A Hybrid Network Architecture for File Transfers

Transcription

1 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 A Hybrid Network Architecture for File Transfers Xiuduan Fang, Meber, IEEE, Malathi Veeraraghavan, Senior Meber, IEEE Abstract In prior work, we proposed a hybrid architecture that copleents the connectionless Internet with a high-speed, dynaically shared circuit-switched network for file-transfer applications. Sall files are directed to the connectionless network while for large files, a high-speed circuit setup is attepted. If the attept is unsuccessful (because all circuits are already in use), the application will fall back to using the connectionless path. This paper addresses the question of how to select appropriate values for operational paraeters in this hybrid architecture. Specifically, we study the questions of what sized files to direct to the circuitswitched network, and how uch bandwidth to allocate per file transfer. To answer these questions, we construct a odel of this hybrid architecture by cobining the Erlang-B call-blocking odel with TCP delay odels. Our odel captures a cobination of utilization and delay considerations in the selection of iniu file size above which transfers should be directed to the circuit-switched network. The optial per-call circuit rate and the optial iniu file size are deterined to axiize the benefits of using the circuit network, which is quantified with an average-delay-reduction etric. Index Ters Network architecture, circuit-switching networks, packet-switching networks, network applications INTRODUCTION IN prior work, we proposed a hybrid architecture that adds a high-speed, dynaically shared circuitswitched network to copleent the connectionless Internet for file-transfer applications [], []. Exaples of high-speed circuit networks are Synchronous Optical Network (SONET) and all-optical Wavelength-Division Multiplexed (WDM) networks. The goal of this paper is to deterine appropriate values for operational paraeters in order to support file transfers efficiently in this hybrid architecture. Specifically, we study the questions of what sized files should be directed to circuit networks, and what circuit rate should be allocated per file transfer. Since the circuit network is proposed as a copleent to the Internet, our hybrid solution calls for a routing decision odule, which assists file-transfer applications at end hosts to deterine whether to attept a circuit setup or directly choose the Internet path. Due to callsetup overhead, a circuit-setup attept is justified only for files that are larger than a iniu file size, θ. If the circuit setup fails, the application falls back to the Internet path. In this paper, we construct a odel for this hybrid solution by cobining an M/G// callblocking odel with analytical odels for TCP fro papers by Padhye et al. [3] and Cardwell et al. [4]. Our odel captures utilization- and delay-based criteria in the selection of θ. We define a etric called average delay reduction, R, to quantify the benefits of using the circuit network, and find an optial per-call circuit rate (circuit rate allocated per file transfer), C/ opt, and X. Fang is with Google Inc., Mountain View, CA, E-ail: xf4c@virginia.edu M. Veeraraghavan is with the University of Virginia, Charlottesville, VA 94. E-ail: v5g@virginia.edu corresponding optial iniu file size, θ opt, at which R is axiized. Results of our analysis show that it is insufficient to siply deterine the effective throughput on the Internet path and use this value as a floor for the percall circuit rate to achieve lower delays for individual transfers. Our odels of the hybrid architecture reveal that a uch larger per-call circuit rate, with a correspondingly large iniu file size, should be used for the good of the overall syste as a whole. For exaple, on a wide-area path with a round-trip tie of 5 s, an Internet-path bottleneck link rate of Mb/s, and a packet loss rate of %, the effective throughput on the Internet path in that exaple is only.87 Mb/s but the optial per-call circuit rate obtained with our odels is 63 Mb/s. With this allocation, given our call-setup overhead consideration, only files larger that 75 MB are directed to the circuit-switched network. Files saller than this size unfortunately experience the slower rate on the Internet path, but by using circuit resources for only large files, the overall delay average is lowered. We carried out sensitivity analysis of the results to three paraeters: call-arrival load, circuit-switched link capacity, and round-trip tie (RTT) on the IP-routed path. Based on these results, we can recoend an adission-control algorith for sharing bandwidth aong file transfers on circuit-switched networks. First, the algorith should be load sensitive, increasing the per-call circuit rate allocations and dropping the iniu file size when loads are low. Second, the relationship between capacity and optial per-call circuit rate is not linear. Third, different optial per-call circuit rates should be used on different paths based on RTT. For low-rtt segents, higher per-call rate and higher iniu file size should be used to irror the higher TCP throughput on the IP-routed path. This paper is organized as follows. Section describes

2 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 our otivation for addressing the above stated proble by reviewing related work. In Section 3, we present our analytical odels for file transfers on this hybrid architecture. Section 4 provides nuerical results that offer insights and answers to our stated questions. Section 5 discusses practical considerations for an ipleentation of this hybrid architecture. Finally, we conclude the paper in Section 6. RELATED WORK There is a growing interest in high-speed optical circuitswitched networks fro the escience counity to support high-end applications [5]. Projects in scientific fields, such as high-energy physics, olecular biology, astrophysics, cliate studies, and oceanography, are expected to generate large-sized files, which then need to be oved between institutions. A nuber of optical testbeds have been deployed for these large-scale scientific projects. To eet the needs of these applications, a nuber of optical testbeds, any of which have been described in articles [5], have ipleented dynaic circuit services, e.g., ESnet4, DRAGON, and CHEETAH in the United States, CANARIE s CA*net 4 in Canada, MUPBED and NOBEL in Europe, and JGN in Japan. Recently, Internet has added a Dynaic Circuit (DC) network to their backbone IP-routed network to offer circuit services copleentary to the connectionless IP service [6]. Most of the project teas deploying these experiental testbeds are focusing on the ipleentation aspect of bandwidth-sharing systes. For exaple, the DOE funded a project called OSCARS to develop a scheduler for ESnet to accept book-ahead reservations for bandwidth [7]. In these schedulers, a fixed value of bandwidth is requested for a certain fixed duration. A question that is not being addressed by these projects, but one in which we have becoe interested, is how uch bandwidth to allocate per file transfer. The goal of the OSCARS and siilar schedulers is ore broad to include other types of applications, but our work has focused on a specific application, i.e., file transfers. As there is no intrinsic requireent for bandwidth for