Titlebook: Stochastic Networks and Queues; Philippe Robert Book 2003 Springer-Verlag Berlin Heidelberg 2003 Applied stochastic calculus.Ergodic theor

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Queues with Poisson Arrivals,or 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 ./∞ queue) and the single server queue with the following service disciplines: FIFO, LIFO and Processor-Sharing. The Proc

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Recurrence and Transience of Markov Chains, Chapter 2, the convergence in distribution of the Markov chain (..) has been obtained by using an explicit representation of the random variable .. as a functional of the random walk associated with the interarrival times and the service times. Markov chains describing the behavior of most queueing

他去就结束

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Ergodic Theory: Basic Results,n probability theory. Results proved in this chapter are classical in a Markovian framework (ergodic theorems, representations of the invariant probability,...). It is nevertheless very helpful to realize that the Markov property does not really play a role to get these results: They also hold in a

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Stationary Point Processes,of their respective sojourn times in the queue (the .th customer arrives at time .. and leaves at .. + ..). The queue transforms a point process {..} (the arrival process) in another point process {.. + ..} (the departure process). In this setting, it is quite natural to investigate the properties o

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The M/M/1 Queue,ced in Chapter 9 to study general queueing networks. A large deviations result concludes this chapter, it gives an estimation of the probability that the sample path of the process of the number of customers follows a very unlikely path.

Outmoded

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Ergodic Theory: Basic Results,truction of ergodic theory is used (the “special flow” defined page 295). Since this subject is not standard in graduate courses on stochastic processes, most of the results are proved. The reference book Cornfeld .. [.] gives a broader point of view of this domain. In the following (Ω,.ℱ, ℙ) is the probability space of reference.

Innocence

Stationary Point Processes,lost for the departure process (the examples of the ./1 queue or some product form networks seen in Chapter 4 are remarkable exceptions to this general rule). For example, if the arrival process is a renewal process, the departure process is not, in general, a renewal process.

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Limit Theorems for ,/1 Queues,get the number of poles and zeros of a complex function in general, and a fortiori to locate them. For this reason, getting some simple qualitative results for the ./1 FIFO queue may turn out to be quite difficult.