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On the relationships among queue lengths at arrival, departure, and random epochs in the discrete-time queue with D-BMAP arrivals

Authors:

Nam K. Kim,

Seok H. Chang,

Kyung C. ChaeAuthors Info & Claims

Operations Research Letters, Volume 30, Issue 1

Pages 25 - 32

https://doi.org/10.1016/S0167-6377(01)00110-9

Published: 01 February 2002 Publication History

Abstract

We consider finite- and infinite-capacity queues with discrete-time batch Markovian arrival processes (D-BMAP) under the assumption of the Late Arrival System with Delayed Access as well as the Early Arrival System. Using simple arguments such as the balance equation, ''rate in=rate out'', we derive relationships among the stationary queue lengths at arrival, at departure, and at random epochs. Such relationships hold for a broad class of discrete-time queues with D-BMAP arrivals.

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On the relationships among queue lengths at arrival, departure, and random epochs in the discrete-time queue with D-BMAP arrivals
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Published In

Operations Research Letters Volume 30, Issue 1

February, 2002

71 pages

ISSN:0167-6377

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Elsevier Science Publishers B. V.

Netherlands

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Published: 01 February 2002

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Samanta SNandi R(2021)Queue-Length, Waiting-Time and Service Batch Size Analysis for the Discrete-Time GI/D-MSP Queueing SystemMethodology and Computing in Applied Probability10.1007/s11009-020-09823-923:4(1461-1488)Online publication date: 1-Dec-2021
https://dl.acm.org/doi/10.1007/s11009-020-09823-9
Horváth G(2020)Waiting time and queue length analysis of Markov-modulated fluid priority queuesQueueing Systems: Theory and Applications10.1007/s11134-020-09650-295:1-2(69-95)Online publication date: 1-Jun-2020
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Moltchanov D(2012)A study of TCP performance in wireless environment using fixed-point approximationComputer Networks: The International Journal of Computer and Telecommunications Networking10.1016/j.comnet.2011.11.01256:4(1263-1285)Online publication date: 1-Mar-2012
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Huo ZTian NWang JYue W(2010)Modeling study of the sleep mode in the IEEE 802.16e wireless networks with correlated trafficProceedings of the 5th International Conference on Queueing Theory and Network Applications10.1145/1837856.1837862(35-40)Online publication date: 24-Jul-2010
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Moltchanov DKoucheryavy YHarju J(2006)An integrated model of packetized VBR teletraffic source for cellular NG All-IP wireless networksComputer Communications10.1016/j.comcom.2005.06.01629:8(957-968)Online publication date: 1-May-2006
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Kim NChae KChaudhry M(2004)An Invariance Relation and a Unified Method to Derive Stationary Queue-Length DistributionsOperations Research10.1287/opre.1040.011652:5(756-764)Online publication date: 1-Oct-2004
https://dl.acm.org/doi/10.1287/opre.1040.0116

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