An Optimal Design Problem for Limited Processor Sharing Systems

An optimal design problem is considered for processor-sharing service systems, where the number of customers served simultaneously is limited to a fixed finite number (called multiplicity). The decision variable is the multiplicity and the optimal criterion is to minimize the mean number of customers in the system, or, alternatively, to minimize the mean sojourn time for a customer. It is proved that the processor-sharing discipline with any multiplicity ameliorates the system performance if a service-requirement distribution is an NWU (new worse than used) type and deteriorates the performance if the distribution type is Erlangian. Moreover, it is conjectured through numerical results that the limited processor-sharing system will ameliorate (deteriorate) the performance if the coefficient of variation of the service-requirement distribution is larger (smaller) than 1.