Robust design of server capability in M/M/1 queues with both partly random arrival and service rates

In this paper we consider a robust design of controllable factors related to the server capability in M/M/1 queues where both arrival and service rates are assumed to be partly random. The performance of an individual queue is measured in terms of the random traffic intensity parameter defined as the ratio of the arrival rate to the service rate where both rates are functions of associated characteristics of an individual queue and a random error. We utilize the empirical Bayes estimator of the traffic intensity parameter and employ a Monte-Carlo simulation to find the optimal levels of server characteristics with respect to mean squared error. An example is given to illustrate how the proposed procedures can be applied to the robust design of a transmission line.