A SINGLE SERVER MARKOVIAN QUEUE WITH MULTIPLE WORKING VACATIONS, CHANGEOVER TIME AND RENEGING

Abstract

In this thesis an in nite capacity single server Markovian queuing system with mul- tiple working vacations, changeover time and reneging was analyzed. It was assumed that customers become impatient only during working vacation in which the arriving units already in the system may abandon the system without receiving any service. The server serves the customers on a rst-come, rst-served basis. The inter-arrival times, service times, the duration of changeover time period, the duration of working vacation period and the impatient times are taken to be mutually independent and exponen- tially distributed. The closed-form solutions for steady state probabilities of the system were obtained by employing the probability generating function methods and continued fractions along with some properties of con uent hypergeometric functions. Various performance measures of the model such as the proportion of time spent in normal ser- vice period, the proportion of time spent in working vacation period, the proportion of time spent in changeover time period, the average number of customers in the system, the average waiting time in the system, the average service rate, the average reneging rate, the loss probability were obtained. Finally, numerical illustrations in the form of tables and graphs were presented to show how various parameters of the model in uence the behavior of the system. The model considered in this study is for continuous-time and in nite capacity queuing systems; therefore, in order to increase its application the study can be extended to discrete-time and nite capacity models under various queuing models.