带服务台故障及启动期和备用服务台的GeomGeom 1+1排队系统
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摘要
在经典Geom/Geom/1离散时间排队系统基础上,加入了一个带启动期的备用服务台,当主服务台故障时使用备用服务台,且两个服务台服务率不同.首先,运用拟生灭过程和矩阵几何解方法,给出该模型稳态队长分布,求出平均队长等系统性能指标的表达式.其次,通过数值例子分析参数对系统指标的影响.最后,通过构造顾客的平均剩余效用和社会效益函数,分析了该排队模型的社会最优策略.
Based on the classical Geom/Geom/1discrete time queue system,a spare server with setup time is added into the system in this paper.The spare server will be used when the main server is in trouble,and the service rates of two servers are different.First of all,using the quasi birth and death process and the matrix-geometric solution method,the steady state distribution of the captain is given in this model,and then the analytical expressions which calculate the mean queue length and other performance indexes are also obtained.Secondly,the influence of parameters on the system indexes is analyzed by numerical examples.Finally,the average residual utility and social benefit function are constructed to analyze the social optimal strategy of the queue system.
Based on the classical Geom/Geom/1discrete time queue system,a spare server with setup time is added into the system in this paper.The spare server will be used when the main server is in trouble,and the service rates of two servers are different.First of all,using the quasi birth and death process and the matrix-geometric solution method,the steady state distribution of the captain is given in this model,and then the analytical expressions which calculate the mean queue length and other performance indexes are also obtained.Secondly,the influence of parameters on the system indexes is analyzed by numerical examples.Finally,the average residual utility and social benefit function are constructed to analyze the social optimal strategy of the queue system.
引文
[1]田乃硕,徐秀丽,马占友.离散时间排队论[M].北京:科学出版社,2008.
[2]刘再明,于森林.一个不同到达率及负顾客的离散工作休假排队[J].山东大学学报(理学版),2015,50(6):1.
[3]SUN Wei,GUO Peng-fei,TIAN Nai-shuo.Equilibrium threshold strategies in observable queueing systerms with setup/closedown Times[J].Central European Journal of Operations Research,2010,18(3):241.
[4]ATENCIA I,MORENO P.The discrete-time Geom/Geom/1 queue with negative customers and disasters[J].Computers&Operations Research,2004,31:1537.
[5]ECONOMOU A,KANTA S.Equilibrium customer strategies and social-profit maximization in the singleserver constant retrial queue[J].Naval Research Logistics,2011,58:107.
[6]田乃硕,岳德权.拟生灭过程与矩阵几何解[M].北京:科学出版社,2002.
[7]ALBRECHER H,BUERLE N,THONHAUSER S.Optimal dividend-payout in random discrete time[J].Statistics and Risk Modeling,2011,28(3):251.
[8]SUN Wei,TIAN Nai-shuo.Contrast of the equilibrium and socially optimal strategies in a queue with vacations[J].Journal of Computational Information Systems,2008,4(5):2167.
[2]刘再明,于森林.一个不同到达率及负顾客的离散工作休假排队[J].山东大学学报(理学版),2015,50(6):1.
[3]SUN Wei,GUO Peng-fei,TIAN Nai-shuo.Equilibrium threshold strategies in observable queueing systerms with setup/closedown Times[J].Central European Journal of Operations Research,2010,18(3):241.
[4]ATENCIA I,MORENO P.The discrete-time Geom/Geom/1 queue with negative customers and disasters[J].Computers&Operations Research,2004,31:1537.
[5]ECONOMOU A,KANTA S.Equilibrium customer strategies and social-profit maximization in the singleserver constant retrial queue[J].Naval Research Logistics,2011,58:107.
[6]田乃硕,岳德权.拟生灭过程与矩阵几何解[M].北京:科学出版社,2002.
[7]ALBRECHER H,BUERLE N,THONHAUSER S.Optimal dividend-payout in random discrete time[J].Statistics and Risk Modeling,2011,28(3):251.
[8]SUN Wei,TIAN Nai-shuo.Contrast of the equilibrium and socially optimal strategies in a queue with vacations[J].Journal of Computational Information Systems,2008,4(5):2167.