Network arrivals are often modeled as Poisson processes for analytic simplicity, even though a number of traffic studies have shown that packet interarrivals are not exponentially distributed. We evaluate 24 wide-area traces, investigating a number of wide-area TCP arrival processes (session and connection arrivals, FTP data connection arrivals within FTP sessions, and TELNET packet arrivals) to determine the error introduced by modeling them using Poisson processes. We find that user-initiated TCP session arrivals, such as remotelogin and file-transfer, are well-modeled as Poisson processes with fixed hourly rates, but that other connection arrivals deviate considerably from Poisson; that modeling TELNET packet interarrivals as exponential grievously underestimates the burstiness of TELNET traffic, but using the empirical Tcplib [Danzig et al, 1992] interarrivals preserves burstiness over many time scales; and that FTP data connection arrivals within FTP sessions come bunched into “connection bursts,” the largest of which are so large that they completely dominate FTP data traffic. Finally, we offer some results regarding how our findings relate to the possible self-similarity of widearea traffic.

We consider the problem of task assignment in a distributed system (such as a distributed Web server) in which task sizes are drawn from a heavy-tailed distribution. Many task assignment algorithms are based on the heuristic that balancing the load at the server hosts will result in optimal performance. We show this conventional wisdom is less true when the task size distribution is heavy-tailed (as is the case for Web file sizes). We introduce a new task assignment policy, called Size Interval Task Assignment with Variable Load (SITA-V). SITA-V purposely operates the server hosts at different loads, and directs smaller tasks to the lighter-loaded hosts.

We consider the standard GI/G/1 queue with unlimited waiting room and the first-in first-out service discipline. We investigate the steady-state waiting-time tail probabilities P(W> x) when the service-time distribution has a long-tail distribution, i.e., when the service-time distribution fails to have a finite moment generating function. We have developed algorithms for computing the waiting-time distribution by Laplace transform inversion when the Laplace transforms of the interarrival-time and service-time distributions are known. One algorithm, exploiting Pollaczek’s classical contour-integral representation of the Laplace transform, does not require that either of these transforms be rational. To facilitate such calculations, we introduce a convenient two-parameter family of long-tail distributions on the positive half line with explicit Laplace transforms. This family is a Pareto mixture of exponential (PME) distributions. These PME distributions have monotone densities and Pareto-like tails, i.e., are of order x − r for r> 1. We use this family of long-tail distributions to investigate the quality of approximations based on asymptotics for P(W> x) as x → ∞. We show that the asymptotic approximations with these long-tail service-time distributions can be remarkably inaccurate for typical x values of interest. We also derive multi-term asymptotic expansions for the waiting-time tail probabilities in the M/G/1 queue. Even three terms of this expansion can be remarkably inaccurate for typical x values of interest. Thus, we evidently must rely on numerical algorithms for determining the waiting-time tail probabilities in this case. When working with service-time data, we suggest using empirical Laplace transforms.

Let f(Xn; Jn)g be a stationary Markov-modulated random walk on R\Theta E (E finite), defined by its probability transition matrix measure F = fF ij g; F ij (B) = P[X 1 2 B; J 1 = jjJ 0 = i]; B 2 B(R); i; j 2 E. If F ij ([x; 1))=(1 \Gamma H(x)) ! W ij 2 [0; 1), as x! 1, for some longtailed distribution function H, then the ascending ladder heights matrix distribution G+ (x) (right Wiener-Hopf factor) has long-tailed asymptotics. If EXn! 0, at least one W ij? 0, and H(x) is a subexponential distribution function, then the asymptotic behavior of the supremum of this random walk is the same as in the i.i.d. case, and it is given by P \Theta sup n0 Sn? x

In present teletraffic applications of queueing theory service time distributions B(t) with a heavy tail occur, i.e. 1 \Gamma B(t) t \Gamma for t !1 with ? 1. For such service time distributions not much explicit information is available concerning the tail probabilities of the inherent waiting time distribution W (t). In the present study the waiting time distribution is studied for a stable M=G=1 model for a class of service time distributions with 1 ! ! 2. For = 1 1 2 the explicit expression for Q(t) is derived. For rational with 1 ! ! 2, an asymptotic series for the tail probabilities of W (t) is derived. 1991 Mathematics Subject Classification: 90B22, 60K25 Keywords and Phrases: M=G=1 model, stable, service time distribution, heavy-tails, waiting time distributions, asymptotic series for tail probabilities. Note: work carried out under project LRD. 1. Introduction In classical applications of teletraffic theory the service time distributions in queueing models are freq...

