Analyzing multi-class, multi-server queueing systems with preemtive priorities

Andrei Sleptchenko, Aart van Harten, Matthijs C. van der Heijden

Research output: Working paper

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Abstract

In this paper we consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple items, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an approximate method to estimate the steady state probabilities with an approximation error that can be made as small as desired at the expense of some more numerical matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system. We illustrate our method with some numerical examples. Comparison to simulation results shows that with a moderate number of matrix iterations (~20) we can estimate key performance measures, such as the mean and variance of the number of items in the system, with an error less than 1% in most cases.
Original languageUndefined
Place of PublicationEnschede, the Netherlands
PublisherUniversity of Twente, Research School for Operations Management and Logistics (BETA)
Number of pages27
Publication statusPublished - 2002

Publication series

NameBETA working paper
PublisherUniversity of Enschede, BETA
No.WP-77

Keywords

  • IR-95692

Cite this

Sleptchenko, A., van Harten, A., & van der Heijden, M. C. (2002). Analyzing multi-class, multi-server queueing systems with preemtive priorities. (BETA working paper; No. WP-77). Enschede, the Netherlands: University of Twente, Research School for Operations Management and Logistics (BETA).
Sleptchenko, Andrei ; van Harten, Aart ; van der Heijden, Matthijs C. / Analyzing multi-class, multi-server queueing systems with preemtive priorities. Enschede, the Netherlands : University of Twente, Research School for Operations Management and Logistics (BETA), 2002. (BETA working paper; WP-77).
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Sleptchenko, A, van Harten, A & van der Heijden, MC 2002 'Analyzing multi-class, multi-server queueing systems with preemtive priorities' BETA working paper, no. WP-77, University of Twente, Research School for Operations Management and Logistics (BETA), Enschede, the Netherlands.

Analyzing multi-class, multi-server queueing systems with preemtive priorities. / Sleptchenko, Andrei; van Harten, Aart; van der Heijden, Matthijs C.

Enschede, the Netherlands : University of Twente, Research School for Operations Management and Logistics (BETA), 2002. (BETA working paper; No. WP-77).

Research output: Working paper

TY - UNPB

T1 - Analyzing multi-class, multi-server queueing systems with preemtive priorities

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AU - van der Heijden, Matthijs C.

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Y1 - 2002

N2 - In this paper we consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple items, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an approximate method to estimate the steady state probabilities with an approximation error that can be made as small as desired at the expense of some more numerical matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system. We illustrate our method with some numerical examples. Comparison to simulation results shows that with a moderate number of matrix iterations (~20) we can estimate key performance measures, such as the mean and variance of the number of items in the system, with an error less than 1% in most cases.

AB - In this paper we consider a multi-class, multi-server queueing system with preemptive priorities. We distinguish two groups of priority classes that consist of multiple items, each having their own arrival and service rate. We assume Poisson arrival processes and exponentially distributed service times. We derive an approximate method to estimate the steady state probabilities with an approximation error that can be made as small as desired at the expense of some more numerical matrix iterations. Based on these probabilities, we can derive approximations for a wide range of relevant performance characteristics, such as the expected postponement time for each item class and the first and second moment of the number of items of a certain type in the system. We illustrate our method with some numerical examples. Comparison to simulation results shows that with a moderate number of matrix iterations (~20) we can estimate key performance measures, such as the mean and variance of the number of items in the system, with an error less than 1% in most cases.

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Sleptchenko A, van Harten A, van der Heijden MC. Analyzing multi-class, multi-server queueing systems with preemtive priorities. Enschede, the Netherlands: University of Twente, Research School for Operations Management and Logistics (BETA). 2002. (BETA working paper; WP-77).