BAIMD: A Responsive Rate Control for TCP over Optical Burst Switched (OBS) Networks

Transcription

1 AIMD: A Responsve Rate Control for TCP over Optcal urst Swtched (OS) Networks asem Shhada 1, Pn-Han Ho 1,2, Fen Hou 2 School of Computer Scence 1, Electrcal & Computer Engneerng 2 U. of Waterloo, Waterloo, Canada Xaohong Jang, Susumu Horguch Graduate School of Informaton Scence JAIST, Ishkawa, Japan Mny Guo School of Computer Scence & Engneerng U. Azu, Azu-Wakamatsu, Japan Hussen Mouftah School of Informaton Technology & Engneerng U. of Ottawa, Ottawa, Canada Abstract Addtve Increase Multplcatve Decrease (AIMD) wndow adjustment mechansm has been embedded n TCP n order to regulate the transmsson rate n modern communcaton networks. In recent years, the AIMD (1,0.5) traffc regulaton mechansm along wth possbly addtonal enhancements, such as false tmeout detecton and explct notfcaton, has been consdered n the carrers wth Optcal urst Swtchng (OS) as the underlyng transmsson technology. Ths paper ntroduces a novel rate control mechansm based on Generalzed AIMD (α,β), called urst AIMD (AIMD), for tunng the rate control parameters (α, β) at each sender. AIMD s desgned to mprove throughput whle mantanng frendlness wth co-exstng AIMD (1,0.5) flows, and s characterzed n the followng two folds: (1) no burst wndow s requred n the TCP sender s level; (2) no explct notfcatons are requred. The above characterstcs make the proposed scheme dstngushed from all the past reported counterparts by mnmzng the sgnallng efforts and control complexty. The smulaton result shows that AIMD can soldly outperform the past reported AIMD-based (1,0.5) rate control schemes under a wde range of traffc loads. We also suggest that AIMD rate control mechansm may serve as a better choce than AIMD (1,0.5) n the bufferless OS networks due to ts dynamc and flexble (α,β) parameter par. I. INTRODUCTION Optcal urst Swtched Network (OS) s envsoned as one of the most promsng underlyng technologes for the next-generaton all-optcal networks. Compared wth the statc Optcal Crcut Swtched (OCS) wth Wavelength Routed Network (WRNs), OS transmsson s dynamc n nature wth on-demand bandwdth allocaton such that a better dynamcty can be acheved [1-2]. Compared wth Optcal Packet Swtched (OPS), OS nduces much less techncal barrers n the practcal mplementaton, and can brng together the best of the OCS and OPS networks. Wth OS, data bursts of varable lengths are launched and asynchronously swtched along predetermned physcal routes to support specfc servces. The control packet s ntated at the source node correspondng to each data burst and s sent pror to the date burst to confgure the swtch fabrcs at each ntermedate OS swtch [1], [2]. OS has been wdely consdered to provson UDP-based servces due to ts hgh dynamcty and unacknowledged resource reservaton. However, the Internet s essentally domnated wth data traffc, n whch the TCP bulk data transfer mechansm wth strct QoS requrements n terms of data ntegrty and relablty are of extremely hgh mportance. To our best survey, only a few studes have been reported dedcatedly on TCP over OS networks [4], [5], [6], where a relatvely lmted understandng on the TCP performance behavours over the OS networks has been ganed n presence of burst drops at a wde range of traffc loads. Most of the currently proposed TCP mplementatons follow the Addtve Increase Multplcatve Decrease (AIMD) (1,0.5) wndow-based congeston control for regulatng data transmsson. Under such a framework, a TCP sender receves an acknowledgment (ACK) for each launched packet or a sequence of packets (or called a segment). The transmsson rate s lnearly ncreased by enlargng the congeston wndow (cwnd) by one packet per round trp tme (RTT) untl ether packet s dropped or the round trp tmer expres [3]. If the packet s dropped, the sender wll receve a trple duplcate acknowledgment (TD) and halves ts cwnd. TCP consders packet loss/delay events to be the two man ndcatons of congeston n the network, and halvng the wndow sze can effectvely resolve the congeston for bulk data transfer applcatons. The abovementoned AIMD (1,0.5) congeston control mechansm s subject to great challenges when OS s adopted n the underlyng transportaton nfrastructure. Wth OS, burst delay and drop could not only be caused due to congeston when the network load s heavy, but also due to some other reasons such as burst assembly, random contenton, and retroblockng, etc. An mproper reacton on an event of burst droppng or delayed arrval of ACK could brng about very negatve mpacts on thousands of TCP senders. The