An I/O request directed to a portion of a storage object managed at a distributed storage service is received. A congestion control parameter value to be used to schedule a storage operation corresponding to the I/O request is determined. The congestion control parameter is based at least in part on an offset within the storage object to which the I/O request is directed. The storage operation is scheduled in accordance with the congestion control parameter at a selected physical storage device to which the portion of the storage object is mapped.