## 2 Integrated Predictive Traffic Resilience Framework
### Traffic Resilience Quantification  
Resilience indexes in transportation system applications can be determined using varying performance metrics, for example, travel time, travel demand, capacity, reliability, and others [31]. This study defines the performance level based on the roadway's volume-to-capacity ratio or loss of service during the evacuation, as defined in Section 2.1. Road traffic performance during evacuation demonstrates a distinct trend compared to any other system performance, as shown in Figure 3.  
In the context of the resilience curve and concept (Figure 2(a)), the system's performance \(P_{R}(t)\) undergoes a degradation phase after being exposed to a disruptive event at time \(t_{p}\). This degradation is depicted as a decline in the resilience curve, indicating a decrease in the system's ability to maintain its desired level of performance. As the disaster propagates, the system's performance reaches a certain level, reflecting the impact and severity of the disruption. Following this degradation phase, the system enters the recovery state at time \(t_{d}\), where efforts are made to restore and improve its performance. The recovery phase is represented by an upward trend in the resilience curve, illustrating the system's gradual recovery and return to its normal performance level by time \(t_{r}\)[32]. The resilience curve visually captures the dynamic behavior of the system's performance over time, highlighting the initial decline, the subsequent recovery process, and ultimately, the restoration of normal performance. On the contrary, the road traffic performance \(P_{TR}(t)\) degrades (volume increases) long before the disaster occurs at time \(tt_{d}\). As the evacuation process is in place following the disaster risk forecast to ensure the safety of the evacuees, a sudden increase in traffic volume is observed, causing congestion as a result of the road disturbance. The traffic volume decreases when a disaster is in progress because it is often not safe to travel when the hazard occurs. After the disaster period ends at time \(tt_{r}\), the traffic flow further restores the normal trend as the evacuees start returning at time \(tt_{s}\). In the context of traffic resilience, the concept of the resilience curve can be related to non-recurring road traffic resilience. This curve defines the behavior of traffic resilience over different stages during a disaster event and evacuation process, as depicted in Figure 2(b). The non-recurring road traffic resilience curve also consists of four distinct stages, each representing a specific phase of the disaster and evacuation scenario as follows:  
Figure 3: A comparison of trends between (**a**) general resilience curve and (**b**) road traffic resilience curve during an evacuation. * Stage 1: Approaching Disaster and Beginning of Evacuation. This stage marks the initial phase where the disaster is imminent and evacuation measures are initiated. Traffic conditions may start to deteriorate as the evacuation process begins;
* Stage 2: Ongoing Disaster; No Evacuation. The disaster is in full effect at this stage, and there is no ongoing evacuation. Traffic conditions may be severely impacted by the disaster, leading to disruptions and congestion on road networks;
* Stage 3: Recovery; