Different Situations Of Service Rate With Vacations Strategy Of M/M/c/m Queuing Model

In this paper,according to the theory of M/M/c queuing system,we analyzed and researched M/M/c/m Queuing Models which portions of the service station were synchronous vacating scientifically and reasonable. Then established multiple service windows waiting system of M/M/c/m Queuing Model,two grade of servicing rate situations of Queuing Model and the Model which is servicing rate linearity grows.Based on steady state analysis,we finally obtained the main index of the queuing system with service rate changes.Firstly,the M/M/c/m queuing system was analyzed.By drawing the state transition diagram, we established multiple service window mixed Queuing Model, two grade of servicing rate situations of Queuing Model and the servicing rate linearity growing of Queuing Model. In order to analysis the difference and mutual,the main indicators were needed to corresponding comparison,Secondly, based on the vacation queuing theory, the service rates were discussed according to the following situation:(1) the service rate is in the traditional situation:(2) the service rate is in two speed situation:(3) the service rate is in linear growth situation:Thirdly, related to the quasi birth and death process and matrix-geometric solution, we drew state transition diagram, described the generator, calculated the rate matrix and then established a multiple service window waiting system of M/M/c/m queuing Model, a two grade of servicing rate situations of Queuing Model and a servicing rate linearity growing Model. According to the steady state distribution, we have made the main index of the three models are extremely calculated and analyzed.Finally, comparing the model from a practical view,analyzing the strengths and weakness of each model and considering the practical significance,some reasonable suggestions are proposed.