## 3 Case Study: Hurricane Irma
### Case Study Description  
The traffic dataset used in the case study was collected during Hurricane Irma from 4 September 2017 to 15 September 2017, which includes various traffic parameters such as hourly vehicle volume around US I-75. These data were collected at different traffic monitoring stations along the US I-75 highway established by the FDOT. The study area considered in this paper includes ten stations (S1-S10) shown in Figure 5a, which are S1(0350), S2(0191), S3(9950), S4(9953), S5(0184), S6(0190), S7(0225), S8(0361), S9(0358),  
Figure 4: Traffic resilience quantification for a travel route. and S10(0329). In this case study, each station is considered a travel segment, and the combination of all stations (or segments) is considered a travel route. The dataset is separated into four traffic condition stages: Stage 1--Prior to the hurricane, during the evacuation period, outbound traffic (4 September 2017 to 8 September 2017); Stage 2--During the hurricane (9 September 2017 and 10 September 2017); Stage 3--After the hurricane, evacueues returned, inbound traffic (11 September 2017 to 13 September 2017); and Stage 4--Normal traffic condition (14 September 2017 to 15 September 2017), as discussed in Section 2.3 and depicted in Figure 3b. During 4-8 September 2017, Category 4 Hurricane Irma approached slowly with a wind speed of 175 mph. The voluntary and mandatory evacuations occurred at this time, leading to a 501-1001% increase in volume, as shown in Figure 5b. As a result, major highways in Florida were congested, slowing the evacuation process for days. On 10 September 2017, Hurricane Irma's landfall occurred, and most Floridians had been evacuated, leaving the significant roads with very little to no traffic due to the severity of the hurricane; no travel was advised. During the post-storm period from 11 September 2017 to 13 September 2017, the residents started returning to their respective homes as the majority of mandatory evacuations were lifted. A high traffic density with an increase above +1001% was observed for some routes or road segments on 13 September 2017, as shown in Figure 5c. As discussed in Section 2, the road traffic volume and capacity conditions with uncertainty factors were calculated with the equations introduced in Section 2.1. The spatial and temporal traffic data were then used for predicting spatial and temporal traffic trends with the augmented LSTM approach presented in Section 2.2. The augmented LSTM algorithm  
Figure 5: Overview of the case study (**a**) the study area along US I-75, (**b**) Stage 1—Traffic volume prior to Hurricane, during evacuation period on 6 September, 2017, and (**c**) Stage 3—Traffic volume post-Hurricane, evacuation lifted, and evacuee returns on 13 September 2017.  
was implemented to predict the post-storm traffic volume \(V(t)\) over the route of US I-75, for all ten stations. Several experiments were performed with different combinations of hyperparameters to ensure the model's accuracy. The final and selected augmented LSTM architecture consisted of one 64-neuron LSTM layer, one flatten layer, and one dense layer. The adopted activation function was the tanh. The loss function adopted was the Adam optimizer with a mean squared error. For both temporal and spatial trend prediction, the same LSTM model was used. With the predicted hourly volume \(V(t)\), the road traffic performance \(P_{TR}(t)\) was calculated for each of the stations using Equations (3) and (12). The uncertainty factor value \(\alpha\) was determined from the predicted \(V(t)\) for the post-storm period. The guide for highway capacity and operations analysis of active transportation and demand management strategies document released by the US Federal Highway Administration (FHWA) determined that the average capacity reduction of a freeway is 1.07% while the wind speed is above 10 and below or equal to 20 mph (\(>10\leq 20\) mph) [34]. The value of the average capacity reduction also increases to 1.47% in the scenario where the wind speed is greater than 20 mph.