Static robustness and mean response time of single-threshold allocation policies

In this section, we analytically study the mean response time and static robustness of two single threshold allocation policies: the T1 policy and the T2 policy. The T1 policy places a threshold, $T_1$, on queue 1, whereby server 2 serves type 1 jobs whenever the length of queue 1 is at least $T_1$. Thus, under T1, the beneficiary queue (queue 1) has control. The T2 policy places a threshold, $T_2$, on queue 2, whereby server 2 serves type 1 jobs whenever the length of queue 2 is below $T_2$. In the T2 policy, the donor queue (queue 2) has control. Our analysis will show that the T1 policy is superior to the T2 policy with respect to minimizing mean response time, but that the T2 policy is superior with respect to static robustness.