A disk scheduling system with bounded request reordering. Disk access requests may be performed during traversals of a disk head across a disk. Each traversal may have a specified direction of motion. A plurality of disk accesses may be performed during a disk head traversal. The overall number of disk access requests for a given disk head traversal may be limited to a maximum number N. By limiting the number of disk requests for each traversal, a bound may effectively be placed on the amount of time it takes to satisfy any single disk request.