Stochastic ordering for Markov processes on partially ordered spaces
Mathematics of Operations Research
Hierarchical Markovian models: symmetries and reduction
Performance Evaluation - Special issue: 6th international conference on modelling techniques and tools for computer performance evaluation
MRAP: a multiservices resource allocation policy for wireless ATM network
Computer Networks and ISDN Systems - Special issue on modeling of wired and wireless ATM networks
Exact performance equivalence: an equivalence relation for stochastic automata
Theoretical Computer Science
Stochastic Automata Networks and Near Complete Decomposability
SIAM Journal on Matrix Analysis and Applications
Multilevel Solutions for Structured Markov Chains
SIAM Journal on Matrix Analysis and Applications
An iterative bounding method for stochastic automata networks
Performance Evaluation
An Algorithmic Approach to Stochastic Bounds
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Bounding the Loss Rates in a Multistage ATM Switch
Proceedings of the 9th International Conference on Computer Performance Evaluation: Modelling Techniques and Tools
Iterative disaggregation for a class of lumpable discrete-time stochastic automata networks
Performance Evaluation
Bound-Preserving Composition for Markov Reward Models
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Bounds based on lumpable matrices for partially ordered state space
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
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The Stochastic Automata Network (SAN in the following) methodology is in general associated to exact numerical analysis taking into account the tensor decomposition of the chain to improve matrix vector product. Here, we advocate a completely different approach: use the automata, their properties and the definition of tensor operations to derive structural properties of the chain and stochastic bounds to simplify the SAN. We focus on lumpability and stochastic bounds. Rather than a complete theory which remains to establish, we present a real example: the computation of the loss rate for a multistage ATM switch.