Daniel P. Heyman

AT&T Labs, Austin, Texas, United States

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Publications (27)16.24 Total impact

  • Source
    D.P. Heyman, D. Lucantoni
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    ABSTRACT: We start with the premise, and provide evidence that it is valid, that a Markov-modulated Poisson process (MMPP) is a good model for Internet traffic at the packet/byte level. We present an algorithm to estimate the parameters and size of a discrete MMPP (D-MMPP) from a data trace. This algorithm requires only two passes through the data. In tandem-network queueing models, the input to a downstream queue is the output from an upstream queue, so the arrival rate is limited by the rate of the upstream queue. We show how to modify the MMPP describing the arrivals to the upstream queue to approximate this effect. To extend this idea to networks that are not tandem, we show how to approximate the superposition of MMPPs without encountering the state-space explosion that occurs in exact computations. Numerical examples that demonstrate the accuracy of these methods are given. We also present a method to convert our estimated D-MMPP to a continuous-time MMPP, which is used as the arrival process in a matrix-analytic queueing model.
    IEEE/ACM Transactions on Networking 01/2004; · 2.01 Impact Factor
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    ABSTRACT: With the rapid growth of Internet applications built on TCP/IP such as the World Wide Web and the standardization of traffic management schemes such as Available Bit Rate (ABR) in Asynchronous Transfer Mode (ATM) networks, it is essential to evaluate the performance of feedback-based protocols using traffic models which are specific to dominant applications. This paper presents a method for analyzing feedback-based protocols with a Web-user-like input traffic where the source alternates between ‘transfer’ periods followed by ‘think’ periods. Our key results, which are presented for the TCP protocol, are as follows: (1) When the round-trip time is the same for all users, the goodputs and the fraction of time that the system has some given number of transferring sources are insensitive to the distributions of transfer (file or page) sizes and think times except through the ratio of their means. Thus, apart from network round-trip times, only the ratio of average transfer sizes and think times of users need be known to size the network for achieving a specific quality of service. (2) The Engset model can be adapted to accurately compute goodputs for TCP and TCP over ATM, with different buffer management schemes. Though only these adaptations are given in the paper, the method based on the Engset model can be applied to analyze other feedback systems, such as ATM ABR, by finding a protocol specific adaptation. Hence, the method we develop is useful not only for analyzing TCP using a source model significantly different from the commonly used persistent sources, but also can be useful for analyzing other feedback schemes. (3) Comparisons of simulated TCP traffic to measured Ethernet traffic shows qualitatively similar second order autocorrelation when think times follow a Pareto distribution with infinite variance. Also, the simulated and measured traffic have long range dependence. In this sense our traffic model, which purports to be Web-user-like, also agrees with measured data traffic.
    Computer Communications. 01/2003;
  • Hans-peter Schwefel, Daniel Heyman
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    ABSTRACT: Despite the fact that most of todays' Internet traffic is transmitted via the TCP protocol, the performance behavior of networks with TCP traffic is still not well understood. Recent research activities have lead to a number of performance models for TCP traffic, but the degree of accuracy of these models in realistic scenarios is still questionable. This paper provides a comparison of the results (in terms of average throughput per connection) of three different `analytic' TCP models: I. the throughput formula in [Padhye et al. 98], II. the modi ed Engset model of [Heyman et al. 97], and III. the analytic TCP queueing model of [Schwefel 01] that is a packet based extension of (II). Results for all three models are computed for a scenario of N identical TCP sources that transmit data in individual TCP connections of stochastically varying size. The results for the average throughput per connection in the analytic models are compared with simulations of detailed TCP behavior. All of the analytic models are expected to show deficiencies in certain scenarios, since they neglect highly inuential parameters of the actual real simulation model: The approach of Model (I) and (II) only indirectly considers queueing in bottleneck routers, and in certain scenarios those models are not able to adequately describe the impact of buffer-space, neither qualitatively nor quantitatively. Furthermore, (II) is insensitive to the actual distribution of the connection sizes. As a consequence, their prediction would also be insensitive of so-called long-range dependent properties in the traffic that are caused by heavy-tailed connection size distributions. The simulation results show that such properties cannot be neglected for certain network topologies: LRD properties can even have counter-intuitive imp...
