(Summary of Talk at Hewlett-Packard) Amarnath Mukherjee. College of Computing. Georgia Institute of Technology. Atlanta, GA

Transcription

1 Trac Signatures for Network Engineering (Summary of Talk at Hewlett-Packard) Amarnath Mukherjee College of Computing Georgia Institute of Technology Atlanta, GA March 20, Introduction Trac over campus-level networks [4, 22, 29], larger multiplexing points such as NSFNET core switches [18], and variable bit-rate video applications [6, 13, 28] exhibit a slowly decaying autocorrelation function. Beyond its observed presence in measured data, there is mounting evidence [2, 3, 11, 13, 16, 21] that a slowly-decaying correlation structure is a trac property that (i) has measurable and practical impact on queueing behavior, (ii) plays a dominant role in a number of packet trac engineering problems (e.g., buer sizing, admission control, trac policing), and (iii) if ignored, typically results in overly optimistic performance predictions and inadequate network resource allocations. Protocols need to exist in this environment and need to be built for this environment. Generating representative workloads is, therefore, an important step towards eective simulations. Similarly, taking advantage of its correlation structure is essential to eective trac control algorithms. The objective of this article is to briey overview our talk, and present it in the context of related results. It is organized as follows. Section 2 presents two trac signature models: (i) a non-parametric trace-sampling model, and (ii) parametric timeseries models (seasonal ARIMA models). Section 3 presents related work in the eld. Section 4 discusses predictive control briey. Section 5 presents some concluding remarks. 2 Trac signature models We present below a couple of examples that illustrate how accurate trac can be generated using (i) trace-sampling, and (ii) a parameterized, seasonal ARIMA model (i.e., an Auto-Regressive Moving-Average model after non-random periodicities, if any, are removed through appropriate dierencing). We will observe through the examples a signicant impact on queue statistics when the arrival process is correlated as in real trac. Research supported by the National Science Foundation under grant NCR This is joint work with A. Adas (GT), S. Basu (Departmental of Statistical Sciences, Southern Methodist University) and S. M. Klivansky (GT). 1

2 2.1 Extracting application signatures with trace-sampling Trace-sampling [17] creates a desired mix of trac traces with statistical properties that are expected to match those of a proled network. The approach is fairly straight-forward and general. By way of example, we present the method we used for reproducing long-range dependence in TCP trac in the NSFNET Simulation Platform[17]. For generating TCP trac with a given proportion of dierent applications (nntp, ftp-data, smtp, etc.), we create a database for each TCP application (in our case, in S+), and store in it sampled conversations. Each sample consists of successive packet arrival times of an observed connection in a measured trace. To generate a trace with a desired trac mix of TCP applications, we sample conversations from the database with the appropriate frequency, and for simplicity, make the inter-conversation arrival times Poisson distributed. The latter is not completely true in observed trac, but it does not appear to make much dierence in packet-level trac statistics and queue statistics. An example of a real trac trace from an NSFNET CNSS and the corresponding trace-sampled trac are shown in Figure 1. A Poisson model is shown for contrast. The data has been aggregated to a level where the Poisson model `attens out' by the law of large numbers. We observe that the match between real and sampled trac is fairly good in most statistics except possibly in the small peaks and valleys in their auto-correlation functions that do not coincide at the same lag values. To see the performance accuracy of trace-sampled trac, Figure 2 shows the 95-percentile of queue length distributions from the three traces. We observe that real and trace-sampled trac are fairly close to each other. The accuracy of sampling of course depends on the representativeness of the database of application signatures. For example, if we have an extremely loud conversation in a trac trace with no parallel in the database (or even if we have it, if it is not sampled), the results will be less accurate. The method of trace-sampling appears to be general enough to apply to other network environments. One needs a way to identify addressable entities that generate trac. For example, for a connection-oriented network, one needs to store the packet arrival timestamps and associate them with a connection identier. For connectionless networks, one may use the host-pair identity and a time-out to create pseudo connections and store timestamps accordingly. For multi-cast communications, one may use a tree routed at the source to generate packet arrivals for a source. (Of course, routing and destination group selection problems will still need to be addressed.) What needs to be accurately modeled depends on the problem being studied. For example, trace-sampled trac is already congestion-controlled, and is therefore, not appropriate for studying congestion control tcplib style statistics [10] is more appropriate in this case. Hence, for the same trac data, multiple library databases are likely to be appropriate, and will be investigated. We expect to draw on our resource management work to determine the issues that are likely to be of interest for a trac library. 2.2 Parameterized trac models We consider next an example of a seasonal ARIMA based parametric model for generating sourcelevel trac, appropriate for studying media access protocols currently being considered for upstream channel access in community networks (by the IEEE standards body). The method was also found to apply to a fairly large class of aggregated Internet trac data. The attached paper [4] gives models and parameter estimates for trac over two campus FDDI rings, an Ethernet, several NSFNET external interfaces, and aggregate trac from popular TCP protocols. Thus far, we have found it to not apply only to aggregate FTP-data trac, for which the burstiness is signicantly larger than these models can capture. 2

