Heavy traffic response times for priority queue with non-linear priorities

Previous work concentrated on providing heavy traffic response times for priority queue with linear priorities. Present paper analyses a priority queue with nonlinear priorities. In the present work, we consider queueing system consisting of a single server, which dispenses service to jobs of K ≥ 1 priority classes. Jobs are assumed to arrive to the queue according to a Poisson point process with a class dependent rate and to have class dependent service demands that are generally distributed. A non-linear priority function of the time spent in the system is specified for each job class and is used to schedule jobs. We provide closed form expressions for the mean class response time under heavy traffic and light load conditions.