The Research Of M/M/c Queuing System With Variable Input Rate And The Asynchronous Multiple Vacation

First the M/M/1 queuing model in [1] with variable input rate has studied. On this basis, these articles discusses with variable input rate of M/M/c queuing model then obtain the stationary distribution of the queuing system and key indicators, finally the relevant results were published in [2].Second, the focus of this paper is to extend asynchronous multiple vacations of partial servers M/M/c queuing model in the Tian Naishuo [3]. It assumes that all the customers entered into the system and received services after they arrived. This article assumes that customers arrive, if they are not in the system help desk is usually idle, the customer with probability p(0≤p≤1)into the system to wait for services to the probability 1-p of leaving the system, that is where the input rate is variable. In this paper, some with variable input rate and asynchronous multiple vacations desk M/M/c queuing model, the use of matrix analytic and quasi birth and death rates of the process of the system matrix obtained by R, and prove the stability of the system, Obtained under the conditions of the system in a smooth distribution of the captain, and the waiting queue length and waiting time for a random decomposition. Finally, take p=1, to solve homogeneous linear equationsπB[R]=0, the result is the same in [3], to a certain extent, verify the correctness of the results.