On the Power of (Even a Little) Resource Pooling

We propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction p of an available resource is deployed in a centralized manner (e.g., to serve a most-loaded station) while the remaining fraction 1 − p is allocated to local servers that can only serve requests addressed specifically to their respective stations. Using a fluid model approach, we demonstrate a surprising phase transition in the steady-state delay scaling, as p changes: in the limit of a large number of stations, and when any amount of centralization is available (p > 0), the average queue length in steady state scales as log11−p11−λ when the traffic intensity λ goes to 1. This is exponentially smaller than the usual M/M/1-queue delay scaling of 11−λ, obtained when all resources are fully allocated to local stations (p = 0). This indicates a strong qualitative impact of even a small degree of resource pooling. We prove convergence to a fluid limit, and ...