Queue proportional scheduling via geometric programming in fading broadcast channels

For fading broadcast channels (BC), a throughput optimal scheduling policy called queue proportional scheduling (QPS) is presented via geometric programming (GP). QPS finds a data rate vector such that the expected rate vector over all fading states is proportional to the current queue state vector and is on the boundary of the ergodic capacity region of a fading BC. Utilizing the degradedness of BC for each fading state, QPS is formulated as a geometric program that can be solved with efficient algorithms. The GP formulation of QPS is also extended to orthogonal frequency-division multiplexing (OFDM) systems in a fading BC. The throughput optimality of QPS is proved, and it is shown that QPS can arbitrarily scale the ratio of each user's average queueing delay. Throughput, delay, and fairness properties of QPS are numerically evaluated in a fading BC and compared with other scheduling policies such as the well-known maximum weight matching scheduling (MWMS). Simulation results for Poisson packet arrivals and exponentially distributed packet lengths demonstrate that compared with MWMS, QPS provides a significant decrease in average queueing delay and has more desirable fairness properties