ACM Transactions on Computer Systems (TOCS)
Stochastic Automata Network of Modeling Parallel Systems
IEEE Transactions on Software Engineering
A distributed numerical/simulative algorithm for the analysis of large continuous time Markov chains
Proceedings of the eleventh workshop on Parallel and distributed simulation
Efficient descriptor-vector multiplications in stochastic automata networks
Journal of the ACM (JACM)
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on modeling and analysis of stochastic systems
Specification of mobile code system using graph grammars
Fourth International Conference on Formal methods for open object-based distributed systems IV
Capacity of Ad Hoc wireless networks
Proceedings of the 7th annual international conference on Mobile computing and networking
Hierarchical Reachability Graph Generation for Petri Nets
Formal Methods in System Design
Superposed Generalized Stochastic Petri Nets: Definition and Efficient Solution
Proceedings of the 15th International Conference on Application and Theory of Petri Nets
INFORMS Journal on Computing
A Data Structure for the Efficient Kronecker Solution of GSPNs
PNPM '99 Proceedings of the The 8th International Workshop on Petri Nets and Performance Models
Efficient Solution of GSPNs Using Canonical Matrix Diagrams
PNPM '01 Proceedings of the 9th international Workshop on Petri Nets and Performance Models (PNPM'01)
Modular Analytical Performance Models for Ad Hoc Wireless Networks
WIOPT '05 Proceedings of the Third International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks
Performance Models For Master/Slave Parallel Programs
Electronic Notes in Theoretical Computer Science (ENTCS)
Modelling Grid5000 point availability with SAN
Electronic Notes in Theoretical Computer Science (ENTCS)
Kronecker descriptor partitioning for parallel algorithms
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Efficient vector-descriptor product exploiting time-memory trade-offs
ACM SIGMETRICS Performance Evaluation Review
Performance evaluation of OpenMP-based algorithms for handling Kronecker descriptors
Journal of Parallel and Distributed Computing
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Many Markovian stochastic structured modeling formalisms like Petri nets, automata networks and process algebra represent the infinitesimal generator of the underlying Markov chain as a descriptor instead of a traditional sparse matrix. A descriptor is a compact and structured storage based on a sum of tensor (Kronecker) products of small matrices that can be handled by many algorithms allowing affordable stationary and transient solutions even for very large Markovian models. One of the most efficient algorithms used to compute iterative solutions of descriptors is the Shuffle algorithm which is used to perform the multiplication by a probability vector. In this paper we propose an alternative algorithm called Split, since it offers a flexible solution between the pure sparse matrix approach and the Shuffle algorithm using a hybrid solution. The Split algorithm puts the Shuffle approach in perspective by presenting a faster execution time for many cases and at least the same efficiency for the worst cases. The Split algorithm is applied to solve two SAN models based on real problems showing the practical contribution of this paper.