【摘要】 研究了在服务员工作量D-策略控制下，不中断单重休假和可变到达率的Geo^λ₁,λ₂/G/1排队的瞬态与稳态性能。使用全概率分解技术和更新过程理论，详细分析了在任意初始状态下队长的瞬态概率分布，得到了在任意时刻n⁺瞬态队长分布的z-变换表达式。在瞬态分析的基础上，通过一些代数运算得到了稳态队长分布的递推表达式，同时推导了系统其他重要的排队性能指标。进一步得到了系统在不同时刻点n、n^-处队长的稳态概率分布的表达式。最后，在建立的费用模型下用数值例子讨论了系统的最小成本问题，并确定了使得系统在长期单位时间内期望成本最小的最优控制策略。更多还原

【Abstract】 This paper studies the transient and steady-state performance of the Geo^λ₁,λ₂/G/1 queue with uninterrupted single vacation and variable arrival rates under the control of server’s workload D-policy. Employing the total probability decomposition technique and the renewal process theory, we present a detailed analysis of the transient probability distribution of the queue length under any initial state, and obtain the expressions of the z-transformation of the transient queue length distribution at any epoch n⁺. Based on the transient analysis, the recursive expressions of the steady-state queue length distribution are derived by using some algebraic operation. Meanwhile, some other important queueing performance measures of the system are obtained. Furthermore, the expressions of the steady-state probability distribution of the queue length at different epochs n and n^-are obtained. Finally, the minimum cost problem of the system is discussed with numerical examples under the established cost model,and the optimal control policies that minimize the long-run expected cost per unit time are determined.更多还原