Queueing systems with long-range dependent input process and subexponential service times

We analyze the asymptotic tail distribution of stationary waiting times and stationary virtual waiting times in a singleserver queue with long-range dependent arrival process and subexponential service times. We investigate the joint impact of the long range dependency of the arrival process and of the tail distribution of the service times. We consider two traffic models that have been widely used to characterize the long-range dependence structure, namely, the M/G/∞ input model and the Fractional Gaussian Noise (FGN) model. We focus on the response times of the customers in a FirstCome First-Serve (FCFS) queueing system, although the results carry through to the backlog distribution of the system with any arbitrary queueing discipline. When the arrival process is driven by an M/G/∞ input model we show that if the residual service time tail distribution Fe is lighter than the residual session duration Ge, then the stationary waiting time is dominated by the long-range dependence ...

• Type: Conference
• Year: 2003
• Where: SIGMETRICS
• Authors: Cathy H. Xia, Zhen Liu
• Keywords: SIGMETRICS 2003, Stationary Waiting Time, Tail Distribution, Waiting Time