SegmentationBased NonPreemptive Scheduling Algorithms for Optical BurstSwitched Networks

 Clare Gilmore
 5 months ago
 Views:
Transcription
1 egmenttionsed NonPreemptive cheduling lgorithms for Opticl urstwitched 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 burstswitched 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 nonpreemptive 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 burstswitched node. These lgorithms re referred to s delyfirst or segmentfirst 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 delyfirst lgorithms re suitble for pplictions which hve higher dely tolernce nd strict loss constrints, while the segmentfirst 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 llopticl trnsport method, which voids electronic buffering while hndling bursty trffic, must be developed. Opticl burstswitching (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 llopticlly. 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 endtoend dely, nd pckets my lso rrive t the destintion outoforder. 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 (LUCVF). 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 tildropping nd heddropping pproches of segmenttion re dopted. Rndomly choosing either tildropping or heddropping 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 segmenttionbsed chnnel scheduling lgorithms cn be either nonpreemptive or preemptive. In the nonpreemptive 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 nonpreemptive 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 nonpreemptive 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 nonpreemptive schemes, we need to use hed dropping on the unscheduled burst for nonvoid 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 nonvoid 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 segmenttionbsed nonpreemptive scheduling lgorithms. These nonpreemptive 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 segmenttionbsed 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 llopticlly 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 burstswitched 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 inputbuffered 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 inputbuffered O node rchitecture shown in Fig. 4(), ech input port is equipped with n FL buffer contining N dely lines. The inputbuffered rchitecture supports the delyfirst scheduling lgorithms. The n dt chnnels re demultiplexed 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. () Inputuffer nd Outputuffer FL rchitecture. In the outputbuffered O node rchitecture, shown in Fig. 4, the FL buffers re plced fter the switch fbric. The outputbuffered rchitecture supports the segmentfirst 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 inputbuffer FL rchitecture. In this pper, we only considered the bove described perport FL rchitectures. In order to minimize switch cost, pernode 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.. NONPRMPTIV 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 fullopticl 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 nonvoid 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 nonvoid 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 worsttime 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 nonpreemptive () NPMOC scheduling lgorithm, nd NPMOCVF scheduling lgorithm. Ltest vilble Unscheduled Chnnel with Void Filling (LUCVF): The LUCVF, 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 worsttime complexity of the LUCVF lgorithm is O(log(WN b ))... egmenttionbsed Nonpreemptive cheduling lgorithms Nonpreemptive Minimum Overlp Chnnel (NPMOC): NPMOC lgorithm is n improvement of the existing LUC scheduling lgorithm. The NPMOC 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. NPMOC 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 NPMOC re given bove. For exmple, pplying the NPMOC 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 worsttime complexity of the NPMOC lgorithm is O(log W ). Nonpreemptive Minimum Overlp Chnnel with Void Filling (NPMOCVF): The NPMOCVF 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 egmenttionbsed Nonpreemptive cheduling lgorithms lgorithm Complexity tte Informtion LUC O(log W ) LU T i, Gp i LUCVF O(log(WN b)) (i;j), (i;j), Gp i NPMOC O(log W ) LU T i, Gp i NPMOCVF O(log(WN b)) (i;j), (i;j), Gp i burst. The detils of NPMOCVF re given below. For exmple, pplying the NPMOCVF 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 LUCVF. The worsttime complexity of the NPMOCVF lgorithm is O(log(WN b )). NPMOCVF 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 nonvoid filling lgorithms is less thn tht of the void filling lgorithms. lso, void filling lgorithms, such s, LUCVF nd NPMOCVF, store more stte informtion s compred to nonvoid filling lgorithms, such s, LUC nd NPMOC. 4. GMNTTION NONPRMPTIV CHULING LGORITHM WITH FL 9,, 4 There hs been substntil work on scheduling using FLs in O. In this section, we propose number of segmenttionbsed nonpreemptive 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 inputbuffer FL node rchitecture re clled delyfirst scheduling lgorithms, while scheduling lgorithms bsed on the outputbuffer FL node rchitecture re clled segmentfirst 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 delyfirst schemes, we resolve contention by wvelength conversion, FLs, nd segmenttion, in tht order, while in segmentfirst 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 delyfirst schemes, FLs re primrily used to dely the entire burst, while in segmentfirst 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 () NPFMOC lgorithm, nd NPFMOCVF 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 () NPFMOC lgorithm, nd NPFMOCVF lgorithm. bursts, pcket order is not lwys mintined. In generl, segmentfirst schemes will incur lower delys thn delyfirst 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 segmenttionbsed nonpreemptive scheduling lgorithms which use segmenttion, wvelength conversion, nd FLs. 4.. elyfirst cheduling lgorithms Nonpreemptive elyfirst Minimum Overlp Chnnel (NPFMOC): The NPFMOC 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 nonoverlpping 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. Nonpreemptive elyfirst Minimum Overlp Chnnel with Void Filling (NPFMOCVF): The NPFMOCVF 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 nonoverlpping 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 nonoverlpping burst segments of the unscheduled burst re scheduled, while the overlpping burst segments re dropped. For exmple, consider Fig. 7. y pplying the NPFMOCVF 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 LUCVF. ely,0 0,0 0,0
