On job assignment for a parallel system of processor sharing queues

Two of the optimality criteria most commonly considered to compare job assignment policies, namely, the stochastic order and the average total completion time criterion, are discussed. It is shown that the latter, while being weaker than the former, still provides a useful criterion when policies are to be evaluated in terms of average performance measures such as the system average response time. Some of the most relevant results available in the literature on job assignment to parallel first come, first served (FCFS) servers are summarized. The assignment problem is discussed for a parallel system of processor sharing (PS) queues with exponential interarrival times and exponential and identical service requirements. The optimality of the join-the-shortcut-queue (JSQ) assignment policy for this case is proven. Feasible policies for general service time distribution are discussed. An approach allowing a meaningful comparison of servers in the perspective of job assignment is proposed. A comparison of the assignment problem for FCFS and PS parallel systems is presented.