Application of empirical Bayesian estimation to the optimal decision of a server-dependent queuing system

This paper presents a decision model that uses empirical Bayesian estimation to construct a server-dependent M/M/2/L queuing system. A Markovian queue with a number of servers depending upon queue length with finite capacity is discussed. This study uses the number of customers for initiating and turning off the second server as decision variables to formulate the expected cost minimization model. In order to conform to the reality, we first collect data of interarrival time and service time by observing a queuing system, then apply the empirical Bayesian method to estimate its traffic intensity. In this research, traffic intensity is used to represent the demand for service facilities. The system initiates another server whenever the number of customers in the system reaches a certain length N and removes the second server as soon as the number of customers in system reduces to Q. Associating the costs with the opening of the second server and the waiting cost of customers, a relationship is developed to obtain the optimal value of N and Q to minimize cost. The mean number of customers in the system and the queue length of customers are derived as the characteristic values of the system. Model development and the implications of the data are discussed in detail.