Large deviations at equilibrium for a large star-shaped loss network
成果类型：
Article
署名作者：
Graham, C; O'Connell, N
署名单位：
Institut Polytechnique de Paris; Ecole Polytechnique; Hewlett-Packard
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/aoap/1019737666
发表日期：
2000
页码：
104-122
关键词：
摘要：
We consider a symmetric network composed of N links, each with capacity C. Calls arrive according to a Poisson process, and each call concerns L distinct links chosen uniformly at random. If each of these links has free capacity, the call is held for an exponential time; otherwise it is lost. The semiexplicit stationary distribution for this process is similar to a Gibbs measure: it involves a normalizing factor, the partition function, which is very difficult to evaluate. We let N go to infinity and keep fixed the rate of call attempts concerning any link. We use asymptotic combinatorics and recent techniques involving the law of large numbers to obtain the asymptotic equivalent fur the logarithm of the partition function and then the large deviation principle for the empirical measure of the occupancies of the links. We give an explicit formula for the rate function and examine its properties.
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