A novel diffusion process with jumps to study an electronic-optical edge router

The article presents a diffusion approximation model applied to investigate the process of filling a large optical packet by smaller and coming irregularly electronic packets. The use of diffusion approximation enables us to include the general distributions of interarrival times, also the self-similarity of the input process, as well as to investigate transient states. We propose a novel diffusion process with jumps representing the end of the filling the buffer due to arrival of too large packet and we give the transient solution to this process. The model allows us to study the distribution of interdeparture times and the distribution of the space occupied in the optical packet

Un modèle d'approximation de diffusion pour la distribution du temps d'acheminement des paquets dans les réseaux de senseurs

Nous proposons un modèle qui s'appuie sur l'approximation de diffusion pour l'estimation de la fonction de densité de probabilité du temps d'acheminement des paquets dans un réseaux de senseurs sans fils à sauts multiples. Dans sa forme générale, le modèle tient compte d'une part de la non homogénéité du milieu de propagation et de la répartition des noeuds intermédiaires dans l'espace et d'autre part, des éventuels changements des caractéristiques du réseau dans le temps. La retransmission des paquets perdus est également pris en compte dans le modèle

A diffusion approximation model of an electronic-optical node

Designing of smart edge routers and shaping the self-similar traffic in optical switched networks arise recently a lot of interest. Here, we propose an analytical approach which we consider useful in modelling and dimensioning of buffers in the edge routers between electronic and optical networks. We study a single buffer where packets of various sizes, classified by the class of service and the destination, are stored to build an optical packet of a fixed size. We already studied this problem with the use of simulation model, remarking that self-similar traffic at the entrance of such a buffer remains self-similar when leaving it. Now we are building analytical model based on diffusion approximation. and our previous contributions to this approach, i.e. a method to solve transient diffusion models. The model is used to analyse the process of buffer filling and a a numerical example proves that this approach may give reasonable results in relatively short (compared to simulation, especially simulation of transient states) time

Diffusion approximation as a modelling tool in congestion control and performance evaluation

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Aggregation for Computing Multi-Modal Stationary Distributions in 1-D Gene Regulatory Networks

International audienc

Numerically Efficient Analysis of a One-Dimensional Stochastic Lac Operon Model

Gene expression models and their analysis play a key role to understand gene regulation mechanisms. The lac operon mechanism has been largely studied to analyze its bistable behavior. In this paper a stochastic quasi steady-state lac operon model which is indeed a one dimensional birth-death process is considered. Nevertheless the well known closed-from solutions, due to the nonlinearity of parameters, the intermediate computed values become out of the representation range with the increase of the state space size. An aggregation-based two step algorithm is proposed to compute the steady-state distribution efficiently. The results of the stochastic model give the same parameter range for the bistable behavior as with the deterministic ODE model

Pontryagin principles for bounded discrete-time processes

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Modelling and performance evaluation of improved access mechanisms in a novel multiservice OPS architecture

International audienceOptical Packet Switching (OPS) technologies are among the most promising solutions for Next Generation Networks. In OPS networks, several mechanisms for Quality of Service (QoS) management have been developed. In this paper, we address QoS and fairness issues in a novel OPS ring architecture with a slotted synchronous transmission. The MAC protocol in the studied architecture is similar to CSMA/CA. Each node may use the available bandwidth in an opportunist manner. Therefore, the chances for each node to find available transmission resources are tightly correlated to the matrix of traffic at the other nodes. In order to remedy this problem, we elaborate two improved access mechanisms with preemptive approaches: Packet Erasing Mechanism (PEM) and Extraction and Reemission Mechanism (ERM). We evaluate the performance of the proposed mechanisms using a discrete-time analytical model. Finally, the results obtained by our model are validated and analyzed through several simulation scenario

Stability and Dynamics of TCP-NCD (DCR) Protocol in Presence of UDP Flows

International audienceThe fluid-flow approximation models investigate with much success the dynamics and stability of TCP/RED connections. Their main assumption is that the fluctuations of variables characterizing the behaviour of the connections are relatively small, that enables the linearization of model and the use of traditional control analysis tools to obtain such measures as Bode gain, phase margins, tracking error or delay margin. In this article, preserving linear fluid-flow model, we propose its extension to the case when a network is composed of wired and wireless part. We consider a variant of TCP algorithm (TCP-DCR or its new version TCP-NCR) and fluid-flow differential equations representing the size of congestion window, mean queue at the bottleneck router and loss probability at a RED queue are supplemented with terms representing constant loss probability due to transmission in wireless part and probability that a fraction of these errors is recovered by a link level mechanism. The decrease of congestion window due to TCP mechanism is delayed to allow the link protocol to deal with the errors. The model considers the presence of uncontrollable UDP flows