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

M. Hlynka, L.M. Hurajt and M. Cylwa

International Journal of Mathematics in Operational Research, 2009, vol. 1, issue 1/2, 20-36

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. (search for similar items in EconPapers)
Date: 2009
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