Optimization Analysis of Controlling Arrivals in the Queueing System with Single Working Vacation Using Particle Swarm Optimization

Abstract

A cost function in the literature of queueing system with single working vacation was formulated as an optimization problem to find the minimum cost. In the approach used, a direct search method is first used to determine the optimal system capacity K and the optimal threshold F followed by the Quasi-Newton method to search for the optimal service rates at the minimum cost. However, this two stage search method restricts the search space and cannot thoroughly explore the global solution space to obtain the optimal solutions. In overcoming these limitations, this study employs a particle swarm optimization algorithm to ensure a thorough search of the solution space in the pursuit of optimal minimum solutions. Numerical results compared with those of the two stage search method and genetic algorithms support the superior search characteristics of the proposed solution.