Part Of The Desk To Leave The Multi-service Queuing System

Based on the research of vacation queue with multiserver, the (finite) queues with vacation of partial servers are considered by using quasi birth and death process and matrix-geometric solutions. These are extension to the previous research of vacation queue with multiserver, and compensate the defect of the research of finite vacation queue with multiserver. We do the following work:Firstly, the queueing theory are introduced briefly. The research status of vacation queue with multiserver is summarized. The theory and method of research are also introduced.Secondly, the M/M/c queue with single asynchronous vacation of partial servers is considered. Based on the transition probability matrix of model, with quasi birth and death process and matrix-geometric solution method, some computational methods for stable indices and results of conditional stochastic decompositions are given. Furthermore, we reveal that the M/M/c queue with single asynchronous vacation is the special case of the model we considered.Finally, the M/M/c/k queue with multiple synchronous vacations of partial servers and its optimization are considered. In the past, it was always assumed that the capacity of the queue was infinite when vacation queue with multiserver was considered. In fact,the real queueing system in our daily life is finite, and it is harder to study the finite queue system. In this paper, we bring the policy of multiple synchronous vacations of partial servers to the classic M/M/c/k queue. By using finite quasi birth and death process and total probability decomposition,the stationary distributions of the queueing system are given. Since the capacity of the system is finite, the more servers going for vacation(auxiliary work), the more customers are lost. Although it increases the income of the auxiliary work, it decreases the income of the main work. How many servers should go for vacation(auxiliary work) when system is idle in order to maximize the income of system? So we discuss the number of server go for vacation(auxiliary work) when system is idle. The computational method and numerical example are given.