Mean response time of single-threshold allocation policies

In this section, we characterize the performance of the T1 and T2 policies. In particular, we will find that

• The characteristics of the T1 policy are quite different depending on whether queue 2 prefers type 1 or type 2 ( $c_1\mu _{12}\leq c_2\mu _2$ or $c_1\mu _{12}> c_2\mu _2$). Specifically, the optimal $T_1$ threshold is typically finite when $c_1\mu _{12}> c_2\mu _2$, and typically infinite when $c_1\mu _{12}\leq c_2\mu _2$, where the optimality is with respect to minimizing mean response time.
• The optimal $T_2$ threshold for the T2 policy is typically small.
• The mean response time under the T1 policy is at least as low as that under the T2 policy for all the cases that we study.