The M/M/c/n+M Queueing System With Asynchronous Vacations And Its Application In The Management Of Call Center

Levy and Yechiali (1976) use classical birth-death process to obtain the probability distribution of the stationary number of servers on working and the average queue length of M / M/c queue model. With the same method we can get the stationary probability distribution and the queue length of M / M/c/n.The M / M/c/n+Mqueueing model with asynchronous single vacation and the M / M/c/n+M queueing model with asynchronous multiple vacations were studied and the stationary probability distribution and the correlation index had been obtained by using the finite quasi birth-death process .The above two models have not studied in the past literatures. In the process of resolution, we try to use a new matrix method. This makes the process be simple.Furthermore, the application and the optimization of the M / M/c/n+Mqueueing model with asynchronous single vacation and the M / M/c/n+M queueing model with asynchronous multiple vacations in personnel management of call center are given here by numerical examples.