    Proc SPIE 10/2001;
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    ABSTRACT: Despite the fact that most of todays' Internet traffic is transmitted via the TCP protocol, the performance behavior of networks with TCP traffic is still not well understood. Recent research activities have lead to a number of performance models for TCP traffic, but the degree of accuracy of these models in realistic scenarios is still questionable. This paper provides a comparison of the results (in terms of average throughput per connection) of three different `analytic' TCP models: I. the throughput formula in [Padhye et al. 98], II. the modified Engset model of [Heyman et al. 97], and III. the analytic TCP queueing model of [Schwefel 01] that is a packet based extension of (II). Results for all three models are computed for a scenario of $N$ identical TCP sources that transmit data in individual TCP connections of stochastically varying size. The results for the average throughput per connection in the analytic models are compared with simulations of detailed TCP behavior. All of the analytic models are expected to show deficiencies in certain scenarios, since they neglect highly influential parameters of the actual real simulation model: The approach of Model (I) and (II) only indirectly considers queueing in bottleneck routers, and in certain scenarios those models are not able to adequately describe the impact of buffer-space, neither qualitatively nor quantitatively. Furthermore, (II) is insensitive to the actual distribution of the connection sizes. As a consequence, their prediction would also be insensitive of so-called long-range dependent properties in the traffic that are caused by heavy-tailed connection size distributions. The simulation results show that such properties cannot be neglected for certain network topologies: LRD properties can even have counter-intuitive impact on the average goodput, namely the goodput can be higher for small buffer-sizes.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
    07/2001;
  • Source
    Daniel P. Heyman
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    ABSTRACT: Measurements of file sizes transported on the World-Wide-Web have led some researchers to propose describing them by probability distributions with infinite variance. The M/G/1 queue often arises as a performance model for components of the WWW, and the service times correspond to file sizes; the infinite variance of the file sizes becomes the variance of the service times. In this paper the effects of very large service-time variances on some performance measures for the M/G/1 queue are explored via numerical examples and analytic arguments.The first main conclusion is that it is the form of the service-time distribution over a wide finite range that controls the steady-state queueing performance, so distributions with very large finite variances can yield the same behavior as distributions with infinite variances. The second main conclusion is that very large service-time variances cause the rate of approach to steady-state performance to be so slow that steady-state performance measures are not likely to be of engineering interest. A third conclusion is that a common device of using the probability that the work in an infinite queue exceeds the level b to approximate the probability that a finite buffer of size b overflows may be very inaccurate. The approximation works better for the fat-tailed distributions studied than for the others.The most important engineering implication of these results is that when service times have a very large variance (such as file transfers on the WWW), performance criteria other than steady-state measures have to be used.
    Proc SPIE 01/2000; 40:47-70.
  • Daniel P. Heyman
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    ABSTRACT: Data teletraffic is characterized by bursty arrival processes. Performance models are characterized by a desire to know under what circumstances is the probability that an arrival finds a full input buffer very small. In this paper I examine how four models proposed in the literature perform on two data sets of local area network traffic. Among my conclusion are (1) the protocol governing the data transmission may have a substantial effect on the statistical propoerties on the packet stream, (2) approximating the probability that a finit buffer of size b overflows may not be adequately approximated by the probability that an infinite buffer has at least b packets in it, and (3) a data-based estimate of large-deviation rate-function does the best job of estimating packet loss on these data sets. This method may overestimate the loss rate by several orders of magnitude, so there is room for further refinements.
