Optimal Control of an M/E_k/1 Queueing System with a Removable Service Station

Abstract

This paper studies the optimal operation of an M/E_k/1 queueing system with a removable service station under steady-state conditions. Analytic closed-form solutions of the controllable M/E_k/1 queueing system are derived. This is a generalization of the controllable M/M/1, the ordinary M/E_k/1, and the ordinary M/M/1 queueing systems in the literature. We prove that the probability that the service station is busy in the steady-state is equal to the traffic intensity. Following the construction of the expected cost function per unit time, we determine the optimal operating policy at minimum cost.

Keywords:

• queues
• control
• service