9 Tble. Comprison of egmenttionbsed Nonpreemptive cheduling lgorithms with FLs lgorithm Complexity tte Informtion 4.. egmentfirst cheduling lgorithms LUC O(log W ) LU T i, Gp i LUCVF O(log(WN b)) (i;j), (i;j), Gp i NPFMOC O(log W ) LU T i, Gp i NPFMOCVF O(log(WN b)) (i;j), (i;j), Gp i NPFMOC O(log W ) LU T i, Gp i NPFMOCVF O(log(WN b)) (i;j), (i;j), Gp i Nonpreemptive egmentfirst Minimum Overlp Chnnel (NPFMOC): The NPFMOC 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 nonoverlpping burst segments re scheduled on the selected chnnel, while the overlpping burst segments re rescheduled. Next, the lgorithm clcultes the overlp on ll the chnnels for the rescheduled burst segments. The rescheduled 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 rescheduled burst segments re delyed for MX LY nd the nonoverlpping 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 rescheduled burst segments re scheduled on. Nonpreemptive egmentfirst Minimum Overlp Chnnel with Void Filling (NPFMOCVF): The NPFMOCVF 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 NPFMOCVF lgorithm is employed. Otherwise, the unscheduled burst is segmented (if necessry) nd the nonoverlpping burst segments re scheduled on the selected chnnel, while the overlpping burst segments re rescheduled. For the rescheduled 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 rescheduled burst segments re delyed until the strt of the first void on the selected chnnel. The nonoverlpping burst segments of the rescheduled 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 rescheduled burst segments re delyed for MX LY nd the nonoverlpping burst segments of the rescheduled 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 segmenttionbsed nonpreemptive 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 nonvoid filling lgorithms is less thn the void filling lgorithms. lso, void filling lgorithms, such s, LUCVF, NPFMOCVF, nd NPFMOCVF, store more stte informtion s compred to nonvoid filling lgorithms, such s, LUC, NPFMOC, nd NPFMOC. 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 fixedsized 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 (Obsed). 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. 4Node 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 endtoend 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 senderreceiver pirs. Fixed minimumhop routing is used to find the pth between ll node pirs. ll the simultion re implemented on the stndrd 4node 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 segmenttionbsed chnnel scheduling lgorithms perform significntly better thn lgorithms without segmenttion. The proposed segmenttionbsed 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 NPMOC suffers lower loss s compred to LUC. lso, NPMOCVF performs better thn LUCVF. We cn lso observe tht NPMOC nd NPMOCVF 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 endtoend dely versus lod for different chnnel scheduling lgorithms, with 8 dt chnnels on ech link. We observe tht the segmenttionbsed chnnel scheduling lgorithms hve higher verge endtoend 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 sourcedestintion 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 perhop FL dely versus lod for different scheduling lgorithms with 8 dt chnnels on ech links, for the NF network. sourcedestintion pirs close to ech other hve higher probbility of mking successful trnsmission, which results in lower verge endtoend pcket dely. We see tht the NPMOC lgorithm hs higher dely thn the LUC lgorithm. lso, the NPMOCVF lgorithm hs higher dely thn the LUCVF lgorithm. We cn lso observe tht LUC hs the lest verge endtoend 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 delyfirst lgorithms hve lower loss s compred to the segmentfirst lgorithms. This is due to the possible blocking of the rescheduled burst segment by the recently scheduled nonoverlpping burst segment in the segmentfirst lgorithms. The loss obtined by delyfirst lgorithms is the lower bound on dely for the segmentfirst lgorithms. We observe tht t ny given lod, the NPFMOC nd NPFMOCVF 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 segmentfirst lgorithms lose pckets proportionl to the switching time every time there is contention, while the LUC nd LUCVF 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, LUCVF performs better thn NPFMOCVF, nd, s the lod increses, NPFMOCVF performs better. Therefore substntil gin is chieved by using segmenttion nd FLs. Figure plots the verge perhop FL dely versus lod for different chnnel scheduling lgorithms. We observe tht the delyfirst lgorithms hve higher perhop FL dely s compred to the segmentfirst 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 perhop FL dely of void filling lgorithms is lower thn nonvoid 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 nonvoid filling lgorithms. Hence, we cn crefully choose either delyfirst or segmentfirst 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, LUCVF, NPFMOC, NPFMOCVF outperform the lgorithms which use segmenttion s the primry contention resolution technique, such s, NPFMOC, NPFMOCVF CONCLUION In this pper, we considered burst segmenttion nd FLs for burst scheduling in opticl burstswitched networks, nd we proposed number of chnnel scheduling lgorithms for O networks. The segmenttionbsed 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 delyfirst lgorithms re suitble
12 for trnsmitting pckets which hve higher dely tolernce nd strict loss constrints, while the segmentfirst 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 nonpreemptive segmenttionbse 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, llopticl Pcketwitched Networks: tudy of Contention Resolution chemes in n Irregulr Mesh Network with Vribleized Pckets, Proceedings, PI OptiComm 000, lls, TX, pp. 546, 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 llopticl Networks, I/CM Trnsctions on Networking, vol., no. 5, pp , Oct cmpor nd I.. hh, Multihop Lightwve Networks: Comprison of torendforwrd nd HotPotto Routing, I Trnsctions on Communictions, vol. 40, no. 6, pp , June ononi, G.. Cstnon, nd O. K. Tonguz, nlysis of HotPotto 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 HotPotto nd ingleuffer 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 urstwitched 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 urstwitched 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 urstwitched 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 urstwitched 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. 808, 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. 669, Jn L. Ru,. Rngrjn,.J. lumenthl, H.F.Chou, Y.J. Chiu, nd J.. owers, Twohop llopticl 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. FF, nheim, C, Mrch 00.
