Fig. 9
From: Structured optimal transmission control in network-coded two-way relay channels
The optimal action \(a_{1}^{*}\) vs. queue state b 1 and channel state g 2 when b 2=3 and g 1=3 (left), and \(a_{2}^{*}\) vs. b 2 and g 1 when b 1=2 and g 2=1 (right). p 1=0.1, p 2=0.2, λ=0.05, τ=1, η=2, ξ o =4 and β=0.95. Two channels are both Rayleigh fading and are both modeled by 8-state equiprobable FSMCs. But, \(\overline {\gamma }_{1}=0\text {dB}\) and \(\overline {\gamma }_{2}=3\text {dB}\). In this case, \(\beta \leq \frac {P_{e}(g_{i})-P_{e}(g_{i}+1)}{\sum _{g'_{i}}P_{g_{i}g'_{i}} (P_{e}(g'_{i})-P_{e}(g'_{i}+1))}\) does not hold for all g i . We can see that \(a_{1}^{*}\) is not monotonic in g 2