Cost Optimization of a Single-Server Queue With Working Breakdowns Under the N Policy

In this paper, we considered a single-server queue with working breakdowns under the N policy. The server was subjected to working breakdowns only when there was at least one customer in the system. We developed the steady-state probabilities of the number of customers in the system as well as several system performance measures. The stability condition was derived using a probability generating function technique. We constructed the total expected cost function per unit time and formulated an optimization problem to find the minimum cost. The two-stage optimization method is implemented to determine the optimal threshold, the optimal fast service rate, and the optimal slow service rate simultaneously at minimum cost. Numerical examples were presented to illustrate the two-stage optimization method. Sensitivity analysis with numerical illustration was also presented.