Segmentation-Based Non-Preemptive Scheduling Algorithms for Optical Burst-Switched Networks

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1 egmenttion-sed Non-Preemptive cheduling lgorithms for Opticl urst-witched Networks Vinod M. Vokkrne nd Json P. Jue eprtment of Computer cience, The University of Texs t lls, Richrdson, TX 7508 fvinod, TRCT One of the key components in the design of opticl burst-switched nodes is the development of chnnel scheduling lgorithms tht cn efficiently hndle dt burst contentions. Trditionl scheduling techniques use pproches such s wvelength conversion nd buffering to resolve burst contention. In this pper, we propose non-preemptive scheduling lgorithms tht use burst segmenttion to resolve contention. We further reduce pcket loss by combining burst segmenttion nd fiber dely lines (FLs) to resolve contentions during chnnel scheduling. We propose two types of scheduling lgorithms tht re clssified bsed on the plcement of the FL buffers in the opticl burst-switched node. These lgorithms re referred to s dely-first or segment-first lgorithms. The scheduling lgorithms with burst segmenttion nd FLs re investigted through simultion. The simultion results show tht the proposed lgorithms cn effectively reduce the pcket loss probbility compred to existing scheduling techniques. The dely-first lgorithms re suitble for pplictions which hve higher dely tolernce nd strict loss constrints, while the segment-first lgorithms re suitble for pplictions with higher loss tolernce nd strict dely constrints.. INTROUCTION The rpid growth of the Internet will result in n incresed demnd for higher trnsmission rtes nd fster switching technologies. In order to efficiently utilize the mount of rw bndwidth in WM networks, n ll-opticl trnsport method, which voids electronic buffering while hndling bursty trffic, must be developed. Opticl burst-switching (O) is one such method for trnsporting trffic directly over bufferless WM network. In O networks, bursts of dt consisting of multiple pckets re switched through the network ll-opticlly. burst heder pcket (HP) is trnsmitted hed of the burst in order to configure the switches long the burst s route. The HP nd the dt burst re seprted t the source, s well s subsequent intermedite nodes, by n offset time, s shown in Fig.. The offset time llows for the HP to be processed t ech node before the dt burst rrives t the intermedite node; thus, no fiber dely lines re necessry t the intermedite nodes to dely the burst while the HP is being processed. The HP my lso specify the durtion of the burst in order to let node know when it my reconfigure its switch for the next burst. This signling technique is known s just enough time (JT). In this pper, we will consider n O network which uses the JT technique. ch WM link consists of control chnnels used to trnsmit HPs, nd dt chnnels used to trnsmit dt bursts. In this pper, we ssume tht every chnnel consists of wvelength nd tht ech O core router hs wvelength conversion cpbility. One of the primry O core network issues is contention resolution. When two or more bursts re destined for the sme output port t the sme time, contention occurs. There re mny contention resolution schemes which my be used to resolve the contention. The primry contention resolution schemes re opticl buffering, wvelength conversion, deflection routing, nd burst segmenttion. In opticl buffering, fiber dely lines (FLs) re used to dely the burst for specified mount of time, proportionl to the length of the dely line, in order to void the contention. In wvelength conversion, if two bursts on the sme wvelength re destined to go out of the sme port t the sme time, then one burst cn be shifted to different wvelength. 4 In deflection routing, one of the two bursts will be routed to the correct output port (primry) t 0 Chnnels Control Chnnel C t ursts Offset Contol Pckets (HPs) Figure. t nd control chnnels in WM Link.

2 Originl urst Contending urst ropped urst egments Originl urst Contending urst ropped urst egments () Contention witching Region witching Contention Region Figure. elective segment dropping for two contending bursts () til dropping policy hed dropping policy. nd the other to ny vilble lternte output port (secondry). The deflected pckets my end up following longer pth to the destintion, leding to higher end-to-end dely, nd pckets my lso rrive t the destintion out-of-order. 5 7 combintion of contention resolution techniques my be used to provide high throughput, low dely, nd low pcket loss probbility. In burst segmenttion, 8 the burst is divided into bsic trnsport units clled segments. ch of these segments my consist of single IP pcket or multiple IP pckets, with ech segment defining the possible prtitioning points of burst when the burst experiences contention in the opticl network. ll segments in burst re initilly trnsmitted s single burst unit. However, when contention occurs, only those segments of given burst tht overlp with segments of nother burst will be dropped, s shown in Fig.. If switching time is not negligible, then dditionl segments my be lost when the output port is switched from one burst to nother. There re two pproches for dropping burst segments when contention occurs between bursts. The first pproch, til dropping, is to drop the til of the originl burst (Fig. ()), nd the second pproch, hed dropping, is to drop the hed of the contending burst (Fig. ). 8 nother importnt issue t every O core router is the scheduling of dt bursts onto outgoing dt chnnels. The scheduling lgorithm must find n vilble dt chnnel for ech incoming burst in mnner which is quick nd efficient, nd which minimizes dt loss. In order to minimize dt loss, the scheduling lgorithm my use one or more contention resolution techniques. t chnnel scheduling lgorithms tht use wvelength conversion nd FLs include ltest vilble unscheduled chnnel (LUC), nd ltest vilble unscheduled chnnel with void filling (LUC-VF). 