Robustness of queuing network formulas
Journal of the ACM (JACM)
A decomposition approach for stochastic reward net models
Performance Evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Using the exact state space of a Markov model to compute approximate stationary measures
Proceedings of the 2000 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Structured analysis approaches for large Markov chains
Applied Numerical Mathematics
On the Best Rank-1 and Rank-(R1,R2,. . .,RN) Approximation of Higher-Order Tensors
SIAM Journal on Matrix Analysis and Applications
Rank-One Approximation to High Order Tensors
SIAM Journal on Matrix Analysis and Applications
IEEE Transactions on Software Engineering
Hierarchical Structuring of Superposed GSPNs
IEEE Transactions on Software Engineering
Product Form Solution for Generalized Stochastic Petri Nets
IEEE Transactions on Software Engineering
Product form solution for an insensitive stochastic process algebra structure
Performance Evaluation - Unified specification and performance evaluation using stochastic process algebras
INFORMS Journal on Computing
Adaptive decomposition and approximation for the analysis of stochastic petri nets
Performance Evaluation - Dependable systems and networks-performance and dependability symposium (DSN-PDS) 2002: Selected papers
Separable equilibrium state probabilities via time reversal in Markovian process algebra
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Convergence of the sequence of parameters generated by alternating least squares algorithms
Computational Statistics & Data Analysis
On the Tensor SVD and the Optimal Low Rank Orthogonal Approximation of Tensors
SIAM Journal on Matrix Analysis and Applications
Methodological construction of product-form stochastic Petri nets for performance evaluation
Journal of Systems and Software
Lumping and reversed processes in cooperating automata
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Algorithmic product-form approximations of interacting stochastic models
Computers & Mathematics with Applications
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Product form solutions have been found for several classes of stochastic models including some networks of stochastic automata or communicating Markov chains. In this paper a theory of approximate and higher order product forms is presented. The idea is to define an approximate product form solution as a Kronecker product of vectors that minimizes the Euclidean norm of the residual vector for arbitrary networks of communicating Markov processes. If the residual becomes zero, the product form becomes exact. By adopting ideas from numerical analysis to approximate a matrix by a sum of Kronecker products of small matrices, higher order product forms that result in better approximations are defined. This paper presents the general theory of product form approximations for communicating Markov processes and it introduces first algorithms to compute product form solutions. By means of some examples it is shown that the approach allows one to compute approximations with increasing accuracy by increasing the order of the product form.