Sharp estimates and a central limit theorem for the invariant law for a large star-shaped loss network.
type: Item
instance of: scholarly article
title: Sharp estimates and a central limit theorem for the invariant law for a large star-shaped loss network.
zbMATH Open document ID: 1058.60088
DOI: 10.1016/S0304-4149(01)00109-0
author: Carl Graham
published in: Stochastic Processes and their Applications
publication date: 2005-02-25T00:00:00Z
review text: An asymptotic behaviour of a star-shaped network is studied. The network is constituted of \(N\) links of capacity \(C\). Calls arrive on the network according to a Poisson process. Each call requires one channel on each of \(L\) distinct links chosen uniformly at random. The call is lost if any of the chosen route is full, else it holds one channel on each of these links for an exponential time, after which it releases the \(L\) channels simultaneously. Arrivals, choices, and holding times are independent. The invariant law for the route occupation process has a semi-explicit expression similar to that for a Gibbs measure. It involves a combinatorial normalizing factor, the partition function, which is very difficult to evaluate. The author studies the large \(N\) limit while keeping the arrival rate per link fixed. The Laplace asymptotic method is used to obtain a sharp asymptotics of the partition function, and to derive the central limit theorem for the empirical measure of the occupancies of the links under the invariant law. A sharp version for the large deviation principle proved in a previous paper is also obtained.
Mathematics Subject Classification ID: 60K35
Mathematics Subject Classification ID: 60F05
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 68M10
Mathematics Subject Classification ID: 90B18
zbMATH DE Number: 2138894
zbMATH Keywords: partition function
zbMATH Keywords: Laplace method
zbMATH Keywords: sharp asymptotics
zbMATH Keywords: central limit theorem
reviewed by: Martin Janžura
MaRDI profile type: Publication
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full work available at URL: s0304-4149(01)00109-0
OpenAlex ID: W2088543570
description: scientific article; zbMATH DE number 2138894