Cookies?
Library Header Image
LSE Research Online LSE Library Services

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.

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
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Research centres and groups > Computational, Discrete and Applicable Mathematics@LSE (CDAM)
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Identification Number: LSE-CDAM-2006-12
Date Deposited: 10 Oct 2008 11:46
URL: http://eprints.lse.ac.uk/13801/

Actions (login required)

Record administration - authorised staff only Record administration - authorised staff only