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Explicit Solutions of M / G / C / / N -type Queueing Loops with Generalizations

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  • Lester Lipsky

    (University of Nebraska, Lincoln, Nebraska)

Abstract

Using recently developed Matrix-Algebraic techniques, we find explicit steady-state solutions of M / G / C / / N -type loops that depend on a set of recursively defined matrices. We show that such systems are special cases of arbitrary service centers that contain (load dependent) exponential servers in which no more than C customers can be active simultaneously. We also outline a recursive algorithm that can be used to evaluate the properties of small- to moderate-sized systems. The solution to the M / G / C open system is then found by letting the overall customer population N go to infinity. The solutions for closed systems in general are not of the matrix geometric type, and only in the limit does the solution become geometric in form.

Suggested Citation

  • Lester Lipsky, 1985. "Explicit Solutions of M / G / C / / N -type Queueing Loops with Generalizations," Operations Research, INFORMS, vol. 33(4), pages 911-927, August.
    • Handle: RePEc:inm:oropre:v:33:y:1985:i:4:p:911-927
    DOI: 10.1287/opre.33.4.911
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