file transfers (in contrast to a coded video or audio signal), this question becoes interesting. Since file transfers can utilize any rate, however high, unlike real-tie audio and video applications in which the circuit rate needs to just atch the codec rates [8], and a file can be streaed out fro a disk fully utilizing a circuit (there is no intrinsic burstiness), these applications see ideal for high-speed circuit-switched networks. A second difference lies in the bandwidth sharing ode. In the iediate-request call-blocking ode, a call arrives for service when needed (hence iediaterequest ), and is iediately accepted if resources are available or rejected if there are no available resources since switch controllers typically do not buffer rejected calls (hence call-blocking ). This work analyzes the usage of high-speed circuit-switched networks in this ode. In contrast, in the OSCARS project, networks are operated in a book-ahead ode in which users specify required bandwidth, call durations, and desired future call-initiation ties, and a scheduler returns an assigned call-initiation tie. We would like to use high-speed circuit-switched networks for run-of-the-ill file-transfer applications, such as content delivery networks, while the escience projects focus priarily on very large files, e.g., terabyte and petabyte sized files, along with other applications. Characterizing the efficiency of bandwidthsharing algoriths becoes ore iportant given that there are any ore sources of run-of-the-ill transfers when copared to escience transfers. In 3, we proposed a novel architecture concept, called CHEETAH, to copleent the existing IP-routed Internet with a high-speed, dynaically shared circuitswitched network, specifically to support file transfers []. In this hybrid architecture, file-transfer applications judiciously choose between the connectionless IP-routed path and the circuit path based on soe paraeters. Our papers in 3 [] and 4 [] studied the perforance of file-transfer applications in this hybrid architecture. However, in these papers, call-blocking probability was not used as an input in the selection of per-call circuit rate. If the selected per-call rate is too high, then while file-transfer delays for aditted calls will be sall, callblocking probability will be high since the nuber of siultaneous file transfers that can be accoodated on a shared link will be sall. But if it is too sall, then the individual transfer delays will be large. Noting this interplay between individual flow perforance and syste perforance averaged across all flows, we noted that the call-blocking probability should be related to per-call circuit rate. In addition to the above-cited papers on analytical odeling [], [], we have published papers reporting experiental work on the CHEETAH testbed [9]. But our question on the optial per-call circuit rate could not be answered using experiental eans because of a lack of a sufficient nuber of data-generating end hosts on this testbed. Therefore, we returned to analytical odeling in our 6 paper []. In this odel, we used call-blocking probability as the priary etric of study. Subsequently we recognized that given our application of interest is file transfers, delay-related etrics are ore iportant than call-blocking probability. Therefore, in this present study, we create new odels focused on delay. We cobine previously validated odels for TCP and callblocking probability. Our ain goal of this study is not to propose new atheatical odels, but rather to use existing odels to study adission-control algoriths for sharing bandwidth aong file transfers on circuit-switched networks, specifically, deterining design paraeters, such as the optial per-call circuit rate for file transfers. Even though several call-adission-control algoriths have been proposed for optical networks, e.g., [] [3],

3 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY N- N Link L, capacity C λ routing decision (RD) odule end host λ'... N- N Link L, capacity C (a) Call based (circuit) sharing odel for (any) single link of a switch Fig. : Switch sharing odel (b) A odel for file transfers these algoriths concentrate on other issues, such as wavelength selection, traffic priority, and service differentiation. 3 DELAY MODEL FOR FILE TRANSFERS ON THE HYBRID ARCHITECTURE For odeling purposes, we liit our analysis to a single-link circuit-switched path, and assue that the IP-routed path can be characterized by three paraeters: round trip tie, RT T, packet loss rate, P loss, and bottleneck link rate, r. Our hybrid architecture odel cobines the Erlang-B M/G// loss odel for a circuit-switched link with TCP odels of [3] and [4]. See Appendix A and Appendix B for a brief review of these odels. A odel of a single-link circuit-switched path is illustrated in Fig. a, in which calls originating fro hosts on the N links share the capacity C of link L. We ake the following assuptions for file-transfer applications: The call-arrival process on each of the N links is Poisson with a rate λ for calls directed to link L, resulting in an aggregate call-arrival rate of λ = Nλ. This assuption is validated for file transfers by easureents reported in [4]. Calls are assued to have identical holding tie distributions with a ean, /µ. This distribution is derived fro the Pareto distribution, since file sizes have been reported in [5] to fit this distribution. Calls are hoogeneous, i.e., all calls are assigned the sae aount of bandwidth. This assuption allows us to treat link L as a link of channels, where the capacity of each channel is C/. Each call is assued to require a circuit whose rate is equivalent to one channel. Given the delay overhead of call setup, circuits are suitable only for large files so that the holding tie of the circuit is significantly longer than call-setup delay. Hence, our design includes a routing decision (RD) odule [] at end hosts, as shown in Fig. b, which decides whether or not to attept a circuit setup for a particular file transfer. A configurable paraeter, iniu file size, θ, is used to odel the behavior of the RD odule. This odule directs files larger than θ to the circuit network.. We use the ters IP-routed path, Internet path, and TCP/IP path interchangeably.. We use the ters channel and circuit interchangeably. A brief overview of our odeling approach is as follows. We first derive offered traffic load, ρ, as a function of θ, and then describe two factors that constrain θ. One factor, θ u, is based on the utilization consideration entioned above, while the other, θ d, is deterined by a coparison of delay estiates across the two paths. Both θ u and θ d are dependent on, the nuber of channels into which the circuit-switched link capacity is divided. An optial value for, opt, is then coputed as one that axiizes our average-delay-reduction etric. By finding an optial opt, we deterine an optial percall circuit rate, C/ opt. The iniu file size corresponding to this optial opt is θ opt. By setting this value in the routing decision odule, and configuring the circuit switch to allocate per-call rates of C/ opt, we ensure that the average delay reduction is axiized. 3. Deterining offered traffic load, ρ, as a function of iniu file size, θ To copute ρ, we should copute the ean call holding tie and ean call-arrival rate. Using the Pareto probability density function (pdf) for file size, f X (x) = αkα x, α+ x k, where α is the shape paraeter (the larger the α, the higher the probability of sall file sizes), and k is sallest file size, we can copute the conditional pdf for files larger than θ (θ k), f X (X>θ) (x). Then the ean size of files directed to the circuit network can be coputed as: E[X (X > θ)] = x f X (X>θ) (x)dx = αθ α Using this ean file size, the ean call holding tie, /µ, can be estiated as: µ = T prop E[X (X > θ)] + = T prop + αθ C α C () where T prop is the round-trip propagation delay, and C/ is the per-call circuit rate. This is a good estiation because there is only one flow on a circuit, there is no congestion in the data plane, and hence no losses related to congestion. Moreover, given the low bit error rates of optical links, the probability of errored fraes and retransissions on a dedicated circuit is assued to be negligibly sall. To aintain a file-transfer rate atched to the circuit rate C/, we proposed the transport protocol Circuit-TCP (CTCP) in [6]. Then, fro Fig. b, we derive the call-arrival rate on ()