9 However, these techniques drop the burst completely if ll of the dt chnnels re occupied t the rrivl time of the burst. Insted of dropping the burst in its entirety, it is possible to drop only the overlpping prts of burst using the burst segmenttion technique. In, 0 burst segmenttion nd FLs re combined to resolve contention during chnnel scheduling. The til-dropping nd hed-dropping pproches of segmenttion re dopted. Rndomly choosing either til-dropping or hed-dropping my result in chnge in the burst length of lredy scheduled bursts. Hence, dditionl signling needs to be sent to the downstrem nodes in order to notify the nodes of the chnge in length nd to void unnecessry contention due to outdted length informtion. In this pper, we consider segmenttion nd buffering for resolving contentions without ffecting lredy scheduled bursts. ue to the inherent property of segmenttion, the segmenttion-bsed chnnel scheduling lgorithms cn be either non-preemptive or preemptive. In the non-preemptive pproch, existing chnnel ssignments re not ltered, while in preemptive scheduling lgorithms, n rriving unscheduled burst Λ my preempt existing dt chnnel ssignments, nd the preempted bursts (or burst segments) my be rescheduled or dropped. The dvntge of non-preemptive pproch is tht the HP of the segmented unscheduled burst cn be immeditely updted with the corresponding chnge in the burst length nd rrivl time (offset time). lso, in non-preemptive chnnel scheduling lgorithms, once burst is scheduled on the output port, it is gurnteed to be trnsmitted without being further segmented. The dvntge of the preemptive pproch cn be observed while incorporting Qo into chnnel scheduling. In this cse, higher priority unscheduled burst cn preempt n lredy scheduled lower priority dt burst. In order to implement non-preemptive schemes, we need to use hed dropping on the unscheduled burst for non-void filling bsed scheduling lgorithms. While, we my need to drop both the hed nd til of the unscheduled burst for void filling bsed scheduling lgorithms. In order to implement preemptive schemes, we need to use til dropping on the scheduled burst for non-void filling bsed scheduling lgorithms. While, we my hve to drop both the hed nd til of the Λ ursts which hve been ssigned dt chnnel re referred s the scheduled bursts, nd the burst which rrives to the node witing to be scheduled s the unscheduled burst.

3 witch Control Module Core Node Control Chnnels O/ Cross br cheduler TX /O Input Trffic Ingress Node gress Node Output Trffic O/ cheduler TX Control ignls /O dge Node WM Link Input Fiber Input Fiber N emux emux Opticl pce witch FL uffer Mux Mux Output Fiber Output Fiber N () Input Trffic t Chnnels Wvelength Converters Opticl witching Fbric Figure. () O trnsport network rchitecture. rchitecture of Core Router. overlpping scheduled burst for void filling bsed scheduling lgorithms. In the void filling cse, if the unscheduled burst overlps more thn two bursts then we hve to execute the bove procedure on per burst bsis. In this pper, we propose new segmenttion-bsed non-preemptive scheduling lgorithms. These non-preemptive scheduling lgorithms perform significntly better in terms of pcket loss probbility compred to existing scheduling lgorithms. The pper is orgnized s follows. In ection, we discuss the O network rchitecture nd describe two core node rchitectures with FLs. ection describes the existing nd proposed dt chnnel scheduling lgorithms with nd without void filling. ection 4 discusses the new segmenttion-bsed scheduling lgorithms with FLs. ection 5 provides numericl results for the different scheduling lgorithms. ection 6 concludes the pper nd proposes directions for future reserch.. O NTWORK RCHITCTUR n O network consists of collection of edge nd core routers (Fig. ()). The edge routers ssemble the electronic input pckets into n opticl burst, which is sent over the O core. The ingress edge node ssembles incoming pckets from the client terminls, into bursts. The bursts re trnsmitted ll-opticlly over O core routers without ny storge t intermedite nodes within the core. The egress edge node, upon receiving the burst, disssembles the bursts into pckets nd provides the pckets to the destintion client terminls. sic rchitectures for core nd edge routers in n O network hve been studied in. 9 Figure shows typicl rchitecture of n opticl burst-switched node, where opticl dt bursts re received nd sent to the neighboring nodes through physicl fiber links. The rchitecture consists primrily of wvelength converters, vrible FLs, n opticl spce switch, nd switch control module. We ssume tht ll the heder pckets incur fixed processing time t every intermedite node. The switch control module processes the HPs nd sends the control informtion to the switching fbric to configure the wvelength converters, spce switch, nd brodcst nd select switch for the ssocited dt burst. It is importnt to note tht the rrngement of the key components depends on the rchitecture of O node considered. number of different O node rchitectures re possible using FLs s opticl buffers. We consider two O node rchitectures with FLs for relizing the proposed scheduling lgorithms. The rchitecture in Fig. 4() shows n input-buffered FL O node with FLs dedicted to ech input port, while Fig. 4 shows n output buffered FL O node with FLs dedicted to ech output port. In the input-buffered O node rchitecture shown in Fig. 4(), ech input port is equipped with n FL buffer contining N dely lines. The input-buffered rchitecture supports the dely-first scheduling lgorithms. The n dt chnnels re de-multiplexed from ech input fiber link nd re pssed through wvelength converters whose function is to convert the input wvelengths to wvelengths tht re used within the FL buffers. The use of different wvelengths in the FL buffers nd on the output links helps to resolve contentions mong multiple incoming dt bursts competing for the sme FL nd the sme output link. In the design of FL buffers, we cn hve fixed dely FL buffers, vrible dely FL buffers, or mixture of both. In this pper, we follow the rchitecture of vrible dely FL buffers.

