Production rate optimization in a two-stage system with finite intermediate storage

Abstract

In this paper two-stage queuing systems with single servers at both stages and finite intermediate storage are considered. Optimization criteria for such systems have been formulated and a survey of so far reported results in analysis and optimization of such systems is presented. Closed form expressions for maximal production rate are obtained for the case when the distribution of service time is exponential, at one of the stages and arbitrary at the other one. The so far published results, pointing out that unbalancing of such a system in the direction of allotting a slightly higher load to the less variable stage increases system's throughput have been shown to be restricted to the case when the coefficient of variation at the non-exponential stage is less than one. If however this coefficient exceeds one, which case hasn't so far been explored, an opposite conclusion holds, at least for the investigated case of hyperexponential distribution. Numerical results illustrating this phenomenon have been included.