Luczak, Malwina J. and McDiarmid, Colin (2006) Asymptotic distributions and chaos for the supermarket model. CDAM research report series (LSE-CDAM-2006-12). Centre for Discrete and Applicable Mathematics, London School of Economics and Political Science, London, UK.
Full text not available from this repository.Abstract
In the supermarket model there are n queues, each with a unit rate server. Customers arrive in a Poisson process at rate n, where 0 < < 1. Each customer chooses d 2 queues uniformly at random, and joins a shortest one. It is known that the equilibrium distribution of a typical queue length converges to a certain explicit limiting distribution as n ! 1. We quantify the rate of convergence by showing that the total variation distance between the equilibrium distribution and the limiting distribution is essentially of order n−1; and we give a corresponding result for systems starting from quite general initial conditions (not in equilibrium). Further, we quantify the result that the systems exhibit chaotic behaviour: we show that the total variation distance between the joint law of a fixed set of queue lengths and the corresponding product law is essentially of order at most n−1
| Item Type: | Monograph (Report) |
|---|---|
| Official URL: | http://www.cdam.lse.ac.uk |
| Additional Information: | © 2006 the authors |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 10 Oct 2008 11:46 |
| Last Modified: | 13 Sep 2024 16:34 |
| URI: | http://eprints.lse.ac.uk/id/eprint/13801 |
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