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
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
Weak stochastic ordering for multidimensional Markov chains
Operations Research Letters
Strong and weak stochastic bounds for multidimensional Markov chains
International Journal of Critical Computer-Based Systems
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End to end QoS (Quality of Service) is crucial in computer networks, but very hard to study as the systems are in general very complex. We suppose that systems can be modeled by multidimensional Markov processes, which could be very hard to analyse if there is no specific solution form. We propose to apply stochastic comparisons of Markov processes in order to solve this problem. We provide new processes, easier to analyze and representing stochastic bounds (upper or lower) for the original model. In this paper, we propose strong and weak bounding processes for a general queueing network model, and discuss their accuracy for QoS constraints.