study n [4] ntroduced a false tmeout (TO) detecton of burst losses due to contenton under a wde range of traffc load. Three dfferent mplementaton scenaros were proposed. The frst soluton s manly based on estmatng the number of TCP packets assembled n one burst wthout necessary knowng the burst assembly mechansm deployed at the OS layer. Along wth the cwnd, TCP mantans a burst congeston wndow burst_wd. When a TCP sender detects a tmeout, t frst compares ts cwnd wth the burst_wd. If the cwnd burst_wd and burst_wd > 3, then the TCP sender treats ths tmeout as a false one by halvng ts cwnd and performng fast retransmsson of the mssng segments. If the cwnd > burst_wd or burst_wd 3, the sender consders ths tmeout as a true tmeout by followng the normal TCP retransmsson procedure. In the second mplementaton, each TCP packet s acknowledged separately by a TCP agent located at the OS edge node. Ths approach can successfully assst TCP from fallng nto false tmeout; however, t volates the end-to-end TCP semantcs snce the ACKs reach the sender before actual completon of the packet delvery. Fnally, a more complcated approach has been proposed by mantanng a TCP agent at

2 each OS core node. Whenever a burst s dropped at the core node, the agent dsassembles the burst and sends a negatve ACK, called NAK, to each correspondng TCP sender, whch s explctly nformed of the mssng segments and probably the network condtons. Generally, the abovementoned solutons could ntroduce ntolerably hgh sgnallng overhead and may not be achevable n practcal Internet. In [5], the authors proposed to persstently retransmt any dropped burst, where each OS edge node buffers a copy of the bursts t launched wthn a certan tme wndow or untl the bursts are successfully delvered. The desgn premse of the scheme s to mprove the TCP throughput by ncreasng the relablty of OS layer transmsson. However, some defcences could be nevtably ntroduced such as the large bufferng capacty and delay. Furthermore, the scheme falls short of the capablty n dealng wth false tmeouts n response to the assocated burst retransmsson delay. The abovementoned TCP congeston control mechansms are subject to dfferent problems, and a TCP rate control scheme that can be responsve to the OS doman network condton wthout takng much extra sgnallng has never been seen. In ths paper, we are commtted to develop a novel approach that can facltate the user doman TCP wndow congeston control. In partcular, the study takes advantage of the Generalzed AIMD (GAIMD) rate control archtecture, whch s more flexble and adaptve to the network condtons wthout losng frendlness wth co-exstng TCP flows. The paper wll frst apply GAIMD to the IP over OS envronment and demonstrate that the proposed scheme can greatly mprove TCP throughput compared wth the past reported counterparts by fully explorng the characterstcs of OS transmsson. The rest of the paper s organzed as follows. Secton II ntroduces the AIMD (α,β) framework n the OS envronment, whch serves as the fundamental part of the study. In Secton III, the formulas for the addtve and multplcatve control parameters are derved. In Secton IV, the derved control parameters are examned and the resultant performance s compared wth the conventonal TCP. Secton V concludes the paper and presents the ssues for our future work. II. GENERALIZED AIMD IN TCP/OS Ths secton ntroduces the archtecture of the proposed GAIMD scheme. We frst start by nvestgatng the concept of congeston n the OS envronment, followed by the effectveness and justfcaton of deployng the GAIMD rate control mechansm n the OS networks. A. Congeston n OS Networks In tradtonal packet-swtched networks, IP packets are stored and forwarded to the next hop at each ntermedate node by lookng up the routng table. In such a swtchng paradgm, network congeston accuses as a result of buffer overflow, and a packet drop event can serve as a clear ndcaton of congeston. Halvng the cwnd for each packet drop event at the TCP senders can effectvely resolve the network congeston. The stuaton s dfferent n the networks wth OS as the underlyng transportaton technology where each data burst cuts through the preconfgured ntermedate core nodes. Some burst drop and TCP tmeout events may not be caused by network congeston but smply random contenton or extra bufferng delay due to the burst assemblng algorthm. In such a crcumstance, halvng the cwnd for each packet loss event at the TCP senders wll certanly lead to unnecessary sendng rate fluctuaton and malcously affect on the throughput. Thus, the desgn of GAIMD s amed to mprove