Steady-State Simulation of Long-Range Dependent Queuing Processes

Abstract

Long-range dependence was first noted in hydrology by H. E. Hurst from a study of the water levels of the Nile river which showed a tendency for a flood year to be followed by another flood year. Long-range dependent processes are relevant not only in telecommunication networks but also in such areas of scientific activity as econophysics, climatology, economics, environmental sciences, geology, geophysics, hydrology, computer science, and computer engineering. They provide good models of packet trac in telecommunication networks, for example, in local area networks and video trac, and good models of persistence analysis in econophysics, especially for short-term interest rates. In this paper, the eects of long-range dependence on the behaviors of queuing systems have been investigated. We have also investigated how the long-range dependence in arrival processes aects the length of sequential steady-state simulations being executed to obtain simulation results with the required level of statistical error. Our results show that the finite buer overflow probability of a queuing system with a long-range dependent input is much greater than the equivalent queuing system with a Poisson or a short-range dependent input process and that the overflow probability increases as the Hurst parameter approaches one.