Counterexamples on the monotonicity of delay optimal strategies for energy harvesting transmitters

TL;DR

This paper investigates the properties of delay optimal transmission strategies for energy harvesting transmitters, revealing that such strategies may not be monotonic in queue and battery states, contrary to initial expectations.

Contribution

The paper provides counterexamples demonstrating that delay optimal policies are not necessarily monotonic in queue and battery states, challenging previous assumptions.

Findings

Counterexamples show non-monotonicity of delay optimal policies.

Delay optimal strategies can outperform monotone policies by 5-13%.

Value function is weakly increasing in queue and decreasing in battery states.

Abstract

We consider cross-layer design of delay optimal transmission strategies for energy harvesting transmitters where the data and energy arrival processes are stochastic. Using Markov decision theory, we show that the value function is weakly increasing in the queue state and weakly decreasing in the battery state. It is natural to expect that the delay optimal policy should be weakly increasing in the queue and battery states. We show via counterexamples that this is not the case. In fact, we show that for some sample scenarios the delay optimal policy may perform 5-13% better than the best monotone policy.