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IMI/Publicaţii/CSJM/Ediţii/CSJM v.29, n.1 (85), 2021/

On a modified M/M/m/n queueing model

Authors: Mario Lefebvre
Keywords: State space, balance equations, queue discipline, priority, cluster-type multiprocessor computing systems.

Abstract

The classic M/M/m/n queueing model is modified by allow- ing a given task to require up to m servers to be performed. Moreover, the maximum time that a task can wait in the queue before being executed is a random variable having an exponen- tial distribution. Both FIFO (First In, First Out) and priority disciplines are considered. The case when m = 2 is treated: the state space needed to fully describe the system is given, its size is calculated and the balance equations are presented when n = 1,2 and 3. The queueing process can be used to model cluster-type multiprocessor computing systems.

Polytechnique Montréal
Department of Mathematics and Industrial Engineering
2500, chemin de Polytechnique
Montréal (Québec), Canada H3T 1J4
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