Asymptotics and Scalings for Large Closed Product-form Networks via the Central Limit Theorem
نویسندگان
چکیده
The asymptotic behaviour of a closed BCMP network, with n queues and m n clients, is analyzed when n and m n become simultaneously large. Our method relies on Berry-Esseen type approximations coming in the Central Limit Theorem. We construct critical sequences m 0 n , which are necessary and sufficient to distinguish between saturated and non-saturated regimes for the network. Several applications of these results are presented. It is shown that some queues can act as bottlenecks, limiting thus the global efficiency of the system. This report contains and extends the results obtained in [2]. asymptotique et charge critique pour les grands réseaux fermésà forme produit via le Théorème de la Limite Centrale Résumé : On analyse le comportement asymptotique d'un réseau BCMP fermé com-portant n files et m n clients, lorsque n et m n tendent vers l'infini simultanément. Notre méthode s'apparente aux approximations de type Berry-Esseen, lí ees au Théo-r` eme de la Limite Centrale. On construit des séquences critiques m 0 n qui séparent de façon nécessaire et suffisante les régimes de saturation et de non saturation du réseau. Plusieurs applications sont présentées, incluant des cas d'engorgement local. Ce travail reprend etétend les résultats présentés dans [2]. Asymptotics and scalings for large closed product-form networks via the CLT 3
منابع مشابه
Asymptotics and Scalings for Large Product-form Networks via the Central Limit Theorem
The asymptotic behaviour of a closed BCMP network, with n queues and m n clients, is analyzed when n and m n become simultaneously large. Our method relies on Berry-Esseen type approximations coming in the Central Limit Theorem. We construct critical sequences m 0 n , which are necessary and suucient to distinguish between saturated and non-saturated regimes for the network. Several application...
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