Numerical transient-state solutions of queueing systems

Abstract

When queueing systems can be modeled in the form of a system of simultaneous first-order difference- differential equations and when the transient-state of such a system is likely to defy analysis, it may be wiser, less expensive, less troublesome, and faster to use some numerical method. The outstanding advantage of numerical methods is that it is rela tively easy to estimate the error (due to truncation of higher-order terms) in the results. The argument for seeking a numerical analysis method for solving a wide class of these models has a strong practical appeal. This paper explores the transient solutions to nonhomogeneous Markov processes (those in which the parameters vary with time), using Runge-Kutta and Hamming methods. For illustration, a simple but rather instructive, single queueing model is solved manually. The solutions obtained by these methods are compared with the corresponding analytical solu tions. Several commonly-used queueing models are solved to demonstrate the wide potential applicabil ity of the numerical methods.