    Proc SPIE 01/1998;
  • D.P. Heyman
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    ABSTRACT: Heyman (1992) examined three sequences giving the number of cells per frame of a VBR encoding of videoconferences (talking heads); these sequences were produced by hardware encoders using different coding algorithms. Each sequence had a gamma marginal distribution, and the autocorrelation function was geometric up to lags of at least 3 s, which includes all autocorrelation values larger than 0.1. We present an easy to simulate autoregressive process that has these properties. The model is tested by comparing the cell-loss rate produced when the data trace was used as the sole source in a simulation of an ATM switch to the cell-loss rates produced when traces generated by the model were used as the source
    IEEE/ACM Transactions on Networking 09/1997; 5(4):554-560. · 2.01 Impact Factor
  • Source
    Daniel P. Heyman, T. V. Lakshman, Arnold L. Neidhardt
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    ABSTRACT: Most of the studies of feedback-based flow and congestion control consider only persistent sources which always have data to send. However, with the rapid growth of Internet applications built on TCP/IP such as the World Wide Web and the standardization of traffic management schemes such as Available Bit Rate (ABR) in Asynchronous Transfer Mode (ATM) networks, it is essential to evaluate the performance of feedback-based protocols using traffic models which are specific to dominant applications. This paper presents a method for analysing feedback-based protocols with a Web-user-like input traffic where the source alternates between "transfer" periods followed by "think" periods. Our key results, which are presented for the TCP protocol, are:(1) The goodputs and the fraction of time that the system has some given number of transferring sources are insensitive to the distributions of transfer (file or page) sizes and think times except through the ratio of their means. Thus, apart from network round-trip times, only the ratio of average transfer sizes and think times of users need be known to size the network for achieving a specific quality of service.(2) The Engset model can be adapted to accurately compute goodputs for TCP and TCP over ATM, with different buffer management schemes. Though only these adaptations are given in the paper, the method based on the Engset model can be applied to analyze other feedback systems, such as ATM ABR, by finding a protocol specific adaptation. Hence, the method we develop is useful not only for analysing TCP using a source model significantly different from the commonly used persistent sources, but also can be useful for analysing other feedback schemes.(3) Comparisons of simulated TCP traffic to measured Ethernet traffic shows qualitatively similar autocorrelation when think times follow a Pareto distribution with infinite variance. Also, the simulated and measured traffic have long range dependence. In this sense our traffic model, which purports to be Web-user-like, also agrees with measured traffic.
    Proceedings of the 1997 ACM SIGMETRICS international conference on Measurement and modeling of computer systems; 06/1997
  • Source
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    ABSTRACT: The Grassmann-Taksar-Heyman algorithm is a direct algorithm for computing the steady-state distribution of a finite irreducible Markov chain. We describe our experience in implementing this algorithm on a single-instruction multiple-data parallel processor computer. Our main conclusions are that a lower-level language has a performance advantage compared to Fortran, and that data storage is the limiting factor that determines the largest problem that can be solved. As a consequence, we devote considerable attention to storing a block tridiagonal transition matrix.
    INFORMS Journal on Computing. 01/1997; 9:218-223.