4 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 4 link L as: λ = N λ = N λ P (X > θ) = N λ ( ) α k (3) θ where λ is the call-arrival rate on each input link before the routing decision odule as shown in Fig. b. Using () and (3), we have the offered traffic load to link L: ρ = λ ( ) α ( k µ = N λ Tprop + αθ θ α ) (4) C This traffic load is used as input while coputing callblocking probability, P b, and link utilization, U b, with (4) and (5), respectively, of Appendix A. 3. Deterining iniu file size, θ The iniu file size, θ, is deterined by θ = ax{θ d, θ u } (5) where θ d and θ u are the iniu file sizes deterined separately through a consideration of file-transfer delay and network utilization, respectively. Fro a delay consideration, for a file of size x, we copare E[T tcp (x)], the expected delay using TCP across the IP-routed path, coputed using the TCP odels suarized in Appendix B, with E[T circuit (x)], the expected delay incurred when a circuit setup is attepted for the transfer. The latter can be represented as: E[T circuit (x)] = ( P b ) (E[T setup ] + T transfer (x)) + P b (E[T fail ] + E[T tcp (x)]) (6) where T transfer (x) is the tie taken to transfer a file of size x over a circuit of rate C/: T transfer (x) = T prop + x C/ = T prop + x C In (6), we odel our hybrid design in which applications fall back to using the Internet path if a call-setup attept fails. We assue that E[T setup ], the ean call-setup delay, is equal to E[T fail ], the ean tie taken by the network to declare setup failure (a setup typically fails when all channels are in use by other calls). We define θ d as the file size for which E[T circuit (θ d )] = E[T tcp (θ d )], and x > θ d, E[T circuit (x)] < E[T tcp (x)] For files whose size, x, is larger than θ d, the end host will first attept a circuit setup because if the setup is successful, the application will enjoy a shorter transfer delay. For files saller than θ d, the lower E[T tcp (x)] justifies the routing-decision odule recoending the Internet path directly with no circuit-setup attept. Next, we describe how we copute θ u, the iniu file size based on a consideration of network utilization, which is an iportant etric for service pricing. The value for θ u is selected to be large enough to ake the call-setup delay a sall fraction of the file-transfer delay (7) (8) over a circuit, T transfer (x). Specifically, using (7) for the file-transfer delay, we define θ u as follows: T prop + θ u C = βe[t setup] (9) where β is a utilization factor. For exaple, if β is, the transfer delay is at least ties the call-setup delay. Since the circuit bandwidth is not used during call setup, we require such a factor to achieve high link utilization. Using (5), the iniu file size, θ, is selected to be the larger of the two values, θ u and θ d. 3.3 Optial per-call circuit rate and corresponding iniu file size The optial per-call circuit rate, C/ opt, should be selected to axiize the benefits of having the circuit network. We define a etric called average delay reduction, R, as follows: R = (E[T tcp (x)] E[T circuit (x)]) f X (x)dx () To obtain R, we approxiate E[T tcp (x)] (see (6) in Appendix B) as: x E[T tcp (x)], when x > θ () r effective where r effective is the effective throughput in the TCP congestion avoidance phase (which is given by B(P loss ) of (7) in Appendix B). This is a good approxiation because for large files, which is the desired region of operation, B(P loss ) is a good estiate of effective TCP throughput. Using the above approxiation and (6) for E[T circuit (x)], we obtain R as: R ( P b ) r effective αk α (α )θ α ( P b) Tprop kα θ α ( P b ) C αk α (α )θ α E[T setup] kα θ α () To copute opt that axiizes R, we use a nuerical approach as there is no closed-for solution for R =. Recall that θ and P b in () depend on. The value of the iniu file size corresponding to opt is θ opt. We define a second etric, R n, the average delay reduction per bit for files larger than θ, i.e., R n = θ (E[T tcp (x)] E[T circuit (x)]) x ( P b) ( P b ) Tprop r effective ( P b ) C E[T setup] α (α + )θ α (α + )θ f X (X>θ) (x)dx Our nuerical results show that the opt value at which a axiu R is attained, also results in an alost axiu R n. Therefore, we only obtain an opt value that axiizes R. (3)

5 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY Liitations of the odel The odel described above characterizes a single flow between a source and destination pair. The Internet path between a particular source-destination pair is characterized by the three paraeters, packet loss rate, round-trip tie and bottleneck link rate, just as is done in [3]. It does not odel the interaction between ultiple flows on the Internet path that will ipact the throughput of the particular flow under consideration. On the circuit-switched path, there is a bottleneck link at which call-blocking probability is the axiu aong all links of that path. This effect is captured by using the single-link call-blocking Erlang-B forula. Siulations are required to understand the interactions of ultiple flows on the Internet path, as well as the ipact of call blocking in the circuit-switched network on the packet loss rate or RTT across the IP-routed path (if routers have large buffers, as is increasingly the trend, RTT, rather than packet loss rate, will increase). Finally, our choice of hoogeneous rate allocations for all calls on the circuit network can be relaxed. After initial subission of this paper, otivated by the results obtained in this work, we undertook an analysis of a heterogeneous-rate-allocation schee. This work is published in [7]. The analysis studied the behavior of a callqueueing usage of the circuit-switched network rather than the call-blocking ode used here; the otivation for this additional change is that very large files ay experience lower delay by waiting for a high-speed circuit to becoe available rather than falling back to the IP path. 4 DETERMINATION OF NUMERICAL VALUES FOR DESIGN PARAMETERS In this section, we use the odel described in Section 3 to deterine appropriate nuerical values for the design paraeters of our hybrid architecture. Specifically, there are two design paraeters, per-call circuit rate, C/, which is deterined by the nuber of channels,, into which the circuit-switched link is divided, and a