3 Real seconds Trace-Sampled seconds Poisson seconds Series: real Rescaled Adjusted Range plot slope=1.0 slope= slope= log10(d) H = Series: sampled Rescaled Adjusted Range plot slope=1.0 slope= slope= log10(d) H = Series: pois Rescaled Adjusted Range plot slope=1.0 slope= slope= log10(d) H = log10(r/s) log10(r/s) log10(r/s) Series : real Series : sampled Series : pois Figure 1: Comparison of real trac with trace-sampled trac from the NSFNET. A Poisson generated stream is shown to provide contrast. The plots show the arrival timeseries, the R/S analysis estimates, the histogram of the arrival processes, and their autocorrelation functions (in that order). The arrival time-series is aggregated over 2-seconds, yet they are bursty (as compared to the Poisson model). 3

4 95% Queue Length Dist Real Trace-Sampled Poisson Utilization Figure 2: 95-percentile of queue length distribution versus mean utilization for real trac, tracesampled trac, and Poisson trac. Observe that the y-axis is in log scale. Therefore, capacity planning using a Poisson trac will seriously under-estimate buer-overow probabilities. The trac data we use in this example is from the GT FDDI backbone. The level of heterogeneity in sources is seen from a 100-sec interval the number of packets transmitted by the top ten sources were as follows. Source-id # Packets in (0; 100] sec Source-id # Packets in (0; 100] sec When the number of packets is aggregated over periods of 0:01-seconds, trac from Source 2 shows a period at lag 4: See it's auto-correlation function in Figure 3. An enlarged plot (not shown) with a larger number of lags on the x-axis shows another potentially period at lag 20: If this series is denoted fy t ; (t = 1; 2; )g; the dierenced sequence fy t = Y t? Y t?4 g shows a correlation at lag 4 and a smaller one at lag 20: y t can therefore, be potentially modeled as an Auto-Regressive Moving-Average (ARMA) process. Two potential models suggest themselves (see [5]): y t = a t? 4 a t?4 ; or (1) y t = a t? 4 a t?4? 20 a t?20 ; (2) where fa t g is a sequence of uncorrelated random variables and 0 s are parameters that need to be i estimated. Once these are estimated, the series fy t g can be generated using (1) or (2), and the distribution of a t : The latter is derived from the data as well see [4] (attached paper). Next fy t g may be generated using Y t = Y t?4 + y t : Some numerical problems arise with such a summation, similar to noise propagation in numerical integration. A detailed look at the problem of generating non-negative integer sequences and a solution are presented in [4]. The end-result is that for Y t > 0; 4