4 witch Control Module Control ignls witch Control Module Control ignls Input Fiber FLuffer Opticl pce witch Output Fiber Input Fiber Opticl pce witch FL uffer Output Fiber Input Fiber Output Fiber Input Fiber Output Fiber t Chnnels Wvelength Converters t Chnnels Wvelength Converters Input Fiber N Output Fiber N Input Fiber N Output Fiber N () rodcst nd elect witch Figure 4. () Input-uffer nd Output-uffer FL rchitecture. In the output-buffered O node rchitecture, shown in Fig. 4, the FL buffers re plced fter the switch fbric. The output-buffered rchitecture supports the segment-first scheduling lgorithms. The input wvelength converters re used to convert the input wvelengths to the wvelengths tht re used within the switching fbric. The functions of the output wvelength converters re the sme s described in the input-buffer FL rchitecture. In this pper, we only considered the bove described per-port FL rchitectures. In order to minimize switch cost, per-node FL rchitecture cn be dopted, in which single set of FLs cn be used for ll the ports in node. This lowering of switch cost results in lower performnce with respect to pcket loss.. NON-PRMPTIV CHNNL CHULING LGORITHM t chnnel scheduling in O networks is the process of ssigning n outgoing dt chnnel for the unscheduled rriving burst. t chnnel scheduling in O networks is different from trditionl IP scheduling. In IP, ech core node stores the pckets in electronic buffers nd schedules them on the desired output port. In O, once burst rrives t node, it must be sent to the next node without storing the burst in electronic buffers. We ssume tht ech O node supports full-opticl wvelength conversion. When HP rrives t node, chnnel scheduling lgorithm is invoked to ssign the unscheduled burst to dt chnnel on the outgoing link. The chnnel scheduler obtins the burst rrivl time nd durtion of the unscheduled burst from the HP. The lgorithm my need to mintin the ltest vilble unscheduled time (), gps, nd voids on every outgoing dt chnnel. Trditionlly, the of dt chnnel is the erliest time t which the dt chnnel is vilble for n unscheduled dt burst to be scheduled. gp is the time difference between the rrivl of the unscheduled burst nd ending time of the previously scheduled burst. void is the unscheduled durtion between two scheduled bursts on dt chnnel. For void filling lgorithms, the strting nd the ending time for ech burst on every dt chnnel must lso be mintined. The following informtion is used by the scheduler for ll the scheduling lgorithms: - L b : Unscheduled burst length durtion. - t ub : Unscheduled burst rrivl time. - W : Mximum number of outgoing dt chnnels. - N b : Mximum number of dt bursts scheduled on dt chnnel. - i : i th outgoing dt chnnel.

5 rriving urst t rriving urst 0 L b 0, L b 0,0 0, 0,0,0 0,0 0,0,0,,,0,0 () Figure 5. Initil dt chnnel sttus () without void filling with void filling. - LU T i : of the i th dt chnnel, i =; ; :::; W, for non-void filling scheduling lgorithms. - (i;j) nd (i;j) : trting nd ending times of ech scheduled burst, j, on every dt chnnel, i, for void filling scheduling lgorithms. - Overlp i : urtion of overlp between the unscheduled burst nd scheduled burst(s). Overlp is used in non-void filling chnnel scheduling lgorithms. The overlp is zero if the chnnel is vilble, otherwise the overlp is the difference between LU T i nd t ub. - Gp i : If the chnnel is vilble, gp is the difference between t ub nd LU T i for scheduling lgorithms without void filling, nd is the difference between t ub nd (i;j) of previous scheduled burst, j, for scheduling lgorithms with void filling. If the chnnel is busy, Gp i is set to 0. Gp informtion is useful to select chnnel for the cse in which more thn one chnnel is free. - Loss i : Number of pckets dropped due to the ssignment of the unscheduled burst on i th dt chnnel. The primry gol of ll scheduling lgorithms is to minimize loss; hence, loss is the primry fctor for choosing dt chnnel. In cse the loss on more thn one chnnel is the sme, then other chnnel prmeters re used to rech decision on the selection of dt chnnel. - V oid (i;k) : urtion of k th void on i th dt chnnel. This informtion is relevnt to void filling lgorithms. void is the durtion between the (i;j+) nd (i;j) on dt chnnel. Void informtion is useful in selecting dt chnnel in cse more thn one chnnel is free. t chnnel scheduling lgorithms cn be brodly clssified into two ctegories: without nd with void filling. The lgorithms primrily differ bsed on the type nd mount of stte informtion tht is mintined t node bout every chnnel. In dt chnnel scheduling lgorithms without void filling, the LU T i on every dt chnnel i, i =0; ; :::; W, is mintined by the chnnel scheduler. In void filling lgorithms, the strting time, (i;j) nd ending time, (i;j) re mintined for ech burst on every dt chnnel, where, i =0; ; :::; W, is the i th dt chnnel nd j =0; ; :::; N b,isthe j th burst on chnnel i. We first describe the existing scheduling lgorithms without nd with void filling. We then describe new segmenttionbsed scheduling lgorithms... xisting Chnnel cheduling lgorithms Ltest vilble Unscheduled Chnnel (LUC): The LUC or Horizon scheduling lgorithm keeps trck of the on every dt chnnel nd ssigns the dt burst to the ltest vilble unscheduled dt chnnel. Let the initil dt chnnel ssignment for the chnnel scheduling lgorithms without void filling (Fig. 5()) nd with void filling (Fig. 5) be s shown. In Fig. 5(), the LU T i on every dt chnnel i, i = 0; ; :::; W, is mintined by the scheduler. In Fig. 5, the strting time, (i;j) nd ending time, (i;j), where i refer to the i th dt chnnel nd j is the j th burst on chnnel i, re mintined for ech burst on every dt chnnel. The LUC lgorithm cn be illustrted in Fig. 5(). No chnnel is vilble for the durtion of the unscheduled burst. Hence, the entire unscheduled burst is dropped, even though the contention period with bursts on dt chnnel is miniml. The worst-time complexity of the LUC lgorithm is O(log W ).

