M/M/2型Bernoulli休假排队系统的率阵及平衡条件  

Rate matric and balance condition of a two server vacation queue with Bernoulli schedules

作　　者：于静[1] 岳德权[1] 殷晓青 王艳禹 郭社平 

机构地区：[1]燕山大学理学院,河北秦皇岛066004

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第3期421-424,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然科学基金资助项目(71071133);河北省自然科学基金资助项目(G2012203136)

摘　　要：针对M/M/2型Bernoulli休假排队模型,假定顾客到达时间服从指数分布,两个服务员向顾客提供异步指数服务.在两个服务员的服务率不同情况下,分别考虑两个模型,模型Ⅰ中,一次服务完成后,两个服务员都可以选择休假,休假的概率分别为1p和2p;模型Ⅱ中,一次服务完成后,两个服务员分别休假,即服务员1休假或者服务员2休假.结果表明:采用拟生灭过程思想,通过矩阵几何解方法得到了两种模型的转移率矩阵以及系统的稳态平衡条件.Considering the M/M/2 vacation queuing model with Bernoulli schedules and assuming me arrivals or customers follow a Poisson process, the two servers provide heterogenous exponential service to customers. This paper studied two models under the circumstance that two servers have different service rates. In the model Ⅰ, after the completion of a service both servers can take a vacation with individual vacation rate p1 and P2 ; in the model Ⅱ, after the completion of a service only one server can take a vacation. Using the theory of quasi-birth and death process and the method of matrix-geometric solution, this study obtained the transfer rate matrix and the stationary balance condition of the system.

关 键 词：BERNOULLI 休假排队 拟生灭过程 率阵 平衡条件 服务率 异步 矩阵几何解 

分 类 号：O226[理学—运筹学与控制论]