NUMERICAL INTEGRATION. The inverse process to differentiation in calculus is integration. Mathematically, integration is represented by.
NUMERICAL INTEGRATION 1 Introduction The inverse process to differentition in clculus is integrtion. Mthemticlly, integrtion is represented by f(x) dx which stnds for the integrl of the function f(x) with
More informationTests for the Ratio of Two Poisson Rates
Chpter 437 Tests for the Rtio of Two Poisson Rtes Introduction The Poisson probbility lw gives the probbility distribution of the number of events occurring in specified intervl of time or spce. The Poisson
More informationAcceptance Sampling by Attributes
Introduction Acceptnce Smpling by Attributes Acceptnce smpling is concerned with inspection nd decision mking regrding products. Three spects of smpling re importnt: o Involves rndom smpling of n entire
More informationNonLinear & Logistic Regression
NonLiner & Logistic Regression If the sttistics re boring, then you've got the wrong numbers. Edwrd R. Tufte (Sttistics Professor, Yle University) Regression Anlyses When do we use these? PART 1: find
More information1 Online Learning and Regret Minimization
2.997 DecisionMking in LrgeScle Systems My 10 MIT, Spring 2004 Hndout #29 Lecture Note 24 1 Online Lerning nd Regret Minimiztion In this lecture, we consider the problem of sequentil decision mking in
More informationContinuous Random Variables
STAT/MATH 395 A  PROBABILITY II UW Winter Qurter 217 Néhémy Lim Continuous Rndom Vribles Nottion. The indictor function of set S is relvlued function defined by : { 1 if x S 1 S (x) if x S Suppose tht
More informationMeasuring Electron Work Function in Metal
n experiment of the Electron topic Mesuring Electron Work Function in Metl Instructor: 梁生 Office: 7318 Emil: shling@bjtu.edu.cn Purposes 1. To understnd the concept of electron work function in metl nd
More informationLECTURE NOTE #12 PROF. ALAN YUILLE
LECTURE NOTE #12 PROF. ALAN YUILLE 1. Clustering, Kmens, nd EM Tsk: set of unlbeled dt D = {x 1,..., x n } Decompose into clsses w 1,..., w M where M is unknown. Lern clss models p(x w)) Discovery of
More informationResources. Introduction: Binding. Resource Types. Resource Sharing. The type of a resource denotes its ability to perform different operations
Introduction: Binding Prt of 4lecture introduction Scheduling Resource inding Are nd performnce estimtion Control unit synthesis This lecture covers Resources nd resource types Resource shring nd inding
More information3.4 Numerical integration
3.4. Numericl integrtion 63 3.4 Numericl integrtion In mny economic pplictions it is necessry to compute the definite integrl of relvlued function f with respect to "weight" function w over n intervl [,
More informationLine Integrals. Partitioning the Curve. Estimating the Mass
Line Integrls Suppose we hve curve in the xy plne nd ssocite density δ(p ) = δ(x, y) t ech point on the curve. urves, of course, do not hve density or mss, but it my sometimes be convenient or useful to
More informationSection 14.3 Arc Length and Curvature
Section 4.3 Arc Length nd Curvture Clculus on Curves in Spce In this section, we ly the foundtions for describing the movement of n object in spce.. Vector Function Bsics In Clc, formul for rc length in
More information1.3 Regular Expressions
56 1.3 Regulr xpressions These hve n importnt role in describing ptterns in serching for strings in mny pplictions (e.g. wk, grep, Perl,...) All regulr expressions of lphbet re 1.Ønd re regulr expressions,
More informationNumerical integration
2 Numericl integrtion This is pge i Printer: Opque this 2. Introduction Numericl integrtion is problem tht is prt of mny problems in the economics nd econometrics literture. The orgniztion of this chpter
More informationData Assimilation. Alan O Neill Data Assimilation Research Centre University of Reading
Dt Assimiltion Aln O Neill Dt Assimiltion Reserch Centre University of Reding Contents Motivtion Univrite sclr dt ssimiltion Multivrite vector dt ssimiltion Optiml Interpoltion BLUE 3dVritionl Method
More informationLecture 1. Functional series. Pointwise and uniform convergence.
