Comparative Simulation on M/M/ c and M/M/1 Queuing Systems

To make a more detailed analysis of the differences in performance between M/M/ c and M/M/1 c parallel systems, in this paper, first, the possible defects in the application of Little formula were analyzed. And then the running process of the model was tracked by AnyLogic. Finally, the service desk utilization, average queue length, maximum queue length, average waiting time of the two queuing system by GPSSJAVA were obtained. The defects of the analytical method for the M/M/1 parallel system were identified. Simulation results show that the service desk utilization is almost identical to the two queuing systems. The average waiting time of customers in M/M/ c system is slightly shorter than that of c parallel M/M/1 system. And the classic conclusion of “compared with the c M/M/1 parallel system, M/M/ c system can significantly improve the service efficiency and reduce the waiting time” conclusion was revised, Moreover, M/M/ c system has more short term waiting customers , its zero waiting and long waiting customers are significantly less than that in c M/M/1 parallel system.