corresponding iniu file size, θ. The values for these design paraeters depend upon the values of input paraeters. We divide input paraeters into three categories: ) Paraeters related to the circuit-switched link: capacity, C, round-trip propagation delay, T prop, callsetup delay, T setup, and the utilization factor, β. ) Paraeters related to the IP-routed path: bottleneck link rate, r, round-trip tie, RT T, and packet loss rate, P loss. 3) Paraeters related to the file-transfer application: aggregate call-arrival rate, Nλ, and file-size Pareto distribution paraeters, α and k. We use a set of values for these input paraeters in a base setting for which we deterine the corresponding design paraeter values in subsection 4.. We then odify the base setting values to study the sensitivity of the design paraeters to these input paraeters in subsections 4., 4.3, and 4.4. First, consider the aggregate call-arrival load, Nλ. In a deployed network, this is an input paraeter, since the nuber of users, N, generating traffic for the shared link is deterined by the network topology and routing. On the other hand, it is a design paraeter in the network planning stages. By controlling N, the service provider can control the effective load for the shared link. For the base setting, we found that a high value of calls/sec was required for Nλ in order to have soe call blocking, and we use a value of for the utilization factor, β, so that call-setup delay does not adversely affect utilization at high loads. When we reduce Nλ to study the syste at low loads, we correspondingly reduce β. Sensitivity of design paraeters to the value of Nλ, and corresponding β, is described in subsection 4.. Next, consider paraeters related to data rate, since for large files, this is likely to be the ost iportant deterinant of delay. In the base setting, we choose C = Gb/s, and r = Mb/s. Recall that the circuitswitched link is subdivided into channels, with channel being assigned to each call, i.e., file transfer. Hence the per-call circuit rate is C/. For exaple, if =, then the per-call circuit rate equals the bottleneck link rate on the TCP/IP path in the base setting. Sensitivity of design paraeters to the value of C is presented in subsection 4.3. Tie-related paraeters include round-trip tie, RT T, on the IP-routed path, and round-trip propagation delay, T prop, across the circuit-switched link. We assue that these two delays to be the sae, in effect, neglecting queueing delays on the IP-routed path. We capture the effect of queueing by using a non-zero packet-loss rate, P loss. We choose RT T = T prop = 5 s and P loss = % for the base setting. This represents a oderately loaded, wide-area path, per the data collected by the Internet End-to-end Perforance Monitoring (IEPM) group [8]. Sensitivity of design paraeters to the value of RT T is presented in subsection 4.4. Paraeters kept unchanged across these sensitivity studies are circuit-switched link capacity, C, bottleneck link rate on the IP-routed path, r, ean call-setup delay, E[T setup ], and the file-size Pareto-distribution paraeters. We choose C = Gb/s, and r = Mb/s. We assue E[T setup ] = sec, based on easureents reported in [9], and set the file-size Pareto-distribution paraeters, α to.9, and k to bytes, based on easureents reported in [5]. The design or output paraeters of interest, as stated earlier, are the nuber of channels,, and iniu file size, θ. As can be noted fro the equations in Section 3, we do not have a closed-for equation for output paraeters, or θ, as a function of input paraeters. For a given, it is straightforward to copute θ u using (9), as all other variables are fixed for a given

6 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 6 setting of the input paraeters. However, it is ore difficult to copute θ d. We use an iterative approach for a given range of file sizes, where the lower-bound is the sallest file size, k (e.g., KB), and the upper-bound is an arbitrarily large value (e.g., TB). For a given, e.g.,, we start with the sallest file size for θ d. We set θ to equal this value of θ d, and solve (4) to find the offered load ρ. Using (4) (see Appendix A), we find P b, which is used in (6), to find E[T circuit (x)] with x set to our arbitrarily chosen θ d. The coputed ean delay E[T circuit (θ d )] is copared to E[T tcp (θ d )] to check if (8) holds for all files larger than θ d, where E[T tcp (θ d )] is coputed using (7) (see Appendix B). If (8) does not hold, we increase the chosen value for θ d by 5 bytes, and repeat the above-described sequence, until it does. We thus copute the correct value of θ d corresponding to each value of. For each value of, we thus obtain two values for the iniu file size, θ d, and θ u. Using (5), we choose the larger of these two values to be the iniu file size, θ, corresponding to each value of. Then using () and (3), we copute R, the average delay reduction, R n, the average delay reduction per bit for files larger than θ, and select an optial opt at which R reaches a axiu. 4. Deterining design paraeter values for the base setting Using the procedure described above, we obtain values of θ d and θ u as a function of, as shown in Fig. a. We see that as increases, θ u decreases (solid line). As increases (i.e., per-call circuit rate decreases), filetransfer delays will increase, which reduces the ipact of the (-second) ean call-setup delay. Therefore, fro a utilization perspective, we can choose saller values of θ u as increases. On the other hand, θ d increases as increases (dashed line), given that the transfer delay on the circuit path will increase (because per-call circuit rate decreases). In the liit, θ d, the iniu file size fro a delay consideration, approaches when becoes large (e.g., θ d = when is larger than 5334 in Fig. a). This is because there is no file size for which the circuit path is a better choice than the Internet path, when the per-call circuit rate, C/, is saller than r effective, the effective throughput on the IP-routed path. In this base setting, r effective =.87 Mb/s. Therefore, the iniu per-call circuit rate should be larger than.87 Mb/s and thus should be saller than 5335 (given C = Gb/s). We refer to 5334 as ax, the axiu-allowed. Fig. b shows the ipact of on the offered load, ρ. While θ is changed correspondingly for different values of using the results fro Fig. a, θ itself has little ipact on ρ. Since α is close to, θ has alost the sae effect on both the nuerator and denoinator ters of (4). Therefore, the ρ vs. plot appears to be linear. Using the values of ρ corresponding to different values, we plot call-blocking probability, P b (solid line), and utilization, U b (dashed line) in Fig. c. These are plots of (4) and (5) fro Appendix A, respectively. Even though ρ increases with, P b drops as increases because has the doinant ipact. Utilization increases with, aking it feasible to operate the link at 9% utilization by choosing to be larger than. Instead of choosing the whole range of fro Fig. a, we consider three values of (i.e.,,, and ) and list in TABLE the corresponding values of per-call circuit rate, iniu file size, traffic load, call-blocking probability, and utilization. We denote the θ values for these three values as θ, θ, and θ, respectively. The iniu file sizes for these values are liited by the utilization-related criteria, θ u, as observed in Fig. a, since