# Hybrid Model-Based Traffic Network Control Using Population Games
## 7 Discussion
### Scenario 3. In this case, the fixed-time strategy, fictitious play, yields superior outcomes compared to the adaptive strategies, replicator and Smith, in certain parameters such as TTT and AS. However, in terms of TST and ASTV, fictitious play is surpassed by them. Once more, the Smith dynamic and replicator demonstrate superior performance, with the replicator dynamic outperforming it in NS and TTT, while Smith dynamics slightly surpass replicator dynamics in TST. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scenario** & **Controller** & **NS[veh]** & **TT[h]** & **TD[tkm]** & **AS[km/h]** & **TST[seg]** & **ASTV[h]** \\ \hline \multirow{4}{*}{1} & FP & \(7917(-6\%)\) & \(183.1(-3\%)\) & \(8526.2(0.1\%)\) & \(46.6(3\%)\) & \(13.7(-11\%)\) & \(22.6(-11\%)\) \\  & RD & \(8257(-2\%)\) & \(188.1(-0.4\%)\) & \(8522.3(0.1\%)\) & \(45.3(0.4\%)\) & \(15.9(3\%)\) & \(26.1(3\%)\) \\  & BNN & \(8618\)\((2\%)\) & \(188.9(0.1\%)\) & \(8568.8(0.6\%)\) & \(45.4(0.7\%)\) & \(15.4(0\%)\) & \(25.4(0\%)\) \\  & Smith & \(7803(-8\%)\) & \(181.9(-4\%)\) & \(8491.7(-0.3\%)\) & \(46.7(3.5\%)\) & \(13.6(-12\%)\) & \(22.4(-11\%)\) \\  & Logit(\(\eta=1\)) & \(8699\)\((3\%)\) & \(189.9(0.6\%)\) & \(8558.3(0.5\%)\) & \(45.1(0\%)\) & \(15.8(3\%)\) & \(26.0(3\%)\) \\ \hline \multirow{4}{*}{2} & FP & \(16,941(-71\%)\) & \(331.5(-18\%)\) & \(13,557.1(1\%)\) & \(40.9(23\%)\) & \(18.1(-29\%)\) & \(47.9(-29\%)\) \\  & RD & \(15,321(-74\%)\) & \(318.8(-21\%)\) & \(13,496.4(1\%)\) & \(42.3(27\%)\) & \(16.24(-37\%)\) & \(42.9(-36\%)\) \\  & BNN & \(17,870(-70\%)\) & \(337.4(-16\%)\) & \(13,569.9(1\%)\) & \(40.2(21\%)\) & \(18.9(-26\%)\) & \(50.0(-26\%)\) \\  & Smith & \(15,608(-74\%)\) & \(320.7(-20\%)\) & \(13,537.8(1\%)\) & \(42.2(27\%)\) & \(16.0(-38\%)\) & \(42.3(-37\%)\) \\  & Logit(\(\eta=1\)) & \(17,885(-70\%)\) & \(337.7(-16\%)\) & \(13,570.6(1\%)\) & \(40.2(21\%)\) & \(18.9(-26\%)\) & \(49.8(-26\%)\) \\ \hline \multirow{4}{*}{3} & FP & \(56,974(-17\%)\) & \(452.1(-6\%)\) & \(14,377.1(6\%)\) & \(31.8(13\%)\) & \(24.7(11\%)\) & \(70.2(18\%)\) \\  & RD & \(52,301(-24\%)\) & \(456.7(-5\%)\) & \(14,209.7(5\%)\) & \(31.1(10\%)\) & \(19.6(-12\%)\) & \(55.7(-7\%)\) \\  & BNN & \(67,506(-1\%)\) & \(470.3(-2\%)\) & \(13,624.5(1\%)\) & \(29.0(3\%)\) & \(20.7(-7\%)\) & \(56.2(-6\%)\) \\  & Smith & \(54,569(-20\%)\) & \(458.5(-4\%)\) & \(14,185.8(5\%)\) & \(30.9(10\%)\) & \(19.5(-12\%)\) & \(54.9(-8\%)\) \\  & Logit(\(\eta=1\)) & \(67,158(-2\%)\) & \(471.6(-2\%)\) & \(13,620.6(1\%)\) & \(28.9(2\%)\) & \(20.9(-6\%)\) & \(56.4(-6\%)\) \\ \hline \multirow{4}{*}{4} & FP & \(21,087(-88\%)\) & \(367.4(-32\%)\) & \(14,164.8(17\%)\) & \(38.6(72\%)\) & \(19.2(-43\%)\) & \(52.9(-35\%)\) \\  & RD & \(19,087(-90\%)\) & \(353.4(-34\%)\) & \(14,192.7(17\%)\) & \(40.2(79\%)\) & \(17.2(-49\%)\) & \(47.4(-42\%)\) \\  & BNN & \(51,206(-72\%)\) & \(432.9(-20\%)\) & \(14,106.1(17\%)\) & \(32.4(44\%)\) & \(23.1(-32\%)\) & \(63.4(-22\%)\) \\  & Smith & \(18,407(-90\%)\) & \(350.3(-35\%)\) & \(14,166.2(17\%)\) & \(40.4(80\%)\) & \(17.0(-50\%)\) & \(46.9(-43\%)\) \\  & Logit (\(\eta=1\)) & \(59,657(-67\%)\) & \(450.8(-16\%)\) & \(14,041.3(16\%)\) & \(31.1(38\%)\) & \(24.0(-29\%)\) & \(65.9(-19\%)\) \\ \hline \multirow{4}{*}{5} & FP & \(52,650(-53\%)\) & \(419.5(-13\%)\) & \(13,823.6(7\%)\) & \(32.9(23\%)\) & \(21.9(-20\%)\) & \(60.7(-14\%)\) \\  & RD & \(25,001(-77\%)\) & \(367.6(-24\%)\) & \(14,206.7(10\%)\) & \(38.6(44\%)\) & \(18.3(-33\%)\) & \(51.4(-28\%)\) \\ \cline{1-1}  & BNN & \(50,421(-55\%)\) & \(430.9(-11\%)\) & \(13,978.1(8\%)\) & \(32.4(21\%)\) & \(22.0(-20\%)\) & \(61.3(-14\%)\) \\ \cline{1-1}  & Smith & \(22,758(-80\%)\) & \(363.0(-25\%)\) & \(14,232.5(10\%)\) & \(39.2(46\%)\) & \(18.1(-34\%)\) & \(50.8(-28\%)\) \\ \cline{1-1}  & [PERSON](\(\eta=1\)) & \(54,132(-51\%)\) & \(435.1(-10\%)\) & \(13,940.7(8\%)\) & \(32.0(19\%)\) & \(21.9(-20\%)\) & \(60.9(-14\%)\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance for control strategies. Scenario 4.