter an optimization rule are efine in Section 2, where APDR is also propose. Section 3 illustrates APDR s results an comparisons with its counterparts through numerical simulations. Finally, this paper is summarize in Section APDR: The Aaptive Parameter Deflection Routing Algorithm OS networ can be represente as a connecte graph G(, E), where represents its noes an E represents its lins. {D i } enotes the istance matrix of G(, E). * Contact Author: Xiaolong Yang ( yxl@uestc.eu.cn, Tel: , Fax: ) is currently with University of Electronic Science an Technology of China, Chengu 60054, China

2 2 Keping Long, Xiaolong Yang, Sheng Huang, Qianbin Chen, Ruyan Wang Assume that the wavelength each lin can support is m, an the +-th priority of burst has preceence over the -th one. Primary Path Priority Contening M/M/m Contening oe A s A Primary lin Alternate Path oe A A M/M/m Alternative lin (a) The eflection routing in the lin A- (b) The analysis moel of the lin A- Fig.. The analytical moel of the APDR scheme As a noe A illustrate by Fig.a, the contention probability L of the primary lin ( ) will worsen with the increase of traffic loa. The contening bursts can be eflecte to other alternate lin (e.g., lin ( )) if it has available resource. Obviously, this can reuce L, an increase the utilization rate of lin ( ). However, when the traffic loa excees a certain threshol, this positive effect will fae away because the premise of eflection exists no more[4]. Here, an aaptive parameter is introuce to control the eflection, which is the eflection probability for the contening burst of priority in the lin ( ). aturally, if the priority of contening burst is higher, an its loa is heavy, then the eflections shoul be restricte more strictly because of the resource preempting of high priority eflecte burst over low priority normal bursts. ase on the requirements, the parameter can be simply efine by the following expression. θ / ( r ) L [, ] () r where enotes the ratio of the iniviual loa of -th priority burst to the overall one, an. enotes LP of the -th priority burst. r L From (), we can observe that the parameter for the lower priority burst is higher. However if its parameter is too high, it is possible that the eflection operation can obtain only a little insignificant LP improvement relative to the resources consume by the low priority eflecte burst. Therefore, it is necessary to mae a traeoff between the priority an the parameter. Here, the traeoff is obtaine through a amper factor θ of the -th priority burst, which can aust the sensitivity of the parameter to the burst priority. Of course, the austment shoul satisfy the constraint. / ( r θ ) (2) As illustrate Fig.a, the noe A eflects the contening burst in the probability to an optimal eflection path from the contening noe A to estination noe D via the noe. Here to easily escribe the eflection path, a oolean variable is efine as follows. x, A

3 An Aaptive Parameter Deflection Routing to Resolve Contentions in OS etwors 3 if Lin( ) Alternat _ Path( D) x (3) 0 otherwise Ν Then a constraint for the eflection path can be euce as follows. if A s x xi, if A s, Ν, an [, ] A i Ν 0 otherwise Assume that the initial loas in ( ) an ( ) are an, respectively. If the -th priority bursts is eflecte to the noe, the eflecte loa will a to the lin ( ), which can be expresse as follows r ) L [, ] (5) A (,,, A A A Known from [7]-[0], if the offset-time ifference between ifferent burst priorities is enough, the overall performance of OS networ can eep steay regarless of the number of priorities. Therefore from Fig. (b), we can get the LP of priority in the lin ( ) after its eflection. (4) L ( ( A + i ), m) i i C C i L i (6) where ( ) enotes Erlang formula, an A enotes the ratio of the iniviual loa of -th priority burst to the overall one in the lin ( ) after eflection, written as follows, C A + + i x i r A i Similarly, the overall LP L in the lin ( ) after eflection can expresse as follows, L ( A M C, +, ) (8) In eflection routing, it is possible that D (ata burst) abnormally arrives at the intermeiate noes prior to its corresponing HP (burst hea pacet). So these Ds must be roppe ue to the offset-time eficit resulting in the previous eflection efforts to be fruitless. For the problem, [3]-[4] propose one solution, i.e., FDL (Fiber Delay Line) buffering. However since it is unnown whether an where a burst to have conflict with others, the location an quantity of FDL to be configure cannot be ecie. Obviously, it is too ifficult to resolve it by FDL buffering[3]-[4]. Here, the paper tries to resolve it by the nonlinear integer programming to search an optimal eflection path. aturally, it can be regare as the following constraint of the optimal path. (7)

4 4 Keping Long, Xiaolong Yang, Sheng Huang, Qianbin Chen, Ruyan Wang xi, ( Di, + t p ) δ i, Ν, [, ] i, (9) where t p an δ enote the HP process time an the initial offset-time, respectively. After δ an D i, normalize by t p, D i, +t p an δ can simplify to D' i, an δ', respectively. Then (9) can be reuce as follows, i, x i, Di i,, δ Ν In terms of LP an the e2e elay involve with the eflection interference, we can esign the obective function to formulate the optimal eflection path by the similar metho of [5], which can be state as follows, (0) Min ε ε [ x + + i, i ( Di Li xi i Di + L,, ),, (, i, )] i, () where ε an ε enote the iniviual an overall burst-loss cost factor, respectively, which can aust the contribution of the burst-loss to the optimization of eflection path. Uner the constraints (2), (4), (9)-(0), we can obtain optimum solution { x i, } to the obect function (), which means that we fin optimal eflection path Fig Manhattan street-base simulation networ 3. Performance Stuy an Simulation umerical Results The following simulation will evaluate the performance of the propose scheme in terms of LP an the e2e elay by the comparisons with Directly Drop, Unconitional Deflection[4] an Limite Deflection[8]. Assume that the simulation networ is a 4 4 Manhattan street moel illustrate by Fig.2, in which each lin can support 4 wavelengths, its istance is one unit, an its ata rate is 0Gbps. For simplicity of analysis, the burst is Poisson arrival, an its length L is fixe to Mbit. It can support 2 priorities, an the loa ratio is assume to be 0.5. For ifferent ecision of eflection conition, Fig.3(a) illustrates their effects in terms of the overall LP uner ifferent traffic loa. Obviously, when traffic loa is not heavy, i.e., ρ<0.6, the behavior of Directly Drop is the worst. Meanwhile the

