摘要
为了研究带启动-关闭期和N策略的单重休假M/G/1排队系统,考虑顾客服务完成后离去时刻系统中的顾客数,推导出其嵌入马尔可夫链的状态转移概率矩阵;再利用拟生灭过程与矩阵几何解的方法,给出稳态队长的母函数及其数学期望的表达式;采用LST变换处理卷积,求出条件等待时间和稳态等待时间的LST变换;采用经典随机分解方法,得到了稳态队长和条件等待时间的随机分解结果;同时,给出了忙期的母函数及数学期望的表达式,讨论了服务员处于忙期、休假期、空闲期、启动期和关闭期的概率等性能指标。丰富了排队系统的研究内容,也为该模型在实际背景下的应用提供了理论基础。
This paper will investigate a continuing time single vacation of M/G/1 queue with set-up and close-down period and N-policy.With the consideration of the moment of customer immediate leaving and the numbers of customers in the system,the paper derives a state transition probability matrix of imbedded Markov chain.Also,under the steady state circumstances,the stochastic decomposition properties of the queue length,the average queue length and the Laplace-Stieltjes transformation of queue waiting time were obtained.Furthermore,the stochastic decomposition properties of the customers,who arrive at a busy time,were derived.The properties of busy period,vacation period,idle period,set-up and close period were calculated.
出处
《辽宁工程技术大学学报（自然科学版）》
CAS
北大核心
2011年第4期607-610,共4页
Journal of Liaoning Technical University (Natural Science)
基金
国家自然科学基金资助项目(10671170)
关键词
N
策略
单重休假
启动-关闭期
队长
等待时间
N-policy
single vacation
set-up period
close period
stochastic decomposition
