Multi-server threshold queues with hysteresis

A queueing system with K servers operates in the following manner. When the system is empty, arriving customers are attended by only one server. A set of forward threshold values is defined so that at epochs at which the number of customers in the system exceeds a forward threshold value an extra server is added. Similarly, a set of reverse threshold values is defined so that at epochs at which the number of customers in the system becomes less than a reverse threshold value one server is removed. The forward and reverse threshold values are assumed to be different. Closed-form occupancy distribution and mean delay of customers in the system are obtained by the Greenʹs function method.