A constrained optimization problem for a processor sharing queue

This article discusses a processor sharing queueing model for a stored program controlled telephone exchange. The model incorporates the effects of both call requests and operator tasks on the load of the processor. Newly arriving call requests and operator tasks can either be admitted or rejected and for this decision the state of the queue at the moment of arrival is available as information. To guarantee a high level of service, a constrained optimization problem is formulated. Two types of access control, viz., partitioning policies and sharing policies, are considered. The optimization problem is solved for partitioning policies and the performance of both types of policies is compared.