MULTI SERVER MARKOVIAN QUEUE WITH MULTIPLE WORKING VACATIONS, WAITING SERVER, FEEDBACK, RENEGING AND RETENTION OF RENEGED CUSTOMERS

Abstract

In this thesis an infinite capacity Multi server Markovian queuing system with multiple working vacations, waiting server, feedback, reneging and retention of reneged customers is examined. If all active servers finish service and these is no customer in the system, the server wait for a duration of time before begin a synchronous WV (waiting server). During WV after completion of each service, customer can either leave the system satisfactorily with probability β or rejoin the queue to get service with feedback com plementary probability 1− β, where 0 ≤ β ≤ 1. The servers serve the customers at a slower rate than the normal busy period during a working vacation and this becomes the cause of customer’s impatience and this impatient customers may remain in the system with probability by employing certain convincing mechanisms. The inter-arrival times, the waiting server times, the feedback times, the service times, the impatient times and the vacation times are taken to be independent and exponentially distributed. The steady state probabilities when the server is in a regular busy period and in a working vacation periods are obtained by using recursive and probability generating function approach, also the steady state probabilities of the system being in any particular state were ob tained by using probability generating function. Various performance measures of the model such as the expected system size during normal busy periods, the expected system size during working vacations periods, the expected system size, the expected number of customer served, the proportion of customers served and the average of reneging and retention rate are obtained by using probability generating function approach. At the end, we have presented some numerical examples to demonstrate the effects of system parameters on some performance measures.