Abstract A finite-buffer queueing system with threshold waking and early setup policy is investigated. The arrival stream is governed by a Poisson process while service times are assumed to be generally distributed. The natural FIFO processing discipline is used. Every time when the system empties, a type-specific energy saving policy is initialized that is a mixture of the classical N-type policy and an early setup mechanism. Namely, if the level of accumulated messages reaches M ≤ N , a generally distributed setup time is started, during which the service station achieves full readiness for processing. If, at the completion epoch of the setup time, the state of the system (the number of accumulated messages) equals at least N , then the service begins immediately. Otherwise, the service station waits (being ready for processing) for the N th arrival. The representation for the Laplace transform of the transient queue-size distribution is obtained using the analytical approach based on the idea of embedded Markov chain, the formula of total probability, linear algebra and renewal theory. A numerical example and simulational study are attached.

中文翻译：

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具有阈值唤醒和早期设置策略的有限缓冲区模型中的瞬态队列大小分布

摘要 研究了具有阈值唤醒和早期设置策略的有限缓冲区排队系统。到达流由泊松过程控制，而假设服务时间通常是分布的。使用自然 FIFO 处理规则。每次系统清空时，都会初始化一个特定类型的节能策略，它是经典的 N 型策略和早期设置机制的混合体。即，如果累积消息的级别达到M≤N，则开始一般分布的建立时间，在此期间服务站实现完全准备好进行处理。如果在设置时间的完成时期，系统状态（累积消息的数量）至少等于 N，则服务立即开始。除此以外，服务站等待（准备处理）第 N 个到达。利用基于嵌入马尔可夫链思想、全概率公式、线性代数和更新理论的解析方法，得到了瞬态队列大小分布的拉普拉斯变换表示。附有数值例子和模拟研究。