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09 Jun 2005
The BMAP/G/1 queue: A tutorial
 David M. Lucantoni
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Abstract
We present an overview of recent results related to the single server queue with general independent and identically distributed service times and a batch Markovian arrival process (BMAP). The BMAP encompasses a wide range of arrival processes and yet, mathematically, the BMAP/G/1 model is a relatively simple matrix generalization of the M/G/1 queue. Stationary and transient distributions for the queue length and waiting time distributions are presented. We discuss numerical algorithms for computing these quantities, which exploit both matrix analytic results and numerical transform inversion. Twodimensional transform inversion is used for the transient results.
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 Title
 The BMAP/G/1 queue: A tutorial
 Book Title
 Performance Evaluation of Computer and Communication Systems
 Book Subtitle
 Joint Tutorial Papers of Performance '93 and Sigmetrics '93
 Pages
 pp 330358
 Copyright
 1993
 DOI
 10.1007/BFb0013859
 Print ISBN
 9783540572978
 Online ISBN
 9783540480440
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 729
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
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 Editors
 Authors

 David M. Lucantoni ^{(1)}
 Author Affiliations

 1. AT&T Bell Laboratories, Room 3K601, 101 Crawfords Corner Rd, 077333030, Holmdel, New Jersey, USA
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