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Point Process Method in Queueing Theory
1982In this paper we shall study a stochastic point process approach to problems in queueing theory. It will appear that many results previously obtained under special assumptions of independence or special distributional assumptions can be obtained under considerably weaker conditions by using the point process theory. In this way we will demonstrate that
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Large deviations ordering of point processes in some queueing networks
Queueing Systems, 1998Authors's abstract: Given a stochastic ordering between point processes (p.p.), say that a p.p. \(N\) is smooth if it is less than the Poisson process with the same average intensity for this ordering. We investigate whether initially smooth processes retain their smoothness as they cross a network of FIFO \(\cdot/\text{D}/1\) queues along fixed routes.
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FiFiQueues: Fixed-Point Analysis of Queueing Networks with Finite-Buffer Stations
2000The tool FiFiQueues analyses a general class of open queueing networks, consisting of queueing stations with limited or unlimited buffer capacity and with arbitrary connections between them. The external arrival processes and the service processes are not limited to Poisson processes but are defined by the first and the second moments of the underlying
Ramin Sadre, Boudewijn R. Haverkort
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Point process channel and capacity of the exponential server queue
2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060), 2002We give a conceptually simple proof for the capacity of the exponential server queue. Our proof links the timing channel to the point process channel with complete feedback. This point process approach enables us to bound capacities of timing channels that arise in multiserver queues, queues in tandem, and other simple configurations.
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Algorithms for the upper bound mean waiting time in the GI/GI/1 queue
Queueing systems, 2020Yan Chen, W. Whitt
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Algorithmic methods in queues and in the exploration of point processes
2013This is a review of the methodology for the algorithmic study of some useful models in point process and queueing theory, as discussed in three lectures at the Summer Institute at Sozopol, Bulgaria. The author provides references to sources where the extensive details of this work are found.
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On the existence of fixed points for the ./GI/1 queue
2003A celebrated theorem of Burke's asserts that the Poisson process is a fixed point for a stable exponential single server queue; that is, when the arrival process is Poisson, the equilibrium departure process is Poisson of the same rate. This paper considers the following question: Do fixed points exist for queues which dispense i.i.d.
Mairesse, Jean, Prabhakar, Balaji
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Extreme Values of Queues, Point Processes and Stochastic Networks.
1985Issued as Subject reports [nos. 1-2], Project report, Annual report, and Final report, Project no.
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