Subdiffusive Load Balancing in Time-Varying Queueing Systems

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The degree to which delays or queue lengths equalize under load-balancing algorithms gives a good indication of their performance. Some of the most well-known results in this context are concerned with the asymptotic behavior of the delay or queue length at the diffusion scale under a critical load condition, where arrival and service rates do not vary with time. For example, under the join-the-shortest-queue policy, the queue length deviation process, defined as the difference between the greatest and smallest queue length as it varies over time, is at a smaller scale (subdiffusive) than that of queue lengths (diffusive).