the TCP throughput when OS s taken underlyng by explorng the characterstc of bufferless transmsson and the hgh frequency of multple TCP segment losses n a sngle RTT. In OS, congeston may occur at ngress and/or at egress node. Precsely, packets may arrve at the ngress node n a bursty manner wth a much hgher arrval rate than that the ngress s capable of dealng wth. Ths could cause the ngress node to drop bursts due to buffer overflow. Smlarly, the egress nodes are subject to recevng a huge number of data bursts queued for dsassembly and forward ther content to ther destnatons. We refer to the congeston happenng at the network edge as edge congeston. In addton to the edge congeston, core congeston must also be defned, whch leads to congeston n the OS core swtch. urst droppng occur at the core swtch s sad to be due to congeston f and only f, the total number of smultaneously arrvng burst (or control packets) surpass the number of avalable wavelengths persstently [9]. The study n [9] proposed an overlappng degree model to determne the number of overlapped bursts n one lnk. The larger the overlappng degree, the more lkely ncomng bursts wll be dropped.. AIMD n TCP/OS The proposed AIMD scheme s based on the framework of GAIMD for the cwnd adjustment. Two parameters are defned: α and β, whch serve as the addtve ncremental and reducton rato on cwnd n each TCP sender as any packet s successfully delvered or dropped, respectvely. Unlke TCP where α and β are constantly set to be 1 and 0.5, AIMD has the TCP senders dynamcally determne the two parameters n such a way that the cwnd s ncreased by α segments for each acknowledged packet n a round trp and s decreases by β (β < 1) as any packet loss occurs. It s clear that AIMD s more general than AIMD (1,0.5) wth much better desgn granularty and flexblty. It s worth notng that the proposed AIMD scheme follows the slow-start and congeston control mechansms as for the conventonal TCP. The only dfference s that upon packet loss, the AIMD senders adjust ther cwnd by manpulate α and β values usng the measured RTT to guarantee the best throughput. Wth AIMD, the sender s not explctly notfed about the used burst assembly mechansm and the reasons of the burst losses. Each sender smply treats a packet loss event as a congeston loss. Obvously, ths could lead to overestmaton of the network congeston by rrelevantly halvng the cwnd for every segment drop. To compensate the overestmaton, the AIMD senders take the value of β larger than 0.5 nstead of β = 0.5 n TCP. As such, the summarzed effect of a burst drop event s estmated when the factors α and β are dynamcally determned n the AIMD senders usng the burst-level states (.e., the traffc load n the OS doman), such that the best throughput can be acheved for each competng flow. For

3 example, f a burst s lost when the network load s low, the lost packets are consdered due to random contenton, and the multplcatve factor s set to be 0.5<β<1. Otherwse, β s set to 0.5 when network load s heavy and the burst droppng s consdered to be due to congeston. One of the most mportant advantages of AIMD s ts smplcty where no burst-level wndow s mantaned n the TCP sender and no explct notfcaton specfc to each launched TCP segment must be performed between the OS edge and each TCP sender. Thus, a clean separaton between the control sgnallng between the TCP senders and OS edge nodes can be ganed. Most notably, the AIMD senders use RTT of each launched segment and the number of TOs as references for sensng the network load. For example, data bursts are subject to extra bufferng delay at the OS ngress nodes n response to serous congeston. Thus, the RTT wll substantally ncrease. On the other hand, f the data burst s dropped due to random contenton, the RTT remans approxmately the same. Thus, t s consdered an ndcaton of low network load. It s clear that the determnaton of the β value for those AIMD senders serves as a crtcal task for mprovng the overall throughput. In the followng secton, an analytcal dervaton for α and β that can guarantee the best performance over OS wll be presented. III. AIMD RATE CONTROL PARAMETERS In ths secton, both the addtve and the multplcatve factors (α, β) of the AIMD over OS are analytcally derved. We denote () W ( T () t and ) W j () t as the cwnd sze of the th TCP and the jth AIMD senders at tme t competng for the common network resources, respectvely. Let K represents the total number of co-exstng flows that traverse through the OS doman at tme t. A. urst Droppng Probablty In OS network, burst droppng occurs due to several reasons