Abstruet-The problem of allocating network resources to the users of an integrated services network is investigated in the context of rate-based flow control. The network is assumed to be a virtual circuiq comection-based packet network. We show that the use of Generalized processor Sharing (GPS), when combined with Leaky Bucket admission control, allows the network to make a wide range of worst-case performance guarantees on throughput and delay. The scheme is flexible in that d~erent users may be given widely different performance guarantees, and is efilcient in that each of the servers is work conserving. We present a practicat packet-by-packet service discipline, PGPS (first proposed by Deme5 Shenker, and Keshav [7] under the name of Weighted Fair Queueing), that closely approximates GPS. This altows us to relate ressdta for GPS to the packet-bypacket scheme in a precise manner. In this paper, the performance of a single-server GPS system is analyzed exactty from the standpoint of worst-case packet delay and burstiness when the sources are constrained by leaky buckets. The worst-case sewdon backlogs are also determined. In the sequel to this paper, these results are extended to arbitrary topology networks with multiple nodes. I.