We present a family of Markov models for analyzing the performance of parallel /distributed processors that execute a job consisting of N independent tasks in parallel using P processors. The model is a Markov Chain with states representing service and failure rates with k (0 ! k P ) active processors. The task-times and processor failures are both exponentially distributed. We derive a number of expressions to determine the mean execution time, probability of success, work, and other measurable quantities, all conditioned on the job finishing successfully. A prototype, implemented using an extended version of ACMPI, is used for actual experiments that are based on simulated task-times and processor failures. We present our results comparing the analytic model with the prototype for a range of values of processor failure rates. We then discuss extensions of the model and issues related to communication costs, approximations and effect of task-time distributions.

this paper, we will plot using logarithmic scales, usually multiplying by 1-ae. The curves are discontinuous because N is an integer function, and have negative slopes for small ae because of the factor 1-ae. Figure 5 shows that although the buffer size can become very large as ae

this paper is the ability to completely characterize the tagged departure process in terms of both first- and second-order statistical properties. The model is also unique in that it incorporates correlations in the packet length distribution as well as the packet interarrival process for each class of traffic. In particular, the model allows us to study all aspects of multiplexed streams in heavy traffic, and answer the questions posed above

Abstract. Jackson networks have been very successful in so many areas in modeling parallel and distributed systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since Jackson networks do not apply to systems where there are population size constraints. Also, the product-form solution of Jackson networks assumes steady state systems exponential service centers with FCFS queueing discipline. In this paper, we present a transient model for Jackson networks. The model is applicable under any population size. This model can be used to study the transient behavior of Jackson networks and if the number of customers in the network is large enough, the model accurately approaches the product-form solution (steady state solution). Finally, an approximation to the transient model using the steady state solution is presented. 1.

We present the results of a parametric study of the buffer size needed to prevent overflow or loss in single and multiple server systems where data arrivals or service times are "bursty", "self-similar", or "fractal". Such erratic behavior can be caused (or adequately described) by renewal processes whose interarrival distributions are power-tail (or Pareto, or L`evy, or "long-tail") with infinite variance. We show that power tails can cause problems for intermediate values of the utilization parameter, ae, and become very serious (beyond the usual 1=(1 \Gamma ae) factor) when ae is close to 1, and/or when ff approaches 1. For systems with a power-tail arrival distribution and multiple servers(PT/M/C), we gain no performence increase by utilizing multiple Poisson servers. However, for systems with a Poisson arrival rate and power-tail service times (M/PT/C), the improvement by using multiple, slower servers over a single faster one can be great indeed. Keywords: Power-tail, long-tail...

1 A short review of what we call "Linear Algebraic Queueing Theory (LAQT)" is presented, including the basic formulas for matrix representations of Phase (or `Matrix Exponential') Distributions. Semi-Markov (or Markov Renewal) Processes are then described in this formulation, with particular emphasis on `Markov Modulated Poisson Processes (MMPP).' The MMPP process is then modified to represent ON-OFF models with non-exponential holding times (the 1Burst model). A `Truncated Power-Tail (TPT)' Distribution with a Phase representation is then described. It is the combination of ON-OFF Processes with TPT ON-times that allows telecommunications systems with self-similar and long-range dependent traffic to be modeled analytically as a point process. We then present some results, showing that there is a range of values for the on-time data rate where performance can go rapidly from very good to very bad even while the overall arrival rate is held constant. We then show how this can be extend...

In this paper we present an analytical model for micro- and pico-ceil wireless networks for any arbitrary topology in a high mobility environment. We introduce an approximation technique which uses a single ceil decomposition analysis which incorporates moment matching of hand-off processes into the ceil. The approximation technique is novel in that it can provide close approximations for non-Poisson arrival traffic and it is easily parallelized. Performance measures such as new cails blocked and hand-off cails lost are presented for any general call arrival distribution in a non-homogeneous traffic environment. We produce some numerical examples for some simple topologies with varying mobility for several call arrival distributions and compare our results to those from simulation studies.

This paper provides a general framework for establishing the relation between various moments of matrix exponential and Markovian processes. Based on this framework we present an algorithm to compute any finite dimensional moments of these processes based on a set of required (low order) moments. This algorithm does not require the computation of any representation of the given process. We present a series of related results and numerical examples to demonstrate the potential use of the obtained moment relations.

Different multi-media traffic sources can have different traffic characteristics which can raise the issue of whether to multiplex (some of) these sources. This issue becomes even more important in traffic engineering in a backbone network when a decision needs to be made on which sources to multiplex when there are constraints on tunneling and capacity along with routing requirements for tunnels. In this paper, we first present a measure of distortion between two different traffic streams and show their effectiveness. Next we use this factor in traffic engineering of backbone networks in the presence of tunneling and capacity constraints by presenting an optimization formulation. We then present a two phase heuristic approach to solve this problem where in the first phase the problem is decoupled into two subproblems and in the second phase we show how the non-linear problem (for one of the subproblems) can be simplified to develop a duality-based method. We then present numerical results to show where and how our approach helps in determining when and which sources to multiplex depending on whether the tunneling and/or capacity constraint is dominant.

The N-Burst model describes traffic in telecommunication systems as the superposition of N packet (or cell) streams of ON/OFF type, i.e., during its ON-time each source generates packets according to a Poisson Process with intra-burst packet rate p . As such, the N-Burst is an analytic Point-Process modeling network traffic on the packet level. When using Power-Tail Distributions for the duration of the ON periods, self-similar properties are observed. A variety of widely used approximate traffic models are shown to be limiting cases of N-Burst/G/1 queues. For very low intra-burst packet rates, the N-Burst/G/1 model reduces to an M/G/1 queue. For p ! 1 all packets in a burst arrive simultaneously and the model reduces to a Bulk arrival, or M (X) =G=1, queue. In the same limit, the packet-based model can be compared to a model on the burst level, an M/G/1 queue where the individual customers represent complete bursts rather than individual packets. Thus the mean system time describes ...