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

Author

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  • M. Hlynka
  • L.M. Hurajt
  • M. Cylwa

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.

Suggested Citation

  • M. Hlynka & L.M. Hurajt & M. Cylwa, 2009. "Transient results for M/M/1/c queues via path counting," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 20-36.
    • Handle: RePEc:ids:ijmore:v:1:y:2009:i:1/2:p:20-36
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    Cited by:

    1. M. Vadivukarasi & K. Kalidass, 2022. "Discussion on the transient solution of single server Markovian multiple variant vacation queues with disasters," OPSEARCH, Springer;Operational Research Society of India, vol. 59(4), pages 1352-1376, December.

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