Impact of dependence on single-server queueing systems

Abstract

This study uses advanced simulation input modeling – the Vector-Auto-Regressi-ve-to-Anything (VARTA) method – to study the impact of bivariate and temporal dependencies among interarrival and service times on the performance of single-server queues. Our initial experiments, with the M/M/1 queue, show that there is nonmonotonic behavior of average waiting time with respect to negative autocorrelation in interarrival and/or service times at high utilization levels; such nonmonotonic behavior with negative autocorrelation in service times is well-known in literature, we are first to show its existence for interarrival times. Our use of VARTA allows us to extend our simulation approach to study dependence among interarrival and service times in nonexponential distributions, enabling us to compare their effects to the M/M/1. We find that the impact of dependence on the performance under nonexponential distributions of interarrival and service times is primarily determined by the second moment of the distribution. Greater (lower) variance of the nonexponential distribution increases (decreases) the average waiting time.