A finite capacity PS queue which models switching times

A processor-sharing queue is considered that has a finite capacity of jobs and a state-dependent service rate. The latter is used to model the switching time that a server (processor) spends transferring control from one job to the next. Assuming that the system’s capacity is large and that the duration of a typical switching time is small compared to the amount of time the processer services a job, asymptotic results are obtained for the mean and second moment of a (tagged) customer’s sojourn time. Several cases of the model parameters are treated, which reflect how heavily the system is loaded. Extensive numerical comparisons are used to back up the asymptotic formulas.