| Título: | Asymptotic distributions and chaos for the supermarket model |
| Autores: |
Luczak, Malwina J; London School of Economics McDiarmid, Colin; University of Oxford |
| Fecha: | 2007-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Supermarket model, join the shortest queue, random choices, power of two choices, load balancing, equilibrium, concentration of measure, law of large numbers, chaos Primary 60C05; secondary 68R05, 90B22, 60K25,60K30, 68M20. |
| Descripción: | In the supermarket model there are $n$ queues, each with a unit rate server. Customers arrive in a Poisson process at rate $\lambda n$, where $0<\lambda<1$. Each customer chooses $d \geq 2$ 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 $n\to\infty$. 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 $1/n$ 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 $1/n$. |
| Idioma: | No aplica |
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