1 Introduction. Lecture 1. Functionl series. Pointwise nd uniform convergence. In this course we study mongst other things Fourier series. The Fourier series for periodic function f(x) with period 2π is
More informationA SignalLevel Fusion Model for ImageBased Change Detection in DARPA's Dynamic Database System
SPIE Aerosense 001 Conference on Signl Processing, Sensor Fusion, nd Trget Recognition X, April 160, Orlndo FL. (Minor errors in published version corrected.) A SignlLevel Fusion Model for ImgeBsed
More informationLecture 14: Quadrature
Lecture 14: Qudrture This lecture is concerned with the evlution of integrls fx)dx 1) over finite intervl [, b] The integrnd fx) is ssumed to be relvlues nd smooth The pproximtion of n integrl by numericl
More informationPrimaryUser Mobility Impact on Spectrum Sensing in Cognitive Radio Networks
2011 IEEE 22nd Interntionl Symposium on Personl, Indoor nd Mobile Rdio Communictions PrimryUser Mobility Impct on Spectrum Sensing in Cognitive Rdio Networks ngel Sr Cccipuoti,InF.kyildiz, Fellow, IEEE
More informationNumerical Integration
Chpter 1 Numericl Integrtion Numericl differentition methods compute pproximtions to the derivtive of function from known vlues of the function. Numericl integrtion uses the sme informtion to compute numericl
More informationBest Approximation. Chapter The General Case
Chpter 4 Best Approximtion 4.1 The Generl Cse In the previous chpter, we hve seen how n interpolting polynomil cn be used s n pproximtion to given function. We now wnt to find the best pproximtion to given
More information1 APL13: Suffix Arrays: more space reduction
1 APL13: Suffix Arrys: more spce reduction In Section??, we sw tht when lphbet size is included in the time nd spce bounds, the suffix tree for string of length m either requires Θ(m Σ ) spce or the minimum
More informationProblem Set 9. Figure 1: Diagram. This picture is a rough sketch of the 4 parabolas that give us the area that we need to find. The equations are:
(x + y ) = y + (x + y ) = x + Problem Set 9 Discussion: Nov., Nov. 8, Nov. (on probbility nd binomil coefficients) The nme fter the problem is the designted writer of the solution of tht problem. (No one
More informationOrdinary Differential Equations Boundary Value Problem
Ordinry Differentil Equtions Boundry Vlue Problem Shooting method Runge Kutt method Computerbsed solutions o BVPFD subroutine (Fortrn IMSL subroutine tht Solves (prmeterized) system of differentil equtions
More informationMath 360: A primitive integral and elementary functions
Mth 360: A primitive integrl nd elementry functions D. DeTurck University of Pennsylvni October 16, 2017 D. DeTurck Mth 360 001 2017C: Integrl/functions 1 / 32 Setup for the integrl prtitions Definition:
More informationMath 8 Winter 2015 Applications of Integration
Mth 8 Winter 205 Applictions of Integrtion Here re few importnt pplictions of integrtion. The pplictions you my see on n exm in this course include only the Net Chnge Theorem (which is relly just the Fundmentl
More informationQueueing Analysis of Early Message Discard Policy
Queueing Anlysis of Erly Messge Discrd olicy rijt Dube Eitn Altmn ; Abstrct We consider in this pper pckets which rrive ccording to oisson process into finite queue. A group of consecutive pckets forms
More informationTimed Automata as Task Models for EventDriven Systems
Timed Automt s Tsk Models for EventDriven Systems Christer Norström 1 nd Anders Wll 1 1 Mälrdlen University Deprtment of Computer Engineering P.O. Box 883, S721 23 Västerås, Sweden fwl,ceng @mdh.se Wng
More informationChapter 4 Contravariance, Covariance, and Spacetime Diagrams
Chpter 4 Contrvrince, Covrince, nd Spcetime Digrms 4. The Components of Vector in Skewed Coordintes We hve seen in Chpter 3; figure 3.9, tht in order to show inertil motion tht is consistent with the Lorentz
More information#6A&B Magnetic Field Mapping
#6A& Mgnetic Field Mpping Gol y performing this lb experiment, you will: 1. use mgnetic field mesurement technique bsed on Frdy s Lw (see the previous experiment),. study the mgnetic fields generted by
More informationLoad Analysis of TopologyUnaware TDMA MAC Policies for AdHoc Networks
Lod Anlysis of TopologyUnwre TDMA MAC Policies for AdHoc Networks Konstntinos Oikonomou 1 nd Ionnis tvrkkis 2 1 INTRACOM.A., Emerging Technologies & Mrkets Deprtment, 19. Km Mrkopoulou Avenue, Pini 190
More informationUSA Mathematical Talent Search Round 1 Solutions Year 21 Academic Year
1/1/21. Fill in the circles in the picture t right with the digits 18, one digit in ech circle with no digit repeted, so tht no two circles tht re connected by line segment contin consecutive digits.
More informationEntropy and Ergodic Theory Notes 10: Large Deviations I
Entropy nd Ergodic Theory Notes 10: Lrge Devitions I 1 A chnge of convention This is our first lecture on pplictions of entropy in probbility theory. In probbility theory, the convention is tht ll logrithms
More informationTHERMAL EXPANSION COEFFICIENT OF WATER FOR VOLUMETRIC CALIBRATION
XX IMEKO World Congress Metrology for Green Growth September 9,, Busn, Republic of Kore THERMAL EXPANSION COEFFICIENT OF WATER FOR OLUMETRIC CALIBRATION Nieves Medin Hed of Mss Division, CEM, Spin, mnmedin@mityc.es
More information4. GREEDY ALGORITHMS I
4. GREEDY ALGORITHMS I coin chnging intervl scheduling scheduling to minimize lteness optiml cching Lecture slides by Kevin Wyne Copyright 2005 PersonAddison Wesley http://www.cs.princeton.edu/~wyne/kleinbergtrdos
More informationA Framework for Scheduling RealTime Systems
182 Int'l Conf. Pr. nd Dist. Proc. Tech. nd Appl. PDPTA'16 A Frmework for Scheduling RelTime Systems Zhuo Cheng, Hito Zhng, Ysuo Tn, nd Yuto Lim School of Informtion Science, Jpn Advnced Institute of
More informationBasic model for traffic interweave
Journl of Physics: Conference Series PAPER OPEN ACCESS Bsic model for trffic interweve To cite this rticle: Dingwei Hung 25 J. Phys.: Conf. Ser. 633 227 Relted content  Bsic sciences gonize in Turkey!
