On using cicuit-switched netwoks fo file tansfes Xiuduan Fang, Malathi Veeaaghavan Univesity of Viginia Email: {xf4c, mv5g}@viginia.edu Abstact High-speed optical cicuit-switched netwoks ae being deployed to suppot highly demanding applications in the escience eseach community. File tansfes wee identified as an ideal application fo high-speed cicuits because such tansfes can utilize any ate, limited only by end-host capabilities. This pape addesses the question of how a cicuit-switched netwok can be shaed efficiently amongst many uses fo file tansfes. Specifically, we study the question of how much bandwidth should be allocated pe file tansfe so that the system pefomance aveaged acoss all flows is optimal in tems of mean esponse time. We exploe a heteogeneous bandwidth-allocation scheme, in which bandwidth is allocated based on file sizes, as well as a homogeneous scheme, in which all tansfes ae allocated the same amount of bandwidth. Ou analytical esults show that bandwidth allocation should be based on loading conditions. Unde low loads, we ecommend a homogeneous scheme and each call should be allocated a high-bandwidth cicuit. Howeve, unde high loads, small files should be allocated low-bandwidth cicuits and lage files high-bandwidth cicuits; this heteogeneous bandwidth-allocation scheme esults in a one-to-thee odes of magnitude eduction in mean esponse time. I. INTRODUCTION Thee is a gowing inteest in high-speed optical cicuitswitched netwoks fom the escience eseach community to suppot highly demanding applications. Pojects in scientific fields, such as high-enegy physics, molecula biology, and oceanogaphy, ae expected to geneate lage-sized files, which then need to be moved between institutions. To meet the needs of these applications, a numbe of optical testbeds, many of which have been descibed in aticles [1], have implemented dynamic cicuit sevices, e.g., ESnet4, DRAGON, and CHEE- TAH in the United States, CANARIE s CA*net 4 in Canada, MUPBED and NOBEL in Euope, and JGN2 in Japan. A natual question that aises with such deployment of dynamic cicuit sevices is what applications ae suitable fo such sevices. Typically, inteactive applications that equie had Quality-of-Sevice (QoS) guaantees (e.g., video confeencing) ae consideed appopiate. Howeve, file tansfes wee identified as an ideal application fo high-speed, host-tohost cicuits because such tansfes can utilize any ate, limited only by end-host capabilities, unlike eal-time audio and video applications whose bandwidth equiements ae on the ode of Mb/s o lowe because of compession technologies [2]. File tansfes have classically been viewed as not having had QoS equiements, and futhemoe bette seved by packet-switched netwoks in which bandwidth allocated to a flow can be elastically adjusted based on the numbe and usage of othe simultaneous flows. Howeve, we ague that any technique that allows fo a eduction in file-tansfe delays is useful. Moeove, we obseve that if, fo each file tansfe, the netwok can allocate a cicuit with a ate matched to the host bottleneck ate 1, then even at low loads, the file-tansfe delay on the patial-ate cicuit will be the same as on a full-ate packet-switched link. In addition, we note that (i) unde high loads, the dedicated allocation of bandwidth pe file tansfe in a cicuit netwok is useful to avoid losses, and the coesponding ecovey times (as occus with TCP), and (ii) high-speed cicuit-switched inteface cads cost much less than packet-switched inteface cads. These obsevations led us to popose the use of high-speed cicuit-switched netwoks fo file tansfes. Since a natual mode of bandwidth shaing fo cicuit netwoks is an immediate-equest call-blocking mode, in which a call simply aives fo sevice when needed and is immediately ejected if thee ae no available esouces, we focus ou study on immediate-equest call-blocking cicuit netwoks. Due to call-setup ovehead in cicuit netwoks, cicuits should be used only fo files lage than a minimum size. At the othe exteme, if a file is vey lage (e.g., on the ode of