Journal of Applied Probability

The output process of an MMPP/M/1 queue

Nigel Bean, David Green, and Peter Taylor

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Abstract

Olivier and Walrand (1994) claimed that the departure process of an MMPP/M/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. They also conjectured that the departure process of an MAP/PH/1 queue is not an MAP unless the queue is a stationary M/M/1 queue. We show that their proof of the first result has an algebraic error, which leaves open the above question of whether the departure process of an MMPP/M/1 can be an MAP.

Article information

Source
J. Appl. Probab. Volume 35, Number 4 (1998), 998-1002.

Dates
First available: 19 September 2002

Permanent link to this document
http://projecteuclid.org/euclid.jap/1032438394

Digital Object Identifier
doi:10.1239/jap/1032438394

Mathematical Reviews number (MathSciNet)
MR1671249

Zentralblatt MATH identifier
0939.60096

Subjects
Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Markov arrival process (MAP) Markov modulated Poisson process (MMPP) (PH) phase-renewal process nonlinear filtering

Citation

Bean, Nigel; Green, David; Taylor, Peter. The output process of an MMPP / M /1 queue. Journal of Applied Probability 35 (1998), no. 4, 998--1002. doi:10.1239/jap/1032438394. http://projecteuclid.org/euclid.jap/1032438394.


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