A queuing system with queue-dependent servers and finite capacity

摘要

This paper deals with a finite source M/M/3 queuing system in steady-state by assuming that the number of servers changes depending on the queue length. It is assumed that the service abilities of each server are different. Whenever the queue length in font of the first server reaches a specific length J, the second server will be provided instantly. At a later time, if the number of customers waiting before the two servers increases to another specified length K(K>J), then the third server will also be provided instantly. We derive the steady-state characteristics of the system such as the average number of customers and the average number of waiting customers. A cost relationship is constructed t determine the optimal queue length J and K simultaneously, in order to gain the maximum net profit.