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
E-mail:
Fulltext
–
0.10 Mb