teabytes), then, given cuent link ates (e.g., 10 Gb/s), even if a lage potion of the link bandwidth is allocated to just a single tansfe (e.g., 1 Gb/s), the cicuit will need to be held fo a long duation (e.g., fo seveal hous). If such lage factions (e.g., one-tenth) of link capacity ae allocated pe file tansfe, then call-blocking pobability will be high at even modeate loads if the bandwidth-shaing mechanism is the immediate-equest call-blocking mode [3]. A way to lowe call-blocking pobability without compomising the high pe-call cicuit-ate allocation o utilization is to use book-ahead mechanisms [4]. Theefoe, we popose the use of immediate-equest call-blocking cicuit netwoks fo files of an intemediate size (modeate-to-lage fo un-of-the-mill tansfes), and assume that small files will be handled with connectionless sevices and vey lage files with book-ahead capable cicuit netwoks. In this pape, we ae inteested in detemining how mediumto-lage sized file tansfes can be suppoted efficiently on an immediate-equest call-blocking cicuit netwok. Specifically, ou metic is esponse time, which includes waiting time fo an available cicuit plus file-tansfe delay ove the allocated cicuit. Since file tansfes can be suppoted at any cicuit ate, a key question is how much bandwidth should be allocated to each call so that the system has a minimum aveage esponse 1 The host bottleneck ate is the maximum ate at which a host, given its disk-access speed and othe limitations, can send/eceive data.
time. The selected pe-call cicuit ate can be any ate equal to o below the host bottleneck ate. If the selected ate is too high, then while file-tansfe delays fo admitted calls will be small, moe calls ae likely to be ejected and have to wait fo an available cicuit since the numbe of simultaneous file tansfes that can be accommodated will be small. Noting this inteplay between individual flow pefomance and system pefomance aveaged acoss all flows, we study this impotant question of what pe-call cicuit ate to use fo each file tansfe. In addition, should all calls be allocated the same amount of bandwidth, i.e., should the bandwidth-allocation scheme be homogeneous? O, should we divide files into multiple classes, and allocate diffeent amounts of bandwidth to each class? We efe to this bandwidth allocation as heteogeneous bandwidth allocation. Ou goal is to undestand whethe this appoach outpefoms the homogeneous one. We constuct analytical models based on M/G/m queueing systems to answe these questions. II. RELATED WORK Most of the poject teams deploying high-speed optical cicuit-switched testbeds ae focusing on the implementation aspect of bandwidth-shaing systems. Fo example, the DOE funded a poject called OSCARS to develop a schedule fo ESnet to accept book-ahead esevations fo bandwidth [5]. A question that is not being addessed by these pojects, but one in which we have become inteested, is how much bandwidth to allocate pe file tansfe. The goal of the OSCARS and simila schedules is moe boad to include othe types of applications, but ou wok has focused on a specific application, i.e., file tansfes. As thee is no intinsic equiement fo bandwidth fo file tansfes, this question becomes inteesting. A second diffeence in ou wok is that we ae inteested in having these high-speed cicuit netwoks be shaed in an immediate-equest mode in contast to the book-ahead mode in the OSCARS poject. Hee again ou goals vay. We would like to use these netwoks fo unof-the-mill file-tansfe applications, such as content delivey netwoks, while the escience pojects focus pimaily on vey lage files, e.g., teabyte and petabyte sized files, along with othe applications. Chaacteizing the efficiency of bandwidthshaing algoithms becomes moe impotant given that thee ae many moe souces of un-of-the-mill tansfes when compaed to escience tansfes. Ou pio wok on the CHEETAH poject [2], [3], [6] analyzed and expeimented with suppoting file tansfes on a hybid netwok consisting of an IP-outed netwok and a high-speed cicuit-switched netwok. In this solution, if a