Optimal Parameter Selection for a Machine Repair System with Servers Vacation and Controlling F-Policy

Abstract

In this article, we proposed an algorithm for determining optimal parameters of the queueing system that allows server vacation under F-policy. The queueing system parameters such as the threshold of the F-policy and the system service rate are designed by minimize the cost associated with the queuing system. We first propose an efficient algorithm to determine steady-state probabilities of the system, and second, a nonlinear integer programming problem is formulated to determine optimal system parameters. The  nonlinear integer programming problem is then relaxed to a nonlinear optimization and is solved using Quasi-Newton’s method. Subsequently, various system performance measures are studied for different system parameters.

Key words and phrases. Warm standby, F-policy, single vacation, setup time, Quasi-Newton method.