A large deviation principle for join the shortest queue

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We consider a join-the-shortest-queue model which is as follows. There are $K$ single FIFO servers and $M$ arrival processes. The customers from a given arrival process can be served only by servers from a certain subset of all servers. The actual destination is the server with the smallest weighted queue length. The arrival processes are assumed to obey a large deviation principle while the service is exponential. A large deviation principle is established for the queue-length process. The action functional is expressed in terms of solutions to mathematical programming problems. The large deviation limit point is identified as a weak solution to a system of idempotent equations. Uniqueness of the weak solution is proved by establishing trajectorial uniqueness.
14 pages

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Probability, 60F10, 60K25

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http://salesiana.dossiersoluciones.com/handle/123456789/107354

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0601010
 http://arxiv.org/abs/math/0601010

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arXiv