θ u is larger than θ d for these values of (see (5)). Fig. d plots E[T tcp ] and E[T circuit ] corresponding to these three values of. As a guideline to reading the plots of Fig. d, copare the dashed line representing E[T tcp ] with the = solid line, which represents the E[T circuit ] of (6), for file sizes larger than θ, which is.6 GB. Siilarly, copare E[T tcp ] with the = plot for file sizes larger than θ, which is 8.9 MB, and with the = plot for file sizes larger than θ, which is.89 MB. Fro Fig. d, we see that if is, for files larger than.89 MB, using a circuit will yield lower delays than using the Internet path. In this scenario, although the Mb/s per-call circuit rate is saller than the Mb/s bottleneck link rate chosen for the Internet path, the circuit path outperfors the Internet path. This is because TCP s congestion-control schee ipacts throughput on wide-area paths with soe level of loading (an RTT of 5 s and a packet loss rate of %). An interesting observation fro Fig. d is that the plots for = and = alost overlap. This is because when =, the call-blocking probability is so high (9.9%, as shown in TABLE ) that any circuit setup attepts fail to obtain a high Gb/s circuit, causing the syste to fall back to the Internet path. Thus alost % of the calls requesting transfers of files larger than.6 GB will experience the higher delay of the Internet path. On the other hand, when =, P b drops to.97%, but for the 99.3% of the calls that do succeed in obtaining a circuit, the circuit rate of Mb/s is low. Thus, the T transfer coponent of E[T circuit ] is high (see (6)). TABLE lists transfer delays for files that are both saller and larger than the iniu file sizes for three values of,,, and. The last colun shows the ean transfer delay, which is E[T tcp ] if the Internet path is chosen directly, and E[T circuit ] if the routing decision odule recoends a circuit-setup attept. Fro TABLE and Fig. d, we observe that for files of size larger than θ, which is 8.9 MB, if the Internet path to the reote host has characteristics atched with our assuptions, then, on average, the least delay is obtained when a circuit setup is attepted

7 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY θ u (bits) 8 θ u θ d 8 θ d (bits) ρ (a) θ u vs. (solid line) and θ d vs. (dashed line) (b) ρ vs U b.95 9 P b P b U b E[T circuit ] or E[T tcp ] (seconds) θ θ tcp = θ (c) P b vs. (solid line) and U b vs. (dashed line) = = 8 9 file size (bits) (d) E[T circuit ] vs. file size (solid lines) or E[T tcp] vs. file size (dashed line) average delay reduction (sec) average delay reduction per MB (sec/mb) (e) R vs. 3 4 (f) R n vs. Fig. : Ipact of on θ u, θ d, ρ, P b, U b, E[T circuit ], R, and R n : α =.9, k = bytes, C = Gb/s, N λ = calls/sec, E[T setup ] = sec, β =, RT T = 5 s, r = Mb/s, P loss = %

8 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 8 TABLE : The values of per-call circuit rate, C/, iniu file size, θ, traffic load, ρ, call-blocking probability, P b, and utilization, U b, when =,, and, C = Gb/s, N λ = calls/sec, E[T setup ] = sec, β =, RT T = 5 s, r = Mb/s, and P loss = % C/ θ ρ P b U b Gb/s 9.975e9 bits (.6 GB) % 77.4% Mb/s 9.975e8 bits ( 8.9 MB) % 9.% Mb/s 9.975e7 bits (.89 MB) % 96.% TABLE : File-transfer delays when =,, and, C = Gb/s, N λ = calls/sec, E[T setup ] = sec, β =, RT T = 5 s, r = Mb/s, and P loss = %; for each file size, the iniu delay aong the three values is denoted with * File size Which path? Mean transfer delay (sec) e7 bits (.9 MB) or or Internet 5.5 e8 bits (.9 MB) or Internet 53.5 Circuit attepted.43* Internet e9 bits ( 9. MB) Circuit attepted 4.43* Circuit attepted 5. Circuit attepted 7.37 e bits (.6 GB) Circuit attepted 45.7* Circuit attepted 4.97 TABLE 3: Average delay reduction, R, and noralized average delay reduction per MB, R n, when =,, 59, and, C = Gb/s, N λ = calls/sec, E[T setup ] = sec, β =, RT T = 5 s, r = Mb/s, and P loss = % R (sec) R n (sec/mb) ( opt ) with a per-call circuit rate of Mb/s (corresponding to = ). For files of size between θ (.89 MB) and θ (8.9 MB), a circuit-setup attept with a percall circuit rate of Mb/s (corresponding to = ) yields the sallest delay. To find opt within the range to 5334, we use Fig. e to show the ipact of on R, the average delay reduction. The first and third ters of () produce opposing effects as is increased. On one hand, as increases, call-blocking probability, P b, decreases, which results in an increase of the first ter. On the other hand, an increase in causes the third ter to increase resulting in a decrease in R. When is increased fro to 59, P b decreases significantly, fro 49.9% to 4.33%, causing the first ter to have the larger ipact on R. However, when is increased fro 59 to larger values, P b decreases at a slower pace, causing the third ter to have the greater ipact. Fig. f shows the relation between R n, the average delay reduction per MB for files directed to the circuit network, and. Coparing Fig. f with Fig. e, we observe that the two plots have siilar trends. As shown in TABLE 3, the axiu R is 4.36 sec at = 59. At this operating point, R n = 3.95 sec/mb, which iplies that for files larger than the iniu file size, θ 59 (about MB), the average delay reduction per MB for files directed to the circuit network is 3.95 sec. In conclusion, it is not sufficient to siply deterine the effective throughput on the Internet path and use this value as a floor for the per-call circuit rate to achieve lower delays for individual transfers. Instead, the percall circuit rate and corresponding iniu file size should be deterined taking into account the overall syste perforance. For exaple, for a wide-area path with an RTT of 5 s, an Internet-path bottleneck link rate of Mb/s, and a packet loss rate of %, the optial per-call circuit rate for a Gb/s circuit-switched Gb/s opt Gb/s link is 63 Mb/s ( = 59 ) and the corresponding iniu file size is about 75 MB. The effective throughput on the Internet path in this exaple is only.87 Mb/s, but the optial per-call circuit rate obtained with our odels is 63 Mb/s. With this allocation, given our call-setup overhead consideration, only files larger than 75 MB are directed to the circuit-switched network. Files saller than this size unfortunately experience the slower rate on the IP-routed path, but by using circuit resources for only large files, the overall delay average is lowered. 4. Sensitivity analysis: aggregate call-arrival rate To study the sensitivity of the design paraeters to Nλ, the aggregate arrival rate of file-transfer requests,

