Queues with Poisson Arrivals
Queues with Poisson Arrivals
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泊松到达队列
DOI：
10.1007/978-3-662-13052-0_7
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
P. Robert
中科院分区：
文献类型：
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作者：
P. Robert
在本章中，假定到达过程是一个有标记的泊松点过程。参见1.11提案第11页和第1.3节。第2页18为泊松标记点过程的定义和主要性质。在此设置下，分析了四种队列模型：具有无限数量服务器的队列（M/G/00队列）和具有先进先出、后进先出和处理器共享服务原则的单服务器队列。处理器共享队列得到了详细的处理，因为一个有趣的分支过程在逗留时间分布的推导中发挥了核心作用。它也是现代通信网络随机模型中的一门重要学科。最后一节专门讨论具有泊松输入的队列的一个常见的、重要的性质。本章还提供了一个机会，让我们在更奇特的状态空间（即非有限维状态空间）中处理带有值的马尔可夫过程。LIFO学科的马尔可夫描述涉及非负有限序列的状态空间。对于处理器共享，状态空间是lER+上的一组点度量。
Throughout this chapter, the arrival process is assumed to be a marked Poisson point process. See Proposition 1.11 page 11 and Section 1.3. 2 page 18 for the definition and the main properties of Poisson marked point processes. In this setting, four queueing models are analyzed: The queue with an infinite number of servers (the M/G/00 queue) and the single server queue with the following service disciplines: FIFO, LIFO and Processor-Sharing. The Processor-Sharing queue receives a detailed treatment because of the central role played by an interesting branching process in the derivation of the distribution of the sojourn time. It is also an important discipline in modern stochastic models of communication networks. The last section is devoted to a common, important property of queues having a Poisson input. This chapter is also an occasion to work with Markov processes with values in more exotic state spaces, ie non-finite dimensional state spaces. A Markovian description of LIFO discipline involves a state space of nonnegative finite sequences. For Processor-Sharing, the state space is a set of point measures on lER+.