Optimal management of a finite M/M/R queueing system with multiple customer classes

We analyzed an M/M/R queueing system with finite capacity N where customers have multiple classes with no priorities under steady-state conditions. It is assumed that any one class of arriving customer is serviced by one or more servers, and that each customer class has equal probability of service. Analytic explicit solutions are obtained with the assumption of exponential distributions for arrival times and service times. A cost model is developed to determine the optimal system capacity and the optimal number of servers. The minimum expected cost, the optimal system capacity, the optimal number of servers, and various system performance measures are obtained for three customer classes and four customer classes, based on assumed numerical values given to the designated system parameters