Transient results for M/M/1/c queues via path counting
by M. Hlynka, L.M. Hurajt, M. Cylwa
International Journal of Mathematics in Operational Research (IJMOR), Vol. 1, No. 1/2, 2009

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.

Online publication date: Sat, 31-Jan-2009

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