9 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 9 TABLE 4: Sensitivity analysis to the aggregate call-arrival rate, Nλ ; all other paraeters are held unchanged except packet-loss rate, P loss, and the utilization factor, β. Nλ (calls/sec) P loss β opt θ opt (θ d or θ u?) P b U b R (sec) R n (sec/mb) 6.% MB (θ u ).3% 5.58% MB (θ u ).3% 5.68% % MB (θ u ).% 78.39% MB (θ u ).5% 78.53%.37.5 % MB (θ u ) 4.33% 9.68% % 59.6 MB (θ u ) 4.86% 97.5% % MB (θ u ) 5.% 98.8% average delay reduction (sec) 5 5 Nλ =9calls/sec, P loss =.3% Nλ =6calls/sec, P loss =.% Nλ =5calls/sec, P loss =% Nλ =3calls/sec, P loss =3% Nλ =calls/sec, P loss =% 3 4 Fig. 3: Sensitivity analysis to the aggregate call-arrival rate, Nλ ; all other paraeters are held unchanged except packet-loss rate, P loss we choose four other values of Nλ : 6 calls/sec, 9 calls/sec, 3 calls/sec, and 5 calls/sec. All other paraeters, except packet loss rate, P loss, are held at their base-setting values. A change in Nλ will have an effect on the offered traffic load to the IP-routed path, and thus on packet loss rate, P loss. An increase in Nλ not only increases the load sent to the IP-routed path directly, but also increases the percentage of requests routed to the IP-routed path due to increased call blocking by the circuit-switched network. As there is no analytical odel capturing the relation between Nλ and P loss, we (soewhat arbitrarily) rely on our intuition to select P loss values corresponding to Nλ values as listed in TABLE 4, with a goal of obtaining an understanding of the trends rather than absolute values for the design paraeters. For actual operation, this relationship needs to be characterized carefully. Fig. 3 shows that as Nλ increases, opt should be increased; in other words, lower per-call circuit rates should be assigned on the circuit-switched path. This is because r effective on the IP-routed path decreases due to increasing P loss. A higher value of results in lower call-blocking probability. While the increase of opt is evident in the right shift of the plots for higher values of Nλ in Fig. 3, the nubers are provided in TABLE 4. The corresponding iniu file size θ opt decreases, which eans ore transfers can use the circuit network without a negative ipact on utilization (our β factor). Our conclusion about the effect of call-arrival load is as follows. If the load is light, ideally, we should increase both the per-call circuit rate and lower the iniu file size. If we keep our utilization criterion, file-transfer duration to call-setup delay ratio, at the sae level as at high loads, then the overall syste perforance is iproved by allocating a higher per-call circuit rate, but the iniu file size increases in keeping with the higher per-call circuit rate. But, if we relax this criterion, given that at low loads the link will be under-utilized anyway, both objectives of increasing the per-call circuit rate and lowering the iniu file size can be achieved (see the β = rows in TABLE 4). 4.3 Sensitivity analysis: circuit-switched link capacity We decrease C to Gb/s fro Gb/s in the base setting, and keep all other paraeters at their base-setting values except the aggregate call-arrival rate, N λ, which is reduced to 9 calls/sec. This is because as C decreases, the ean call holding tie, /µ, increases for a given (see ()). To operate the network at reasonable values of call-blocking probability and utilization, we reduce N λ correspondingly to achieve alost the sae traffic load as in the base setting. We show the results in Fig. 4 and TABLE 5. Fig. 4 shows that when C is decreased to Gb/s, the axiu-allowed, ax, is 534. Naely, when is larger than 534, θ d, the delay-related crossover file size, approaches and thus R, the average delay reduction, equals. Copared with the base setting, the value of ax decreases an order of agnitude. Recall that per-call circuit rate, C/, should be larger than r effective, the expected effective throughput on the

10 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 TABLE 5: Sensitivity analysis to the circuit-switched link capacity, which is decreased to Gb/s, while all the other paraeters are the sae as in the base setting, except Nλ, which is decreased to 9 calls/sec; the base-setting row is denoted with ** C (Gb/s) Nλ (calls/sec) opt θ opt (θ d or θ u?) P b U b R (sec) R n (sec/mb) MB (θ u ) 4.3% 76.3% ** MB (θ u ) 4.33% 9.68% TABLE 6: Sensitivity analysis to RTT, which is decreased to s, while all the other paraeters are the sae as in the base setting; the base-setting row is denoted with ** RTT (s) opt θ opt (θ d or θ u?) P b U b R (sec) R n (sec/mb) MB (θ u ) 7.58% 79.66%.9.8 5** MB (θ u ) 4.33% 9.68% average delay reduction (sec) base setting: C=Gb/s, Nλ =calls/sec C=Gb/s, Nλ =9calls/sec average delay reduction (sec) RTT = s base setting: RTT=5s Fig. 4: Sensitivity analysis to the circuit-switched link capacity, which is decreased to Gb/s, while all the other paraeters are the sae as in the base setting, except Nλ, which is decreased to 9 calls/sec IP-routed path. Since we do not change the paraeters related to the IP-routed path but decrease C by an order of agnitude, ax should correspondingly decrease an order of agnitude to aintain the iniu per-call circuit rate. In contrast with ax, which shows a linear relation with C, opt does not. When we changed the link capacity fro Gb/s as in the base setting to Gb/s, the optial per-call circuit rate does not decrease by one-tenth. Instead the value drops fro 63 Mb/s to 35.7 Mb/s. The corresponding inial file size is 4 MB. This is because the absolute transfer-delay values change with this change in circuit-switched link capacity, but call setup delay was kept unchanged. This allows for use of the circuit network for saller files. 4.4 Sensitivity analysis: round-trip tie Since round-trip tie, RT T, has a significant ipact on the effective throughput, r effective, on the IP-routed Fig. 5: Sensitivity analysis to RTT, which is decreased to s, while all the other paraeters are the sae as in the base setting path, we study the effect of RT T on the design paraeters. We decrease RT T to s and keep all other paraeters at the base-setting values. As a result, r effective increases to Mb/s. To atch this increase in r effective, the per-call circuit rate should be increased, which results in a decrease of both ax (see Fig. 5) and opt (see TABLE 6). The corresponding iniu file size, θ opt, is still liited by the utilization-based criterion, and hence needs to be increased. Copared with the large-rtt base setting, the average delay reduction, R, is relatively sall. Two factors contribute to this saller value of R. First, r effective in this sall-rtt setting is uch larger than in the large- RTT setting, and thus the delay reduction per file transfer is itself saller. Second, the relatively large iniu file size, θ opt, liits the proportion of transfers that are directed to the circuit option. The optial per-call circuit rate is sensitive to RTT because TCP throughput on a loaded IP-routed path is sensitive to RTT. When considering short paths with an RTT of s (instead of 5 s as in the base setting), we

