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 the 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 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 follows by trajectorial uniqueness.