Optimal control of a service system with emergency vacation using bat algorithm

Abstract

The novelty of this research article is to study the effect of new introduced emergency vacation of a single service provider in service system via queueing-theoretic approach and comparative analysis of some metaheuristic and heuristic optimization techniques for optimal control. According to this vacation policy, the working state server takes a vacation in an emergency without completing the ongoing service of the waiting customer in the system. For the modeling purpose, it is assumed that the inter-arrival times, service times and vacation times are exponentially distributed. A cost optimization problem is developed to obtain the optimal values of system design parameters. The comparative analysis of proposed metaheuristic technique bat algorithm (BA) with another well-known metaheuristic technique: particle swarm optimization (PSO), and heuristic technique: Quasi-Newton method has been done to achieve the optimal operating conditions with minimal expected cost. Finally, numerical simulations and illustrations are provided to get an understanding of the mathematical modeling in detail and performance analysis of the queueing measures is also done. Numerical results are summarized in tables and graphs to provide a quick insight into critical issues related to the studied model. Concluding remarks are also drawn along with the future scope of the present study.