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

The literature [1] and [2] have studied an M/M/1 queuing system and mixed queuing system M/M/n/m with variable service rate,an M / M / 1 preemptive priority queuing system and non-preemptive priority M/G/1 queue.This paper is studying theM / M / n / mqueuing system with variable service rate and priority.The model in this paper is focuses on the literature [1] for promotion, the literature [1] has been studied of M/M/1 queuing system with preemptive priority and an M/G/1 queue system with non-preemptive priority, however, this paper is to extend it to an M/M/n/m queuing system, and assuming that the system as captain for k, at that time 0≤ k≤ n, μ= kμ1,at that time n＜k≤m, μ= nμ2. Here, the service rate is variable. This paper has done the following work:① The proposed with variable service rate and preemptive priority of M/M/n/m queuing system. From the system’s stability, obtains the stationary distribution, so as to get the corresponding index system in different levels of customers queuing. At that time μ1=μ2, the results are agree with the results of literature [1],thereby verifying to correct of the results in this article partly. Finally illustrated the application of the model by example.② Proposed non-preemptive priority M/M/n/m queuing system with variable service rate,generalizes the related results in literature [1].When μ1= μ2 and n = 1, the results are consistent with the results of literature [1],thereby verifying to correct of the results in this article partly. Finally illustrated the application of the model by example.