5 Series : Y(t) Series : Y(t) - Y(t-4) Figure 3: Left: auto-correlation function of original sequence fy t g shows a potential period at lag 4: Right: auto-correlation function of dierenced sequence fy t? Y t?4 g damps out for most lags (except lags 4 and 20), and may potentially admit to an Auto-Regressive Moving-Average (ARMA) model quantile of queue 0.95 quantile of queue length mean load points=generated, lines=trace Figure 4: 95-percentile of queue length distribution versus mean utilization for seasonal ARIMA model of Source 2. Points correspond to the generated sequence. The solid line corresponds to the real trace. it is truncated with a probability u and rounded with probability (1?u); where u is derived from the data by minimizing a weighted objective function that attempts to match the correlation structure of the generated sequence with that of the real trac data. In practice we have found it to be in the range 0:1? 0:3: If Y t < 0; however, it is set to zero (boundary condition). For our example trac source, parameter estimates were found to be ^ 4 = 0: in Eq. (1), and (^ 4 ; ^ 20 ) = (0:967855; 0:012218) in Eq. (2). u was 0:15 in both cases. The performance of the second model and that of the trace data are shown in Figure 4. It was found that Eq. (2) produced more accurate results than Eq. (1). At mean utilization levels of 0:9 or higher, however, even Eq. (2) is not satisfactory. More study is needed to determine accurate models in this regime. Based on the absolute values for the measured trac, however, systems running at this load level would not give acceptable performance. To complete the example, Figure 5 shows a section of the trac trace and its auto-correlation function, and Figure 6 shows the corresponding plots for a synthetic non-negative integer sequence using a seasonal ARIMA model with degree of dierencing equal to 4: While no agreement can be 100%, the generation does not appear to be too inaccurate. A discrepancy at lag 20 still exists, and needs more work. For the theory behind generation (and noise suppression), please see [4]. The appendix in that paper also gives a list of seasonal ARIMA models for aggregate data trac from 5

6 Section of trace data t #Packets Series : Trace Figure 5: Section of trace data (Source 2 in Section II-D), and its. Section of generated sequence t #Packets Series : Generated Figure 6: Section of corresponding generated sequence and its. FDDI, Ethernet, NSFNET External Interfaces and popular TCP protocols. 3 Related Work Properties of network trac have been the subject of considerable recent interest, see for example [8, 7, 9, 18, 22, 29, 30]. Our current approach is to model dierenced series as ARMA processes. Dierencing makes a non-stationary series stationary when there is a drift in the data. However, not all classes of non-stationarities admit a dierencing strategy. Some example datasets are given in [4]. These show quite a few non-random periodicities that are dicult to capture with seasonal models. In [4], we were able to model Bellcore's Ethernet trac data as seasonal ARIMA processes with a non-random period of approximately 80msec. This trac data has also been shown [22, 35] to possess the properties of a second-order self-similar process which is dened as a widesense stationary process (constant, time-independent, mean, variance and auto-covariance function) possessing long-memory (sum of the auto-correlations diverge), and further, the auto-correlation function is the same for all time scales over which the data is aggregated. The self-similar/longmemory model has subsequently led to insights into the burstiness properties of individual TCP connections that constitute aggregate trac [18, 29] based on processes that are known to 6

