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A large deviation principle for join the shortest queue

Anatolii A. Puhalskii·Alexander A. Vladimirov
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Abstract

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.

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Anatolii A. Puhalskii, Alexander A. Vladimirov. 2005-12-31. A large deviation principle for join the shortest queue. https://arxiv.org/abs/math/0601010

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