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
Stochastic bounds on partial ordering: application to memory overflows due to bursty arrivals
ISCIS'05 Proceedings of the 20th international conference on Computer and Information Sciences
Weak stochastic ordering for multidimensional Markov chains
Operations Research Letters
Accuracy of strong and weak comparisons for network of queues
MMB&DFT'10 Proceedings of the 15th international GI/ITG conference on Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance
Necessary and sufficient conditions for strong comparability of multicomponent systems
Discrete Event Dynamic Systems
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Stochastic monotonicity is one of the sufficient conditions for stochastic comparisons of Markov chains. On a partially ordered state space, several stochastic orderings can be defined by means of increasing sets. The most known is the strong stochastic (sample-path) ordering, but weaker orderings (weak and weak*) could be defined by restricting the considered increasing sets. When the strong ordering could not be defined, weaker orderings represent an alternative as they generate less constraints. Also, they may provide more accurate bounds. The main goal of this paper is to provide an intuitive event formalism added to stochastic comparisons methods in order to prove the stochastic monotonicity for multidimensional Continuous Time Markov Chains (CTMC). We use the coupling by events for the strong monotonicity. For weaker monotonicity, we give a theorem based on generator inequalities using increasing sets. We prove this theorem, and we present the event formalism for the definition of the increasing sets. We apply our formalism on queueing networks, in order to establish monotonicity properties.