More informationINVESTIGATION OF MATHEMATICAL MODEL OF COMMUNICATION NETWORK WITH UNSTEADY FLOW OF REQUESTS
Trnsport nd Telecommuniction Vol No 4 9 Trnsport nd Telecommuniction 9 Volume No 4 8 34 Trnsport nd Telecommuniction Institute Lomonosov Rig LV9 Ltvi INVESTIGATION OF MATHEMATICAL MODEL OF COMMUNICATION
More informationIntro to Nuclear and Particle Physics (5110)
Intro to Nucler nd Prticle Physics (5110) Feb, 009 The Nucler Mss Spectrum The Liquid Drop Model //009 1 E(MeV) n n(n1)/ E/[ n(n1)/] (MeV/pir) 1 C 16 O 0 Ne 4 Mg 7.7 14.44 19.17 8.48 4 5 6 6 10 15.4.41
More informationMATHS NOTES. SUBJECT: Maths LEVEL: Higher TEACHER: Aidan Roantree. The Institute of Education Topics Covered: Powers and Logs
MATHS NOTES The Institute of Eduction 06 SUBJECT: Mths LEVEL: Higher TEACHER: Aidn Rontree Topics Covered: Powers nd Logs About Aidn: Aidn is our senior Mths techer t the Institute, where he hs been teching
More informationDesign Data 1M. Highway Live Loads on Concrete Pipe
Design Dt 1M Highwy Live Lods on Concrete Pipe Foreword Thick, highstrength pvements designed for hevy truck trffic substntilly reduce the pressure trnsmitted through wheel to the subgrde nd consequently,
More informationC Dutch System Version as agreed by the 83rd FIDE Congress in Istanbul 2012
04.3.1. Dutch System Version s greed y the 83rd FIDE Congress in Istnul 2012 A Introductory Remrks nd Definitions A.1 Initil rnking list A.2 Order See 04.2.B (Generl Hndling Rules  Initil order) For pirings
More informationHow to simulate Turing machines by invertible onedimensional cellular automata
How to simulte Turing mchines by invertible onedimensionl cellulr utomt JenChristophe Dubcq Déprtement de Mthémtiques et d Informtique, École Normle Supérieure de Lyon, 46, llée d Itlie, 69364 Lyon Cedex
More informationThe Wave Equation I. MA 436 Kurt Bryan
1 Introduction The Wve Eqution I MA 436 Kurt Bryn Consider string stretching long the x xis, of indeterminte (or even infinite!) length. We wnt to derive n eqution which models the motion of the string
More informationChapter 9: Inferences based on Two samples: Confidence intervals and tests of hypotheses
Chpter 9: Inferences bsed on Two smples: Confidence intervls nd tests of hypotheses 9.1 The trget prmeter : difference between two popultion mens : difference between two popultion proportions : rtio of
More informationJob No. Sheet 1 of 8 Rev B. Made by IR Date Aug Checked by FH/NB Date Oct Revised by MEB Date April 2006
Job o. Sheet 1 of 8 Rev B 10, Route de Limours 78471 St Rémy Lès Chevreuse Cedex rnce Tel : 33 (0)1 30 85 5 00 x : 33 (0)1 30 5 75 38 CLCULTO SHEET Stinless Steel Vloristion Project Design Exmple 5 Welded
More informationA. Limits  L Hopital s Rule ( ) How to find it: Try and find limits by traditional methods (plugging in). If you get 0 0 or!!, apply C.! 1 6 C.
A. Limits  L Hopitl s Rule Wht you re finding: L Hopitl s Rule is used to find limits of the form f ( x) lim where lim f x x! c g x ( ) = or lim f ( x) = limg( x) = ". ( ) x! c limg( x) = 0 x! c x! c
More informationNumerical quadrature based on interpolating functions: A MATLAB implementation
SEMINAR REPORT Numericl qudrture bsed on interpolting functions: A MATLAB implementtion by Venkt Ayylsomyjul A seminr report submitted in prtil fulfillment for the degree of Mster of Science (M.Sc) in
More informationPreSession Review. Part 1: Basic Algebra; Linear Functions and Graphs
PreSession Review Prt 1: Bsic Algebr; Liner Functions nd Grphs A. Generl Review nd Introduction to Algebr Hierrchy of Arithmetic Opertions Opertions in ny expression re performed in the following order:
More informationPART 1 MULTIPLE CHOICE Circle the appropriate response to each of the questions below. Each question has a value of 1 point.
PART MULTIPLE CHOICE Circle the pproprite response to ech of the questions below. Ech question hs vlue of point.. If in sequence the second level difference is constnt, thn the sequence is:. rithmetic
More informationZ0103/07/09 series. Blocking voltage to 800 V (NA and NN types)
Rev. September Product dt. Product profile. Description Pssivted trics in conventionl nd surfce mounting pckges. Intended for use in pplictions requiring high bidirectionl trnsient nd blocking voltge cpbility.
