Abstract: In a master/slave multiprocessor system, process execution tasks are allocated on the basis of anticipated execution time. Work which can be performed by either the master or the slave is entered on a double ended queue in a non-descending order of anticipated execution times. Processes having high anticipated execution times are selected for execution by the slave processor and processes having low anticipated execution times are selected for execution by the master processor. Anticipated holding times are computed on the basis of the time spent by the slave computer in the execution of a segment of a process without requiring interaction with the master processor. The slave processor records the time spent in execution each time a segment of the process is completed and the process has to be returned to the master. The master uses the recorded time as a measure of the anticipated execution time for a next segment of the same process.