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Journal ArticleDOI

The Single Server Queue

Jacob Cohen1
01 May 1970-Vol. 146, Iss: 1, pp 92-92
TL;DR: In this paper, the basic models of queueing theory are described and a dual aim is to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.
Abstract: Hardbound. This classic work, now available in paperback, concentrates on the basic models of queueing theory. It has a dual aim: to describe relevant mathematical techniques and to analyse the single server queue and its most important variants.
Citations
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Journal ArticleDOI
12 May 2005-Nature
TL;DR: It is shown that the bursty nature of human behaviour is a consequence of a decision-based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times.
Abstract: What determines the timing of human actions? A big question, but the science of human dynamics is here to tackle it. And its predictions are of practical value: for example, when ISPs decide what bandwidth an institution needs, they use a model of the likely timing and activity level of the individuals. Current models assume that an individual has a well defined probability of engaging in a specific action at a given moment, but evidence that the timing of human actions does not follow this pattern (of Poisson statistics) is emerging. Instead the delay between two consecutive events is best described by a heavy-tailed (power law) distribution. Albert-Laszlo Barabasi proposes an explanation for the prevalence of this behaviour. The ‘bursty’ nature of human dynamics, he finds, is a fundamental consequence of decision making. The dynamics of many social, technological and economic phenomena are driven by individual human actions, turning the quantitative understanding of human behaviour into a central question of modern science. Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes1,2,3. In contrast, there is increasing evidence that the timing of many human activities, ranging from communication to entertainment and work patterns, follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity4,5,6,7,8. Here I show that the bursty nature of human behaviour is a consequence of a decision-based queuing process9,10: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, with most tasks being rapidly executed, whereas a few experience very long waiting times. In contrast, random or priority blind execution is well approximated by uniform inter-event statistics. These finding have important implications, ranging from resource management to service allocation, in both communications and retail.

2,186 citations

Journal ArticleDOI
TL;DR: The purpose of this paper is to collect a number of useful results about Markov-modulated Poisson processes and queues with Markov -modulated input and to summary of recent developments.

882 citations

Journal ArticleDOI
TL;DR: In this article, a particular problem is addressed but results lead to a computationally reasonable solution which applies to very general two dimensional random walks, where the unknown functions are the generating functions for a stationary distribution of the studied process.
Abstract: Many problems arising from the coupling of processors require the solution of functional equations. Generally, the unknown functions are the generating functions for a stationary distribution of the studied process. In this paper, a particular problem is addressed but results lead to a computationally reasonable solution which applies to very general two dimensional random walks.

355 citations

Journal ArticleDOI
TL;DR: A bibliography of material concerned with modeling of production and transfer lines using queueing networks, which denotes production lines as flow lines with asynchronous part transfer, while transfer lines have synchronous part transfer.

323 citations

Book ChapterDOI
01 Jun 1988
TL;DR: In this paper, the authors summarize the lines of research that are currently being pursued, and explain what new results would be regarded as breakthroughs and have the most impact on the use of this modeling technique in the application field.
Abstract: Petri nets in which random firing delays are associated with transitions whose firing is an atomic operation are known under the name “stochastic Petri nets” These models are discussed, with the purpose of explaining why they were proposed in the performance evaluation field, why random delays with negative exponential probability density functions are mainly used, and what are their strong and weak points An effort is made to summarize the lines of research that are currently being pursued, and to explain what new results would be regarded as breakthroughs and have the most impact on the use of this modeling technique in the application field

319 citations