This paper studies the optimal operation of an M/Ek/1 queueing system with a removable service station under steady-state conditions. Analytic closed-form solutions of the controllable M/Ek/1 queueing system are derived. This is a generalization of the controllable M/M/1, the ordinary M/Ek/1, and the ordinary M/M/1 queueing systems in the literature. The paper provides 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, the paper determines the optimal operating policy at minimum cost.
