摘要
本文考虑具有温储备失效特征和单重休假Min(N,V)-控制策略的M/G/1可修排队系统.在该系统中,服务台有两类故障:一类是服务台在服务员"广义忙期"中可能发生的故障,另一类是服务台在没有为顾客服务的时间段内可能发生的温储备故障,且假设两类故障具有不同的故障率和修复率.运用全概率分解技术、拉普拉斯变换工具以及更新过程理论,研究了系统的瞬态队长分布和稳态队长分布,获得了瞬态队长分布的拉普拉斯变换的递推表达式,得到了在系统容量的优化设计中有重要应用价值的稳态队长分布的递推结果,并证明了稳态队长的随机分解性质.同时还讨论了当休假时间V=0,V→∞与温储备寿命时间Y→∞时的特殊情形.最后,建立了系统长期单位时间内总成本费用函数,用数值计算例子讨论了最优控制策略N~*.
This paper considers an M/C/1 repairable queueing system with warm standby failure and Min（N,v）-policy based on single vacation in which there are two types of breakdowns. One is that the service station may break during the ＂generalized busy period＂ of the servers, and another is warm standby failure during the period of not providing service for customers. We assume that two breakdowns are enjoyed different failure rate and repair rate. Applying the total probability decomposition technique, laplace transform and the renewal process theory, we study the transient queue distribution and the steady-state queue distribution. The recursive expression of the laplace transformation for transient queue length distribution is obtained. And, the recursive expression for the steady-state queue length distribution, which have important value in the system capacity design, is also given. Then, the stochastic decomposition property of the steady state queue length distribution is proved. Meanwhile some special cases are also or v→∞, and the warm standby life time Y→∞ cost per unit for system is developed, and the discussed when the single vacation time v-0 Finally, the total long-run expected average optimal control policy N＊ is discussed by the numerical example.
作者
蔡晓丽
唐应辉
CAI XIAOLI TANG YINGHUI(School of Mathematics ＆ Software Science, Sichuan Normal University, Chengdu 610068 School of Fundamental Education, Siehuan Normal University, Chengdu 610068)
出处
《应用数学学报》
CSCD
北大核心
2017年第5期702-726,共25页
Acta Mathematicae Applicatae Sinica
基金
国家自然科学基金(71571127)
国家自然科学基金青年基金(71301111)资助项目
