Journal of Applied Mathematics and Stochastic Analysis
Volume 11 (1998), Issue 2, Pages 115-162
Analysis of the asymmetrical shortest two-server queueing model
CWl, P.O. Box 94079, 1090 GB, Amsterdam, The Netherlands
Received 1 September 1997; Revised 1 February 1998
Copyright © 1998 J. W. Cohen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This study presents the analytic solution for an asymmetrical two-server
queueing model for arriving customers joining the shorter queue for the
case of Poisson arrivals and negative exponentially distributed service
times. The bivariate generating function of the stationary joint distribution of the queue lengths is explicitly determined.
The determination of this bivariate generating function requires a construction of four generating functions. It is shown that each of these functions is the sum of a polynomial and a meromorphic function. The poles
and residues at the poles of the meromorphic functions can be simply calculated recursively; the coefficients of the polynomials are easily found, in
particular, if the asymmetry in the model parameters is not excessively
large. The starting point for the asymptotic analysis for the queue lengths
is obtained. The approach developed in the present study is applicable to
a larger class of random walks modeling asymmetrical two-dimensional