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This paper addresses the problem of how to service web requests quickly in order to minimize the client response time. Some of the recent work uses the idea of the shortest remaining processing time scheduling (SRPT) in Web servers in order to give preference to requests for short files. However by considering only the size of the file for determining the priority of requests, the previous works lack in capturing potentially useful scheduling information contained in the interaction between networks and end systems. To address this, this paper proposes and implements an algorithm, SWIFT that focuses on both server and network characteristics in conjunction. Our approach prioritizes requests based on the size of the file requested and the distance of the client from the server The implementation is at the kernel level for a finer-grained control over the packets entering the network. We present the results of the experiments conducted in a WAN environment to test the efficacy of SWIFT The results show that for large-sized files, SWIFT shows an improvement of 2.5% - 10% over the SRPT scheme for the tested server loads.