11 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 Optical Switching Node Router Site IP network Dynaic Circuit network Fig. 6: The Internet backbone topology found that the per-call circuit rate should be increased to 769 Mb/s (fro 63 Mb/s in the base setting) and the corresponding iniu file size increased to 97 MB. The iplication of this finding is that circuit rate allocations should be ade based on an estiate of RTT, which is a (relatively) easily deterined easure. 5 PRACTICAL CONSIDERATIONS In this section, we consider the question of how to translate the nuerical results fro Section 4 into a practical call-adission-control algorith. There are two issues: (i) dynaic data collection for the input paraeters, and (ii) use of this data to deterine the per-call circuit rate and iniu file size for different paths. As an illustration, we use the Internet backbone topology as shown in Fig. 6 [6]. This backbone consists of an IP-routed network, and a high-speed SONET-based circuit-switched network, referred to as the Dynaic Circuit (DC) network. As otivation for file transfer applications across just this backbone, consider Content Delivery Network (CDN) service. CDN servers are typically located in Points-of-Presence (PoPs) in ajor cities. Large file transfers occur between these CDN servers. We could conceivably use Internet s hybrid architecture to support file transfers between CDN servers, oving files below a coputed iniu file size across the IProuted path and larger files across the DC network. Using this exaple hybrid architecture, let us consider how to obtain easureents for the input paraeters of our odel. We listed three categories of input paraeters in Section 4. For the first set, paraeters related to the circuit-switched path, capacity on all links in the DC network is known to be Gb/s (OC9). Call-setup delay across different paths can be obtained through easureents as we did on the CHEETAH network [9]. Propagation delays can be obtained using ping between coputers at different PoPs. For the second category of input paraeters, those related to the IP-routed path, the packet loss rate, and RTT, could vary significantly on the sae path. More iportantly, we found that in new releases of server operating systes, different versions of TCP are being deployed. For exaple, Linux, by default, now runs BIC TCP [9], not TCP-Reno, which is the version on which the TCP odels used in our hybrid-architecture odel are based. Thus, if we obtained easureents for the input paraeters, bottleneck link rate (for which there are tools such as pathrate []), RTT, and packet-loss rate, and then used these in our odel, the predicted r effective ay vary significantly fro the actual throughput on the TCP/IP path. Therefore, we recoend a easureent-based approach rather than a odel-based approach. Specifically, we can ipleent software to run on end hosts (e.g., CDN servers) that collect file-transfer delay easureents for different file sizes across each path with tie-of-day tiestaps as transfers occur. This data can be uploaded to web services based network anageent systes (NMS) periodically. Given the daily cyclical nature of IP load, to obtain r effective on a specific path, the appropriate historical tie-of-day data can be requested fro the NMS. For the final set of paraeters, call-arrival rate and

12 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 file-size distribution, the forer can be tracked through Manageent Inforation Bases (MIBs), related to the signaling protocol, such as Resource reservation Protocol with Traffic Engineering (RSVP-TE), while the latter can be easured through collected traffic analysis on a slow cycle. call-arrival rates typically exhibit a well-known daily pattern of variation. These changes in call-arrival rate can be handled by a network anageent syste initiating changes in the paraeter settings based on the forecasted load on a periodic, e.g., hourly, basis. As for the second issue raised at the start of this section, i.e., deterination of per-call circuit rate and iniu file size, alternative designs are feasible. The end hosts that execute the file-transfer applications could run software to obtain data for input paraeters fro the web services based NMS to copute the per-call circuit rate and iniu file size, or switch controllers could be tasked to perfor this coputation. In the latter solution, end-host software issuing a request for circuit would siply indicate a axiu-acceptable data rate. For exaple, if a host has ordinary IDE disks and file systes that allow for a source and sink of data at approxiately 4 Mb/s, the application issuing the call-setup essage can indicate this axiu rate. The switch controller s call-adission-control algorith needs to then use the NMS databases to obtain RTT and other data to decide what circuit rate to allocate for this particular transfer. An issue of fairness between long-rtt and short-rtt paths arise. For exaple, the link between New York and Washington, DC, on the Internet backbone illustrated in Fig. 6 will be siultaneously shared by file transfers between these two locations (short-rtt path) as well as transfers between New York and Atlanta or other nodes on the southern route (long-rtt paths). If the calladission-control algorith treats both types of calls in the sae anner, then long-rtt paths will suffer fro a higher call-blocking probability than short-rtt paths because the forer needs resources to be allocated on a larger nuber of links. In such cases, typically algoriths such as trunk reservation schees are used to set a threshold and adit only long-rtt calls if link occupancy is at or higher than that threshold. We see such enhanceents to the basic call-adission-control algorith as a future work ite. 6 CONCLUSIONS This work enhanced our understanding of how to support file transfers on a hybrid network, consisting of a connectionless IP-routed network and a high-speed circuit-switched network. Specifically, we addressed the adission-control question of how to select an optial circuit rate per file transfer, and corresponding iniu file size. To deterine the optial values of these two design paraeters, we constructed a odel that cobines the Erlang-B call-blocking odel with TCP delay odels. We defined a etric called average delay reduction. Our goal was to deterine the optial values for the design paraeters at which the average delay reduction reaches a axiu. Our findings are as follows: (i) under high loads, the optial per-call circuit, at which the average delay reduction reaches a axiu, is considerably higher than the effective throughput on the TCP/IP path, which iplies that an adissioncontrol algorith based on benefitting the syste as a whole could penalize a certain range of files by denying the access to the high-speed circuit network, (ii) at low loads, higher per-call circuit rates should be allocated, and at the sae tie, by relaxing our utilization criterion on the file-transfer duration to call-setup delay ratio, the iniu file size can be siultaneously lowered, (iii) the optial per-call circuit rate and corresponding iniu file size are saller for lower-speed links, and (iv) the optial per-call circuit rate should be higher, along with the iniu file size, for short-rtt paths relative to long-rtt paths. APPENDIX A WELL-KNOWN QUEUEING THEORY RESULTS The call-blocking probability, P b, in an M/G// callblocking syste is given by the Erlang-B forula [] 3 : P b = ρ! ρ i i! i= (4) where ρ, the offered traffic load, is λ/µ, λ is the callarrival rate, and /µ is the ean call holding tie. The utilization, U b, of link L is given by: APPENDIX B TCP DELAY MODELS U b = ρ ( P b) (5) The ean file-transfer delay using TCP/IP over the Internet path, E[T tcp (x)], is obtained using the odels of [4], which capture four types of delays: (a) the tie spent in the initial slow start phase, E[T ss ], (b) the expected cost of recovery fro a packet loss at the end of the initial slow start phase, E[T loss ], (c) the expected tie to send the reaining data in the congestion avoidance phase, E[T ca ], and (d) the expected cost for the first delayed ACK, E[T delack ]. E[T tcp (x)] = E[T ss ] + E[T loss ] + E[T ca ] + E[T delack ] (6) The first two ters on the right hand side of (6) are derived as closed-for expressions in [4]. The third ter, E[T ca ], is priarily obtained fro the throughput odel 3. Recall that the Erlang-B forula holds for arbitrary holding tie distributions [].

