Quality-Dependent Stochastic Networks: Is FIFO Always Better Than LIFO?

Abstract

In various service and production systems, such as metal processing, fresh food industry, polymer forming, etc., the quality of the final product is a function of its total sojourn time in the system. We consider (i) an M/G/1-type single-server queue, as well as (ii) open tandem Jackson networks, and analyze the quality of products traversing through each system under two service disciplines -- FIFO and LIFO. Although the mean sojourn times in an M/G/1 queue are equal under both service disciplines (that is, E [WLIFO] = E [WFIFO]), the variance of WLIFO is larger than the variance of WFIFO. We show that, when quality is the measure of performance, FIFO is not necessarily better than LIFO. We consider several service-time distributions and show under what values of the parameters one discipline is better (or worse) than the other. In particular, the mean quality under LIFO is better than the mean quality under FIFO for all values of the traffic intensity. Moreover, the mean quality under the FIFO service regime drops sharply to 0 when the traffic intensity approaches 1, while the mean quality under LIFO is bounded below. Numerical results as functions of the system parameters are presented and discussed for both the M/G/1 queue and the tandem Jackson network.