Simulation Analysis Of M/pM+M/c And (pM/M)M/M/c Queuing System

Queuing theory derives from life, and it also has a wide range of applications in practice. Many previous researches on the queuing system are based on the number of service stations and the adjustment of vacation policies. It is ordinary believed that customers arrive service system with no obstacle, they receive service immediately when there is a free server. This report will through two kind of queuing system, the first one is that customers may have a preparation period between arrival and service, the second one is that a block time may happen during the customer arrival process. Then, we evaluate vacation policies to simulate a situation which is more close to normal life.Using Monte Carlo method and programming by computer to study two kind of queuing system. Variable control method is adopted to analysis the affect brought by preparation period and block period when we change the value of preparation rate and block rate. The quantitative indicators include average waiting time, average staying time and average queuing length. Adjusting parameter valuesto simulate different systems, preparation period and block period will aggravate congestion in a crowd system, increase waiting time and reduce service rate. Therefore we should avoid preparation situation and block situation, so that customers can obtain better service. The simulation results are compared with theoretical value to test the correctness of program. We also discuss queuing system with vacation policies, propose the vacation time.In this article, we analysis customers may have a preparation period between arrival and service and a block time may happen during the customer arrival process, compare the simulation results to theoretical value and evaluate vacation policies.