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A desirable behavior of an Internet server is that a request's queuing delay depends on its service time in a linear fashion. Measuring the quality of service in terms of slowdown, the ratio of a request's queuing delay to its service time, provides a simple way to attain the objective. Moreover, it treats client requests equally regardless of their service time, whereas response time favors requests that need more processing resources. In this paper, we propose a proportional slowdown differentiation (PSD) service model on Internet servers. It aims to maintain prespecified slowdown ratios between different classes of client requests. To provide PSD services, we first derive a closed-form expression of the expected slowdown in an M/G/1 FCFS queuing system with a typical heavy-tailed service time distribution, the bounded Pareto distribution. Based on the closed-form expression, we design a queuing-theoretic strategy of processing-rate allocation. The rate allocation is realized by deploying a virtual server for each class. Simulation results show that the strategy can provide controllable PSD services on Internet servers. It, however, comes along with large variance and weak predictability due to the dynamics of Internet traffic. To address these issues, we design an integral feedback controller and integrate it into the queuing-theoretic strategy. Simulation results demonstrate that the integrated strategy is robust and can deliver predictable PSD services at a superior fine-grained level. We modified the Apache Web server with an implementation of the integrated processing-rate allocation strategy. Experimental results further demonstrate its effectiveness and feasibility in practice.
Index Terms- Quality of Service, slowdown, queuing theory, feedback control, rate allocation.

X. Zhou, J. Wei and C. Xu, "Robust Processing Rate Allocation for Proportional Slowdown Differentiation on Internet Servers," in IEEE Transactions on Computers, vol. 54, no. , pp. 964-977, 2005.
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