An Efficient Solution to the Waiting Time Distribution in a Correlated Single Server Queue

摘要

In this paper, we compute the steady state waiting time distribution of a single sever queue where the arrival and the service processes are possibly correlated using a spectral decomposition of a coupling matrix. This approach is computationally more efficient than existing iterative approaches and it is possible, under certain conditions, to obtain analytical closed form solutions. This is illustrated in length by looking at some examples. For the special case of the MEP/M/1 system, we present closed form expressions for the waiting time distribution in terms of the free parameters of the arrival process. The method has applicability in solving the inverse problem i.e., characterizing the arrival stream given the (moments of the) waiting time distribution and the service time distribution. Using empirical trace driven simulations, we provide insightful information about the effects of the source model parameters.