A bus arbitration algorithm precisely controls the relative bus channel bandwidth allocated to each master device by considering the direction of, and/or the bus channel bandwidth consumed by, a bus transaction. At least one weighting register is associated with each master device; in one embodiment, one weighting register per bus channel. The register is periodically loaded with a proportionate share of the available bus bandwidth. Upon being granted a bus transaction on a bus channel, the corresponding weighting register is decremented by an amount that reflects the bus channel bandwidth consumed by the transaction, measured in amount of data transferred or number of bus data transfer cycles required to complete the transaction. In the case of equal initial allocation of relative bandwidth share, master devices that consume bus channel bandwidth will have relatively low priority; master devices that do not consume bus channel bandwidth retain relatively high priority.