Markovian network processes: congestion-dependent routing and processing
Proceedings of the workshop held at the Mathematical Sciences Institute Cornell University on Mathematical theory of queueing systems
Product form equilibrium distributions and a convolution algorithm for stochastic Petri nets
Performance Evaluation
Open, Closed, and Mixed Networks of Queues with Different Classes of Customers
Journal of the ACM (JACM)
Turning back time in Markovian process algebra
Theoretical Computer Science
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
State-dependent rates and semi-product-form via the reversed process
EPEW'10 Proceedings of the 7th European performance engineering conference on Computer performance engineering
Methodological construction of product-form stochastic Petri nets for performance evaluation
Journal of Systems and Software
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In the last few years some novel approaches have been developed to analyse Markovian stochastic models with product-form solutions. In particular RCAT [4] has proved to be a very powerful result capable to derive most of the well-known product-forms previously formulated in queueing theory or stochastic Petri net analysis contexts as well as new ones. The main idea is to define a joint-process as a cooperation among a set of models and give the condition for and the expression of the equilibrium probability distribution of the joint-states as product of the equilibrium distributions of each model considered in isolation. This paper aims to formulate an approach to deal with models whose transition rates depend on the resulting joint-states. In practice, we extend what has been introduced to solve the same problem for queueing networks [8,9] and stochastic Petri nets [5]. However, since RCAT is more general than the results that are derived for a specific model, we show that some conditions on the transition rate specification that are not present in the original formulation arise. Several examples are given to point out the application of this result and strength the intuition about the implications of the formulated conditions.