The Vacation Queueing System With Balking And Reneging

Queueing systems with balking and reneging have been widely used in telecommunication networks, inventory management, call centers, computer and among others. Vacation queueing models with balking and reneging can describe the practical problem precisely, so vacation queueing models with balking and reneging have important theoretic and practical significance.In this paper, we study three vacation queueing models with balking and reneging. These are new vacation queueing models, which are the extension of the relevant models in the previous literatures.In Chapter 1, we briefly introduce the development of the classic queueing theory, mainly elaborate the research content of the queueing systems with balking, reneging and vacation.In Chapter 2, we study the N policy GI/M/1/L vacation queueing system with balking and reneging. Firstly, we develop the differential equations by supplementary variables, and solve these equations by discrete transform of matrix form. Furthermore, we derive the steady-state probabilities and some performance measures. Then, we consider the effect of the threshold N on some system performance measures. Finally, we derive the Laplace transform of the busy period. In Chapter 3, we introduce N policy into the M/G/1/L queueing system with balking and reneging. We firstly derive the steady-state distribution of the system by the supplementary variables and discrete transform of algebra form, and get some system performance measures such as the average number of customers in the system, etc. Then, using the queueing length during the busy period, we derive the Laplace transform of the busy period and the mean length. Finally, we numerically analyze some system performance measures.In Chapter 4, we study the M/G/1/N queueing system with balking and reneging under multiple adaptive vacations. Firstly, we discuss the distribution of the busy period which starts with a number of customers. We get the mean length of the busy period and the distribution of the number of customers during the busy period. Then, we study the instantaneous-state queueing length in the system. Using the renewal process theory, we derive the steady-state queueing length in the system, which is the same as the steady-state queueing length when the customer arrives at the system. Finally, we derive the Laplace transform of the waiting time of customer who joins the system.