Optimal load distribution for asynchronously scheduled homogeneous multiprocessor and distributed systems

The problem of distributing m interacting tasks over N identical processors for minimizing job completion time is examined. The processors are independently and asynchronously scheduled with distinct execution initiation times corresponding to their earliest instant of availability. The criteria specify, for any given values of load and system parameters, the subset of processors that should be assigned to execute the given job and the number of tasks allocated to each processor. Unlike previously published criteria, which assume synchronously scheduled processors, the present results show that minimizing job completion time does not always require engaging all available processors in job execution and that the optimal load allocation is generally an uneven distribution of modules over engaged processors