A New Tool to Model Parallel Systems and Protocols

We present a new performance evaluation tool based on the analysis of large Markov chains and Stochastic Automata Networks. Using some graph theoretical arguments, we show how to systematically perform state reduction. The graph properties can be checked easily because we take advantage of the tensorial construction of the Markov chain from the Stochastic Automata Network. 1 Introduction We present a new modeling tool based on Stochastic Automata Networks (SAN). Stochastic Automata Networks have been introduced as an efficient method to represent complex systems with interacting components such as parallel systems or distributed systems [Plateau et al. 1988]. This new method automatically provides an analytic derivation of the generator matrix of the Markov chain using tensor algebra. The SAN seem to be more efficient than Queueing Networks or Stochastic Petri Nets to model systems with a large number of states and complex synchronizations. Queueing Networks give a very compact repres..

Analyse par Diffusion d'un Multiplexeur Statistique à Intégration de Services: Analyse Stationnaire

Diffusion approximation is a method which consists in replacing a discrete valued process with an appropriate continuous one. Using this method, we study the performances of a statistical multiplexer for integrated services in an ATM network. We compute several performance measures such as buffer queue length distribution and cell loss probabilities

Performance Modelling of Hierarchical Cellular Networks using PEPA

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Multiple Class G-Networks with list-oriented deletions

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Diffusion Approximation to Study the Flow Synchronization in ATM Networks

Diffusion approximation is a method which consists in replacing a discrete valued process with an appropriate continuous one. Using this method, we study some problems related to the flow synchronization in ATM networks. We model the end-to-end transmission delay and introduce a synchronization station at the receiver level to compensate the dispersion effect that can be drawn by the jitter phenomenon. We compute several performance measures such as buffer queue length distribution and cell loss probabilities. 1 Introduction In ATM networks, the agreement terms between the user and the network establish the connection characteristics and the quality of service that the network should guarantee. Certain applications such as voice transmission have strong constraints of end-to-end transmission delay. We know however that in such networks cells are subjected to random transmission delays: this is the multiplexing jitter. Jitter is a phenomenon introduced by the variation of cell transfer..

Multiple Class Generalized Networks with iterated deletions

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Multiple Class G-Networks with Jumps back to Zero

We consider multiple class G-networks of processor sharing queues with negative customers which destroy all the customers in a queue. We prove that these networks have a product form solution for steady-state distribution. These networks may have some applications in reliability or performability as the negative customers may clearly model breakdown of computer or communication systems. We also show that under simple assumptions these networks always have a stationary distribution. Finally, we present some asymptotic results on the average number of customers and the average sojourn time when the arrival rate goes to infinity

Performance Modelling of Hierarchical Cellular Networks using PEPA

. We present a performance evaluation study of hierarchical cellular networks using PEPA. These networks constitute a new application area for this process algebra formalism. We show that this formalism can easily be used to model such systems. We also show that the strong equivalence aggregation technique behind PEPA allows a significant reduction of the state space of the underlying Markov process. Using the resulting model, we derive performance criteria such as new call blocking and dropping handover probabilities. 1 Introduction Hierarchical cellular networks [2] have been proposed for future Personal Communications Systems [4] in the frame of third generation of wireless networks (UMTS). In these networks, a service area is called a cell and is defined as the area where the received signal power from a base station is stronger than the signals from all other base stations. Depending on the expected traffic density and on their sizes, cells are of two types: large cells or macroc..