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    ABSTRACT: Intuition suggests that a finite buffer limits the effect of traffic auto-correlations on the queue length. We investigate the extent to which finite buffers can, therefore, be expected to mitigate the effects of long-range dependence (LRD). With traffic sequences generated by the fractional autoregressive integrated moving average (f-ARIMA) models for LRD, and by AR models for short range dependence (SRD), we investigate the traffic performance for a range of finite buffers, both for single and multiplexed streams. For design, the aim is to `match' a given LRD auto-correlation function with a suitable SRD function whose performance provides, for a wide range of traffic intensities and buffer sizes, a conservative bound on the performance associated with the LRD function. The results suggest that by suitably `dominating' an LRD auto-correlation function by an SRD function, one can obtain conservative performance bounds for a realistic range of traffic intensities and buffer sizes (delays). Also, in several cases, a `cross-over' phenomenon is observed for cell-loss probabilities as the buffer size increases, i.e., the loss probabilities are smaller for LRD than for SRD for small buffers, with the converse true for large buffers. This suggests that finite buffers, can in some cases, counteract the effects of LRD in traffic arrivals, and thus enable conservative designs to be based on Markovian traffic models
    Global Telecommunications Conference, 1996. GLOBECOM '96. 'Communications: The Key to Global Prosperity; 12/1996
  • D.P. Heyman, T.V. Lakshman
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    ABSTRACT: The authors explore the influence of long-range dependence in broadband traffic engineering. The classification of stochastic processes {X<sub>t</sub>} into those with short or long-range dependence is based on the asymptotic properties of the variance of the sum S<sub>m </sub>=X<sub>1</sub>+X<sub>2</sub>+···+X<sub>m </sub>. Suppose this process describes the number of packets (or ATM cells) that arrive at a buffer; X<sub>t</sub> is the number that arrive in the tth time slice (e.g., 10 ms). We use a generic buffer model to show how the distribution of S<sub>m</sub> (for all values of m) determines the buffer occupancy. From this model we show that long-range dependence does not affect the buffer occupancy when the busy periods are not large. Numerical experiments show this property is present when data from four video conferences and two entertainment video sequences (which have long-range dependence) are used as the arrival process, even when the transmitting times are long enough to make the probability of buffer overflow 0.07. We generated sample paths from Markov chain models of the video traffic (these have short-range dependence). Various operating characteristics, computed over a wide range of loadings, closely agree when the data trace and the Markov chain paths are used to drive the model. From this, we conclude that long-range dependence is not a crucial property in determining the buffer behavior of variable bit rate (VBR)-video sources
    IEEE/ACM Transactions on Networking 07/1996; · 2.01 Impact Factor
  • D.P. Heyman, T.V. Lakshman
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    ABSTRACT: Traffic from video services is expected to be a substantial portion of the traffic carried by emerging broadband integrated networks. For variable bit rate (VBR) coded video, statistical source models are needed to design networks that achieve acceptable picture quality at minimum cost and to design traffic shaping and control mechanisms. For video teleconference traffic Heyman et al. (1992) showed that traffic is sufficiently accurately characterized by a multistate Markov chain model that can be derived from three traffic parameters (mean, correlation, and variance). The present authors describe modeling results for sequences with frequent scene changes (the previously studied video teleconferences have very little scene variation) such as entertainment television, news, and sports broadcasts. The authors analyze 11 long sequences of broadcast video traffic data. Unlike video teleconferences, the different sequences studied have different details regarding distributions of cells per frame. The authors present source models applicable to the different sequences and evaluate their accuracy as predictors of cell losses in asynchronous transfer mode (ATM) networks. The modeling approach is the same for all of the sequences but use of a single model based on a few physically meaningful parameters and applicable to all sequences does not seem to be possible
    IEEE/ACM Transactions on Networking 03/1996; · 2.01 Impact Factor
  • Sigrún Andradóttir, Daniel P. Heyman, Teunis J. Ott
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    ABSTRACT: We consider the application of importance sampling in steady-state simulations of finite Markov chains. We show that, for a large class of performance measures, there is a choice of the alternative transition matrix for which the ratio of the variance of the importance sampling estimator to the variance of the naive simulation estimator converges to zero as the sample path length goes to infinity. Obtaining this ‘optimal’ transition matrix involves computing the performance measure of interest, so the optimal matrix cannot be computed in precisely those situations where simulation is required to estimate steady-state performance. However, our results show that alternative transition matrices of the form Q=P+E/T, where P is the original transition matrix and T is the sample path length, can be expected to provide good results. Moreover, we provide an iterative algorithm for obtaining alternative transition matrices of this form that converge to the optimal matrix as the number of iterations increases, and present an example that shows that spending some computer time iterating this algorithm and then conducting the simulation with the resulting alternative transition matrix may provide considerable variance reduction when compared to naive simulation.
