We design three types (random, first-fit, and busy-first) of harmonic, static pinwheel, and dynamic pinwheel bandwidth allocation schemes for real-time constant-bit-rate connections on ATM. From the blocking probability point of view, busy-first harmonic scheme is better than the other two types, and the random type has the least overhead. Dynamic pinwheel scheme has the lowest blocking probability, and the blocking probability of harmonic scheme is highest. The disadvantage of pinwheel is bandwidth waste, because the pinwheel scheduler needs to offer more bandwidth than required to have a cyclic sequence of schedule.