Optimization Analysis of the N Policy M/G/1 Queue with Working Breakdowns

Abstract

This paper deals with the N policy M/G/1 queue with working breakdowns. The supplementary variable and probability generating function techniques are implemented to develop the steady-state results. The stability condition of a stable queue, as well as several system performance measures, are also derived. A two-stage optimization method is employed to determine the optimal threshold N and the optimal joint values of two mean service rates until the stability constraint is satisfied. To demonstrate the effectiveness of two-stage optimization method, some numerical results are presented. Finally, we carry out sensitivity analysis for the expected cost function with numerical illustrations.

Keywords

• N policy M/G/1 queue
• sensitivity analysis
• supplementary variable technique
• two-stage optimization method
• working breakdowns