With the rapid development of Internet multimedia applications, the next generation of networks is required to schedule not only the best effort traffic but also the traffic with bandwidth and delay guarantees. Currently, there are two types of fair scheduling algorithms in the literature. The time stamp based schedulers achieve very good fairness and delay guarantees but have high O(log N) time complexity, where N is the number of flows. While the round robin based schedulers reach O(1) time complexity, their delay guarantees are O(N). This paper aims at a fair scheduling algorithm with constant time complexity as well as good fairness and delay guarantees. We first present a credit/balance based fair scheduling algorithm called Most Credit First (MCF). We theoretically prove that MCF can provide O(log N) fairness, delay and delay jitter guarantees, and demonstrate experimentally that it actually can achieve O(1) guarantees. In order to reduce the O(log N) time complexity of MCF,...