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

O.J. Boxma, B.J. Prabhu

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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.
Original languageEnglish
Title of host publicationProceedings of the 5th International Conference on Network Games, Control and Optimization (NetGCoop 2011, Paris, France, October 12-14, 2011)
PublisherInstitute of Electrical and Electronics Engineers
ISBN (Print)978-1-4673-0383-5
Publication statusPublished - 2011


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