such as, burst random contenton, persstent congeston, and retro-blockng. In the lterature, many burst droppng probablty models have been proposed to evaluate the burst droppng for dfferent OS desgn characterstcs. For Just-In-Tme sgnallng scheme (JIT), the output port s modeled as an M/G/k/k queue and s solved by usng Erlang s- loss probablty formula to obtan the burst droppng. In [10] two-state Markov Chan model s used to approxmate the packet loss for Just-Enough-Tme (JET) sgnallng usng Frst Ft wth Vod Fllng (FF-VF) as a lnk schedulng algorthm. In [11] a burst droppng probablty model s obtaned whle consderng dfferent fber delay lnes (FDL) optcal bufferng granulartes. In [5], a burst droppng probablty model s derved consderng burst retransmsson technque. Each of the abovementoned burst droppng probablty models were desgned to hghlght the burst droppng behavors regardng specfc OS transmsson characterstcs. However, none of them have consdered the stuaton that a burst loss event can be caused under a number of network states. In ths secton, an analyss on burst droppng probablty s conducted whch further consders the classfcaton of burst droppng events due to ether persstent congeston or random contenton. In our analytcal model an OS swtch s connected wth an adjacent OS swtch wth N output ports each consstng of M number of wavelength channels wthout wavelength converson. For smplcty, the followng dscussons wll be based on the case wth N = 1, where one output port s consdered. The derved model can be easly generalzed. The correspondng state transton dagram s shown n Fg. 1. The state represents the case where there are reserved channels n the output port. State jumps to state +1 f a reservaton request arrve at the port, or jump to state -1 f a burst fnshes traversng the OS swtch. We assume that the burst arrval at the state follows the Posson dstrbuton wth arrval rate, and each burst s served wth servce rate of µ. When = M, the arrved bursts must be dropped. However, n the state where 0 < < M, an ncomng burst s subject to be dropped n the case where more than M 1 bursts arrve n the prevous RTT. Thus, the droppng probablty for an ncomng burst to be dropped n the state M, denoted as p. M Let π be the probablty that the system s n the state. We wrte the state equatons are as follows, As 0 < < M, As = 1, M π ( + µ ) π 1 π+ 1 ( + 1) µ = 0 (1) π µ π 1 = 0 (2) where π M denotes to the probablty of an ncomng burst fnds all output port channels occuped and snce π = 1. µ M = 0 2 µ ( m 1) µ Fgure 1. State transton dagram for obtanng burst droppng From the balance equatons of the Markov chan, the probablty we have a burst droppng event at state, where = 0, 1, 2, M, can be gven as follows, p0ρ P = ρ = / µ,! 1 M k ρ 0 = 0! P = k k = 0,1,2... M On the other hand, the burst droppng probablty due to congeston s denote as l cgst and can be expressed n Eq. (4): Mµ (3)

4 l cgst M. Dervng the Multplcatve Factor (β) = =0 π p (4) In order to derve the multplcatve factor β n AIMD, our system classfes the network condton nto ether one of the followng two states: wth low (contenton) or wth hgh (congeston) overlappng degree probablty. In the TCP layer, when a packet loss occurs at tme t and all the connected TCPs as well as AIMD are notfed through TD or TO smultaneously, the maxmum lnk capacty has been reached at the moment. When the jth AIMD sender receves a packet loss notfcaton, ts cwnd s reduced by a factor of β, whle the cwnd of each competng TCP sender s reduced by a factor of 0.5. ased on ths, the followng two relatons can thus be derved: AIMD senders ncrease by one packet n each 1/α RTT. However, burst droppng may occur due to random contenton, where the cwnd s decreased; thus, the actual ncrease rate of the cwnd wll never reach α segment. For ths reason, α should nteract wth the burst droppng condton and network load dynamcally nstead of merely n response to each burst droppng event. Therefore, the followng rule s summarzed for confgurng α: If the cwnd s large, then α s set accordng to Eq. (8) or (9) dependng on whether a notfcaton of TD or TO s detected. If cwnd s mnmal, then AIMD behaves smlar to TCP wth α=1. When the cwnd sze s n the mddle, α s set dynamcally to ensure a hgher throughput and TCPfrendlness. The followng flowchart summarzes the functonalty of the proposed congeston control scheme. ( ) ( j) T = W W ( ) ( t + ) = β W ( t), (5) + ( j) ( t ) 0.5 W ( t) (6) In the congeston state ( l cgst 0. 6 ), the AIMD senders behave the same as TCP senders wth β = 0.5. Otherwse, β follow = 1 l cgst T β where, 0 < 0. 