Optimal management of the N-policy M/Ek/1 queuing system with a removable service station: a sensitivity investigation

This paper deals with optimal management problem of the N-policy M/Ek/1 queuing system with a removable service station under steady-state condition. The server is in a controllable position that the manager can turn the single server on at any arrival epoch, or off at any service completion. Arrival time and service time of the customers are assumed to follow the negative exponential distribution and the Erlang k type distribution, respectively. In this paper, we consider a practical application of such model. A cost formula is established to determine the optimal management policy of the removable service station to minimize the total expected cost per customer per unit time. We apply the analytic solution of the queuing model and use an efficient Matlab computer program to calculate the optimal value of N and some system performance measures. Analytical results for sensitivity analysis are derived. We provide extensive numerical computation for illustration purpose, and demonstrate how the model could be used in real applications.