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Asymptotic distributions and chaos for the supermarket model

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.

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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:
Additional Information: © 2006 the authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Date Deposited: 10 Oct 2008 11:46
Last Modified: 24 Jun 2020 23:13

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