6 () 0 rriving urst L b t 0 0, 0, 0,,, rriving urst L b, , 0,0 0,0 Figure 6. Illustrtion of non-preemptive () NP-MOC scheduling lgorithm, nd NP-MOC-VF scheduling lgorithm. Ltest vilble Unscheduled Chnnel with Void Filling (LUC-VF): The LUC-VF, scheduling lgorithm mintins the strting nd ending times for ech scheduled dt burst on every dt chnnel. The gol of this lgorithm is to utilize voids between two dt burst ssignments. The chnnel with void tht minimizes the gp is chosen. The LUC- VF lgorithm is illustrted on Fig. 5. No chnnel is vilble for the durtion of the unscheduled burst; hence, the entire unscheduled burst is dropped, even though the contention period with bursts on dt chnnel 0 is miniml. If N b is the number of bursts currently scheduled on every dt chnnel, then binry serch lgorithm cn be used to check if dt chnnel is eligible. Thus, the worst-time complexity of the LUC-VF lgorithm is O(log(WN b ))... egmenttion-bsed Non-preemptive cheduling lgorithms Non-preemptive Minimum Overlp Chnnel (NP-MOC): NP-MOC lgorithm is n improvement of the existing LUC scheduling lgorithm. The NP-MOC scheduling lgorithm keeps trck of the on every dt chnnel. For given unscheduled burst, the scheduling lgorithm considers ll outgoing dt chnnels nd clcultes the overlp on every chnnel nd chooses the dt chnnel with minimum overlp. NP-MOC LGORITHM (t ub ) tempoverlp ψ INFINITY ; tempgp ψ INFINITY ; tempchnnel ψ ; for 8 ech i t Chnnel < if (Overlp i is ZRO) nd (Gp i < tempgp) ρ tempgp ψ Gpi ; : tempchnnel ψ i; if (tempchnnel <> ) ρ chedule the U nscheduled urst on i ; top; 8 >< 8for ech i t Chnnel < if else ρ (Overlp i < tempoverlp) tempoverlp ψ Overlpi ; >: : tempchnnel ψ i; if 8 (tempchnnel <> ) < Resolve Contention using N on preemptive egmenttion chedule the U nscheduled urst on i ; : top; ρ rop U nscheduled urst; else top; The detils of NP-MOC re given bove. For exmple, pplying the NP-MOC lgorithm to the exmple in Fig. 5(), we see tht dt chnnel hs the minimum overlp, nd the unscheduled burst is scheduled on (Fig. 6()). Here, only the overlpping segments of the unscheduled burst re dropped insted of the entire unscheduled burst s in the cse of LUC. The worst-time complexity of the NP-MOC lgorithm is O(log W ). Non-preemptive Minimum Overlp Chnnel with Void Filling (NP-MOC-VF): The NP-MOC-VF scheduling lgorithm mintins the strting nd ending times of ech dt burst on every dt chnnel. The gol is to utilize the voids between dt burst ssignments on every dt chnnel. The dt chnnel with void tht minimizes the Gp i is chosen in cse of more thn one vilble chnnel. If no chnnel is free, the chnnel with minimum loss is ssigned to the unscheduled,0,0,0,0 0,0

7 Tble. Comprison of egmenttion-bsed Non-preemptive cheduling lgorithms lgorithm Complexity tte Informtion LUC O(log W ) LU T i, Gp i LUC-VF O(log(WN b)) (i;j), (i;j), Gp i NP-MOC O(log W ) LU T i, Gp i NP-MOC-VF O(log(WN b)) (i;j), (i;j), Gp i burst. The detils of NP-MOC-VF re given below. For exmple, pplying the NP-MOC-VF lgorithm to the exmple in Fig. 5(), we see tht dt chnnel 0 hs the minimum overlp, nd the unscheduled burst is scheduled on 0 (Fig. 6). Here, only the overlpping segments of the unscheduled burst re dropped insted of the entire unscheduled burst s in the cse of LUC-VF. The worst-time complexity of the NP-MOC-VF lgorithm is O(log(WN b )). NP-MOC-VF LGORITHM (t ub ) temploss ψ INFINITY ; tempgp ψ INFINITY ; tempchnnel ψ ; for 8 ech i t Chnnel < if ρ (Loss i is ZRO) nd (Gp i < tempgp) tempgp ψ Gpi ; : tempchnnel ψ i; if (tempchnnel <> ) ρ chedule the U nscheduled urst on i ; top; 8 >< 8for ech i t Chnnel < if (Loss else i < temploss) ρ temploss ψ Lossi ; >: : tempchnnel ψ i; if 8 (tempchnnel <> ) < Resolve Contention using N on preemptive egmenttion chedule the U nscheduled urst on i ; : top; ρ rop U nscheduled urst; else top; Tble I compres ll the bove chnnel scheduling lgorithms in terms of time complexity nd the mount of stte informtion stored. We observe tht the time complexity of the non-void filling lgorithms is less thn tht of the void filling lgorithms. lso, void filling lgorithms, such s, LUC-VF nd NP-MOC-VF, store more stte informtion s compred to non-void filling lgorithms, such s, LUC nd NP-MOC. 4. GMNTTION- NON-PRMPTIV CHULING LGORITHM WITH FL 9,, 4 There hs been substntil work on scheduling using FLs in O. In this section, we