Pierre-Jacques Courtois

On time and space decomposition of complex structures

Models of large and complex systems can often be reduced to smaller sub-models, for easier analysis, by a process known as decomposition. Certain criteria for successful decompositions can be established.

Computable Bounds for Conditional Steady-State Probabilities in Large Markov Chains and Queueing Models

A method is presented to compute, for the steady-state conditional probabilities of a given Markov subchain, the best lower and upper bounds derivable from the submatrix of transition probabilities between the states of that subchain only. The bounds can be improved when additional information, even fragmentary, on the entire chain is available. When the submatrix has a special structure, analytical expressions of the bounds can be obtained. The method is shown to be useful and economical to bound performance measures in large nonproduct-form queueing network models of computer communication systems.

The M/G/1 Finite Capacity Queue with Delays

A steady-state analysis of the M/G/1 finite capacity queue with delays is being made. In this model every busy period is followed by the execution of a noninterruptable task other than the servicing of ordinary customers; the duration of this task, called a delay, is a random variable with general distribution. Closed form expressions, easy to evaluate, are given for the distribution of the queue length and the first two moments of the queueing time distribution. A variant is also studied in which a busy period is followed by as many delays as possible, new delays being reinitiated as long as no customer has arrived.

An algorithm for the optimization of nonbifurcated flows in computer communication networks

Abstract For practical reasons, many computer communications networks currently in operation use single path routing, also called nonbifurcated routing: the traffic of every end to end communication is constrained to follow at most one single path at a time. The determination of optimal nonbifurcated flows is therefore a problem which confronts many network designers. In this paper, two important features of the classical nonbifurcated flow deviation algorithm, originally proposed by Fratta et al. are improved: the path length metric and the starting flow calculation. Tested on different examples, the essential gain is brought by a heuristic which provides a starting flow which is already a reasonable approximation of the global nonbifurcated optimum. Compared with the initial algorithm, this starting flow leads, with less computing time, to solutions which are closer to the optimum.

Analysis of Large Markovian Models by Parts. Applications to Queueing Network Models

The Markov chain remains one of the most useful and flexible techniques for the evaluation of the performances and of the reliability characteristics of models of communication and computer systems.

Some Results on Traffic Control and Resource Allocation in ATM networks

We first consider the problem of minimizing the loss in a system of two finite capacity queues in series with no blocking at the first queue. The issue is to choose an optimal ratio of the service rates and an optimal distribution of the buffer space between the two queues. Then we address the same optimization problem for a three queue system with multiplexing at the third queue and we discuss the potential applications of the results obtained for dimensioning broadband ISDN networks based on ATM.

Minimizing the loss of non-blocking tandem buffer stages

Abstract We consider the problem of minimizing the loss in a system of two finite capacity queues in series with no blocking at the first queue. The issue is to choose an optimal ratio of the service rates and an optimal distribution of the buffer space between the two queues. We also discuss the potential applications of the results obtained for the design of broadband communication networks using asynchronous transfer mode.