Router Performance Evaluation Of Two Priority Queuing Model

With the fast development of information technology, some new subjects are proposed in queueing systems. On the one hand, the number of network clients increase rapidly, which results in the flux of data of the network increasing exponentially. This demands larger bandwidth in network transmision. On the other hand, routers are always bottleneck in network transmision before adopting the optical exchange. This limits the bandwidth to a large extend. However, the reqirement of the quality of service of the custmers is improving, so new routers are hoped to sustain QoS and to schedule according to the priority of custmers. Thus, priority queueing systems are usually adopted in the performance analysis of a router.In computer and communication fields, each operation actually needs time in the fulfillment of hardware of any algorithm. If the decision time is very small relative to the service time, it may be ignorded. This is classical queueing system. Otherwise the decision time must be considered in modelling of systems. The third chapter of the paper is about a question like this. This paper is divided into three chapters, the first chapter gives a brief summary about developments of correlative fields currently.The second chapter deals with a nonpreemptive priority queueing system with three priority queues. Using the method of imbedded Markov chain, probability generating funtion and laplace transform, we can obtain the mean queue length, mean waiting time for eachqueue and generalize this conclusion to multi-priority queues. This chapter includes four sections. In the first section, the detailed description of the system is given, and the set of stationary equations of the imbedded Markov chain is obtained. Then, the union generating funtion of the three queue length is derived in the second section. In the third section, we get the mean queue length of the .three queues using the results of the second section. In the fourth section, we obtain the laplace transform of the waiting time of the three queues and the mean waiting time of them by using the results of the second section.The third chapter deals with a non-absolute priority queueing system B/D/1 with decision time and two priority. This is a discrete time system. Also adopting the method of imbedded Markov chain, we can obtain the mean queue length for each queue. In fact, we can further obtain some other results about the mean waiting time using the results. All these results are of significance in application of engineering.