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

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