7 be second-order self-similar. For instance, the distribution of connection lifetimes and number of packets transmitted are both heavy-tailed, the latter being close to a Pareto distribution: F (x) = 1? x? ; with 1 < < 2; (which leads to a nite mean and innite variance; in practice the estimated variance can never be innite for nite datasets, but they are large). On the other hand, the models that we study are adequate and appropriate for the purposes of generating and forecasting. However, no model is true reality, and its usefulness lies in one's ability to ask and obtain answers to questions of interest from the model. Alternative models and paradigms allow for answering dierent questions on the same real phenomenon. The theoretical assumptions for the two models are dierent. Second-order self-similar models are dened for the family processes that are wide-sense stationary. The correlations for these processes extend into far lags, and by denition, the sum of their autocorrelations diverge. ARMA models for the dierenced sequences, on the other hand, result in the original sequence to be nonstationary. In practice, whether the mean, the variance and the auto-covariance are all stationary or non-stationary is often dicult to determine. Both classes of models appear to be useful, and although, theoretically, stationarity and non-stationarity are exclusive of one another, we believe that they ought to be considered inclusively in modeling repertoire (based on the results obtained from the two classes on the same datasets). In other related work on Internet trac, Clay et al studied ow-parameterization and trac characteristics of the T1 NSFNET backbone [7, 9]. Danzig et al [10] developed a trac library for TCP conversations based on empirical burst distributions they studied in [8]. Klivansky et al studied the impact of dierent factors on potential long-range dependence in aggregate TCP trac over NSFNET core switches, see [18]. Paxson developed statistical distributions for TCP burst distributions, see [30]. Paxson and Floyd reported signicant dependence among conversation arrivals for specic TCP protocols (e.g., for FTP-data and NNTP conversations), and independence among others (e.g., for TELNET and FTP-control conversations). They also showed that Danzig et al's TCP trac library produces similar variance-time plots as measured TCP trac, see [29]. Willinger et al [35] explained the presence of self-similarity in trac auto-correlation structure at multiple time-scales through a heavy-tailed distribution of source on-periods. Trac traces on variable bit-rate video have been collected and studied by several research groups, for example, [6, 12, 13, 19, 20, 28, 33, 34]. Some of the earlier studies (e.g., [33, 34]) have provided interesting data. The studies in [19, 20] model VBR video trac as TES processes [15]. The study in [20] investigates a hierarchically encoded video stream with two priorities. The studies in [6, 12, 13, 28] provide the important insight that there exists a slowly decaying auto-correlation function in many VBR video applications. TES processes [15] provide an alternate parametric method for short-memory trac with arbitrary marginal distributions. ARMA and TES models should be considered as non-exclusive alternatives for model forms. The above trac studies are an excellent resource to the networking community. However, there is still a need for a larger and broader base of applications for realistic evaluation of protocols 7

8 for quality of service guarantees. Their signatures need to be understood and used in studying resource management (e.g., in predictive controls, admission control, policing). Regarding control algorithms, networking algorithms that we are aware of do not really attempt to exploit the correlation structure in the underlying trac. Example studies are [14, 23, 24, 25, 27, 31, 32]. The studies in [23, 32] develop a controller of the class discussed under sender-initiated controls, assuming a known ARMA model. However, since trac data is not used, no attempt is made to match models with measured trac signatures. Our experience is that (i) accurate trac models are a pre-requisite for eective prediction, and apparently small model inaccuracies can lead to signicant departure in performance, and (ii) the precise denition of the problem depends on where the control is initiated (sender-initiated versus network or receiver-initiated, because of dierent information available, and dierent objectives) [1, 26]. 4 Predictive Control 4.1 Sender-initiated forecasting For trac with a slowly decaying auto-correlation function, static channel and buer allocations are likely to result in low utilizations; a dynamic allocation strategy is necessary. Studies have shown that multiplexing gains are also dependent on the coecient of variation of the number of arrivals in a xed interval [2, 13], although precise queueing results on this are not yet available. Therefore, sender-initiated forecasting for adaptive bandwidth reservation are likely to be more eective at end-points where the coecient of variation is typically larger (e.g., through adaptive leaky bucket token rates). In order to achieve a forecast, it is necessary at time n to forecast and reserve a portion of channel and switch buers for a future time-point n + j given the history until time n: In a recent paper [1], A. Adas (Ph.D. student working with AM) studies the performance of several prediction algorithms applied to six one-half-hour MPEG-I traces (made available in the public domain by Oliver Rose). One such algorithm, the Normalized Least Mean Square (NLMS) computes weights of the prediction lter adaptively, so (i) it does not require advanced knowledge of the auto-correlation structure of the arrival process, and (ii) it adapts to changing levels due to scene changes in the video stream without knowing anything of the contents. The relative buer-sizes with xed and adaptive reservations are shown in Figure 7. Note that the y-axis scales are markedly dierent. A signicant reduction in the queue length process is achieved with adaptive reservation. See also Tables 1 and 2. The forecast ^Xn+j can be chosen so as to minimize the mean squared error dened as E[( ^X n+j? X n+j ) 2 ]. However, this can lead to unacceptable performance, especially for heavytailed distributions. We investigate methods for forecasting the uth percentile (at the higher tails) of the distribution of X n+j given the past history (X 1 ; ; X n ) in [4]. This amounts to obtaining an accurate predictive distribution of X n+j and obtaining the appropriate percentiles from the predictive distribution. As an illustration of how the forecast compares with true values, consider an example trace of aggregate SMTP trace over the Georgia Tech campus FDDI backbone. We look at 15 minute segments of the data separately. Dierent percentile values used in the forecast, and corresponding observed under-forecasts are shown in Table 3. See [4] for details. Online updating of the parameter values that are used in the forecast function is important, and need to be investigated. 8

