Stochastic Automata Networks Formalism Research Articles

Numerical solution of reliability models described by stochastic automata networks

This paper presents the solution of Markov chain reliability models with a large state-space. To specify a system reliability model, we use our previously proposed methodology, which is based on the Stochastic Automata Networks formalism. We model parts of the system by arrowhead matrices with functional transition rates. As a result, the infinitesimal generator matrix of the reliability model has a distinctive structure. In this paper, we demonstrate that a block Gauss–Seidel method can be applied very efficiently to such a structure. The application of the proposed methodology is illustrated by an example of a standard 3/2 substation configuration. Even though its Markov chain reliability model has almost two million states, its steady-state probabilities can be estimated in just a few seconds of CPU time.

Markov Chain Reliability Model of Cogeneration Power Plant Substation

The paper presents a Markov chain reliability model of a cogeneration power plant substation. Stochastic automata networks formalism and functional transition rates were used to specify the reliability behavior of a system. Iterative solution techniques were used to find steady-state solution of Markov models with different sets of randomly generated failure and repair rates. Modeling results were used to perform uncertainty and sensitivity analysis of the reliability model. DOI: http://dx.doi.org/10.5755/j01.eee.19.5.1214

Admission control mechanism and performance analysis based on stochastic automata networks formalism

IEEE 802.16 has been designed to support QoS (Quality of Service) in Wireless broadband Metropolitan Networks (WMAN), and specifically in the access networks. To achieve this, the IEEE 802.16.e amendment introduces the service differentiation by five service classes (UGS, ertPS, rtPS, nrtPS and BE). To maintain the QoS of active connections and to avoid any congestion in the network, an Admission Control (AC) is defined. AC aims to accept or reject a new connection according to the negotiated parameters and the availability of resources in the network. This mechanism is not standardized and let to the operators. We tackle this point, by proposing in this study a new Admission Control (AC) that improves the QoS of BE traffic by avoiding a strict bandwidth assignment of other traffics (rtPS and nrtPS) as is defined in major previous studies. The proposed mechanism is based on token bucket for rtPS, nrtPS and BE traffics in order to reduce lightly the number of accepted connections and to improve considerably the number of accepted BE connections. To evaluate the performance of the proposed scheme, we use PEPS (Performance Evaluation of Parallel Systems) which is a powerful tool based on models which can be described with Stochastic Automata Networks (SAN). PEPS can solve complex models with a large state space and with many synchronized events. Therefore, we show that this tool is suitable for wireless network, and specifically for the proposed scheme, toward numerical results we show as we expected that our proposed AC outperform the classical one by reducing lightly the performance of other service classes.

Réseaux d'automates stochastiques à temps discret

Markov Chains facilitate the performance analysis of dynamic systems in many areas of application. They are often used through a high-level formalism. Several of these are currently used, specially for continuous-time systems, and we work on Stochastic Automata Networks (SAN). Discrete-time systems are more difficult to model, because several events can occur during the same time slot (conflicting events). We define a SAN formalism for discrete-time models, and we present an algorithm to generate the equivalent Markov chain.

Modelling buffer admission mechanisms using stochastic automata networks

The stochastic automata networks formalism is an attractive technique to model complex systems with interacting components. Each component of the system is modelled by a single automaton; interactions between components are modelled by labels on the arcs which may represent synchronization and state-dependent transitions. Every automaton is associated with some matrices which allow to build the transition matrix of the underlying Markov chain, using tensor algebra. To illustrate this methodology, we introduce two buffer policies which could be used inAtm switching node. Every policy manages two priority levels which have distinct cell loss requirements. The first buffer policy is based on the push-out mechanism : a high priority cell replaces a low priority cell when the buffer is full. The second policy causes the discarding of all the low priority cells when the user transmits a request to send a burst of cells. In both studies, we compute the loss probabilities of each type of cells under various assumptions.