The Effect of the Future in Work Distribution.

A controller is considered which routes arrivals among several servers of different speeds. A decision which sends work to the server which will complete it soonest does not optimize the average completion time (mean flow time) because it doesn't take into account the impact of the decision on future arrivals. This impact on future arrivals, the 'future effect', can be significant at high arrival rates. An estimate of the size of the future effect is derived and controllers which take it into account in routing decisions can reduce the average completion time to near optimum. The effect is most pronounced when the service requirements for arrivals are nearly constant, server speeds are markedly different, and the arrival rate is close to the system's capacity. A controller considering the future effect will more heavily weigh a potential server's backlog than the arrival's service time when making a routing decision