Markovian working vacation queue with imperfect service, balking and retrial

Abstract

Markovian queue with working vacation, retrial and impatient customers has been investigated by including the feature of imperfect service during working vacation. If the server is occupied, an incoming customer may either decide to balk from the system or join the retrial orbit following the classical retrial policy. When there is no customer in the system, the server switches over to a working vacation (WV) mode. The customers who enter into the system during working vacation are also served at a slower speed. The probability generating functions (PGFs) are derived for evaluating the distributions of the number of customers in the system and orbit, which are further utilized to derive several performance metrics in closed form. The sensitivity analysis has been done to explore the sensitiveness of various descriptors on the system performance measures. Finally, a cost function is constructed and minimized using quasi-Newton method (QNM) and genetic algorithm (GA).