propose number of segmenttion-bsed non-preemptive scheduling lgorithms incorporting FLs. sed on the two FL rchitectures presented in ection, we hve two fmilies of scheduling lgorithms. cheduling lgorithms bsed on the input-buffer FL node rchitecture re clled dely-first scheduling lgorithms, while scheduling lgorithms bsed on the output-buffer FL node rchitecture re clled segment-first scheduling lgorithms. In both schemes, we ssume tht full wvelength conversion, FLs, nd segmenttion techniques re used to resolve burst contention for n output dt chnnel. However, the order of pplying the bove techniques depends on the FL rchitecture. In dely-first schemes, we resolve contention by wvelength conversion, FLs, nd segmenttion, in tht order, while in segment-first schemes, we resolve contention by wvelength conversion, segmenttion, nd FLs, in tht order. efore going on to the detiled description of the schemes, it is necessry to discuss the motivtion for developing two different schemes. In dely-first schemes, FLs re primrily used to dely the entire burst, while in segment-first schemes, FLs re primrily used to dely the segmented bursts. elying the entire burst nd then segmenting the burst keeps the pckets in order; however, when delying segmented

8 rriving urst t ub nd trt rriving urst () () 0 0 L b MX_LY old witching ely 0 0, 0, 0, L b MX_LY 0,,0,0 witching ely 0,0 0,0,,,0,0 Figure 7. Illustrtion of () NP-FMOC lgorithm, nd NP-FMOC-VF lgorithm. rriving urst t ub L b MX_LY old old witching ely 0 0, nd 0, 0, rriving urst trt, L b MX_LY 0, 0,0 0,0,0,0 witching,,,0 00,0 00 Figure 8. Illustrtion of () NP-FMOC lgorithm, nd NP-FMOC-VF lgorithm. bursts, pcket order is not lwys mintined. In generl, segment-first schemes will incur lower delys thn dely-first schemes. In both the schemes, the scheduler hs to dditionlly know MX LY, i.e., the mximum dely provided by the FLs. We will now describe the segmenttion-bsed non-preemptive scheduling lgorithms which use segmenttion, wvelength conversion, nd FLs. 4.. ely-first cheduling lgorithms Non-preemptive ely-first Minimum Overlp Chnnel (NP-FMOC): The NP-FMOC lgorithm clcultes the overlp on every chnnel nd then selects the chnnel with minimum overlp. If chnnel is vilble, then the unscheduled burst is scheduled on the free chnnel with the minimum gp. If ll chnnels re busy nd the minimum overlp is greter thn or equl to the sum of the unscheduled burst length nd MX LY, then the entire unscheduled burst is dropped. Otherwise, the unscheduled burst is delyed for the durtion of the minimum overlp nd scheduled on the selected chnnel. In cse the minimum overlp is greter thn MX LY, the unscheduled burst is delyed for MX LY nd the non-overlpping burst segments of the unscheduled burst is scheduled, while the overlpping burst segments re dropped. For exmple, in Fig. 7(), the dt chnnel hs the minimum overlp, thus the unscheduled burst is scheduled on fter providing dely using FLs. Non-preemptive ely-first Minimum Overlp Chnnel with Void Filling (NP-FMOC-VF): The NP-FMOC-VF lgorithm clcultes the dely until the first void on every chnnel nd then selects the chnnel with minimum dely. If chnnel is vilble, the unscheduled burst is scheduled on the free chnnel with minimum gp. If ll chnnels re busy nd the strting time of the first void is greter thn or equl to the sum of the end time,, of the unscheduled burst nd MX LY, then the entire unscheduled burst is dropped. Otherwise, the unscheduled burst is delyed until the strt of the first void on the selected chnnel, where the non-overlpping burst segments of the unscheduled burst re scheduled, while the overlpping burst segments re dropped. In cse the strt of the first void is greter thn the sum of the strt time,, of the unscheduled burst nd MX LY, then the unscheduled burst is delyed for MX LY nd the non-overlpping burst segments of the unscheduled burst re scheduled, while the overlpping burst segments re dropped. For exmple, consider Fig. 7. y pplying the NP-FMOC-VF lgorithm, the dt chnnel 0 hs the minimum dely, thus the unscheduled burst is scheduled on 0 fter delying the burst using FLs. In this cse, only the overlpping segments of the burst re dropped insted of the entire burst s in the cse of LUC-VF. ely,0 0,0 0,0

