A Large Deviation Principle for Join the Shortest Queue

Anatolii A. Puhalskii · Alexander Vladimirov

19 citations0/0 files storedMathematics of Operations Research

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Advanced Queuing Theory Analysis Stochastic processes and statistical mechanics Probability and Risk Models

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 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.

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References

1987Limit Theorems for Stochastic Processes 1989Theory of Martingales 1991Discrete Flow Networks: Bottleneck Analysis and Fluid Approximations 2019Large Deviations For Performance Analysis 2001Join the shortest queue: stability and exact asymptotics 1995The Large Deviation Principle for a General Class of Queueing Systems I 1999Large deviations and queueing networks: Methods for rate function identification 2000Large deviations of Jackson networks

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2010Large Deviations of Max-Weight Scheduling Policies on Convex Rate Regions 2009Importance Sampling for Weighted-Serve-the-Longest-Queue 2009Asymptotic behavior for MAP/PH/ queue with shortest queue discipline and jockeying 2009Two Sided DQBD Process and Solutions to the Tail Decay Rate Problem and Their Applications to the Generalized Join Shortest Queue

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