filetansfe application s equest fo a cicuit is blocked, which would happen if at the time of call aival all cicuits ae occupied, then the application outes the tansfe to the IPouted path iespective of the file size. Fo lage files, this may not be the best option; instead waiting and tying again fo a high-speed cicuit may yield a lowe delay. Theefoe, in this new wok, we assume that once a file-tansfe equest is outed to the cicuit netwok, it waits fo esouces to become available on the cicuit netwok, which effectively means that calls ae not blocked, but athe queued. Anothe impotant diffeence in this pape is ou novel heteogeneous bandwidthallocation scheme based on file sizes. In all ou pio wok, we only consideed the homogeneous scheme. III. BANDWIDTH SHARING MODELS Fo modeling puposes, we limit ou analysis to a singlelink cicuit-switched path. We make the following assumptions fo file-tansfe applications: The call aival pocess is Poisson with ate λ. This assumption is validated fo file tansfes by measuements epoted in [7]. The file-size distibution is Paeto, P (α, k) (whee α is the exponent of the powe law, and k is the smallest file size) [8]. We assume that l (l k) and u (u >l)aethe smallest and lagest sizes of files outed to the immediateequest cicuit netwok, espectively. Files smalle than l will be seved by a connectionless netwok (e.g., the Intenet), and files lage than u, by a book-ahead cicuit netwok [4]. The file-size distibution fo files outed to the immediate-equest cicuit netwok is bounded Paeto, BP(α, l, u), with a pobability density function (pdf): { α lα x α 1 f X (x) = 1 (l/u) α if l<x u (1) 0 othewise All the moments of X ae finite and the jth moment is denoted by E[X j ]. The time to establish and elease a cicuit is a constant, denoted by T setup. A. Homogeneous bandwidth-allocation scheme In this scheme, all calls ae assigned cicuits of the same ate. Hence if a link of capacity C is divided into m equalate channels, each file tansfe is assigned a cicuit of ate = C/m. Let sevice time, i.e., file-tansfe delay ove an allocated cicuit, be denoted by S. Neglecting popagation delay in the actual file tansfe, we estimate S as: S = T setup + X (2) We neglect popagation delay in the actual tansfe because the emission delays fo the ange of file sizes being handled by the cicuit netwok will be much lage than popagation delay. The fist two moments of S ae: E[S] =T setup + E[X] (3) E[S 2 ]=T 2 setup +2 T setup E[X] + E[X2 ] 2 (4) Ou single-link M/G/m system model is illustated in Fig. 1a. Calls ae queued if all m seves ae busy, and seved on a Fist-Come-Fist-Seved (FCFS) basis. To implement call queueing in a multi-link system, we designed two algoithms
λ classifie A call equests the sevice of a seve 1 λ link capacity C call queue m m identical seves (a) A homogeneous system p 1 λ p n λ Q 1 Q n 1 m 1 1 m n subsystem 1 with m 1 identical seves the whole system has the link capacity of C A class i call equests the sevice of a single seve fom subsystem i subsystem n with m n identical seves (b) A completely patitioned heteogeneous system Fig. 1: Bandwidth shaing queueing models fo a single-link cicuit-switched netwok called Fixed-Bandwidth Delayed Stat (FBDS) and Vaying- Bandwidth Delayed Stat (VBDS) as epoted in [9]. In this pape howeve, we only model the single-link system to focus ou study on undestanding how to set design paametes, such as pe-call cicuit ate, in ou homogeneous and heteogeneous bandwidth-shaing mechanisms. Thus, ou goal is not to design new models, but athe use existing queueing models to detemine how to set design paametes fo system opeation. The pe-seve taffic intensity fo the M/G/m model, ρ, is defined as ρ = λ E[S] m. This is also the utilization facto fo the system [10]. The system is stable (i.e., a system with finite aveage delays and queue lengths) when 0 ρ<1. Due to call-setup ovehead, we define the, U, as: E[X] U = ρ E[S] = λ E[X] (5) C Let W epesent waiting time in the queue. The aveage waiting time, E[W ], can be appoximated as in [11]: E[S 2 ] E[W ] E[W ] M/M/m 2 E[S] 2 (6) whee E[W ] M/M/m is the mean waiting time of an M/M/m queueing system [10]. The mean esponse time is E[T ]=E[W ]+E[S] (7) B. Heteogeneous bandwidth-allocation scheme In this scheme, file-tansfe equests ae divided into multiple classes based on file sizes. Calls within a cetain filesize ange ae assigned to a class and ae allocated the same amount of bandwidth. Calls fom diffeent classes ae seved by cicuits of diffeent ates. Assume that thee ae n classes in total. Calls ae divided into n classes by cutoff points, χ k (k =0, 1,..., n), whee l = χ 0 < χ 1 <... < χ n = u. Calls with file sizes in (χ i 1,χ i ] (1 i n) ae assigned to the ith class. Let p i be the faction of class-i calls among all calls: p i = P (χ i 1 <X χ i )= (l/χ i 1) α (l/χ i ) α 1 (l/u) α (8) p i =1 (9) Let X i (1 i n) epesent file size fo the ith class. The distibution of X i is bounded Paeto, BP(α, χ i 1,χ i ).We deive the following elation between the jth moments of X and X i : E[X j ]= p i E[X j i ] (10) Since file sizes coesponding to diffeent calls ae independent of each othe, and a call belongs to class i with pobability p i, we can chaacteize the call aival pocess as being a Poisson pocess with ate λ i : λ i = p i λ (11) Assume that a call fom the ith class is allocated a cicuit of ate, i. Let sevice time fo class-i calls be S i : S i = T setup + X i (12) i E[S i ] and E[Si 2] can be computed using E[X i] and E[Xi 2]. As shown in Fig. 1b, we assume a complete patitioning of the link capacity. We will conside moe complex class-based shaing mechanisms such as uppe-limit, guaanteed minimum (ULGM) [12] fo simulation studies. Analytical models fo such schemes exist fo only call-blocking netwoks, not callqueueing netwoks, as assumed in this wok. Given ou assumption of complete patitioning, we can model the heteogeneous system as n independent M/G/m i subsystems (see Fig. 1b). The ith subsystem handles class-i calls with a capacity of C i : C i = m i i, subject to C i C (13) Using (5), (6), and (7), we can compute the following thee metics fo each subsystem:, U i, mean waiting time, E[W i ], and mean esponse time, E[T i ]. The mean esponse time fo the whole system is E[T ]= p i E[T i ] (14)
Using (5), (10), and (11), the fo the whole system is deived as: λ i E[X i ] C i U = C U i = = λ E[X] (15) C C Note that this is the same as (5) in the homogeneous system. A complete-patitioning system can be opeated efficiently if a netwok management system is used to monito taffic loads of all classes and dynamically (on a slowe scale than call aivals) adjust the capacity allocations fo each class, C i (1 i n). IV. NUMERICAL RESULTS A. Homogeneous bandwidth-allocation scheme Given that a file-tansfe session can use a cicuit of any ate, ou goal is to detemine an optimal value of pe-call cicuit ate, opt (and a coesponding optimal numbe of channels into which the cicuit-switched link capacity is divided, m opt ; opt = C/m opt ), so that the homogeneous system can be opeated with minimum mean esponse time, E[T min ],ata given, U. Using the analytical model of Section III-A, we solve this optimization poblem. Specifically, the input paametes, output paametes, and the algoithm ae descibed below: Input: 1) Thee paametes of the bounded-paeto distibution fo file sizes, α, l, and u 2) Link capacity C, call-setup time T setup, and a set of values, U = {0.01, 0.02,..., 0.99} Output: 1) Design paamete opt 2) Intemediate esults such as m opt and E[T min ] Algoithm: 1) Fo each value of U a) Compute call aival ate, λ, using(5) b) Compute mean esponse time, E[T ], using (7) and (6). These fomulas assume knowledge of. We use the optimization tool NMinimize of Mathematica to solve fo opt at which E[T ] eaches a minimum. c) Compute intemediate esults Fig. 2 shows the analytical esults. As the tageted effective utilization inceases, the optimal pe-call cicuit ate, opt, deceases significantly. This esult is intuitive. Deceasing has opposing effects on the two components of mean esponse time, E[T ]: mean sevice time, E[S], and mean