Load balancing system under Join the Shortest Queue: Many-Server-Heavy-Traffic Asymptotics
arXiv:2004.04826 · doi:10.1007/s11134-022-09847-7
Abstract
We study the load balancing system operating under Join the Shortest Queue (JSQ) in the many-server heavy-traffic regime. If is the number of servers, we let the difference between the total service rate and the total arrival rate be with . We show that for the average queue length behaves similarly to the classical heavy-traffic regime. Specifically, we prove that the distribution of the average queue length multiplied by converges to an exponential random variable. Moreover, we show a result analogous to state space collapse. We provide two proofs for our result: one using the one-sided Laplace transform, and one using Stein's method. We additionally obtain the rate of convergence in the Wasserstein's distance.
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