An experimental analysis of steady state convergence in simple queueing systems: Implications for flexible manufacturing system models

Abstract

Queueing models are widely used for performance analysis of Flexible Manufacturing Systems (FMS). Most studies are done under steady state assumptions. The inherent flexibility of FMS in terms of input, volume, and mix makes such an assumption hard to justify. In this paper, we investigate the convergence rate to steady state in simple queueing models that constitute the basic building blocks of more complex FMS models. The study reveals that steady-state conditions are not achieved during the execution of batches of moderate size. We therefore conclude that although equilibrium models are appropriate for studying long-term planning problems, for the operational control of FMSs, it is highly desirable to study the transient behaviour of the system. On a broader scope, our investigation also shows that steady-state assumptions used in the analysis of any inherently transient system should be carefully validated.