A queueing approximation of MMPP/PH/1

Asanjarani, Azam and Nazarathy, Yoni (2016). A queueing approximation of MMPP/PH/1. In: Tien van Do, Yutaka Takahashi, Wuyi Yue and Viet-Ha Nguyen, Queueing Theory and Network Applications. 10th International Conference on Queueing Theory and Network Applications (QTNA 2015), Ha Noi and Ha Long, Vietnam, (41-51). 17-20 August 2015. doi:10.1007/978-3-319-22267-7_4

Author Asanjarani, Azam
Nazarathy, Yoni
Title of paper A queueing approximation of MMPP/PH/1
Conference name 10th International Conference on Queueing Theory and Network Applications (QTNA 2015)
Conference location Ha Noi and Ha Long, Vietnam
Conference dates 17-20 August 2015
Proceedings title Queueing Theory and Network Applications   Check publisher's open access policy
Journal name Advances in Intelligent Systems and Computing   Check publisher's open access policy
Series Advances in Intelligent Systems and Computing
Place of Publication Heidelberg, Germany
Publisher Springer
Publication Year 2016
Year available 2016
Sub-type Fully published paper
DOI 10.1007/978-3-319-22267-7_4
Open Access Status Not Open Access
ISBN 9783319222660
ISSN 2194-5357
Editor Tien van Do
Yutaka Takahashi
Wuyi Yue
Viet-Ha Nguyen
Volume 383
Start page 41
End page 51
Total pages 11
Chapter number 4
Total chapters 16
Language eng
Formatted Abstract/Summary
We consider the well-studied MMPP/PH/1 queue and illustrate a method to find an almost equivalent model, the MTCP/PH/1. MTCP stands for Markovian Transition Counting Process. It is a counting process that has similar characteristics to MMPP (Markov Modulated Poisson Process). We prove that for a class of MMPPs there is an equivalent class of MTCPs. We then use this property to suggest an approximation for MMPP/PH/1 in terms of the first two moments. We numerically show that the steady state characteristics of MMPP/PH/1 are well approximated by the associated MTCP/PH/1 queue. Our numerical analysis leaves some open problems on bounds of the approximations. Of independent interest, this paper also contains a lemma on the workload expression of MAP/PH/1 queues which to the best of our knowledge has not appeared elsewhere.
Keyword MAP/PH/1
Markov modulated poisson process
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Conference Paper
Collections: School of Mathematics and Physics
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