Abstract:
In this thesis an infinite capacity single server Markovian queuing system with single
working vacation, reneging and retention of reneged customers is examined. Whenever
a customer arrives at the system, it activates an impatience timer for his service to
begun. If it has not begun before the customer’s impatience timer expires, then the
customers get impatient and may leave the system without getting service with some
probability and may remain in the system with probability by employing certain con vincing mechanisms for his service. It is assumed that the impatience timer depends
on the server’s states. During a working vacation, customers are served at a slower
rate than usual service rate. The server serves the customers on a first-come, first served basis. The inter-arrival times, the service times, the impatient times and the
vacation times are taken to be independent and exponentially distributed. The closed
form expressions of steady state probabilities when the server is in a regular busy period
and in a working vacation period are obtained by using probability generating function
approach and the steady state probabilities of the system being in any particular state
were obtained by using continued fractions and incomplete gamma function along with
some properties of confluent hypergeometric function. Various performance measures
such as the expected system size, the expected sojourn time of a customer served, the
proportion of customers served and other performance measures are derived. Finally,
numerical illustrations generated by MATLAB(R2019a) software were presented in the
form of tables and graphs to demonstrate how the various parameters of the model in fluence the performance measures of the system. The model considered in this study can
be extended to Markovian queue with state dependent retention of reneged customers,
working vacations and Bernoulli scheduled vacation interruption.
