Calculation of steady-state probabilities of M/M queues: Further approaches.
Smith, David K. (2002)
Journal of Applied Mathematics and Decision Sciences
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Smith, David K. (2002)
Journal of Applied Mathematics and Decision Sciences
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Jesús Artalejo, Gennadi Falin (2002)
Revista Matemática Complutense
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We describe main models and results of a new branch of the queueing theory, theory of retrial queues, which is characterized by the following basic assumption: a customer who cannot get service (due to finite capacity of the system, balking, impatience, etc.) leaves the service area, but after some random delay returns to the system again. Emphasis is done on comparison with standard queues with waiting line and queues with losses. We give a survey of main results for both single server...
Saulius Minkevičius, Stasys Steišŭnas (2005)
Control and Cybernetics
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Wood, David R. (2005)
Discrete Mathematics and Theoretical Computer Science. DMTCS [electronic only]
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Oleg Tikhonenko, Wojciech M. Kempa (2013)
Kybernetika
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A multi-server -type queueing system with a bounded total volume and finite queue size is considered. An AQM algorithm with the “accepting” function is being used to control the arrival process of incoming packets. The stationary queue-size distribution and the loss probability are derived. Numerical examples illustrating theoretical results are attached as well.
Bramson, Maury (2008)
Probability Surveys [electronic only]
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Wojciech M. Kempa (2014)
Kybernetika
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A queueing system with batch Poisson arrivals and single vacations with the exhaustive service discipline is investigated. As the main result the representation for the Laplace transform of the transient queue-size distribution in the system which is empty before the opening is obtained. The approach consists of few stages. Firstly, some results for a ``usual'' system without vacations corresponding to the original one are derived. Next, applying the formula of total probability, the...
Andrzej Chydziński, Łukasz Chróst (2011)
International Journal of Applied Mathematics and Computer Science
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Queueing systems in which an arriving job is blocked and lost with a probability that depends on the queue size are studied. The study is motivated by the popularity of Active Queue Management (AQM) algorithms proposed for packet queueing in Internet routers. AQM algorithms often exploit the idea of queue-size based packet dropping. The main results include analytical solutions for queue size distribution, loss ratio and throughput. The analytical results are illustrated via numerical...