Analysis Of Queueing Systems With Impatient Customers And K-Vacation Policy

Vacation queueing systems with impatient customers have wide applications inmany fields such as wireless communication systems, computer technology, and publicservices. It has been paid much attention by scholars. In this thesis, we extend thequeueing systems with single vacation policy and multiple vacation policy to the queueingsystem with K-vacation queueing policy. The research of K-vacation policy is morecomplex in theory, and more flexible in practical applications. Therefore, the analysis ofqueueing systems with impatient customers and K-vacation policy has application valueand theoretical significance.In this thesis, we consider several models of the queueing systems with theK-vacation policy and the impatient customers, such as the queueing systems with singleserver, with infinite servers, and the queueing system with two-phase service.Firstly, we analyze the K-vacation queueing system with single server and infiniteservers, respectively. If the arrival customer finds that the server is on vacation, thecustomer waits in the system for service, but he may be impatient for waiting and thenreneges. By applying the Markov process theory and probability generating functions, weobtain the closed-form expressions for some performance measures of the system,including the mean system size when server is on vacation and the proportion ofabandonment due to impatience. Aiming at the characteristics of K-vacation queueingsystem, we analyze the monotonicity of some system performance measures on K. At last,by numerical experiment, we study on the effects of the system parameters on propertiesof some system performance.Secondly, we investigate the M/M/1queueing system with K-vacation policy andtwo-phase service by considering two kind of customer impatience phenomenon, i.e.,balking and reneging. Using the balance equations and probability generating functions,we further obtain the closed-form expressions of some performance measures of thesystem, including the mean system size when server is on vacation, the mean system sizewhen server is on the first-phase service and the second-phase service, and the rate of abandonment due to balking and reneging. At last, by numerical experiment, we study onthe effects of in the system parameters on properties of some system performance.