Optimal Scheduling Policies in Small Generalized Switches

We consider small generalized switches with less than or equal to four links, and study scheduling policies designed to minimize the total number of packets in the system. By focusing on very small switches, we are able to derive optimal or heavy-traffic optimal policies whose performance can then be compared to previously conjectured optimal policies. In particular, it has been conjectured that the max-weight policy with weight q^alpha is optimal in heavy-traffic when alpha rarr 0. Our results show that this conjecture is not true.