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Slowdown, defined as the ratio of a request's queueing delay to its service time, is accepted as an important quality of service metric of Internet servers. In this paper, we investigate the problem of providing proportional slowdown differentiation (PSD) services to various applications and clients on cluster-based Internet servers. We extend a closed-form expression of the expected slowdown of a popular Internet workload model with a typical heavy-tailed service time distribution from a single server mode to a server cluster mode. Based on the closed-form expression, we design a two-tier resource allocation approach, which integrates a dispatcher-based node partitioning scheme and a server-based dynamic process allocation scheme. We evaluate the two-tier resource allocation approach via extensive simulations and compare it with an one-tier node partitioning approach. Simulation results show that the two-tier approach can provide fine-grained PSD services on cluster-based Internet servers. We implement the two-tier approach on a cluster testbed. Experimental results further demonstrate the feasibility of the approach in practice.