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

Lester Lipsky
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Lester Lipsky: University of Nebraska, Lincoln, Nebraska

Operations Research, 1985, vol. 33, issue 4, 911-927

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.

Keywords: 693 networks of queues; 694 explicit solutions of M/G/C//N-type loops (search for similar items in EconPapers)
Date: 1985
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