13 JOURNAL OF IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, VOL. 6, NO., JANUARY 9 3 of [3]: B(P loss ) ( W in ax RT T, bploss 3bPloss RT T 3 +T in(,3 8 )P loss (+3Ploss ) ) (7) where the throughput B(P loss ) is expressed in the nuber of packets. The three key paraeters are round-trip tie, RT T, packet loss rate, P loss, and bottleneck link rate, r. The values chosen for these three paraeters are described in this paper. The other paraeters are selected as follows. First, we assue a axiu segent size, MSS, of 5 bytes. Second, we assue an ACK-everyother-segent strategy, i.e, the nuber of packets that are acknowledged by a received ACK, b, is set to be packets/ack. Third, we set the receiver s axiu window size, W ax, as the bandwidth delay product easured in packets (i.e., W ax = RT T r). Next, we choose the average duration of the first tieout in a sequence of one or ore successive tieouts, T, to equal. RT T. Finally, we assue that the sender s initial congestion window size is packets, and that the delayed acknowledgent cost, E[T delack ], is. ACKNOWLEDGMENTS This work was carried out under the sponsorship of NSF ANI-3359 grant. REFERENCES [] M. Veeraraghavan, X. Zheng, H. Lee, M. Gardner, and W. Feng, CHEETAH: Circuit-switched High-speed End-to-End Transport ArcHitecture, in Proc. of Optico 3, Proceedings of the SPIE, Dallas, TX, Oct. 3, pp [Online]. Available: [] M. Veeraraghavan and X. Zheng, A reconfigurable Ethernet/SONET circuit based etro network architecture, IEEE JSAC, vol., no. 8, pp , Oct. 4. [3] J. Padhye, V. Firoiu, D. Towsley, and J. Kurose, Modeling TCP throughput: A siple odel and its epirical validation, in Proceedings of the ACM SIGCOMM, Aug. 998, pp [4] N. Cardwell, S. Savage, and T. Anderson, Modeling TCP latency, in IEEE INFOCOM, Mar., pp [5] G. Karous-Edwards and A. Jukan, Eds., IEEE Coun. Mag., Special issue on An Optical Control Plane for the Grid Counity: Opportunities, Challenges, and Vision, vol. 44, no. 3, Mar. 6. [6] Internet Dynaic Circuit Network. [Online]. Available: http: // [7] ESnet On-deand Secure Circuits and Advance Reservation Syste (OSCARS). [Online]. Available: oscars/index.htl [8] X. Zheng, M. Veeraraghavan, N. S. V. Rao, Q. Wu, and M. Zhu, CHEETAH: Circuit-switched High-speed End-to-End Transport ArcHitecture testbed, IEEE Coun. Mag., vol. 43, no. 8, pp. 7, Aug. 5. [9] X. Zhu, X. Zheng, and M. Veeraraghavan, Experiences in ipleenting an experiental wide-area GMPLS network, IEEE JSAC, vol. 5, no. 4, pp. 8 9, Apr. 7. [] M. Veeraraghavan, X. Fang, and X. Zheng, On the suitability of applications for GMPLS networks, in Proc. of IEEE GLOBECOM, San Francisco, CA, Nov. 6, pp. 6. [] Baruch Awerbuch, Yossi Azar, Aos Fiat, Stefano Leonardi, Adi Rosn, On-line copetitive algoriths for call adission in optical networks, Algorithica, vol. 3, no., pp. 9 43,. [] Boudriga, N. and Obaidat, M.S., Adission control and resource anageent of uncertain duration traffic in optical networks, Electronics, Circuits and Systes, 3. ICECS 3. Proceedings of the 3 th IEEE International Conference on, vol. 3, pp. 8, Dec. 3. [3] Mosharaf, K. and Tali, J. and Labadaris, I., A call adission control for service differentiation and fairness anageent in WDM grooing networks, Broadband Networks, pp. 6 69, Oct. 4. [4] H. Wu, M. Zhou, and J. Gong, Investigation on the IP Flow Inter- Arrival Tie in Large-Scale Network, in Wireless Counications, Networking and Mobile Coputing, 7. WiCo 7. International Conference on, 7, pp [5] Allen B. Downey, Lognoral and Pareto distributions in the Internet, Coput. Coun, vol. 8, pp. 79 8, 5. [6] A. P. Mudabi, X. Zheng, and M. Veeraraghavan, A transport protocol for dedicated end-to-end circuits, in Proc. of IEEE ICC 6, Istanbul, Turkey, Jun. 6, pp [7] X. Fang and M. Veeraraghavan, On using circuit-switched networks for file transfers, in Proc. of IEEE GLOBECOM, New Orleans, LA, Nov. 8, pp. 6. [8] The Internet End-to-end Perforance Monitoring (IEPM) PingER History Tables. [Online]. Available: stanford.edu/cgi-wrap/table.pl [9] L. Xu, K. Harfoush, and I. Rhee, Binary increase congestion control for fast long-distance networks. in Proceedings of IEEE INFOCOM, Hong Kong, Mar. 4, pp [] Pathrate: a easureent tool for the capacity of network paths. [Online]. Available: Constantinos.Dovrolis/pathrate.htl [] M. Schwartz, Telecounication networks: protocols, odeling and analysis. Boston, MA: Addison-Wesley, 986. Xiuduan Fang received the BEng and MEng degrees in Coputer Science fro Fuzhou University, China in 999 and, respectively, and the MS and PhD degrees in Coputer Science fro University of Virginia in 6 and 8, respectively. She is a software engineer of Google Inc. Her research interests include dynaic high-speed circuit-switched network with ephasis on bandwidth sharing and perforance analysis. Malathi Veeraraghavan is a professor of the Charles L. Brown Departent of Electrical & Coputer Engineering at the University of Virginia. Dr. Veeraraghavan received her BTech degree fro Indian Institute of Technology (Madras) in 984, and MS and PhD degrees fro Duke University in 985 and 988, respectively. After a ten-year career at Bell Laboratories, she served on the faculty at Polytechnic University, Brookyln, New York fro Her current research work on optical networks is supported by NSF and DOE. She holds twenty-five patents and has received five Best-Paper awards. She served as the Technical Progra Coittee Chair for IEEE ICC.