Markovian queueing network with complex synchronizations: Product form and tensor

Authors:
T. H. Dao Thi;J. M. Fourneau
Affiliations:
-;-
Venue:
Performance Evaluation
Year:
2012

Citing 16
Cited 0

Markovian Petri Nets protocols with product form solution

Performance Evaluation
Superposed stochastic automata: a class of stochastic Petri nets with parallel solution and distributed state space

Performance Evaluation
Efficient descriptor-vector multiplications in stochastic automata networks

Journal of the ACM (JACM)
On the stochastic structure of parallelism and synchronization models for distributed algorithms
The ubiquitous Kronecker product

Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
G-Networks with resets

Performance Evaluation
A Characterization of Independence for Competing Markov Chains with Applications to Stochastic Petri Nets

IEEE Transactions on Software Engineering
An Efficient Kronecker Representation for PEPA Models

PAPM-PROBMIV '01 Proceedings of the Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Compositional reversed Markov processes, with applications to G-networks

Performance Evaluation
Product form for stochastic automata networks

Proceedings of the 2nd international conference on Performance evaluation methodologies and tools
Zero-Automatic Networks

Discrete Event Dynamic Systems
Product Form Steady-State Distribution for Stochastic Automata Networks with Domino Synchronizations

EPEW '08 Proceedings of the 5th European Performance Engineering Workshop on Computer Performance Engineering
Discrete Time Markov Chains Competing over Resources: Product Form Steady-State Distribution

QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
An algebraic condition for product form in stochastic automata networks without synchronizations

Performance Evaluation
Stochastic Automata Networks with Master/Slave Synchronization: Product Form and Tensor

ASMTA '09 Proceedings of the 16th International Conference on Analytical and Stochastic Modeling Techniques and Applications
Computing the steady-state distribution of g-networks with synchronized partial flushing

ISCIS'06 Proceedings of the 21st international conference on Computer and Information Sciences

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider complex synchronizations in a generalized network of queues with signals (Gnetwork) or Stochastic Automata Networks without functions. Both models allow to describe their continuous time Markov chain as a summation of tensor (or Kronecker) products and sums of local description of queues (or automata). We give a purely algebraic proof of the product form results based on properties of the tensor products. These results generalize many well-known results in queueing theory but also on all the models which allow a tensor based representation such as Stochastic Petri Nets or Stochastic Process Algebra.