Cost investigation of a batch arrival retrial G-Queue with working  malfunction and working vacation using particle swarm optimization

Shweta Upadhyaya; Sutrishna Ghosh; Geetika Malik

Shweta Upadhyaya Department of Mathematics, Amity University Amity Institute of Applied Science ,NOIDA-201301 (U.P.), India
Sutrishna Ghosh Department of Mathematics, Amity University Amity Institute of Applied Science ,NOIDA-201301 (U.P.), India
Geetika Malik Department of Mathematics, Amity University Amity Institute of Applied Science ,NOIDA-201301 (U.P.), India

Abstract

A retrial model with working malfunction (WM) (or working breakdown), working vacation (WV) and state dependent arrivals is scrutinized. Disaster leads to the evacuation of the entire unit from the system, and then the mainframe is sent to repair. The system may still be capable of performing activities but at lower speed during breakdown and it will perform some maintenance jobs as soon as all units depart from the system. When the mainframe is occupied and a unit arrives ,then it has to wait in the orbit. We have used supplementary variable technique (SVT) and probability generating function (PGF) approach to derive explicit formulas for various queueing and reliability measures. Numerical illustrations are used to investigate the impact of different parameters on performance measures. We have also derived optimal values of certain sensitive parameters using Direct Search Method (DSM) and then compare our results with that of Particle Swarm Optimization (PSO).