# An Optimal Policy for Competitive Processing of High and Low Priority Arrivals

Abstract —We consider two mutually independent traffic streams whose arrivals are stored in an infinite capacity buffer. The two arrival traffics are modelled by renewal processes, and are competing for service by a single processor, where one of the processes requires 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, we first find the optimal processing sharing policy, which attains throughput one and minimizes the expected delays of both traffic streams. We then analyze the delays induced by the latter policy. We present numerical results, in the case where the two renewal processes have exponentially distributed interarrival intervals.