The Research Of M/M/n/m Queuing System With Variable Input Rate And The Priority

Many scholars have studied the multi-server platform with priority or variable input rateand had got a lot of results in recent years, but generally only involve one side.This articlewill talk over the multi-server queuing model with variable input rate and priority.The focus of this article will extend the M/M/1queuing model with preemptive priorityand M/G/1queuing model with non-preemptive priority, which was introduced by LuChuanlai[1].In Lu Chuanlai's article, he assumed the system provides customers serviceswhen customers come to the system. This article considers a scenario where there is no idleservice desk, customers have to waiting for service of system in accordance with a certainprobabilityα_k(0≤α_k≤1)(k is meaning that the customer number of waiting for service inthe waiting area),that is to say: here the input rate is variable. The article described primarilyas follows:(1)Made with variable input rates M/M/n/m of preemptive priority queuing model, usedmatrix-vector method to prove stability of the system and got the indicators of stationarydistributions and some important queues. When α_k≡1,the results are consistent with onesof the at literature[1], thereby verifying to correct of the results in this article partly. Finallyillustrated the practical application of the model by examples.(2)Proposed non-preemptive priority M/M/n/m queuing model with variable input rates,extended the results of the known non-preemptive priority M/G/1queuing model; Whenα_k≡1,n=1the results are consistent with ones of the at literature[1], thereby verifying tocorrect of the results in this article partly. Finally illustrated the practical application of themodel by examples.