9 U Sequence 50-percentile 75-percentile 99.9-percentile 0:9 Jurassic Park Star Wars Gold Finger Terminator Talk Show Soccer :8 Jurassic Park Star Wars Gold Finger Terminator Talk Show Soccer Table 1: Queue length percentiles for dierent mean utilizations, U; when bandwidth reserved is xed. U Sequence 50-percentile 75-percentile 99.9-percentile one twelve one twelve one twelve 0:9 Jurassic Park Star Wars Gold Finger Terminator Talk Show Soccer :8 Jurassic Park Star Wars Gold Finger Terminator Talk Show Soccer Table 2: Queue length percentiles for dierent mean utilizations, U; when bandwidth reserved is dynamic. The column `one' refers to using a one-frame-ahead prediction. The column `twelve' refers to a 12-frame prediction. In general, the further away the forecast is, less its accuracy. Data Period % Under-forecasts (u) 0:5 0:8 0:9 0:95 0:99 First 15-min 41:7 19:1 11:3 5:3 1:8 Second 15-min 40:8 13:3 5:1 1:9 0:1 Third 15-min 43:7 22:8 13:6 8:0 1:6 Fourth 15-min 45:0 18:4 9:4 5:0 0:6 Table 3: Percent of times the forecasting procedure under-forecasted using the one step ahead forecast for an SMTP trace data. u is the percentile used to forecast as given in [4]. The results are based on 1000 out-of-sample forecasts. 9

10 Jurassic Park Kbits Kbits (a) (b) Jurassic Park Figure 7: Queue length process for the Jurassic Park movie (a) Fixed reservation (b) Dynamic reservation using 1-step NLMS prediction. 4.2 Network-initiated or receiver-initiated control In [26], hop-by-hop ow control of aggregate upstream trac is studied in the context of current Internet trac models. For each multiplexing point, control decision is centralized at the downstream side of transmission. Two optimization models over a nite time horizon are considered. One assumes a time-series model for the arrival process at a down-stream station; the other assumes a Brownian motion model for it. For time-series based models, equations relating (i) current and previous assigned-rates to each of the upstream switches, and (ii) corresponding departures from these switches over a time horizon, are investigated. A number of such transfer-function models are necessary, and their precise formulation is dictated by the desired optimization formulation. Model parameter estimates for example Internet trac traces are developed. The modeling method admits feedback delay. However, prediction accuracy decays with the distance between the current time and the time for which a prediction is desired. The transfer-function based approach has been applied in other engineering domains. Box et al [5] give an example of controlling the rate of reaction in a chemical plant by controlling an oxygen feed for which a transfer function between oxygen feed-rate and reaction rate is rst developed. This study needed to control one variable (reaction rate), so the model form was simple and elegant. The need to control multiple entities simultaneously requires multiple transfer functions, and makes the networking problem more challenging. This method may also have potential in receiver-initiated control, and needs to be investigated. 5 Concluding Remarks It is important to measure, characterize, and create trac libraries from emerging applications from dierent networks, each providing a window into a class of new signatures. These need to be put into a database of application signatures suitable for studying and validating resource management algorithms. Such a trac library and associated statistical models are of practical interest in the management of broadband networks. In conjunction with signature databases generated by colleagues in the community, our trac 10

11 signature library can serve as the network equivalent of standardized benchmarks that are currently available in the Database and Processor worlds. At some point in future, these could be used to study (and perhaps enable) quality of service across multiple network providers. Based on current knowledge of trac and the need to provide dependable quality of service to multi-media applications, a multi-disciplinary eort between Networking and Statistics appears to be a necessity. Our research and that of colleagues in the networking community, is addressed to meet this need. Acknowledgment This is joint work with A. Adas (GT), S. Basu (Departmental of Statistical Sciences, Southern Methodist University), and S. M. Klivansky (GT). References [1] A. Adas, \Supporting real time VBR video using dynamic reservation based on linear prediction," Proc. IEEE INFOCOM, San Francisco, March 1996 (to appear). [2] Adas, A. and A. Mukherjee, \On resource management and QoS guarantees for long range dependent trac," Proc. IEEE INFOCOM, pp , Boston, April Extended version: reports/index.94.html/git-cc [3] Adas, A. and A. Mukherjee, \Delay-jitter bound and statistical loss bound for heterogeneous correlated trac architecture and equivalent bandwidth," College of Computing Technical Report GIT-CC-96-6, Georgia Inst. of Technology. (In preparation for IEEE Journal on Selected Areas in Communications, special issue on supporting heterogeneous VBR video, due date: April 15, 1996.) reports/index.96.html/git-cc [4] Basu, S., A. Mukherjee and S. M. Klivansky, \Time-series models of Internet trac," (in review), IEEE Transactions on Networking. Preliminary version to appear in Proc. IEEE IN- FOCOM, San Francisco, March 1996 (to appear). Also College of Computing Tech Report GIT- CC-95-27, July ( reports/index.94.html/git-cc ) [5] Box, G.E.P, G.M. Jenkins, and G.C. Reinsel, Time series analysis: forecasting and control, Prentice Hall, [6] Beran, J., R. Sherman, M.S. Taqqu and W. Willinger, \Variable-bit-rate video trac and long-range dependence," accepted for publication in IEEE Trans. Networking, [7] Clay, K. C., H. W. Braun, and G. C. Polyzos, \A parameterizable methodology for Internet trac proling," IEEE Journal on Selected Areas in Communications. [8] Caceres, R., P.B.Danzig, S.Jamin and D.J.Mitzel, \Characteristics of wide-area TCP/IP conversations," Proc of ACM Sigcomm, pp , Zurich, Sept [9] Clay, K. C., G. C. Polyzos and H. W. Braun, \Trac characteristics of the T1 NSFNet backbone," Proc. IEEE Infocom, San Francisco, [10] Danzig P. B., S. Jamin, R. Caceres, D.J. Mitzel, and D. Estrin, \An Empirical Workload Model for Driving Wide-Area TCP/IP Network Simulations", Journal of Internetworking: Practice and Experience, 3; No. 1, March

