In this paper, we present an efficient resource allocation scheme forscheduling and buffer management in a bottleneck hybrid Internetgateway. We use Fair Queueing in conjunction with Probabilistic FairDrop, a new buffer management policy, to allocate bandwidth and bufferspace in the gateway to ensure that all TCP flows threading thegateway achieve high end-to-end throughput and fair service. Wepropose the use of buffer dimensioning to alleviate the inherent biasof the TCP algorithm towards connections with large Round Trip Timeand validate our scheme through simulations.