Optimal control of a removable server in an M/Ek/1 queueing system with finite capacity

Abstract This paper deals with the economic behavior of a removable server in the N policy M/E k /1 queueing system with finite capacity. Expressions for the probability mass functions of the number of customers in the system are derived and taken in closed-form. As special cases, the probability mass functions of the number of customers for the N policy M/M/1 queueing system, the ordinary M/K k /1 queueing system, and the ordinary M/M/1 queueing system are obtained. The cost structure includes a holding cost per unit time spent in the system for each customer, costs per unit time for keeping the server on or off, a server start-up cost, a server shut-down cost, and fixed cost for every lost customer. Following the construction of the total expected cost per unit time, we determine the optimal operating policy at minimum cost.