A Linear Programming Approach to Markov Reward Error Bounds for Queueing Networks

Xinwei Bai*, Jasper Goseling

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


In this paper, we present a numerical framework for constructing bounds on stationary performance measures of random walks in the positive orthant using the Markov reward approach. These bounds are established in terms of stationary performance measures of a perturbed random walk whose stationary distribution is known explicitly. We consider random walks in an arbitrary number of dimensions and with a transition probability structure that is defined on an arbitrary partition of the positive orthant. Within each component of this partition the transition probabilities are homogeneous. This enables us to model queueing networks with, for instance, break-downs and finite buffers. The main contribution of this paper is that we generalize the linear programming approach of [10] to this class of models.

Original languageEnglish
Title of host publicationQueueing Theory and Network Applications - 14th International Conference, QTNA 2019, Proceedings
EditorsTuan Phung-Duc, Shoji Kasahara, Sabine Wittevrongel
Number of pages20
ISBN (Print)9783030271800
Publication statusPublished - 2019
Event14th International Conference on Queueing Theory and Network Applications, QTNA 2019 - Ghent, Belgium
Duration: 27 Aug 201929 Aug 2019
Conference number: 14

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11688 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference14th International Conference on Queueing Theory and Network Applications, QTNA 2019
Abbreviated titleQTNA 2019


  • Error bound
  • Linear programming
  • Markov reward approach
  • Multi-dimensional random walk
  • Stationary performance measures

Cite this