 Sharp estimates and a central limit theorem for the invariant law for a large star-shaped loss networkCarl Graham Stochastic Processes and their Applications, 2001, vol. 95, issue 2, 177-202 Abstract: Calls arrive in a Poisson stream on a symmetric network constituted of N links of capacity C. Each call requires one channel on each of L distinct links chosen uniformly at random; if none of these links is full, the call is accepted and holds one channel per link for an exponential duration, else it is lost. 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. We study the large N limit while keeping the arrival rate per link fixed. We use the Laplace asymptotic method. We obtain the sharp asymptotics of the partition function, then the central limit theorem for the empirical measure of the occupancies of the links under the invariant law. We also obtain a sharp version for the large deviation principle proved in Graham and O'Connell (Ann. Appl. Probab. 10 (2000) 104). Keywords: Partition; function; Laplace; method; Sharp; asymptotics; Central; limit; theorem (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:95:y:2001:i:2:p:177-202 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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