The PEPA workbench: a tool to support a process algebra-based approach to performance modelling
Proceedings of the 7th international conference on Computer performance evaluation : modelling techniques and tools: modelling techniques and tools
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
Computable Error Bounds for Aggregated Markov Chains
Journal of the ACM (JACM)
An Efficient Algorithm for Aggregating PEPA Models
IEEE Transactions on Software Engineering
Computer Performance Modeling Handbook
Computer Performance Modeling Handbook
Decomposition of general queueing networks with MMPP inputs and customer losses
Performance Evaluation
Turning back time in Markovian process algebra
Theoretical Computer Science
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
Bounding stationary results of Tandem networks with MAP input and PH service time distributions
SIGMETRICS '06/Performance '06 Proceedings of the joint international conference on Measurement and modeling of computer systems
Performance Analysis Using Stochastic Petri Nets
IEEE Transactions on Computers
An Extension of Norton's Theorem for Queueing Networks
IEEE Transactions on Software Engineering
Product form for stochastic automata networks
Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Parametric analysis of queuing networks
IBM Journal of Research and Development
Product form approximations for communicating Markov processes
Performance Evaluation
Simple O(m log n) time Markov chain lumping
TACAS'10 Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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Performance evaluation of computer software or hardware architectures may rely on the analysis of a complex stochastic model whose specification is usually given in terms of a high level formalism such as queueing networks, stochastic Petri nets, stochastic Automata or Markovian process algebras. Compositionality is a key-feature of many of these formalisms and allows the modeller to combine several (simple) components to form a complex architecture. However, although these formalisms allow for relative compact specifications of possibly complex models, the derivation of the interested performance indices may be very time and space consuming since the set of possible states of the model tends to grow exponentially with the number of components. In this paper we focus on models with underlying continuous time Markov chains and we show sufficient conditions under which exact lumping of the forward or the reversed process can be derived, allowing the exact computation of marginal stationary probabilities of the cooperating components. The peculiarity of our method relies on the fact that lumping is applied at component-level rather than to the CTMC of the joint process, thus reducing both the memory requirement and the computational cost of the subsequent solution of the model.