Sojourn-time approximations for a multi-server processor sharing system with priorities

We study mean sojourn times in a multi-server processor sharing system with two priority classes and with general service-time distributions. For high-priority customers, the mean sojourn time follows directly from classical results on symmetric queues. For low-priority customers, in the absence of exact results, we propose a simple and explicit approximation for the mean sojourn time. Extensive numerical experiments demonstrate that the approximations are highly accurate for a wide range of parameter settings.