具有Bernoulli反馈和Min(N,D)-策略控制的Geo^(λ1,λ2)/G/1离散时间可修排队的可靠性分析

RELIABILITY ANALYSIS OF DISCRETE-TIME Geo^(λ_1,λ_2)/G/1 REPAIRABLE QUEUE WITH BERNOULLI FEEDBACK AND MIN(N,D)-POLICY

考虑具有Bernoulli反馈,可变到达率以及Min(Ⅳ,D)-策略控制的Geo/G/1离散时间可修排队系统的可靠性指标.服务台在服务过程中可能发生故障,顾客的到达率依赖于服务员的状态.使用更新理论,全概率分解技术和概率母函数方法,首先讨论了服务员在任意时刻n^+处于忙的瞬态概率和稳态概率.其次,分析了一些可靠性指标,如服务台的瞬态和稳态不可用度、时间段(0^+,n^+]内服务台的平均故障次数和稳态故障频度.所得结果揭示了可靠性指标的随机分解性质.利用本文的结论直接给出了一些特殊离散时间可修排队系统的可靠性指标.最后,通过数值实例分析了系统参数对可靠性指标的影响.

This paper considers reliability indices for a Geo/G/1 discrete-time re- pairable queue with Bernoulli feedback, variable arrival rate and Min（N, D）-policy. The service station may be subject to breakdowns at random during serving cus- tomers. Customers arrive at the system in variable input rates according to the states of the server. Using the renewal theory, the total probability decomposition technique and the probability generating function method, the transient and the steady-state probabilities that the server is busy at any time epoch n＋ are discussed. Furthermore, some reliability indices such as the transient and steady-state unavailability, the ex- pected number of failures during time interval （0＋, n＋] and the equilibrium failure frequency are analyzed. The results obtained in our study reveal that the reliability measures meet the stochastic decomposition property. Moreover, some correspond- ing results of reliability indices for special discrete-time repairable queues are directly given by our results. Finally, the effects of system parameters on the reliability indices are analyzed by numerical examples.