Asymptotic distributions and chaos for the supermarket model
| dc.creator | Luczak, Malwina J. | |
| dc.creator | McDiarmid, Colin | |
| dc.date | 2007-12-13 | |
| dc.date.accessioned | 2026-07-07T08:48:58Z | |
| dc.date.available | 2026-07-07T08:48:58Z | |
| dc.description | In the supermarket model there are n queues, each with a unit rate server. Customers arrive in a Poisson process at rate λn, where 0<λ<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 -> oo. 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}. | |
| dc.description | Published in Electronic Journal of Probability | |
| dc.identifier | https://arxiv.org/abs/0712.2091 | |
| dc.identifier | http://arxiv.org/abs/0712.2091 | |
| dc.identifier | EJP, vol. 12 (2007), 75--99 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/144135 | |
| dc.subject | Probability | |
| dc.subject | 60C05; 68R05; 90B22; 60K25; 60K30; 68M20 | |
| dc.title | Asymptotic distributions and chaos for the supermarket model | |
| dc.type | text |