The Impact of Dependence on Queueing Systems

The effect of dependence is mostly ignored in queueing systems due to the difficulty in its analysis; the existing studies about dependent queueing systems have restrictive assumptions, such as considering only the M/M/1 queue with order of dependence lag-1 in interarrival and service times. In this paper, we conduct a simulation study to observe the impact of dependence in a single server queue, by using different probability distributions and higher orders of dependence. For generating multivariate input for our simulation, we use Vector-Auto-Regressive-to-Anything (VARTA) method that has never been used in queueing systems. We invesitage nonmonotonic behavior of the performance of a single server queue with autocorrelated service times, which is a known observation in the literature but it hasn’t been explained by using VARTA as a novel approach to generate multivariate input. ∗email: [email protected] †email: [email protected] ‡email: [email protected]