Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
NECESSARY AND SUFFICIENT CONDITIONS FOR THE STOCHASTIC COMPARISON OF JACKSON NETWORKS
Probability in the Engineering and Informational Sciences
Performance measure bounds in mobile networks by state space reduction
MASCOTS '05 Proceedings of the 13th IEEE International Symposium on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
Loss rates bounds for IP switches in MPLS networks
AICCSA '06 Proceedings of the IEEE International Conference on Computer Systems and Applications
Aggregated bounding Markov processes applied to the analysis of tandem queues
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Weak Stochastic Comparisons for Performability Verification
ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Stochastic Monotonicity in Queueing Networks
EPEW '09 Proceedings of the 6th European Performance Engineering Workshop on Computer Performance Engineering
Weak stochastic ordering for multidimensional Markov chains
Operations Research Letters
On the choice of the stochastic comparison method for multidimensional Markov chains analysis
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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Quality of performance measure bounds is crucial for an accurate dimensioning of computer network resources. We study stochastic comparisons of multidimensional Markov processes for which quantitative analysis could be intractable if there is no specific solution form. On partially ordered state space, different stochastic orderings can be defined as the strong or the less constrained weak ordering. The goal of the present paper is to compare these two orderings with respect the quality of derived bounds. We propose to study a system similar to a Jackson network except that queues have finite capacity. Different bounding systems are built either in the sense of the strong ordering with hard constraints, or in the sense of the weak ordering with less ones. The proofs of the stochastic comparisons are done using the coupling and the increasing set methods, with an intuitive event based formalism. The qualities of bounding systems are compared regarding to blocking probabilities.