More informationexpression simply by forming an OR of the ANDs of all input variables for which the output is
2.4 Logic Minimiztion nd Krnugh Mps As we found ove, given truth tle, it is lwys possile to write down correct logic expression simply y forming n OR of the ANDs of ll input vriles for which the output
More information12.1 Nondeterminism Nondeterministic Finite Automata. a a b ε. CS125 Lecture 12 Fall 2016
CS125 Lecture 12 Fll 2016 12.1 Nondeterminism The ide of nondeterministic computtions is to llow our lgorithms to mke guesses, nd only require tht they ccept when the guesses re correct. For exmple, simple
More informationDeteriorating Inventory Model for Waiting. Time Partial Backlogging
Applied Mthemticl Sciences, Vol. 3, 2009, no. 9, 42428 Deteriorting Inventory Model for Witing Time Prtil Bcklogging Nit H. Shh nd 2 Kunl T. Shukl Deprtment of Mthemtics, Gujrt university, Ahmedbd. 2
More informationPOLYPHASE CIRCUITS. Introduction:
POLYPHASE CIRCUITS Introduction: Threephse systems re commonly used in genertion, trnsmission nd distribution of electric power. Power in threephse system is constnt rther thn pulsting nd threephse
More informationCS/CE/SE 6367 Software Testing, Validation and Verification. Lecture 4 Code Coverage (II)
CS/CE/SE 6367 Softwre Testing, Vlidtion nd Verifiction Lecture 4 Code Coverge (II) 2/54 Lst Clss Code coverge Controlflow coverge Sttement coverge Brnch coverge Pth coverge Coverge Collection Tools EclEmm
More informationMinimum Energy State of Plasmas with an Internal Transport Barrier
Minimum Energy Stte of Plsms with n Internl Trnsport Brrier T. Tmno ), I. Ktnum ), Y. Skmoto ) ) Formerly, Plsm Reserch Center, University of Tsukub, Tsukub, Ibrki, Jpn ) Plsm Reserch Center, University
More information1 Nondeterministic Finite Automata
1 Nondeterministic Finite Automt Suppose in life, whenever you hd choice, you could try oth possiilities nd live your life. At the end, you would go ck nd choose the one tht worked out the est. Then you
More informationTime Optimal Control of the Brockett Integrator
Milno (Itly) August 8  September, 011 Time Optiml Control of the Brockett Integrtor S. Sinh Deprtment of Mthemtics, IIT Bomby, Mumbi, Indi (emil : sunnysphs4891@gmil.com) Abstrct: The Brockett integrtor
More informationDistance And Velocity
Unit #8  The Integrl Some problems nd solutions selected or dpted from HughesHllett Clculus. Distnce And Velocity. The grph below shows the velocity, v, of n object (in meters/sec). Estimte the totl
More informationMACsolutions of the nonexistent solutions of mathematical physics
Proceedings of the 4th WSEAS Interntionl Conference on Finite Differences  Finite Elements  Finite Volumes  Boundry Elements MACsolutions of the nonexistent solutions of mthemticl physics IGO NEYGEBAUE
More informationMA123, Chapter 10: Formulas for integrals: integrals, antiderivatives, and the Fundamental Theorem of Calculus (pp.
MA123, Chpter 1: Formuls for integrls: integrls, ntiderivtives, nd the Fundmentl Theorem of Clculus (pp. 27233, Gootmn) Chpter Gols: Assignments: Understnd the sttement of the Fundmentl Theorem of Clculus.
More informationSOME relationships among events happening in
Possible nd Impossible Vector Clock Sets Estebn Meneses nd Frncisco J. TorresRojs Abstrct It is well known tht vector clocks cpture perfectly the cuslity reltionship mong events in distributed system.
More informationA027 Uncertainties in Local Anisotropy Estimation from Multioffset VSP Data
A07 Uncertinties in Locl Anisotropy Estimtion from Multioffset VSP Dt M. Asghrzdeh* (Curtin University), A. Bon (Curtin University), R. Pevzner (Curtin University), M. Urosevic (Curtin University) & B.
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics
SCHOOL OF ENGINEERING & BUIL ENVIRONMEN Mthemtics An Introduction to Mtrices Definition of Mtri Size of Mtri Rows nd Columns of Mtri Mtri Addition Sclr Multipliction of Mtri Mtri Multipliction 7 rnspose
More informationSection 4.8. D v(t j 1 ) t. (4.8.1) j=1
Difference Equtions to Differentil Equtions Section.8 Distnce, Position, nd the Length of Curves Although we motivted the definition of the definite integrl with the notion of re, there re mny pplictions
More information1 Error Analysis of Simple Rules for Numerical Integration
cs41: introduction to numericl nlysis 11/16/10 Lecture 19: Numericl Integrtion II Instructor: Professor Amos Ron Scries: Mrk Cowlishw, Nthnel Fillmore 1 Error Anlysis of Simple Rules for Numericl Integrtion
More informationUsing QM for Windows. Using QM for Windows. Using QM for Windows LEARNING OBJECTIVES. Solving Flair Furniture s LP Problem
LEARNING OBJECTIVES Vlu%on nd pricing (November 5, 2013) Lecture 11 Liner Progrmming (prt 2) 10/8/16, 2:46 AM Olivier J. de Jong, LL.M., MM., MBA, CFD, CFFA, AA www.olivierdejong.com Solving Flir Furniture
More informationThe final exam will take place on Friday May 11th from 8am 11am in Evans room 60.
