Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Queueing networks with blocking
Queueing networks with blocking
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
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
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
On the delay of network coding over line networks
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Stochastic comparisons for performability of telecommunication systems
ASMTA'10 Proceedings of the 17th international conference on Analytical and stochastic modeling techniques and applications
Bounding techniques for transient analysis of G-networks with catastrophes
Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools
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
Strong and Weak orderings for an accurate resource dimensioning
VECoS'11 Proceedings of the Fifth international conference on Verification and Evaluation of Computer and Communication Systems
Strong and weak stochastic bounds for multidimensional Markov chains
International Journal of Critical Computer-Based Systems
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Performance evaluation of telecommunication and computer systems is essential but a complex issue in general. Quantitative analysis of systems represented by multidimensional Markov processes models is very difficult and may be intractable if there is no specific solution form. In this study, we propose an algorithm in order to derive aggregated Markov processes providing upper and lower bounds on performance measures. We prove using stochastic comparisons that these aggregated Markov processes give bounds on performance measures defined as increasing reward functions on the transient and stationary distributions. The stochastic comparison has been largely applied in performance evaluation however the state space is generally assumed to be totally ordered which induces less accurate bounds for multidimensional Markov processes. Our proposed algorithm assumes only a preorder on the state space, and is applied to the analysis of an open tandem queueing network with rejection in order to derive loss probability bounds. Numerical results are computed from two parametric aggregation schemes: a fine and a coarse in order to show the improvement of the accuracy of the bound with respect to the state space size. We propose an attractive solution to the performance study: given a performance measure threshold, we study if it is guaranteed or not by studying less complex aggregated bounding processes.