A Non-Markovian Queue with Second Optional Service, Disasters, Working Breakdowns and Working Vacation

Abstract

Inside this research article, we look at a non-Markovian queue (M/G/1) with second optional service, disaster events, working breakdowns and working vacation. There are two servers in the system: a primary and a backup. First Essential Service (FES) is delivered by a primary (backup) server to all arriving customers. A customer may choose the Second Optional Service (SOS) after his initial service is finished. When a disaster happens, all customers are made to evacuate the system, as well as the primary server crashes. The primary server is dispatched to repair at the first sign of a breakdown and the repair period begins right away. While a primary server is being repaired, a backup server is servicing customers at such a reduced rate. If a system is inactive while it is operating, the primary server will just go on vacation. The primary server, which is on working vacation mode and serving at a reduced rate, subsequently serves the new customers. The disasters have no effect on working vacation period. The supplementary variable methodology is used to determine the probability generating function (PGF) of the number of customers throughout typical peak times, working breakdown periods and working vacation periods, as well as specific metrics of effectiveness. Some statistical outcomes are shown at the end.