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

Abstract

The classic M/M/$m$/$n$ queueing model is modified by allowing 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 exponential 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.

Keywords

• state space
• balance equations
• queue discipline
• priority
• cluster-type multiprocessor computing systems