A queueing system with queue-dependent servers and finite capacity

This paper deals with a finite source M/M/3 queueing 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 front 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 to determine the optimal queue lengths J and K simultaneously, in order to gain the maximum net profit. (C) 2000 Elsevier Science Inc. All rights reserved.