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.
