Читать книгу Queueing Theory 1 - Nikolaos Limnios - Страница 11

Attahiru Sule ALFA

University of Manitoba, Canada and University of Pretoria, South Africa

Discrete time single-server queues in which the interarrival and service times are interdependent are presented. First, we study the simple Geo/Geo/1 system, let the interarrival times depend on the service times and then consider special cases. The idea is then extended to the PH/PH/1 system. We then consider the case where the interarrival times are constructed from a combination of a set of interarrival times driven by the service times distribution. The initiating vector for the resulting combined PH distribution for the interarrival times is constructed as a function of the service times distribution, so that any changes in the service time distributions are reflected in this initiating vector. We capitalize on the structures of discrete phase type distributions in generalizing the resulting interarrival times. Finally, we introduce a general case where there is interdependence between service and interarrival times. We present a generalized matrix version of the bivariate geometric distribution, which can be used to capture some interdependence between the interarrival and service times.