含负顾客的M/M/1两种休假体制的排队系统的平稳性态  

Stationary behavior of the M/M/1 queue with negative customers andtwo vacation policies

作　　者：闫俊娜 杨永燕 Yan Junna;Yang Yongyan(Department of Basic Education,Linzhou College of Architectural Technology,Linzhou 456500,Henan,China;Mathematics&Science College,Anyang University,Anyang 455000,Henan,China;Puyang Petrochemical Vocational&Technical College,Puyang 457000,Henan,China)

机构地区：[1]林州建筑职业技术学院基础教学部,河南林州456500 [2]安阳学院数理学院,河南安阳455000 [3]濮阳石油化工职业技术学院,河南濮阳457000

出　　处：《江苏师范大学学报（自然科学版）》2022年第2期46-51,共6页Journal of Jiangsu Normal University：Natural Science Edition

基　　金：河南省高等学校重点科研项目(20B110002,21A110002)。

摘　　要：研究两类顾客(正顾客、负顾客)、两种休假体制(单次工作休假(半休假)体制与多重休假体制(M/M/1/SWV+MV))下的M/M/1系统.若服务系统中有正顾客,则到达的负顾客一对一抵消掉正在接受服务的正顾客;若服务系统中无正顾客,则负顾客自动消失,且此类顾客不接受系统服务.在服务期结束后,系统会进入工作休假(即半休假)模式,其间以较低的速率为顾客提供服务.工作休假结束后,系统中如果有顾客,则恢复正常服务期;否则,进入正常休假模式,其间不向任何顾客提供服务.正常休假结束后,系统中如果仍然没有顾客,则再次正常休假,以此类推,直到有新顾客到达,然后才开始一个正常服务期.通过建立一个拟生灭过程得出马尔可夫链的无穷小生成元,利用矩阵几何解的方法得出了系统的平稳条件、平稳队长及其相关成果,最后通过数值模拟验证了模型.The M/M/1 system with two types of customers(positive customers and negative customers)and two vacation policies(single working vacation policy(semi vacation policy)and multiple vacation policies(M/M/1/SWV+MV))is studied.If there are positive customers in the service system,the arriving negative customers will offset the customers who are serving one by one.If there are no positive customers in the service system,the negative customers will automatically disappear,and such customers will not accept the service of the system.After the normal service period,a working vacation mode will be conducted,during which customers will be served at a lower rate.After the holiday,if there are customers,the service system will resume the normal service period.Otherwise,the service system will enter another vacation mode—normal vacation mode,during which,no service will be provided to any new customers.If there are still no customers after the normal vacation,the service system will take another normal vacation,and so on,until a new customer arrives,and then the service system starts a normal service period.In this paper,the infinitesimal generator of Markov chain is obtained by establishing a quasi-birth-death process,and the stationary condition,stationary captain and related results of the system are obtained by using the method of matrix geometric solution.Finally,the model is verified by numerical simulation.

关 键 词：负顾客 工作休假(半休假) 正常休假 矩阵几何解 

分 类 号：O226[理学—运筹学与控制论]