Abstract
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 language | English |
---|---|
Title of host publication | Queueing Theory and Network Applications - 14th International Conference, QTNA 2019, Proceedings |
Editors | Tuan Phung-Duc, Shoji Kasahara, Sabine Wittevrongel |
Publisher | Springer |
Pages | 201-220 |
Number of pages | 20 |
ISBN (Print) | 9783030271800 |
DOIs | |
Publication status | Published - 2019 |
Event | 14th International Conference on Queueing Theory and Network Applications, QTNA 2019 - Ghent, Belgium Duration: 27 Aug 2019 → 29 Aug 2019 Conference number: 14 |
Publication series
Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|
Volume | 11688 LNCS |
ISSN (Print) | 0302-9743 |
ISSN (Electronic) | 1611-3349 |
Conference
Conference | 14th International Conference on Queueing Theory and Network Applications, QTNA 2019 |
---|---|
Abbreviated title | QTNA 2019 |
Country/Territory | Belgium |
City | Ghent |
Period | 27/08/19 → 29/08/19 |
Keywords
- Error bound
- Linear programming
- Markov reward approach
- Multi-dimensional random walk
- Stationary performance measures