9 Tble. Comprison of egmenttion-bsed Non-preemptive cheduling lgorithms with FLs lgorithm Complexity tte Informtion 4.. egment-first cheduling lgorithms LUC O(log W ) LU T i, Gp i LUC-VF O(log(WN b)) (i;j), (i;j), Gp i NP-FMOC O(log W ) LU T i, Gp i NP-FMOC-VF O(log(WN b)) (i;j), (i;j), Gp i NP-FMOC O(log W ) LU T i, Gp i NP-FMOC-VF O(log(WN b)) (i;j), (i;j), Gp i Non-preemptive egment-first Minimum Overlp Chnnel (NP-FMOC): The NP-FMOC lgorithm clcultes the overlp on every chnnel nd then selects the dt chnnel with minimum overlp. If chnnel is vilble, the unscheduled burst is scheduled on the free chnnel with the minimum Gp i. If ll chnnels re busy nd the minimum overlp is greter thn or equl to the sum of the unscheduled burst length nd MX LY, then the entire unscheduled burst is dropped. Otherwise, the unscheduled burst is segmented (if necessry) nd the non-overlpping burst segments re scheduled on the selected chnnel, while the overlpping burst segments re re-scheduled. Next, the lgorithm clcultes the overlp on ll the chnnels for the re-scheduled burst segments. The re-scheduled burst segments re delyed for the durtion of the minimum overlp nd scheduled on the selected chnnel. In cse the minimum overlp is greter thn MX LY, then the re-scheduled burst segments re delyed for MX LY nd the non-overlpping burst segments of the rescheduled burst segments re scheduled, while the overlpping burst segments re dropped. For exmple, in Fig. 8(), we observe tht the dt chnnel hs the minimum overlp for the unscheduled burst, thus the unscheduled burst is scheduled on, nd the re-scheduled burst segments re scheduled on. Non-preemptive egment-first Minimum Overlp Chnnel with Void Filling (NP-FMOC-VF): The NP-FMOC-VF lgorithm clcultes the loss on every chnnel nd then selects the chnnel with minimum loss. If chnnel is vilble, the unscheduled burst is scheduled on the free chnnel with minimum gp. If ll chnnels re busy nd the strting time of the first void is greter thn or equl to the sum of the end time,, of the unscheduled burst nd MX LY, then the entire unscheduled burst is dropped. If the strting time of the first void is greter thn or equl to the end time,, of the unscheduled burst, the NP-FMOC-VF lgorithm is employed. Otherwise, the unscheduled burst is segmented (if necessry) nd the non-overlpping burst segments re scheduled on the selected chnnel, while the overlpping burst segments re re-scheduled. For the re-scheduled burst segments, the lgorithm clcultes the dely required until the strt of the next void on every chnnel nd selects the chnnel with minimum dely. The re-scheduled burst segments re delyed until the strt of the first void on the selected chnnel. The non-overlpping burst segments of the re-scheduled burst re scheduled, while the overlpping burst segments re dropped. In cse the strt of the next void is greter thn the sum of the strt time,, of the unscheduled burst nd MX LY, the re-scheduled burst segments re delyed for MX LY nd the non-overlpping burst segments of the re-scheduled burst re scheduled, while the overlpping burst segments re dropped. For exmple, in Fig. 8, we observe tht the dt chnnel 0 hs the minimum loss, thus the unscheduled burst is scheduled on 0, nd the unscheduled burst segments re scheduled on (s it incurs the minimum dely) fter providing dely using FLs. Tble II compres ll of the discussed segmenttion-bsed non-preemptive chnnel scheduling lgorithms with FLs in terms of time complexity nd the mount of stte informtion stored. We cn observe tht the time complexity of the non-void filling lgorithms is less thn the void filling lgorithms. lso, void filling lgorithms, such s, LUC-VF, NP-FMOC-VF, nd NP-FMOC-VF, store more stte informtion s compred to non-void filling lgorithms, such s, LUC, NP-FMOC, nd NP-FMOC. 5. NUMRICL RULT In order to evlute the performnce of the proposed chnnel scheduling lgorithms, simultion model is developed. urst rrivls to the network re Poisson, nd ech burst length is n exponentilly generted rndom number rounded to the nerest integer multiple of the fixed-sized pcket length of 50 bytes. The verge burst length is 00 μs. The link trnsmission rte is 0 Gb/s. Current switching technologies provide us with rnge of switching times from few ms (MMs) 5 to few ps (O-bsed). 6 We ssume conservtive switch reconfigurtion time of 0 μs. The burst heder processing time t ech node depends on the rchitecture of the scheduler nd the complexity of the scheduling lgorithm.

