An approximation for the waiting time distribution in single server queues

Abstract

Single server queues with general interarrival and service times are approximated by queues with two-point (Bernoulli) interarrival times and exponential service times. The parameters are chosen such that the first four moments of the difference of the service times and interarrival times in the approximating system equal those of the original system. The aptness of the approximation is discussed and some examples are presented comparing the exact and approximate waiting time distributions. A more complicated approximation is presented using the dual system (exponential arrivals, Bernoulli service) for those cases where the original approximation cannot be used.