waiting time, E[W ]. On one hand, as deceases, E[S] inceases linealy (see (3)). On the othe hand, at a given taffic load, E[W ] deceases as deceases, because a call is moe likely to obtain an unoccupied cicuit without waiting in the queue. Unde light loads, if pe-call cicuit ate is too small (i.e., the numbe of channels into which the cicuit-switched link optimal pe call cicuit ate (Mb/s) opt E[T min ] Fig. 2: E[T min ] vs. U and opt vs. U when C =10Gb/s, T setup =1sec, α =1.0, l =1MB, and u =1TB capacity is divided is too lage), some channels ae likely to be idle, causing the link capacity to be undeutilized. Theefoe, pe-call cicuit ate should be high to achieve minimum mean esponse time. Convesely, unde heavy loads, moe calls will be queued upon aival and thus waiting time plays a significant ole in esponse time. Hence, to obtain minimum mean esponse time, we should decease pe-call cicuit ate to counteact the impact of incease in mean waiting time. In conclusion, to minimize mean esponse time, we should allocate bandwidth based on loading conditions. Unde light taffic, we should choose a high pe-call cicuit ate but unde heavy taffic, we should lowe the pe-call cicuit ate. B. Heteogeneous bandwidth-allocation scheme Ou goal is to undestand whethe a completely patitioned heteogeneous system outpefoms a homogeneous system in tems of mean esponse time, E[T ], at a given effective utilization, U, assuming compaable input paametes. Unlike a homogeneous system whee thee is a single design paamete of pe-call cicuit ate, opt, to minimize E[T ], ina heteogeneous system, we have moe design paametes, e.g., 1) What ae cutoff points (χ i ) fo the classes? 2) How much bandwidth (C i ) should each subsystem be allocated? 3) What ae ideal pe-call cicuit ates ( i ) fo each class? In this section, we study a 2-class system (i.e., n = 2) and exploe thee scenaios to answe these design questions. These scenaios diffe in seveal input paametes but have six common input paametes as the homogeneous scheme in Section IV-A. 1) Scenaio 1: given the pe-call cicuit ate fo each subsystem ( 1, 2 ), what is an appopiate value fo the middle cutoff point (χ 1 ), and how much total capacity should be assigned to each subsystem (C 1 and C 2 ): In effect, we have two unknown paametes, χ 1 and C 1, since C 2 = C C 1.We use a simila optimization algoithm as in Section IV-A, and input the equations of the analytical model fo a heteogeneous system into Mathematica to solve fo the χ 1 and C 1 values that minimize E[T ]. Fig. 3a compaes a heteogeneous system with pe-call cicuit ates of 10 Mb/s and 100 Mb/s fo its two subsystems, with two homogeneous systems with pe-call minimum esponse time (sec)
mean esponse time (sec) 10 5 class 2 fo the heteogeneous system the homogeneous system: =100Mb/s the homogeneous system: =10Mb/s the whole heteogeneous system: 1 =10 Mb/s, 2 =100 Mb/s 10 1 class 1 fo the heteogeneous system (a) heteogeneous vs. homogeneous optimal middle cutoff point (MB) 10 1 (b) optimal middle cutoff point bandwidth allocated to the class 2 subsystem (Gb/s) 10 9 8 7 6 5 4 (c) bandwidth allocated to the class-2 subsystem Fig. 3: Results fo a heteogeneous system with pe-call cicuit ate of 10 Mb/s fo class 1 and 100 Mb/s fo class 2; common input paametes: C =10Gb/s, T setup =0sec, α =1.0, l =1MB, and u =1TB TABLE I: Two example points in Fig. 3a Homogeneous systems Heteogeneous system U =10 Mb/s =100 Mb/s whole system class-1 subsystem class-2 subsystem E[W ] E[T ] E[W ] E[T ] E[T ] χ 1 p 1 E[W 1 ] E[T 1 ] C 2 E[W 2 ] E[T 2 ] (sec) (sec) (sec) (sec) (sec) (MB) (sec) (sec) (Gb/s) (sec) (sec) 20% 0 11.63 0 1.16 1.16 1.001 0.10% 0 0.84 7.4 0 1.16 50% 0 11.63 0 1.16 1.16 1.001 0.10% 0 0.84 9.9 0 1.16 98% 653.86 665.49 1229.51 1230.67 14.91 1222.300 99.92% 3.67 9.64 4.8 5680.69 6553.46 cicuit ates of 10 Mb/s and 100 Mb/s, espectively. TABLE I lists two example points fom Fig. 3a fo the thee systems. Fom Fig. 3a, we see that unde low loads (i.e., when U < 73%), the whole heteogeneous system, its class-2 subsystem, and the