Structural Properties of LDP for Queue-Length Based Wireless Scheduling Algorithms

In this paper, we are interested in wireless scheduling algorithms for the downlink of a single cell that can minimize the queue-overflow probability. Assuming that a samplepath large-deviation principle holds for the backlog process, we first study structural properties of the minimum-cost-pathto-overflow for a class of scheduling algorithms collectively referred to as the “α-algorithms.” For a given α ≥ 1, the α-algorithm picks the user for service at each time that has the largest product of the transmission rate multiplied by the backlog raised to the power α. We show that when the overflow metric is appropriately modified, the minimum-cost-to-overflow under the α-algorithm can be achieved by a simple linear path, and it can be written as the solution of a vector-optimization problem. Using this structural property, we then show that when α approaches infinity, the α-algorithm asymptotically achieves the largest value of the minimum-cost-to-overflow under all scheduling algorithms.