A single server queue with cyclically indexed arrival and service rates

Abstract

In this paper we consider a queueing model that results from at least two apparently unrelated areas. One motivation to study a system of this type results from a test case of a computer simulation factor screening technique calledfrequency domain methodology. A second motivation comes from manufacturing, where due to cyclic scheduling of upstream machines, the arrival process to downstream machines is periodic. The model is a single server queue with FIFO service discipline and exponential interarrival and service times where the arrival and/or service rates are deterministic cyclic functions of the customer sequence number. We provide steady state results for the mean number in the system for the model with cyclic arrival and fixed service rates and for the model with fixed arrival and cyclic service rates. For the model with both cyclic arrival and service rates, upper and lower bounds are developed for the steady state mean waiting time in the system. Throughout the paper various implications and/or insights derived from the results of this study are discussed for frequency domain methodology.