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Analysis of an M/G/1 queue with customer impatience and adaptive arrival process

Abstract : We study an M/G/1 queue with impatience and an adaptive arrival process. The rate of the arrival process changes according to whether an incoming customer is accepted or rejected. We analyse two different models for impatience : (i) based on workload, and (ii) based on queue-length. For the workload-based model, we obtain the Laplace-Stieltjes Transform of the joint stationary workload and arrival rate process, and that of the waiting time. For the queue-length based model we obtain the analogous z-transform. These queueing models might also be useful for capturing the interaction between congestion control algorithms and queue management schemes in the Internet.
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https://hal.inria.fr/hal-00644866
Contributor : Service Ist Inria Sophia Antipolis-Méditerranée / I3s Connect in order to contact the contributor
Submitted on : Friday, November 25, 2011 - 1:47:17 PM
Last modification on : Wednesday, June 1, 2022 - 4:34:36 AM
Long-term archiving on: : Sunday, February 26, 2012 - 2:30:12 AM

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  • HAL Id : hal-00644866, version 1

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Onno Boxma, Balakrishna Prabhu. Analysis of an M/G/1 queue with customer impatience and adaptive arrival process. NetGCOOP 2011 : International conference on NETwork Games, COntrol and OPtimization, Telecom SudParis et Université Paris Descartes, Oct 2011, Paris, France. ⟨hal-00644866⟩

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