Consider a single server queue with i.i.d. arrival and service processes, fA; A n ; n 1g and fC; C n ; n 1g, respectively, and finite buffer B. The queue content process fQ B n ; n 0g is recursively defined as Q B n+1 = min((Q B n + A n+1 \Gamma C n+1 ) + ; B), q + = max(0; q). When E(A \Gamma C) ! 0, and A has a subexponential distribution, we show that the stationary expected loss rate for this queue E(Q B n + A n+1 \Gamma C n+1 \Gamma B) + has the following explicit asymptotic characterization E(Q B n +A n+1 \Gamma C n+1 \Gamma B) + ¸ E(A \Gamma B) + as B !1; independently of the server process C n . For a fluid queue with capacity c, M/G/1 arrival process a t , characterized by intermediately regularly varying On periods ø on , that arrive with Poisson rate , the average loss rate B loss satisfies B loss ¸ E(ø on j \Gamma B) + as B !1; where j = r + ae \Gamma c, ae = Ea t ! c, and r; r c, is the rate at which the fluid is arriving during an On per...

In this paper, the performance of ATM switches with self-similar input traffic is analyzed. The ATM switch is a non-blocking, output-buffered switch, and input traffic is approximated by a Poisson-Zeta process, which is an asymptotically second-order self-similar process. The upper and lower bounds of the buffer overflow probability of the switch are obtained by stochastically bounding the number of cells arriving in any interval of time. These upper and lower bounds are very tight and give reliable estimates of the buffer overflow probability. The self-similar behavior of traffic has serious implications on the buffer overflow probability of the switches. In contrast to typical ATM traffic models currently considered in the literature, the buffer overflow probability decreases non exponentially with buffer size. This work was supported in part by NSERC Operating grant No. A-8450 2 1. Introduction Performance analysis of ATM switches has been extensively studied. From previous studi...

We examine the question of whether to employ the first-come-first-served (FCFS) discipline or the processor-sharing (PS) discipline at the hosts in a distributed server system. We are interested in the case in which service times are drawn from a heavy-tailed distribution, and so have very high variability. Traditional wisdom when task sizes are highly variable would prefer the PS discipline, because it allows small tasks to avoid being delayed behind large tasks in a queue. However, we show that system performance can actually be significantly better under FCFS queueing, if each task is assigned to a host based on the task's size. By task assignment, we mean an algorithm that inspects incoming tasks and assigns them to hosts for service. The particular task assignment policy we propose is called SITA-E: Size Interval Task Assignment with Equal Load. Surprisingly, under SITA-E, FCFS queueing typically outperforms the PS discipline by a factor of about two, as measured by mean waiting t...

Real-time traffic processes, such as video, exhibit multiple time scale characteristics, as well as subexponential first and second order statistics. We present recent results on evaluating the asymptotic behavior of a network multiplexer that is loaded with such processes.

The Intensity Of Long-range Dependence (LRD) for communications network traffic can be measured using the Hurst parameter. LRD characteristics in computer networks, however, present a fundamentally different set of problems in research towards the future of network design. There are various estimators of the Hurst parameter, which differ in the reliability of their results. Getting robust and reliable estimators can help to improve traffic characterization, performance modelling, planning and engineering of real networks. Earlier research [1] introduced an estimator called the Hurst Exponent from the Autocorrelation Function (HEAF) and it was shown why lag 2 in HEAF (i.e. HEAF (2)) is considered when estimating LRD of network traffic. This paper considers the robustness of HEAF(2) when estimating the Hurst parameter of data traffic (e.g. packet sequences) with outliers.