Optimal power allocation for a time-varying wireless channel under heavy-traffic approximation

• Published in: IEEE transactions on automatic control Vol. 51; no. 4; pp. 580 - 594
• Main Authors: Wei Wu, Arapostathis, A., Shakkottai, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.04.2006; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Allocations; Applied sciences; Approximation; Channels; Computer science; control theory; systems; Control theory. Systems; Controlled diffusion; Delay; Diffusion processes; Energy efficiency; Energy resources; Exact sciences and technology; Fading; fading channel; heavy-traffic; Mathematical analysis; Network servers; Optimization; Policies; power allocation; Power control; Queueing analysis; Queues; Queuing theory; Scheduling; Studies; Thresholds; Time-varying channels; Process dynamics; Fading; Monotonic function; Markov process; fading channel; Resource allocation; Optimal policy; Controlled diffusion; Transmission channel; heavy- traffic; power allocation; Delay system; Arrival time; Time varying system; Queue length; Optimal allocation; Heavy traffic; Arrival process; Channel allocation; Diffusion process; Wireless network; Time allocation; Peak power; Queue
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2006.872838

This paper studies the problem of minimizing the queueing delay for a time-varying channel with a single queue, subject to constraints on the average and peak power. First, by separating the time-scales of the arrival process, the channel process and the queueing dynamics it derives a heavy-traffic limit for the queue length in the form of a reflected diffusion process. Given a monotone function of the queue-length process that serves as a penalty, and constraints on the average and peak available power, it shows that the optimal power allocation policy is a channel-state based threshold policy. For each channel state j there corresponds a threshold value of the queue length, and it is optimal to transmit at peak power if the queue length exceeds this threshold, and not transmit otherwise. Numerical results compare the optimal policy for the original Markovian dynamics to the threshold policy which is optimal for the heavy-traffic approximation, to conclude that that latter performs very well even outside the heavy-traffic operating regime.