10 Figure 9. 4-Node NF Network Pcket Loss Probbility > LUC NP MOC LUC VF NP MOC VF Lod (in rlng) > verge nd to nd Pcket ely (in ms) > LUC 9.05 NP MOC LUC VF NP MOC VF Lod (in rlng) > Figure 0. () Pcket loss probbility versus lod, nd verge end-to-end dely versus lod for different scheduling lgorithms with 8 dt chnnels on ech link, for the NF network. sed on current CPU clock speeds nd conservtive estimte of the number of instructions required, we ssume burst heder processing time to be.5 μs. We know tht in ny opticl buffer rchitecture, the size of the buffers is severely limited, not only by signl qulity concerns, but lso by physicl spce limittions. To dely single burst for 5 μs requires over kilometer of fiber. ue to this size limittion of opticl buffers, we consider mximum FL dely of 0:0 ms. Trffic is uniformly distributed over ll sender-receiver pirs. Fixed minimum-hop routing is used to find the pth between ll node pirs. ll the simultion re implemented on the stndrd 4-node NF network shown in Fig. 9, where link distnces re in km. Figure 0() plots the totl pcket loss probbility versus lod for different chnnel scheduling lgorithms, with 8 dt chnnels on ech link. We observe tht the segmenttion-bsed chnnel scheduling lgorithms perform significntly better thn lgorithms without segmenttion. The proposed segmenttion-bsed scheduling lgorithms perform better thn the lgorithms without segmenttion becuse, when contention occurs, only the overlpping pckets from one of the bursts re lost insted of the entire burst. We see tht NP-MOC suffers lower loss s compred to LUC. lso, NP-MOC-VF performs better thn LUC-VF. We cn lso observe tht NP-MOC nd NP-MOC-VF re the best lgorithms without nd with void filling respectively. lso, the lgorithms with void filling perform better thn lgorithms without void filling s expected. Figure 0 plots the verge end-to-end dely versus lod for different chnnel scheduling lgorithms, with 8 dt chnnels on ech link. We observe tht the segmenttion-bsed chnnel scheduling lgorithms hve higher verge endto-end pcket dely thn existing chnnel scheduling lgorithms without segmenttion. The higher dely for scheduling lgorithms with segmenttion is due to the higher probbility of successful trnsmission between source-destintion pirs which re frther prt, while in trditionl scheduling lgorithms the entire burst is dropped in cse of contention; hence,

11 0 0 Pcket Loss Probbility > Lod (in rlng) > MX_LY = 0.0 ms LUC NP FMOC NP FMOC LUC VF NP FMOC VF NP FMOC VF verge Per Hop FL ely (in ms) > MX_LY = 0.0 ms LUC 0 7 NP FMOC NP FMOC LUC VF NP FMOC VF NP FMOC VF Lod (in rlng) > Figure. () Pcket loss probbility versus lod, nd verge per-hop FL dely versus lod for different scheduling lgorithms with 8 dt chnnels on ech links, for the NF network. source-destintion pirs close to ech other hve higher probbility of mking successful trnsmission, which results in lower verge end-to-end pcket dely. We see tht the NP-MOC lgorithm hs higher dely thn the LUC lgorithm. lso, the NP-MOC-VF lgorithm hs higher dely thn the LUC-VF lgorithm. We cn lso observe tht LUC hs the lest verge end-to-end pcket dely mong ll the lgorithms. Figure () plots the totl pcket loss probbility versus lod for different chnnel scheduling lgorithms. We observe tht the chnnel scheduling lgorithms with burst segmenttion perform better thn lgorithms without burst segmenttion t most lods. lso, the dely-first lgorithms hve lower loss s compred to the segment-first lgorithms. This is due to the possible blocking of the re-scheduled burst segment by the recently scheduled non-overlpping burst segment in the segment-first lgorithms. The loss obtined by dely-first lgorithms is the lower bound on dely for the segment-first lgorithms. We observe tht t ny given lod, the NP-FMOC nd NP-FMOC-VF lgorithms perform the best, since the unscheduled burst is delyed; nd in cse there is still contention, the burst is segmented nd only the overlpping burst segment is dropped. The segment-first lgorithms lose pckets proportionl to the switching time every time there is contention, while the LUC nd LUC-VF lgorithms dely the burst in cse of contention nd schedule the burst if the chnnel is free fter the provided dely. Hence, t low lods, LUC-VF performs better thn NP-FMOC-VF, nd, s the lod increses, NP-FMOC-VF performs better. Therefore substntil gin is chieved by using segmenttion nd FLs. Figure plots the verge per-hop FL dely versus lod for different chnnel scheduling lgorithms. We observe tht the dely-first lgorithms hve higher per-hop FL dely s compred to the segment-first lgorithms, since FL is the primry contention resolution technique in the former nd segmenttion is the primry contention resolution technique in the ltter. We lso observe tht the per-hop FL dely of void