A stochastic model of TCP/IP with stationary ergodic random losses
نویسندگان
چکیده
We consider here a ow control mechanism in which the rate at which data is sent increases linearly in time until a loss occurs. At that point the transmission rate decreases by a multiplicative factor. This mechanism is a good approximation to TCP/IP, the congestion control in the Internet. Losses are generated by some exogenous random process, which is assumed to be stationary ergodic; no Markovian assumptions are made. We obtain an explicit expression for the average transmission rate and obtain bounds in the case that there is a limit on the maximum rate. Key-words: TCP/IP, Performance evaluation, Stationary ergodic point processes, Palm calculus. Un modèle stochastique de TCP/IP en présence d'un processus de perte de paquets aléatoire, stationnaire et ergodique Résumé : On présente dans ce papier un modèle stochastique pour un protocole de contrôle de ux similaire à TCP, le fameux protocole contrôlant la congestion dans l'Internet. Le protocole modélisé augmente linéairement le débit de transmission jusqu'à l'apparition d'une congestion. Il divise alors le débit par deux et recommence l'augmentation. Ceci est similaire à TCP où la congestion est détectée par l'apparition d'une perte d'un paquet. On suppose que les pertes de paquets, donc les signaux de congestion, sont générées par un processus aléatoire supposé être stationnaire, ergodique et indépendant du ux contrôlé. Aucune hypothèse Markovienne n'est faite. On obtient une expression explicite du débit moyen en fonction des paramètres du processus de pertes. Dans le cas où une limite existe sur le débit de transmission, on trouve deux bornes pour le débit moyen. Le modèle est à la n étendue pour modéliser le mécanisme Timeout du protocole TCP. Mots-clés : TCP/IP, Évaluation de performance, Processus ponctuel ergodique et stationnaire, Calcul de Palm A stochastic model of TCP/IP 3
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