Mth 104: finl informtion The finl exm will tke plce on Fridy My 11th from 8m 11m in Evns room 60. The exm will cover ll prts of the course with equl weighting. It will cover Chpters 1 5, 7 15, 17 21, 23
More informationDepartment of Physical Pharmacy and Pharmacokinetics Poznań University of Medical Sciences Pharmacokinetics laboratory
Deprtment of Physicl Phrmcy nd Phrmcoinetics Poznń University of Medicl Sciences Phrmcoinetics lbortory Experiment 1 Phrmcoinetics of ibuprofen s n exmple of the firstorder inetics in n open onecomprtment
More informationWhere did dynamic programming come from?
Where did dynmic progrmming come from? String lgorithms Dvid Kuchk cs302 Spring 2012 Richrd ellmn On the irth of Dynmic Progrmming Sturt Dreyfus http://www.eng.tu.c.il/~mi/cd/ or50/15265463200250010048.pdf
More informationEnergy Bands Energy Bands and Band Gap. Phys463.nb Phenomenon
Phys463.nb 49 7 Energy Bnds Ref: textbook, Chpter 7 Q: Why re there insultors nd conductors? Q: Wht will hppen when n electron moves in crystl? In the previous chpter, we discussed free electron gses,
More information20 MATHEMATICS POLYNOMIALS
0 MATHEMATICS POLYNOMIALS.1 Introduction In Clss IX, you hve studied polynomils in one vrible nd their degrees. Recll tht if p(x) is polynomil in x, the highest power of x in p(x) is clled the degree of
More informationMonotonic Parallel and Orthogonal Routing for SingleLayer Ball Grid Array Packages
Monotonic Prllel nd Orthogonl Routing for SingleLyer Bll Grid Arry Pckges Yoichi Tomiok Atsushi Tkhshi Deprtment of Communictions nd Integrted Systems, Tokyo Institute of Technology 2 12 1 S3 58 Ookym,
More informationSection 6.1 Definite Integral
Section 6.1 Definite Integrl Suppose we wnt to find the re of region tht is not so nicely shped. For exmple, consider the function shown elow. The re elow the curve nd ove the x xis cnnot e determined
More informationWe know that if f is a continuous nonnegative function on the interval [a, b], then b
1 Ares Between Curves c 22 Donld Kreider nd Dwight Lhr We know tht if f is continuous nonnegtive function on the intervl [, b], then f(x) dx is the re under the grph of f nd bove the intervl. We re going
More informationESTIMATING DYNAMIC ORIGIN DESTINATION DEMANDS FROM LINK AND PROBE COUNTS
ESTIMATING DYNAMIC ORIGIN DESTINATION DEMANDS FROM LINK AND PROBE COUNTS by Bruce R. Helling A thesis submitted to the Deprtment of Civil Engineering in Conformity with the requirements for the degree
More informationMetrics for Finite Markov Decision Processes
Metrics for Finite Mrkov Decision Processes Norm Ferns chool of Computer cience McGill University Montrél, Cnd, H3 27 nferns@cs.mcgill.c Prksh Pnngden chool of Computer cience McGill University Montrél,
More informationConstruction and Selection of Single Sampling Quick Switching Variables System for given Control Limits Involving Minimum Sum of Risks
Construction nd Selection of Single Smpling Quick Switching Vribles System for given Control Limits Involving Minimum Sum of Risks Dr. D. SENHILKUMAR *1 R. GANESAN B. ESHA RAFFIE 1 Associte Professor,
More informationDEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS
3 DEFINITION OF ASSOCIATIVE OR DIRECT PRODUCT AND ROTATION OF VECTORS This chpter summrizes few properties of Cli ord Algebr nd describe its usefulness in e ecting vector rottions. 3.1 De nition of Associtive
More informationPrecalculus Spring 2017
Preclculus Spring 2017 Exm 3 Summry (Section 4.1 through 5.2, nd 9.4) Section P.5 Find domins of lgebric expressions Simplify rtionl expressions Add, subtrct, multiply, & divide rtionl expressions Simplify
More informationLecture Notes PH 411/511 ECE 598 A. La Rosa Portland State University INTRODUCTION TO QUANTUM MECHANICS
Lecture Notes PH 4/5 ECE 598. L Ros Portlnd Stte University INTRODUCTION TO QUNTUM MECHNICS Underlying subject of the PROJECT ssignment: QUNTUM ENTNGLEMENT Fundmentls: EPR s view on the completeness of
More informationAnalytical Methods for Materials
Anlyticl Methods for Mterils Lesson 7 Crystl Geometry nd Crystllogrphy, Prt 1 Suggested Reding Chpters 2 nd 6 in Wsed et l. 169 Slt crystls N Cl http://helthfreedoms.org/2009/05/24/tblesltvsunrefinedsesltprimer/
More informationLecture 17. Integration: Gauss Quadrature. David Semeraro. University of Illinois at UrbanaChampaign. March 20, 2014
Lecture 17 Integrtion: Guss Qudrture Dvid Semerro University of Illinois t UrbnChmpign Mrch 0, 014 Dvid Semerro (NCSA) CS 57 Mrch 0, 014 1 / 9 Tody: Objectives identify the most widely used qudrture method
More informationSynthesis from Quantitative Specifications
This reserch ws supported in prt by the Europen Reserch Council (ERC) Advnced Investigtor Grnt QUAREM nd by the Austrin Science Fund (FWF) project S11402N23. Synthesis from Quntittive Specifictions Arjun
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics GENERALIZATIONS OF THE TRAPEZOID INEQUALITIES BASED ON A NEW MEAN VALUE THEOREM FOR THE REMAINDER IN TAYLOR S FORMULA volume 7, issue 3, rticle 90, 006.