filling lgorithms is lower thn non-void filling, since the scheduler cn of ssign the rriving bursts to closer voids tht incur lower FL dely s compred to scheduling the bursts t the end of the horizon () in the cse of non-void filling lgorithms. Hence, we cn crefully choose either dely-first or segment-first schemes bsed on loss nd dely tolernces of input IP pckets. When high MX LY vlue is used, lgorithms which use FLs s the primry contention resolution technique, such s, LUC, LUC-VF, NP-FMOC, NP-FMOC-VF outperform the lgorithms which use segmenttion s the primry contention resolution technique, such s, NP-FMOC, NP-FMOC-VF CONCLUION In this pper, we considered burst segmenttion nd FLs for burst scheduling in opticl burst-switched networks, nd we proposed number of chnnel scheduling lgorithms for O networks. The segmenttion-bsed scheduling lgorithms perform better thn the existing scheduling lgorithms with nd without void filling in terms of pcket loss. We lso introduced two ctegories of scheduling lgorithms bsed on the FL rchitecture. The dely-first lgorithms re suitble

12 for trnsmitting pckets which hve higher dely tolernce nd strict loss constrints, while the segment-first lgorithms re suitble for trnsmitting pckets which hve higher loss tolernce nd strict dely constrints. res of future works include extending the proposed lgorithms to support Qo. In the cse of providing Qo support, the priority of the burst cn be stored in the HP, nd the scheduling lgorithm cn dynmiclly decide which of contending bursts or burst segments to drop using burst segmenttion or to dely using FLs. Hence combintion of preemptive nd non-preemptive segmenttion-bse techniques cn be used to provide service differentition. It would lso be useful to develop n nlyticl model for the proposed scheduling lgorithms. RFRNC. C. Qio nd M. Yoo, Opticl urst witching (O) - New Prdigm for n Opticl Internet, Journl of High peed Networks, vol. 8, no., pp , Jn Yo,. Mukherjee,.J.. Yoo, nd. ixit, ll-opticl Pcket-witched Networks: tudy of Contention Resolution chemes in n Irregulr Mesh Network with Vrible-ized Pckets, Proceedings, PI OptiComm 000, lls, TX, pp. 5-46, Oct I. Chlmtc,. Fumglli, L. G. Kzovsky, et l., COR: Contention Resolution by ely Lines, I Journl on elected res in Communictions, vol. 4, no. 5, pp , June R. Rmswmi nd K.N. ivrjn, Routing nd Wvelength ssignment in ll-opticl Networks, I/CM Trnsctions on Networking, vol., no. 5, pp , Oct cmpor nd I.. hh, Multihop Lightwve Networks: Comprison of tore-nd-forwrd nd Hot-Potto Routing, I Trnsctions on Communictions, vol. 40, no. 6, pp , June ononi, G.. Cstnon, nd O. K. Tonguz, nlysis of Hot-Potto Opticl Networks with Wvelength Conversion, I Journl of Lightwve Technology, vol. 7, no. 4, pp , pril F. Forghieri,. ononi, nd P. R. Prucnl, nlysis nd Comprison of Hot-Potto nd ingle-uffer eflection Routing in Very High it Rte Opticl Mesh Networks, I Trnsctions on Communictions, vol. 4, no., pp , Jn V.M. Vokkrne, J.P. Jue, nd. itrmn, urst egmenttion: n pproch for Reducing Pcket Loss in Opticl urst-witched Networks, Proceedings, I Interntionl Conference on Communictions (ICC) 00, New York, NY, vol. 5, pp , pril Y. Xiong, M. Vnderhoute, nd H.C. Cnky, Control rchitecture in Opticl urst-witched WM Networks, I Journl on elected res in Communictions, vol. 8, no. 0, pp , Oct V.M. Vokkrne, G.P.V. Thodime, V..T. Chllgull, nd J.P. Jue, Chnnel cheduling lgorithms using urst egmenttion nd FLs for Opticl urst-witched Networks, Proceedings, I Interntionl Conference on Communictions (ICC) 00, nchorge, K, vol., pp , My 00.. V.M. Vokkrne nd J.P. Jue, Prioritized Routing nd urst egmenttion for Qo in Opticl urst-witched Networks, Proceedings, Opticl Fiber Communiction Conference (OFC) 00, nheim, C, WG6, pp. -, Mrch 00.. J.. Turner, Terbit urst witching, Journl of High peed Networks, vol. 8, no., pp. -6, L. Tncevski,. Ge, G. Cstnon, nd L. Tmil, New cheduling lgorithm for synchronous, Vrible Length IP Trffic Incorporting Void Filling, Proceedings, Opticl Fiber Communiction Conference (OFC) 999, vol., pp. 80-8, Feb C. Guger, imensioning of FL uffers for Opticl urst witching Nodes, Proceedings, IFIP Opticl Network esign nd Modeling (ONM 00), Torino, Neukermns nd R. Rmswmi, MM Technology for Opticl Networking pplictions, I Communictions Mgzine, vol. 9, no., pp. 6-69, Jn L. Ru,. Rngrjn,.J. lumenthl, H.-F.Chou, Y.-J. Chiu, nd J.. owers, Two-hop ll-opticl Lbel wpping with Vrible Length 80 Gb/s Pckets nd 0 Gb/s Lbels using Nonliner Fiber Wvelength Converters, Unicst/Multicst Output nd ingle M for 80- to 0 Gb/s Pcket emultiplexing, Proceedings, Opticl Fiber Communiction Conference (OFC) 00, pp. F--F-, nheim, C, Mrch 00.

NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.

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