一类服务率可变的M/M/s/K排队模型研究

全文下载：2014010095

韩玉群，梁希泉*

（青岛科技大学 数理学院,山东 青岛 266061）

 摘要：针对M/M/s/K混合制排队服务模型，考虑服务系统的服务率随着系统的状态发生变化的情形，并假设服务系统有两个不同的服务率，当系统服务台有空闲时,每个服务台的工作效率相对较小,但是当系统服务台全部处于繁忙状态并且有顾客等待时,服务台的服务速度提高。利用生灭过程获得了模型的状态转移图和平稳分布，然后计算获得了系统的损失概率，平均损失顾客数，系统中正在接受服务的平均顾客数，平均队长（包括平均等待队长和平均顾客数），平均等待时间和逗留时间等相关指标。

关键词：M/M/s/K排队；服务率可变；生灭过程；平稳分布

 图分类号： O 226文献标志码： A

 Analysis of a Class of M/M/s/K Queuing Model with Variable Service Rate

 HAN Yuqun , LIANG Xiquan

 （College of Mathtematics and Physics, Qingdao University of Science and Technology, Qingdao,266061，China）

 Abstract: According to the M/M/s/K mixed system queuing service model, we considered the situation of the service rate along with the change of the state of the system, and the hypothesis that service system has two different service rate, when the system service stations have free time，each desk efficiency is relatively low. But when the system service station all is busy and have customers waiting，desk efficiency will increased. Get the state transition diagram and stationary distribution according to birth and death process model，and then obtained system loss probability, the average loss customer number, the average number of customers being served in the system, the average captain (including average waiting for captain and average customer number), the average waiting time and residence time and other related index by computing.

Key words:M/M/s/K queuing; variable service rate; birth and death process; stationary distribution

收稿日期： 20121203

作者简介： 韩玉群（1987—），男，硕士研究生.*通信联系人.