Proves diffusion limits for ranked queue lengths under marginal JSQ routing in extreme heavy traffic, yielding a reflected Atlas process with explicit product-form stationary gap distributions and sharp asymptotics for imbalance and delay.
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Rank Based Routing in Large Server Systems under Extreme Congestion
Proves diffusion limits for ranked queue lengths under marginal JSQ routing in extreme heavy traffic, yielding a reflected Atlas process with explicit product-form stationary gap distributions and sharp asymptotics for imbalance and delay.