A HETEROGENEOUS TWO-SERVER MARKOVIAN QUEUE WITH DIFFERENTIATED VACATION, WAITING SERVER, RENEGING AND RETENTION OF RENEGING CUSTOMERS

Abstract

In this thesis a heterogeneous two servers Markovian queue with differentiated vacations, waiting server, reneging and retention of reneged customers was analyzed. The server serves the customers on a first-come, first-served basis. The solutions for steady state probabilities and performance measures of the model were obtained by employing the shift operator, the recursive methods and PGFs. Numerical illustrations in the form of tables and graphs generated by using MATLAB were presented to show how various parameters of the model influence the performance measures of the system. This model reveals that the existence of server waiting time duration maintains the stability of the system by reducing the loss of customers. Finally, for the future research work it will be interesting to consider a multi-server queueing system with heterogeneous server with differentiated working vacations, waiting server and impatient customers depending on the state of the servers