Pathwise optimality of the exponential scheduling rule for wireless channels

We consider the problem of scheduling the transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate of the channel varies randomly with time and asynchronously for different users. We study a scheduling policy called the exponential scheduling rule, which was introduced in an earlier paper. Given a system with N users, and any set of positive numbers {an}, n = 1, 2, . .., N, we show that in a heavy-traffic limit, under a nonrestrictive "complete resource pooling' condition, this algorithm has the property that, for each time t, it (asymptotically) minimizes max an in (t), where \n (t) is the queue length of user n in the heavy-traffic regime.