An optimal policy for competitive processing of high and low priority arrivals

Two mutually independent traffic streams whose arrivals are stored in an infinite capacity buffer are considered. The two arrival traffics are modeled by renewal processes and compete for service by a single processor, with one of the processes requiring a strict upper bound on the total delay per arrival. It is assumed that the processing time per arrival for each process is a constant; the value of this constant is different for each of the two traffic streams. Given the above model, the authors find the optimal processing sharing policy, which attains throughput one and minimizes the expected delays of both traffic streams. The delays induced by the optimal policy are analyzed. Numerical results for the case in which the two renewal processes have exponentially distributed interarrival intervals are presented