Title: Transient results for M/M/1/c queues via path counting

Authors: M. Hlynka, L.M. Hurajt, M. Cylwa

Addresses: Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario N9B 3P4, Canada. ' Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario N9B 3P4, Canada. ' Department of Mathematics and Statistics, University of Windsor, Windsor, Ontario N9B 3P4, Canada

Abstract: We find combinatorially the probability of having n customers in an M/M/1/c queueing system at an arbitrary time t when the arrival rate λ and the service rate µ are equal, including the case c = ∞. Our method uses path-counting methods and finds a bijection between the paths of the type needed for the queueing model and paths of another type which are easy to count. The bijection involves some interesting geometric methods.

Keywords: M/M/1; M/M/1/c; paths; queueing models; transient results; path counting.

DOI: 10.1504/IJMOR.2009.022874

International Journal of Mathematics in Operational Research, 2009 Vol.1 No.1/2, pp.20 - 36

Published online: 31 Jan 2009 *

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