    Advances in Applied Probability 01/1996; 28(1). · 0.90 Impact Factor
  • Source
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    ABSTRACT: The main contributions of this paper are two-fold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their models are of high dimension. Second, we apply our analytic approximation to statistical models of video teleconference traffic, obtain the multiplexing system's capacity as determined by the number of admissible sources for given cell-loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulations, which are driven by actual data from coders. The results are surprisingly close. Our bounds are based on large deviations theory. The main assumption is that the sources are Markovian and time-reversible. Our approximation to the steady-state buffer distribution is called Chenoff-dominant eigenvalue since one parameter is obtained from Chernoffs theorem and the other is the system's dominant eigenvalue. Fast, effective techniques are given for their computation. In our application we process the output of variable bit rate coders to obtain DAR(1) source models which, while of high dimension, require only knowledge of the mean, variance, and correlation. We require cell-loss probability not to exceed 10<sup>-6 </sup>, trunk bandwidth ranges from 45 to 150 Mb/s, buffer sizes are such that maximum delays range from 1 to 60 ms, and the number of coder-sources ranges from 15 to 150. Even for the largest systems, the time for analysis is a fraction of a second, while each simulation takes many hours. Thus, the real-time administration of admission control based on our analytic techniques is feasible
    IEEE Journal on Selected Areas in Communications 09/1995; · 3.12 Impact Factor
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    ABSTRACT: The main contributions of this paper are two-fold. First, we prove fundamental, similarly behaving lower and upper bounds, and give an approximation based on the bounds, which is effective for analyzing ATM multiplexers, even when the traffic has many, possibly heterogeneous, sources and their models are of high dimension. Second, we apply our analytic approximation to statistical models of video teleconference traffic, obtain the multiplexing system's capacity as determined by the number of admissible sources for given cell loss probability, buffer size and trunk bandwidth, and, finally, compare with results from simulations, which are driven by actual data from coders. The results are surprisingly close. Our bounds are based on Large Deviations theory. Our approximation has two easily calculated parameters, one is from Chernoff's theorem and the other is the system's dominant eigenvalue. A broad range of systems are analyzed and the time for analysis in each case is a fraction of a second.
    Proceedings of the 1995 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems; 01/1995
  • 01/1995
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    ABSTRACT: The authors analyze teleconference traffic, with moderate motion and scene changes, generated by different video codecs. These codecs differ in several aspects of coding, such as in the use of DCT and motion compensation. The results are that, even when traffic is generated using different coding schemes, the number of cells per frame can be described by a gamma (or equivalently negative binomial) distribution and a DAR(1) model determined by three traffic parameters (the mean, variance, and correlation) can be used to accurately model the source. The main contribution of the paper is in showing that the authors' previously published results on source modeling and marginal distributions, which were based on analysis of traffic generated by one type of coder, hold for coders which differ in various ways and particularly differ in the use of motion compensation
    Communications, 1994. ICC '94, SUPERCOMM/ICC '94, Conference Record, 'Serving Humanity Through Communications.' IEEE International Conference on; 06/1994
  • D.P. Heyman, T.V. Lakshman
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    ABSTRACT: Not Available
    Computer-Aided Modeling, Analysis, and Design of Communication Links and Networks, 1994. (CAMAD '94) Fifth IEEE International Workshop on; 02/1994
  • IEEE Transactions on Circuits and Systems for Video Technology - TCSV. 01/1994;
  • Source
    Sigrún Andradóttir, Daniel P. Heyman, Teunis J. Ott
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    ABSTRACT: We consider the simulation of a discrete Markov chain that is so large that numerical solution of the steady-state balance equations cannot be done with available computers, We propose smoothing methods to obtain variance reduction when simulation is used to estimate a function of a subset of the steady-state probabilities. These methods attempt to make each transition provide information about the probabilities of interest. We give an algorithm that converges to the optimal smoothing operator, and some guidelines for picking the parameters of this algorithm. Analytical arguments are used to justify our procedures, and they are buttressed by the results of a numerical example,
    ACM Transactions on Modeling and Computer Simulation 01/1993; 3:167-189. · 0.53 Impact Factor