1. A method for performing backfilling on an incoming flow of incoming parallel programs provided by a population of clients to a facility, the method comprising: using a computer-controlled process to generate a current run-time prediction for at least some of the incoming parallel programs; performing backfilling on the incoming flow of incoming parallel programs based, at least in part, on at least some of the current run-time predictions and on client estimated run-times, wherein at least an individual one of the client estimated run-times is implied from an attribute of the parallel program associated with the individual client estimated run-time rather than being explicitly provided by the client; and if the current run-time of a particular incoming parallel program currently in process exceeds the current run-time prediction corresponding to the particular incoming parallel program, generating an updated run-time prediction to exceed the current run-time, re-defining the current run-time prediction to equal the updated run-time prediction, and continuing to execute said performing backfilling based on the updated run-time prediction.