More information63. Representation of functions as power series Consider a power series. ( 1) n x 2n for all 1 < x < 1
3 9. SEQUENCES AND SERIES 63. Representtion of functions s power series Consider power series x 2 + x 4 x 6 + x 8 + = ( ) n x 2n It is geometric series with q = x 2 nd therefore it converges for ll q =
More information7.6 The Use of Definite Integrals in Physics and Engineering
Arknss Tech University MATH 94: Clculus II Dr. Mrcel B. Finn 7.6 The Use of Definite Integrls in Physics nd Engineering It hs been shown how clculus cn be pplied to find solutions to geometric problems
More information3.1 Review of Sine, Cosine and Tangent for Right Angles
Foundtions of Mth 11 Section 3.1 Review of Sine, osine nd Tngent for Right Tringles 125 3.1 Review of Sine, osine nd Tngent for Right ngles The word trigonometry is derived from the Greek words trigon,
More informationTypes of Finite Automata. CMSC 330: Organization of Programming Languages. Comparing DFAs and NFAs. NFA for (a b)*abb.
CMSC 330: Orgniztion of Progrmming Lnguges Finite Automt 2 Types of Finite Automt Deterministic Finite Automt () Exctly one sequence of steps for ech string All exmples so fr Nondeterministic Finite Automt
More informationC1M14. Integrals as Area Accumulators
CM Integrls s Are Accumultors Most tetbooks do good job of developing the integrl nd this is not the plce to provide tht development. We will show how Mple presents Riemnn Sums nd the ccompnying digrms
More information5: The Definite Integral
5: The Definite Integrl 5.: Estimting with Finite Sums Consider moving oject its velocity (meters per second) t ny time (seconds) is given y v t = t+. Cn we use this informtion to determine the distnce
More information15. Quantisation Noise and Nonuniform Quantisation
5. Quntistion Noise nd Nonuniform Quntistion In PCM, n nlogue signl is smpled, quntised, nd coded into sequence of digits. Once we hve quntised the smpled signls, the exct vlues of the smpled signls cn
More informationIII. Lecture on Numerical Integration. File faclib/dattab/lecturenotes/numericalinter03.tex /by EC, 3/14/2008 at 15:11, version 9
III Lecture on Numericl Integrtion File fclib/dttb/lecturenotes/numericalinter03.tex /by EC, 3/14/008 t 15:11, version 9 1 Sttement of the Numericl Integrtion Problem In this lecture we consider the
More informationIntegrals along Curves.
Integrls long Curves. 1. Pth integrls. Let : [, b] R n be continuous function nd let be the imge ([, b]) of. We refer to both nd s curve. If we need to distinguish between the two we cll the function the
More informationWeek 10: Riemann integral and its properties
Clculus nd Liner Algebr for Biomedicl Engineering Week 10: Riemnn integrl nd its properties H. Führ, Lehrstuhl A für Mthemtik, RWTH Achen, WS 07 Motivtion: Computing flow from flow rtes 1 We observe the
More informationPreview 11/1/2017. Greedy Algorithms. Coin Change. Coin Change. Coin Change. Coin Change. Greedy algorithms. Greedy Algorithms
Preview Greed Algorithms Greed Algorithms Coin Chnge Huffmn Code Greed lgorithms end to e simple nd strightforwrd. Are often used to solve optimiztion prolems. Alws mke the choice tht looks est t the moment,
More informationArtificial Intelligence Markov Decision Problems
rtificil Intelligence Mrkov eciion Problem ilon  briefly mentioned in hpter Ruell nd orvig  hpter 7 Mrkov eciion Problem; pge of Mrkov eciion Problem; pge of exmple: probbilitic blockworld ction outcome
More informationPlanar Graph Isomorphism is in LogSpace
Plnr Grph Isomorphism is in LogSpce Smir Dtt 1 Nutn Limye 2 Prjkt Nimbhorkr 2 Thoms Thieruf 3 Fbin Wgner 4 1 Chenni Mthemticl Institute sdtt@cmi.c.in 2 The Institute of Mthemticl Sciences {nutn,prjkt}@imsc.res.in
More informationModule 2. Analysis of Statically Indeterminate Structures by the Matrix Force Method. Version 2 CE IIT, Kharagpur
Module Anlysis of Stticlly Indeterminte Structures by the Mtrix Force Method Version CE IIT, Khrgpur esson 8 The Force Method of Anlysis: Bems Version CE IIT, Khrgpur Instructionl Objectives After reding
More information