Explicit and Iterative Numerical Approaches to Solving Queueing Models

Patricia M. Snyder and William J. Stewart
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Patricia M. Snyder: North Carolina State University, Raleigh, North Carolina
William J. Stewart: North Carolina State University, Raleigh, North Carolina

Operations Research, 1985, vol. 33, issue 1, 183-202

Abstract: This paper considers two approaches to the numerical solution of single node queueing models. Both approaches use a phase-type distribution to model very general service processes. The first approach is explicit and sometimes can exploit the structure of certain balance equations to reduce the global balance equations from a set of second order difference equations to a set of first order difference equations. This reduction permits the steady-state probability distribution to be written explicitly as a function of the model parameters. The second approach, due to Neuts, uses the fact that most queues that have a matrix-geometric steady-state probability distribution can be solved by means of a recursive technique. We compare the approaches and present a theorem that specifies necessary conditions for the computation of an explicit solution. A number of examples are provided.

Keywords: 564 phase-type distribution in queuing approximations; 683 iterative approaches (search for similar items in EconPapers)
Date: 1985
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Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:33:y:1985:i:1:p:183-202

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