具有两类失效模式的D-策略M/G/1可修排队系统分析

Analysis of the M/G/1 repairable queueing system with D-policy and two types of failure modes

研究具有两类失效模式的D-策略M/G/1可修排队系统,其中第一类失效是服务台在服务顾客期间发生的失效,第二类失效是服务台在空闲期间发生的失效,且两类失效模式的失效率不同.使用全概率分解技术和利用拉普拉斯变换与母函数等工具,从任意初始状态出发,讨论了系统队长的瞬时分布和稳态分布,获得了系统稳态队长分布的递推表达式与稳态队长的随机分解结果.进一步,在建立费用模型的基础上,通过数值计算实例讨论了使得系统在长期单位时间内达到最小值的最优控制策略D~*,并在同一组参数取值下与服务台不发生故障时的最优控制策略进行了比较.

This paper studies the M/G/1 repairable queueing system with D-policy and two types of failure modes.The first type of failure is the failure of the service desk during the service of a customer,the second type of failure is the failure of the service desk during the idle period,and the failure efficiency of the two types of failure modes is different.By using the total probability decomposition,L-transform,generating function and other tools,the transient distribution and equilibrium distribution of the system queue-length are discussed from any initial state.The recursive expression of the steady-state queue length distribution and the random decomposition results of the steady-state queue length are obtained.Furthermore,on the basis of establishing the cost model,the optimal control strategy D*is discussed,which makes the system reach the minimum value in a long-term unit time by numerical examples.The optimal control strategy under the same set of parameters is compared with the optimal control strategy when the service desk does not fail.