Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Multiple Class G-Networks with Jumps back to Zero
MASCOTS '95 Proceedings of the 3rd International Workshop on Modeling, Analysis, and Simulation of Computer and Telecommunication Systems
Turning back time in Markovian process algebra
Theoretical Computer Science
Compositional reversed Markov processes, with applications to G-networks
Performance Evaluation
Separable equilibrium state probabilities via time reversal in Markovian process algebra
Theoretical Computer Science - Quantitative aspects of programming languages (QAPL 2004)
Automated product-forms with Meercat
SMCtools '06 Proceeding from the 2006 workshop on Tools for solving structured Markov chains
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
A queueing network model with catastrophes and product form solution
Operations Research Letters
Performance engineering with product-form models: efficient solutions and applications
Proceedings of the 2nd ACM/SPEC International Conference on Performance engineering
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Markovian models play a pivotal role in system performance evaluation field. Several high level formalisms are capable to model systems consisting of some interacting sub-models, but often the resulting underlying process has a number of states that makes the computation of the solution unfeasible. Product-form models consist of a set of interacting sub-models and have the property that their steady-state solution is the product of the sub-model solutions considered in isolation and opportunely parametrised. The computation of the steady-state solution of a composition of arbitrary and possibly different types of models in product-form is still an open problem. It consists of two parts: a) deciding whether the model is in product-form and b) in this case, compute the stationary distribution efficiently. In this paper we propose an algorithm to solve these problems that extends that proposed in [14] by allowing the sub-models to have infinite state spaces. This is done without a-priori knowledge of the structure of the stochastic processes underlying the model components. As a consequence, open models consisting of non homogeneous components having infinite state space (e.g., a composition of G-queues, G-queues with catastrophes, Stochastic Petri Nets with product-forms) may be modelled and efficiently studied.