# Hidden Markov Model-Based Dynamic Hard Shoulders Running Strategy in Hybrid Network Environments
## 4 Numerical Results and Discussion
### Experimental Analysis of Hard Shoulder Opening Strategies
#### 4.2.2 Analysis of Results  
Figure 13 illustrates the parameters of the four hard shoulder opening strategies. As shown in Figure 13a, the average travel speed of the road section under the four hard shoulder openings is shown. At the beginning of the simulation, since the starting conditions of the four hard shoulder opening approaches were not reached, the average travel speeds of the road section under the four opening approaches remained the same from 0 to 2800 s, and all of them gradually decreased with the occurrence of accidents within the road section. Starting at 2800 s, the hard shoulders were opened according to their respective opening thresholds with the occurrence of HMMD, HMM, and LMD predicted traffic breakdowns. Eventually, with the disappearance of the bottleneck and the reduction in loaded traffic at 8500 s, the bottleneck speed within the road section gradually returned to the free-flow speed. As can be seen in Figure 13a, when the HMMD-HSR was taken, the time period when the average speed of the road segment did not collapse was significantly higher than that of HMM-HSR, LMD-HSR, and N-HSR, while the average speed within the road segment was always low when the N-HSR was taken. The average upstream traffic density and accumulated density under the four hard shoulder opening approaches are shown in Figure 13b,d. From 0 to 2800 s, the upstream density remained the same during this period because the hard shoulder was not opened for all four approaches. With the opening of the hard shoulder after 2800 s, respectively, the section density upstream of the bottleneck started to produce significant differences, and the maximum section density upstream of the bottleneck under HMMD-HSR, HMM-HSR, LMD-HSR, and N-HSR reached 99 veh/km, 114 veh/km, 128 veh/km, and 177 veh/km, respectively. The average section density and accumulated density of the upstream of the bottleneck under the hard shoulder opening modes were the same for all four modes  
Figure 13: Parameters of hard shoulder opening strategies under different traffic breakdown prediction models under the influence of \(\rho\): (**a**) Speed; (**b**) Upstream traffic density; (**c**) Accumulated travel time; (**d**) Accumulated upstream traffic density. during this period. HMMD-HSR had a lower section density than HMM-HSR, which proves that considering the effect of \(\rho\) when opening the hard shoulder will significantly improve the opening effect. In addition, from the accumulated density, it can be seen that the accumulated upstream traffic density sections were lower under HMMD-HSR than under LMD-HSR, with values of 7.4762 \(\times\) 10\({}^{5}\) veh/km and 7.8466 \(\times\) 10\({}^{5}\) veh/km, respectively. The accumulated travel time of the road segments under the four hard shoulder opening modes are shown in Figure 13c. From 0 to 2800 s, the accumulated travel time of the road segments remained the same during this period because the hard shoulder was not opened for all four modes. As the hard shoulders opened after 2800 s, respectively, the accumulated travel time of the road segments started to differ significantly. The accumulated travel time of the road segments under HMMD-HSR and LMD-HSR were lower than those under HMM-HSR. In addition, the accumulated travel time of the road segments under HMMD-HSR were lower than those under LMD-HSR, with the values of 5.5199 \(\times\) 10\({}^{6}\) s and 5.8385 \(\times\) 10\({}^{6}\) s, respectively. Since there are differences in the probability of traffic breakdown under different permeability \(\rho\), there are also differences in the degree of hard shoulder opening enhancement effect under different permeability \(\rho\).