Research On Multifunctional And Single-node Queues

In the recent years, call center is a brand-new and modern service, which uses the existing technology of communication and computer. The business of call center developed very quickly all over the world. Nowadays, the research of this field is mostly centered on the realization of hardware technology; however, there is little research on the quality of call center, which is based on the queue model.And it comes to light that feedback, changeable service rate, impatience and priority are main characteristics of call center. On the other hand, queuing system with working vacations, which has been applied in the performance evaluation of the access router that is used in optical access network, is an emerging research hotspot in queuing system in recent years. At the same time, literatures regarding queuing models incorporating negative customers are extensively discussed by researchers worldwide. In view of the facts listed, we study queuing systems taking together the above mentioned features in this thesis. And we try to establish Multifunctional and Single-node Queues, which have both characteristics of call center and access router. The organization of the thesis is as follows:Firstly, a flow controlledqueue with negative customers and preemptive priority is studied. An algorithm for caculating the steady-state distribution is designed by using the matrix analytic method,and a numerical example is given in the end.Secondly, an M/M/1 Bernoulli feedback queue with slow service period and impatient customers is studied. We derive the queue-length distributions by using analytic solutions, calculate the probabilty generating function and the mean queue size of the queue-length from the established differential equations.Finally, an M/M/c queue with negative customers and single working vacation is studied. A quasi-birth-and-death process and infinitesimal generator for the process are obtained from the model that has been described. Matrix-geometric approach is utilized to obtain the steady-state distributions of queue length and some system characteristics.