Performance decay in a single server exponential queueing model with long range dependence

We discuss how long-range dependence can influence the characteristics of a single server queue. We take the analogue of the G/M/1 queue except that the input stream is altered to exhibit long-range dependence. The equilibrium queue size and equilibrium waiting time distributions have heavy tails. By suitably selecting the parameters of the inputs, the queue size or waiting time can be made to possess infinite variance and even infinite mean. Some simulations dramatically illustrate the potential for undetected long-range dependence to significantly alter the queueing behavior compared to what is anticipated with traditional inputs.