Distribution of crossings of level in a busy cycle of the M/G/1 queue
J. W. Cohen, I. Greenberg (1968)
Annales de l'I.H.P. Probabilités et statistiques
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J. W. Cohen, I. Greenberg (1968)
Annales de l'I.H.P. Probabilités et statistiques
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Loris-Teghem, Jacqueline (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Loris-Teghem, J. (2000)
Journal of Applied Mathematics and Stochastic Analysis
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Choi, Bong Dae, Kim, Yeong Cheol, Shin, Yang Woo, Pearce, Charles E.M. (2001)
Journal of Applied Mathematics and Stochastic Analysis
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R. G. Rani (1974)
RAIRO - Operations Research - Recherche Opérationnelle
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Władysław Szczotka
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CONTENTS1. Introduction...................................................................52. Preliminaries................................................................113. Departure process......................................................194. Joint distribution of waiting time and queue size..........325. New forms of Little's formula.......................................38References.....................................................................53
Frey, Andreas, Takahashi, Yoshitaka (1999)
Journal of Applied Mathematics and Stochastic Analysis
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Shin, Yang Woo (1999)
Journal of Applied Mathematics and Stochastic Analysis
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Ghosal, A., Madan, S. (1988)
International Journal of Mathematics and Mathematical Sciences
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Arianna Brugno, Ciro D'Apice, Alexander Dudin, Rosanna Manzo (2017)
International Journal of Applied Mathematics and Computer Science
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A novel customer batch service discipline for a single server queue is introduced and analyzed. Service to customers is offered in batches of a certain size. If the number of customers in the system at the service completion moment is less than this size, the server does not start the next service until the number of customers in the system reaches this size or a random limitation of the idle time of the server expires, whichever occurs first. Customers arrive according to a Markovian...
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...