Bilevel hysteric service rate control for bulk arrival queue

A particular queue is discussed. The number of customers in each arriving unit is a random variable. There are two control threshold values K and N, with K smaller than N. Service rate is switched from u to tu whenever the system size increases to N. The tu rate is switched to u when the system size drops to the value K. The steady-state probabilities of the number of customers in system and the expected number of customers in system are derived. A cost model is introduced for the service cost, queuing cost, and switching cost.