We first consider single threshold policies, T1 and T2, and find that the T1 policy is superior with respect to (overall weighted) mean response time. That is, the threshold for resource allocation is better determined by the beneficiary queue length (queue 1) than by the donor queue length (queue 2), in all cases studied.
We then compare single threshold policies to a multiple threshold policy, the adaptive dual threshold (ADT) policy, with respect to mean response time, assuming that the load is fixed and known. We find that when the threshold value is chosen appropriately, the mean response time of the T1 policy is at worst very close to the best mean response time achieved by the ADT policy. This is surprising, since the optimal policy appears to have infinitely many thresholds, but evidently the improvement these thresholds generate is marginal.
We next study static robustness, where the load is constant, but may have been misestimated. We find that the ADT policy not only provides low mean response time but also excels in static robustness, whereas the T1 policy does not. The increased flexibility of the ADT policy enables it to provide low mean response time under a range of loads. Hence, when the load is not exactly known, the ADT policy is a much better choice than the T1 policy.
Finally, and surprisingly, our analysis shows that this improvement in static robustness does not necessarily carry over to dynamic robustness, i.e. robustness against load fluctuation. We observe that when the load is fluctuating, the T1 policy, which lacks static robustness, can often provide low mean response time, comparable to ADT. This can occur for example because the mean response time of jobs arriving during the high load period may dominate the overall mean response time.
The results in this chapter have implications to the multiserver systems studied in previous chapters. For example, in Chapter 5, we have proposed size-based task assignment policies with cycle stealing, SBCS-ID and SBCS-CQ, but these task assignment policies can be improved upon by a threshold-based policy, whereby the server for long jobs processes short jobs when the number of long jobs is below a threshold value, as in the T1 policy, or by a more complex threshold-based policy like the ADT policy. In designing such threshold-based task assignment policies, lessons learned in this chapter would be useful.
Also, robustness is more or less a common issue in resource allocation policies that have parameters to be tuned. For example, in Chapter 6, we have studied a threshold-based policy for reducing switching costs in cycle stealing, but the optimal threshold values depend on loads. When these resource allocation policies are used where the load is not known, it would be important to study the robustness of these allocation policies and to design robust allocation policies based on the lessons learned in this chapter.