A methodology for solving Markov models of parallel systems
Journal of Parallel and Distributed Computing
On the self-similar nature of Ethernet traffic (extended version)
IEEE/ACM Transactions on Networking (TON)
Bounds for quasi-lumpable Markov chains
Performance '93 Proceedings of the 16th IFIP Working Group 7.3 international symposium on Computer performance modeling measurement and evaluation
Wide area traffic: the failure of Poisson modeling
IEEE/ACM Transactions on Networking (TON)
Composition and behaviors of probabilistic I/O automata
Theoretical Computer Science
Exact performance equivalence: an equivalence relation for stochastic automata
Theoretical Computer Science
INFORMS Journal on Computing
Lumpability and nearly-lumpability in hierarchical queueing networks
IPDS '95 Proceedings of the International Computer Performance and Dependability Symposium on Computer Performance and Dependability Symposium
A Novel Approach for Phase-Type Fitting with the EM Algorithm
IEEE Transactions on Dependable and Secure Computing
Bound-Preserving Composition for Markov Reward Models
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
A minimal representation of Markov arrival processes and a moments matching method
Performance Evaluation
KPC-Toolbox: Simple Yet Effective Trace Fitting Using Markovian Arrival Processes
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Convergence of the sequence of parameters generated by alternating least squares algorithms
Computational Statistics & Data Analysis
Using underapproximations for sparse nonnegative matrix factorization
Pattern Recognition
Stochastic Petri nets with matrix exponentially distributed firing times
Performance Evaluation
On the Complexity of Nonnegative Matrix Factorization
SIAM Journal on Optimization
Composition and Equivalence of Markovian and Non-Markovian Models
QEST '11 Proceedings of the 2011 Eighth International Conference on Quantitative Evaluation of SysTems
EPEW'05/WS-FM'05 Proceedings of the 2005 international conference on European Performance Engineering, and Web Services and Formal Methods, international conference on Formal Techniques for Computer Systems and Business Processes
Aggregation of Markovian Models -- An Alternating Least Squares Approach
QEST '12 Proceedings of the 2012 Ninth International Conference on Quantitative Evaluation of Systems
Compositional approximate markov chain aggregation for PEPA models
EPEW'12 Proceedings of the 9th European conference on Computer Performance Engineering
Nonnegative Matrix Factorization: A Comprehensive Review
IEEE Transactions on Knowledge and Data Engineering
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State based analysis of Markovian models is faced with the problem of state space explosion. To handle huge state spaces often compositional modeling and aggregation of components are used. Exact aggregation resulting in exact transient or stationary results is only possible in some cases, when the Markov process is lumpable. Therefore approximate aggregation is often applied to reduce the state space. Several approximate aggregation methods exist which are usually based on heuristics. This paper presents a new aggregation approach for Markovian components which computes aggregates that minimize the difference according to some algebraically defined function which describes the difference between the component and the aggregate. If the difference becomes zero, aggregation is exact, which means that component and aggregate are indistinguishable in the sense that transient and stationary results in any environment are identical. For the computation of aggregates, an alternating least squares approach is presented which tries to minimize the norm-wise difference between the original component and the aggregate. Algorithms to compute aggregates are also introduced and the quality of the approximation is evaluated by means of several examples.