Weighted fair queueing (WFQ)-based packet scheduling schemes require processing at line speeds for tag computation and tag sorting. This requirement presents a bottleneck for their implementation at high transmission speeds. We propose an alternative and lower complexity approach to packet scheduling, based on modifications of the classical round-robin scheduler. Contrary to conventional belief, we show that appropriate modifications of the weighted round-robin (WRR) service discipline can, in fact, provide tight fairness properties and efficient delay guarantees to multiple sessions. Two such modifications are described: 1) list-based round robin, in which the server visits different sessions according to a precomputed list which is designed to obtain the desirable scheduling properties; 2) multiclass round robin, a version of hierarchical round robin with controls designed for good scheduling properties. The schemes considered are compared with well-known WFQ schemes and with deficit round robin (a credit-based WRR), on the basis of desirable properties such as bandwidth guarantees, fairness in excess bandwidth sharing, worst-case fairness, and efficiency of latency (delay guarantee) tuning. The scheduling schemes proposed and analyzed here operate with fixed packet sizes, and hence can be used in applications such as cell scheduling in ATM networks, time-slot scheduling on wireless links as in GPRS air interface, etc. A credit-based extension of the proposed schemes to handle variable packet sizes is also possible.