Study And Application On Priority Multi-server Queuing System

Priority multi-server queuing system has played an important role in many fields. This system is modeled on the classical queuing system, combining priority service to carry on research results. In this article, firstly, we modeled a multi-server queuing system with priority, and after using matrix geometric method of Nuets, got several performance indicators which expressed by matrix; secondly, applied this model to bank service system, worked out the number solution about important performance index of bank service system by editing Matlab program; finally, seeing different customer arrival rate and service rate as known, solved the problem about the designing capacity of the service system.In the priority multi-server queuing system, the process of customer arrival and service both follow Markov distribution. In This paper, the research on priority multi-server queuing system goes as follows:Firstly, in the chapter tow we modeled priority three-server queuing system. When the system got steady, using matrix geometric method of Nuets, we got the quantity of the customer all in the system, customer being served and customer queuing and so on. Then change the number of server, we supposed that the quantity of server was C, and analysis about the relationship among different customers.Secondly, we apply the priority M/M/C queue to bank service system. Think about designing the scale of bank, we got the capacity of the bank service system on known different customer rate and service rate, which provides the important operation reference for designer.As far, all the solutions of priority multi-server queuing system are formal. In this paper, we computed the numerical solution of several important performance indicators by Matlab.