Explicit and Iterative Numerical Approaches to Solving Queueing Models
Patricia M. Snyder, William J. Stewart
Operations Research · 1985 · Volume 33 · Issue 1
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
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