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The delay distribution of a type k customer in a first-come-first-served MMAP[K]/PH[K]/1 queue

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

B. Van Houdt  and
C. Blondia
B. Van Houdt*
Affiliation:
University of Antwerp
C. Blondia*
Affiliation:
University of Antwerp
*
∗ Postal address: Department of Mathematics and Computer Science, Performance Analysis of Telecommunication Systems Research Group, Universiteitsplein, 1, B-2610 Antwerp, Belgium.
∗ Postal address: Department of Mathematics and Computer Science, Performance Analysis of Telecommunication Systems Research Group, Universiteitsplein, 1, B-2610 Antwerp, Belgium.
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Abstract

This paper presents an algorithmic procedure to calculate the delay distribution of a type k customer in a first-come-first-served (FCFS) discrete-time queueing system with multiple types of customers, where each type has different service requirements (the MMAP[K]/PH[K]/1 queue). First, we develop a procedure, using matrix analytical methods, to handle arrival processes that do not allow batch arrivals to occur. Next, we show that this technique can be generalized to arrival processes that do allow batch arrivals to occur. We end the paper by presenting some numerical examples.

Keywords

Queueing theorydelay distributionfirst-come-first-servedmultiple customer typesmatrix analytic methodsphase-type distributionMarkovian arrival process

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 1 , March 2002 , pp. 213 - 223
Copyright
Copyright © Applied Probability Trust 2002 

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