Summary of results

A wide range of threshold-based allocation policies for the Beneficiary-Donor model can be analyzed via DR by modeling the system as GFB processes, as discussed in Section 3.4. This allows us to analytically study static and dynamic robustness as well as mean response time of these allocation policies. In particular, DR allows us to evaluate the mean response time under the T1 policy, proposed by Squillante et. al. and Williams [181,205], for which only coarse approximations exist. Our analysis will lead to the following conclusions.

• We first consider single-threshold policies, and study which queue should control the single threshold. We find that it is better to determine when help is provided based on the beneficiary queue length (the T1 policy) rather than the donor queue length for all the cases that we study (not just in the heavy traffic limit, as proved in [17]).
• Surprisingly, we find that the use of multiple thresholds improves upon the T1 policy only by a small amount with respect to mean response time, although the optimal allocation policy appears to be a ``flexible'' T1 policy, which uses an infinite number of thresholds [4,125].
• We introduce two types of robustness: static robustness and dynamic robustness, and analytically study a wide range of threshold-based allocation policies with respect to both types of robustness via DR. Surprisingly, we will see that policies that excel in static robustness do not necessarily excel in dynamic robustness.
• Specifically, we find that an allocation policy with multiple thresholds can experience significant benefit over allocation policies with a single threshold with respect to static robustness. Illustrating this, we introduce the adaptive dual threshold (ADT) policy, which places two thresholds on queue 1, and show this has significant advantage over single-threshold allocation policies with respect to static robustness. The ADT policy operates like a T1 policy, but the threshold value is self-adapted to the load.
• In contrast to this, we find that multiple thresholds surprisingly offer only small advantage over a single threshold with respect to dynamic robustness.

The rest of this chapter is organized as follows. Section 7.2 discusses single-threshold allocation policies, including the T1 policy. Section 7.3 discusses multiple threshold allocation policies, including the ADT policy. In Sections 7.2-7.3, we evaluate the policies with respect to mean response time and static robustness. In Section 7.4, we shift our interest to dynamic robustness.