6 < cgst l (7) C. Dervng the Addtve Factor (α) Wth the AIMD congeston control mechansm, the relaton between α and β can be obtaned by Eq. (8) or (9) [7], [8] n order to ensure the frendlness of the AIMD flows wth the other co-exstng TCP flows n the case of TD: 3(1 β ) α = 1 + β whle n the case of TO, the relaton between α and β becomes: 4 2 (8) α = (1 β ) (9) 3 It s clear that n the case where β s larger than 0.5, α should be less than 1. The network s n the under-loaded regon, and W T () t of the th TCP and W () t of the jth AIMD evolve as follows, ( ) ( ) WT ( t) = WT ( t) + 1 t, (10) ( j) ( j) W ( t) = W ( t) + α t (11) The lnk capacty and the average RTT are the two factors that determne the cwnd [8]. When the cwnd s small due to hgh droppng rate, the AIMD flow wth larger β has lower throughput compared wth that of the other TCP flows. In the case where few burst droppng occurs, the cwnd n the Fgure 2. Flow chard demonstratng AIMD congeston control IV. NUMERICAL RESULTS To verfy the proposed scheme, smulaton s conducted usng Network Smulator NS-2, where the NSF network topology shown n Fg. 3 s adopted. The dstances shown are n km. The TCP senders and recevers are connected to the ngress and egress OS edge nodes, whch assemble the ncomng TCP packets nto bursts and dssemble the bursts back to TCP packets, respectvely. Each core OS swtch s connected to ngress/egress edge node. The number of co-exstng TCP and AIMD does not mpact the overall loss performance of the network. The network conssts of background traffc to ensure the low and hgh congeston scenaros n the smulaton. The mxed tme/length based burst assembly algorthm s used, where the burst tmeout threshold s set to 1ms and the maxmum burst length s set to 100K. The core nodes mplement the LAUC- VF channel schedulng algorthm [1], [2], where one bdrectonal control channel s allocated along each lnk. The number of wavelengths on each lnk s 8 and the transmsson

5 rate on a wavelength s set to be 10 Gb/s. The data traffc traverses through 4 ngress-egress node pars, where the fxed path routng algorthm s used. Fgure 3. NSF topology The control packet processng tme s set to 1µs at both core and edge nodes. No wavelength converson s used, and no burst retransmsson faclty s mplemented. A Fle Transfer Protocol (FTP) applcaton s adopted for generatng TCP traffc wth a 1K average packet sze. We have equpped each core node wth one FDL wth 3 wavelengths operatng at 2, 5, and 8 ms delay granulartes. The throughput s obtaned over a 10 6 s smulaton perod. In order to avod the phase effect, the traffc flows are launched wth a random delay between each other. The study n [4] has shown that TCP wth Selectve Acknowledgment (Sack) can acheve decent throughput behavours when deployed over OS networks. Ths s due to the selectve acknowledgement mechansm. Therefore, TCP Sack mplementaton and TCP Reno are taken n our performance evaluaton. manly due to random contenton nstead of congeston. On the other hand, the AIMD senders can acheve better throughput because AIMD does not rgdly react to a burst loss as a congeston loss at ths low level loads. Instead, the factor of β s manpulated n each AIMD sender to guarantee a smoother wndow sze cut n response to any packet loss, whch summarzes the effect of both contenton and congeston losses. Fg. 5 shows the throughput by TCP Sack, Reno, and AIMD under heavy network loads. In the experment, up to 5 flows are launched for each scheme (whch results n totally 15 competng flows at the core OS node). Snce the traffc load s above the congeston threshold, the AIMD senders dynamcally derve the β value accordng to the evaluated burst droppng probablty due to congeston, whch can acheve a smoother congeston wndow adjustment upon each burst loss event. The smulaton result also shows that AIMD can yeld better throughput compared wth that by TCP Reno and Sack over heavy network loads snce t consders the number of sessons whle computng β. Fgure 5. Throughput by TCP Reno, TCP Sack, and AIMD under hgh network loads. Fgure 4. Throughput by TCP Reno, TCP Sack, and AIMD under low network loads. Fg. 4 shows the performance of the case where the flows of Sack, Reno, and AIMD are competng n the OS doman. It s observed that the throughput by TCP Sack and Reno s dramatcally reduced even when the burst droppng rate s qute low because the AIMD (1,0.5) senders always take a burst loss event as due to congeston. It s qute clear that under such a low network traffc load, a burst loss event s Fg. 6 shows the throughput by TCP wth ACK/NAK [4], whch s compared wth that by AIMD. Wth