12 [11] A. Erramilli, O. Narayan and W. Willinger, \Experimental queuing analysis with long-range dependent trac," Preprint, September 28, [12] Garrett, M., \Contributions toward real-time services on packet-switched networks," Ph.D. Thesis, Columbia University, [13] Garrett, M., and W. Willinger, \Analysis, modeling and generation of self-similar VBR video trac," Proc. ACM Sigcomm, pp , London, [14] Jacobson, V., \Congestion avoidance and control," Proc. of the ACM Sigcomm, pp , Aug [15] D.L. Jagerman and B. Melamed, \The Transition and Autocorrelation Structure of TES Processes Part I: General Theory", Stochastic Models 8, , [16] Jelenkovic, P. R., and A. A. Lazar, \On the Dependence of the Queue Tail Distribution on Multiple Time Scales of ATM Multiplexors," Proceedings of the 1995 Conference on Information Sciences and Systems, The Johns Hopkins University, Baltimore, MA, March 22-24, [17] Klivansky, S. M., and A. Mukherjee, \Disclosure on trac-models for performance analysis of a class of wide-area network problems." Provisional patent led with the US patent oce under the title \Trace-Sampling," serial number 60/005,112, July [18] Klivansky S., A. Mukherjee and C. Song, \On long-range dependence in NSFNET trac," 7th IEEE LAN/MAN Conference, Marathon, March Also, College of Computing Tech Report GIT-CC-94-61, December ( reports/index.94.html/git-cc ) [19] Lazar, A. A., G. Pacici and D. E. Pendarakis, \Modeling Video Sources for Real Time Scheduling," Multimedia Systems, 1, 6, , April [20] Lee, D. S., B. Melamed, A. R. Reibman and B. Sengupta, \TES modeling for analysis of a video multiplexor," Performance Evaluation, 16, 21-34, [21] Livny, M., B. Melamed and A.K. Tsiolis, \The impact of auto-correlation on queueing systems," Management Science, pp , March [22] Leland, W.E., M.S. Taqqu, W. Willinger and D.V. Wilson, \On the self-similar nature of Ethernet trac (extended version)," IEEE Trans. Networking, 2, (1), 1-15, February, [23] Mishra, P.P., and H. Kanakia \A hop-by-hop rate-based congestion control scheme," Proc. ACM Sigcomm, Baltimore, pp , August [24] Mitra, D. and J. Seery, \Dynamic adaptive windows for high speed data networks: theory and simulations," Proc. ACM Sigcomm, pp 30-37, Philadelphia, September [25] Mitra, D., \Asymptotically optimal design of congestion control for high speed data networks," IEEE Trans. Commun., 40, (2), , February [26] Mukherjee, A., and B. Sengupta, \Modeling considerations in the rate assignment of heterogeneous aggregate trac streams," (in preparation). 12

13 [27] Mukherjee, A. and J.C. Strikwerda, \Analysis of Dynamic Congestion Control Protocols A Fokker-Planck Approximation," Journal of High Speed Networks, 3, (1), 1994, (Previously appeared in Proc. ACM Sigcomm, Zurich, pp , September 1991.) [28] Pancha P., and M. El Zarki, \Variable bit rate video transmission\ IEEE Commun. Mag., Vol.32, No.5, pp , May [29] Paxson, V. and S. Floyd, \Wide-area trac: the failure of Poisson modeling," IEEE/ACM Trans. on Networking, 3, (3), , June [30] Paxson, V., \Empirically-derived analytical models of wide-area TCP connections: extended report," IEEE/ACM Transactions on Networking, 2, (4), , August [31] Ramakrishnan, K.K., and R. Jain, \A Binary Feedback Scheme for Congestion Avoidance in Computer Networks with a Connectionless Network Layer," ACM Trans. Computer Systems, vol. 8, pp , May [32] Ramamurthy, G., and B. Sengupta, \A predictive congestion control policy for high-speed wide-area networks," Proc. IEEE INFOCOM, San Francisco, [33] Sen, P., B. Maglaris, N.E. Rikli and D. Anastassiou, \Models for packet switching of variablebit-rate video sources," IEEE Journal on Selected Areas in Communications, pp , [34] Verbiest, W., and Pinnoo, L., \A Variable Bit Rate Video Codec for Asynchronous Transfer Mode Networks," IEEE Journal on Selected Areas in Communications, Vol. 7, pp , June [35] W. Willinger, M.S. Taqqu, R. Sherman, and D. Wilson, \Self-similarity through highvariability: statistical analysis of Ethernet LAN trac at the source level," Proc. ACM Sigcomm,, pp , Boston, Aug