A sample path analysis of theM/M/1 queue
- 1 June 1989
- journal article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 26 (2) , 418-422
- https://doi.org/10.2307/3214049
Abstract
The exact solution for the transient distribution of the queue length and busy period of theM/M/1 queue in terms of modified Bessel functions has been proved in a variety of ways. Methods of the past range from spectral analysis (Lederman and Reuter (1954)), combinatorial arguments (Champernowne (1956)), to generating functions coupled with Laplace transforms (Clarke (1956)). In this paper, we present a novel approach that ties the computation of these transient distributions directly to the random sample path behavior of theM/M/1 queue. The use of Laplace transforms is minimized, and the use of generating functions is eliminated completely. This is a method that could prove to be useful in developing a similar transient analysis for queueing networks.Keywords
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