TCP, a TCP agent s placed at the ngress nodes to enable the explct loss notfcaton faclty and ACKs for the TCP senders. The proposed AIMD scheme outperforms TCP whch requres the exchange of extra notfcaton sgnallng. In the experment, up to 5 flows are launched for each scheme (whch results n totally 20 competng flows at the core OS node). The superorty of AIMD les n the fact that the AIMD senders can ntellgently estmate the burst loss probablty due to congeston to determne the correspondng transmsson parameters α and β, whch s an mportant desgn n makng the cwnd sze stable to result better throughput. In Fg. 7, we addtonally consder UDP sessons whch coexst wth TCP Sack, Reno, and AIMD. Snce no congeston avodance mechansm n UDP s devsed, the UDP traffc does not respond to any burst or packet drop event and

6 yelds much hgher throughput. Whle the TCP Sack, Reno and AIMD mplementatons have started to reduce ther transmssons due to the ncreased network load, the UDP senders probe for any avalable bandwdth and ncrease ther transmsson rates. However, t has been seen from the smulaton result that AIMD scheme can acheve the best throughput performance n presence of UDP traffc. Fgure 6. Throughput by TCP wth ACK/NAK, TCP Sack, and AIMD scheme. Throughout the above smulaton study, we verfed the proposed AIMD scheme and concluded that AIMD can acheve sgnfcantly better throughput than that by a number of TCP mplementatons based on AIMD (1,0.5) mechansm n the carrer wth OS transmsson. In addton, the proposed scheme can effectvely mantan farness among competng TCP flows and keep awareness on non-congeston burst droppng by manpulatng the α and β values n the TCP layer. Fgure 7. Throughput by the TCP mplementatons n presence of UDP traffc. V. CONCLUTION The paper has tackled the problems of regulatng the TCP traffc n the carrer networks supported by Optcal urst Swtchng (OS). A novel congeston control scheme called urst AIMD (AIMD) s proposed, whch s amed to resolve the vcous effect of non-congeston burst drops n the OS doman whch unnecessarly halve the TCP senders congeston wndows by usng the conventonal AIMD scheme. The proposed scheme s characterzed by the fact that no extra sgnallng s requred between the AIMD senders and the OS edge nodes. Furthermore, t has demonstrated a clean separaton between the transmsson layer and the underlyng OS layers. Analyss on burst droppng probablty s conducted to evaluate the rate control ratos α and β for achevng the best throughput wthout losng TCP frendlness. The proposed AIMD scheme s further verfed by extensve smulaton and compared wth a number of past reported counterparts, such as TCP Sack, Reno, and TCP, under a wde range of dfferent crcumstances n terms of burst loss probablty, the number of competng flows, and the number of co-exstng non-tcp traffc. We proved that the proposed AIMD scheme can yeld sold advantages aganst the schemes based on the tradtonal AIMD framework n every aspect of nterest by the TCP scheme desgners, whch can serve as a better canddate n the bufferless OS networks. REFERENCES [1] Y Chen, C. Qao, X. Yu, An optcal burst swtchng: a new area n optcal networkng research, IEEE Network, vol. 18, pp , [2] C. Qao, M. Yoo Optcal burst swtchng (OS), a new paradgm for an optcal nternet Journal of Hgh Speed Networks, vol. 8, pp , [3] W. Stevens, TCP/IP Illustrated, Volume 1, Addson Wesley Longman, [4] X. Yu, C. Qao, and Y. Lu, TCP mplementaton and false tme out detecton n OS networks, IEEE Infocom, pp , Hong Kong, Chna, [5] Q. Zhang, V. Vokkarane, Y. Wang, and J. Jue, TCP over optcal burstswtched networks wth optcal burst retransmsson, Submtted to IEEE Journal on Selected Areas n Communcatons Optcal Communcaton and Networkng Seres, [6] X. Cao, J. L, Y. Chen, and C. Qao, "Assemblng TCP/IP packets n optcal burst swtched networks", IEEE Globecom, vol. 3, pp , Tawan, [7] Y. Yang, S. Lam, Generalzed AIMD congeston control, Unversty of Texas, Techncal Report TR-2000, avalable at [8] L. Ca, X. Shen, J. Pan, and J. W. Mark, Performance analyss of TCPfrendly AIMD algorthms for multmeda applcatons, IEEE Transacton on Multmeda, vol. 7, no. 2, pp , [9] J. L, C. Qao, J. Xu, and D. Xu, "Maxmzng throughput for optcal burst swtchng networks", IEEE Infocom, pp , Hong Kong, Chna, [10] A. Kaheel, H. Alnuwer, F. Gebal, "Analytcal Evaluaton of blockng probablty n optcal burst swtchng networks", IEEE ICC, vol. 3, pp , France, [11] X. Zhu, J. Kahn, Queung models of optcal delay lnes n synchronous and asynchronous optcal packet-swtchng networks, Optcal. Engneerng, vol. 42, no. 6, pp , 2003.