Sequencing Tasks with Exponential Service Times to Minimize the Expected Flow Time or Makespan

The problems of minimizing the expected makespan and minimizing the expected tic for a finite set of independent tasks with exponential service-time distributions on m ~ 2 it processors are considered. It is shown that a scheduling policy minimizes the expected flow timq only if it is shortest expected processing time tint, and that a policy minimizes the expected make and only if it is longest expected processing time fast.