homogeneous system with of 100 Mb/s have the same mean esponse time (e.g., E[T ]=1.16 sec as shown in the U =20% and U =50% ows of TABLE I). This is because unde low loads, mean waiting time, E[W ], is negligible. To minimize E[T ], the heteogeneous system should allocate all calls the lage value of pe-call cicuit ate, i.e., 100 Mb/s. In othe wods, all calls should be assigned to the class-2 subsystem by setting the cutoff point χ 1 to equal l, which is 1 MB 2. Coespondingly, the class-2 subsystem should be allocated almost all of the total link capacity. That is why in Fig. 3c, 9.9 Gb/s bandwidth out of 10 Gb/s is allocated to the class-2 subsystem when 40% < U < 73%. Unde extemely low loads, the heteogeneous system can obtain minimum E[T ] with an even smalle bandwidth allocation fo class-2 calls. Fo example, when U = 20%, 7.4 Gb/s bandwidth is sufficient fo the class-2 subsystem to achieve minimum E[T ] (see the U = 20% ow in TABLE I). Howeve, unde high loads (i.e., when U>73%), the heteogeneous system outpefoms both homogeneous systems. In paticula, when U>90%, thee is a one-to-thee odes of magnitude eduction in mean esponse time with the heteogeneous system. This pefomance impovement is pimaily due to a eduction in the vaiance of file sizes fo the class-1 subsystem. Intuitively, by dividing calls into two classes, small file-tansfe equests in the class-1 subsystem will not suffe 2 Given the estiction of l<χ 1 <u, the solution of χ 1 is the smallest allowable value appoaching l, which is set to be 1.001 MB, as shown in Fig. 3b and the U =20%andU =50%owsofTABLEI. fom waiting fo an extemely lage job to complete. This is confimed by the small mean esponse time fo the class-1 subsystem (see Fig. 3a). Due to the heavy-tailed natue of the taffic, a lage popotion of file-tansfe equests (e.g., 99.92% in the heteogenous system at U =98% as shown in TABLE I) belong to the class-1 subsystem. Theefoe, the oveall mean esponse time fo the heteogeneous system is dominated by its class-1 subsystem even though its class-2 subsystem has a much lage mean esponse time at high U. In addition, as load inceases, the cutoff point, χ 1, should be inceased, which implies that moe files ae assigned to the class-1 subsystem as shown in Fig. 3b. To accommodate moe taffic being assigned to the class-1 subsystem, moe bandwidth should be allocated to this subsystem. This is illustated in Fig. 3c, whee unde heavy taffic, the amount of bandwidth allocated to the class-2 subsystem deceases as load inceases. In conclusion, we ecommend that when the taffic load is low, link capacity should be shaed with a simple, homogeneous bandwidth-shaing mechanism with a pedetemined value of (high) pe-call cicuit ate. As taffic load inceases, bandwidth patitions fo each class should be pogammed into the switch contolle, along with pecomputed optimal peclass bandwidth levels and the contolle instucted to switch to the heteogenous mode of opeation. A netwok management system that monitos taffic load and dynamically updates the contolle is equied to suppot this admission-contol algoithm. 2) Scenaio 2: given total capacity assigned fo each subsystem (C 1 and C 2 ), what is an appopiate value fo the middle cutoff point (χ 1 ), and the pe-class, pe-call cicuit ates ( 1 and 2 ): Fig. 4 compaes a heteogeneous system, the two subsystems of which ae allocated equal amounts
mean esponse time (sec) class 2 in the heteogeneous system homogeneous system whole heteogeneous system class 1 in the heteogeneous system (a) heteogeneous vs. homogeneous optimal cutoff point (MB) 1000 800 600 400 200 0 (b) optimal middle cutoff point optimal pe call cicuit ate (Mb/s) class 2 in the heteogeneous system class 1 in the heteogeneous system homogeneous system 10 1 (c) optimal pe-call cicuit ate Fig. 4: Results fo a heteogeneous system with equal amounts of bandwidth allocated to class 1 and class 2; common input paametes: C =10Gb/s, T setup =1sec, α =1.0, l =1MB, and u =1TB of capacity, with a homogeneous system that is designed to minimize mean esponse time, E[T ]. Fom Fig. 4a, we see that the heteogeneous system yields lowe E[T ] than the homogeneous system at diffeent values of U. In paticula, unde high loads, the impovement is significant. As in Scenaio 1, this pefomance impovement is pimaily due to the small E[T ] of the class-1 subsystem, which is a dominant popotion of the heavy-tailed taffic. Moeove, unde high loads, both subsystems can enjoy highe pe-call cicuit ates than in the homogeneous system (see Fig. 4c). In paticula, small files ae allocated lowebandwidth cicuits than lage files. Fig. 4b shows the impact of load on the optimal cutoff point fo the heteogeneous system. As in Scenaio 1, unde highe loads, moe files ae assigned to the class-1 subsystem to counteact the significant incease in mean waiting time of the class-2 subsystem. 3) Scenaio 3: given the middle cutoff point (χ 1 ), what ae optimal total capacity allocations pe subsystem (C 1 and C 2 ) and pe-call cicuit ates ( 1 and 2 ): We have left out the details due to space constaints. Howeve, fom ou analytical esults, we daw the same conclusion: heteogeneous bandwidth allocation yields smalle mean esponse time than homogeneous bandwidth allocation unde high loads. V. CONCLUSIONS We studied the question of how an immediate-equest cicuit netwok can be shaed efficiently fo file tansfes. As thee is no intinsic equiement fo bandwidth fo file tansfes, a key question is how much bandwidth should be allocated fo each file tansfe so that the system pefomance is optimized in tems of mean esponse time. We exploed two bandwidthallocation schemes: homogeneous and heteogeneous. Ou analytical esults show that bandwidth allocation should be based on loading conditions. Unde low loads, we ecommend a homogeneous scheme and each call should be allocated a cicuit with a elatively high ate. Howeve, unde high loads, a heteogeneous bandwidth-allocation scheme based on file sizes can impove mean esponse time by one-to-thee odes of magnitude. This pefomance impovement is pimaily due to a eduction in the vaiance of file sizes in the small-file subsystem. ACKNOWLEDGMENT This wok was caied out unde the sponsoship of NSF ANI-0335190 gant. REFERENCES [1] G. Kamous-Edwads and A. Jukan, Eds., IEEE Commun. Mag., Special issue on An Optical Contol Plane fo the Gid Community: Oppotunities, Challenges, and Vision, vol. 44, no. 3, Ma. 2006. [2] M. Veeaaghavan and X. Zheng, A econfiguable Ethenet/SONET cicuit based meto netwok achitectue, IEEE JSAC, vol. 22, no. 8, pp. 1406 1418, Oct. 2004. [3] M. Veeaaghavan, X. Fang, and X. Zheng, On the suitability of applications fo GMPLS netwoks, in Poc. of IEEE GLOBECOM, San Fancisco, CA, Nov. 2006. [4] X. Zhu and M. Veeaaghavan, Analysis and design of book-ahead bandwidth-shaing mechanisms, accepted by IEEE Tansactions on Communications, 2007. [5] ESnet On-demand Secue Cicuits and Advance Resevation System (OSCARS). [Online]. Available: http://www.es.net/oscas/index.html [6] M. Veeaaghavan, X. Zheng, H. Lee, M. Gadne, and W. Feng, CHEE- TAH: Cicuit-switched High-speed End-to-End Tanspot AcHitectue, in Poc. of Opticomm 2003, Dallas, TX, Oct. 2003. [7] V. Paxson and S. Floyd, Wide aea taffic: The failue of Poisson modeling, IEEE/ACM Tansactions on Netwoking, vol. 3, no. 3, Jun. 1995. [8] M. Covella and A.Bestavos, Self-similaity in Wold Wide Web taffic evidence and possible causes, IEEE/ACM Tansactions on Netwoking, vol. 5, no. 6, Dec. 1997. [9] X. Zhu, A study of bandwidth-shaing mechanisms in connectionoiented netwoks, Ph.D. dissetation, Univesity of Viginia, Viginia, Feb. 2008. [10] L. Kleinock, Queueing Systems. Volume 2: Compute Applications. USA: Wiley-Intescience, John Wiley & Sons, 1976. [11] G. Bolch, S. Geine, H. de Mee, and K. S. Tivedi, Queueing Netwoks and Makov Chains: Modeling and Pefomance Evaluation with Compute Science Applications, 2nd Edition. Hoboken, NJ: Wiley, 2006. [12] G. L. Choudhuy and K. K. Leung and W. Whitt, An invesion algoithm fo loss netwoks with state-dependent ates, in Poc. of IEEE INFOCOM 95, Washington, DC, USA, 1995, pp. 513 521.