The Application Of Queueing System In ATM Communications Network

During the development of communications network, we can analyze and evaluate the performance of communications network then improve it by using the results of queueing theory besides using advanced industrial manufacture technology. This is an indispensable link which develops the communications network through enhancing its utilization ratio and satisfying the needs of users.In this paper, we analyze the application of queueing system in ATM communications network. The performances of various queueing models in the virtual channel connection of ATM communications network are analyzed in the second part of this paper. We first consider the M/M/s queueing model with two priorities. Through the analysis of state transition-rate equations of two priorities, the average queue length at the input or output of communications systems is derived. We then consider the N policy M/G/1 queueing model with two priorities. By using the supplementary variable method to analyze the state probability equations, we derive the generating function of queueing length distribution and the mean queue length in the buffer of the communications network. And through further discussing for the queue with various priorities, we derive the generating function of queueing length distribution and the stationary queueing length in queue models with various priorities. The cell' s average waiting time and average queueing length in the N policy MX/G/1 vacation queueing system with server set up and close down time are discussed. We finally applied the results of some on-off input processes to obtain the calculating formulae for the performances of communications network.The performances of ATM switches with different butter queueing model are analyzed in the third part of this paper. We discuss the performances of input queue switch, shared memory switch and output queue switch respectively. Among them, the cell input is taken the extended method for input queue switch. The arrival of cells is restricted by threshold in the model of shared memory switch. The arrival and service of cells have geometric distribution in the model of output queue switch. Through the analysis of the three kinds of queue model switches, the throughput, average delay and mean waiting cell numbers in the buffer are given for different models of queueing switches in this paper.The component of communications network is described in the fourth part. And the performances of queueing network with two nodes are analyzed.