5 An Aaptive Parameter Deflection Routing to Resolve Contentions in OS etwors 5 traffic loa is much heavier, APDR can aaptively aust the eflection probability accoring to the traffic loa while Limite Deflection is insensitive to the variation of traffic loa. aturally, APDR behaves better than Limite Deflection. Compaere with Directly Drop, APDR can obtain the maximum gain 47% in terms of the overall LP. Overall urst Loss Probability Directly Drop Unconitional Deflection Limite Deflection Tunable Parameter Deflection Offere Loa (a)the traffic loa ρ versus the overall LP (θεε) urst Loss Probability ormalize ΔDelay Pri_2 (Unconitional Deflection ) Pri_2 (Tunable Parameter Deflection ).00 Pri_ (Unconitional Deflection ) Pri_ (Tunable Parameter Deflection ) Offset Time Difference etween urst Priorities tiff Offere Loa (b)the iniviual LP versus tiff (c) The traffic loa ρ versus the average e2e elay (θεε, ρ0.6) (θεε) Tunable Parameter Deflection Shortest Path -base Deflection Fig. 3. The performance comparisons of APDR with other schemes ext, let us further compare the QoS guarantee capacity between Unconitional Deflection an APDR uner ifferent offset-time ifference t iff. Assume that their QoS schemes are base on the offset-time. As illustrate Fig.3(b), when LP. 0-3, APDR can support the ifferentiate service if t iff is about 6L. ut for unconitional eflection, its t iff is about 8L. For other LP case, there is the same tren, i.e., the t iff for unconitional eflection is more than t iff for APDR. Finally comparing with the shortest-path base eflection, we will evaluate the en-en elay of APDR. Here, we concern the en-en elay suffere only by the burst successfully arriving at the estination. Certainly, the elay of the shortest-pathbase eflection is less than that of APDR. As illustrate Fig.3(c), the elay of APDR increases along with the traffic loa. At the worst case, the elay of APDR is higher than that of the shortest-path base eflection about 0%. It shows that APDR behaves very well in terms of its en-en elay. This benefit roots in the item ( i D i, ) in the expression (), which can aust the relationship between the eflection path length an the input traffic loa, that is, if traffic loa is heavier, then the eflecte burst shoul choose much shorter eflection path. 4. Conclusion This paper propose an aaptive parameter-base eflection routing algorithm, calle as APDR, which can aaptively aust the eflection probability accoring to the traffic loa an the burst priority. Using the metho in literature [5], this paper esigne an obect function base on the eflection probability. Uner the three constraints (2), (4) an (0), we can fin an optimum eflection path erive from the linear programming solutions.

6 6 Keping Long, Xiaolong Yang, Sheng Huang, Qianbin Chen, Ruyan Wang The simulation results show that APDR outperforms irectly rop, unconitional eflection an the limite eflection in the improvement of the overall LP an the guarantee of ifferentiate service. In aition, APDR can efficiently circumvent the offset-time eficit, an requires less t iff to support QoS. This is very helpful to reuce the en-en elay of APDR, which cannot excee that of the shortest-path-base eflection about 0%. Acnowlegements This wor is supporte in part by the ational atural Science Founation of China (SFC) uner Grant o , Hi-Tech Research an Development Program of China (863) uner Grant o. 2005AA2230, the Program for ew Century Excellent Talents in University (CET) of the Ministry of Eucation of China, the Proect of the Eucation Council of Chongqing, an the Proects of the Science an Technology Council of Chongqing ( , 2005AC2089). Reference [] X. Y. Yang, M. R. Dang, Y. J. Mao, an L. M. Li, A ew urst Assembly Technique for Supporting QoS in Optical urst Switching etwors, Chinese Optics Letters, (5): , May [2] M. Yoo, C. Qiao, S. Dixit, A comparative stuy of contention resolution policies in optical burst switche WDM networs, SPIE vol. 423, pp [3] Hsu, T. Liu,. Huang, Performance analysis of eflection routing in optical burstswitche networs, Proc. of IEEE Infocom 02 (ew Yor, US June 2002), : [4] X. Wang, H. Moriawa, T. Aoyama, urst optical eflection routing protocol for wavelength routing WDM networs, Proc. of SPIE Opticomm 2000, ,Oct [5] S.K. Lee, H.S. Kim, J.S. Song, D. Griffith, A Stuy on Deflection Routing in Optical urst-switching etwors, Photonic etwor Communications, 6(): 5-59 [6] Y. Chen, H. Wu, D. Xu, C. Qiao, Performance Analysis of Optical urst Switche oe with Deflection Routing, Proc. of IEEE ICC, 2: , 2003 [7] M. Yoo, C. Qiao, S. Dixit, QoS performance in IP over WDM networs, IEEE Journal on Selecte Areas in Communications, 8(0): , October [8] H. Kim, S. Lee, J. Song, Optical burst switching with limite eflection routing rules, IEICE Transactions on Communications, E86-(5): , 2003 [9] K. Dolzer, C. Gauger, J. Späth, S. oamer, Evaluation of reservation mechanisms for optical burst switching, AEÜ Int. J. Electron. Commun., 55(): -8, Jan [0] H. Vu, M. Zuerman, locing probability for priority classes in optical burst switching networs, IEEE Communications Letters. 6(5): 24-26, May 2002