Abstract: Computer-based devices, whether initiators or targets, are assured access to a bus having a fixed priority arbitration scheme (such as a SCSI bus) by assigning to each initiator a “fair share” of the bus bandwidth. This share is defined as a number of bytes per a unit of time such as a time period. The shares together total a fraction of the total bus bandwidth, with a margin of bus bandwidth left unassigned. To prevent initiator starvation, each initiator monitors its bus requests to determine if it is being prevented by higher-priority initiators from using its assigned share of the bandwidth. If not, the initiator periodically pings each higher-priority initiator to indicate that it is not being starved. So long as a higher-priority initiator continues to receive pings from all lower-priority initiators, the higher-priority initiator can continue to use as much bandwidth as it needs.