We wish to thank Tom Fairgrieve for influential discussions related to the generalization of the allocation policies and Ken Sevcik for helping us to arrive at a proper formulation. Nian Gu and Minas Spetsakis provided help in solving various equations and with using Maple. Mary Vernon encouraged us to consider job models that also have limited degrees of parallelism and whose speedup can decrease when allocated more processors (detailed results obtained using such models are presented in [12]). We wish to thank the anonymous referees for their suggestions for improving the presentation of this paper. We gratefully acknowledge the efforts of Raul Flores who quickly and accurately converted this document from troff to latex format and Lucia Dow and Nian Gu who read and provided helpful comments on various drafts of this paper. Finally, both authors thank the Natural Sciences and Engineering Research Council (NSERC) for a grant which partially supported this research.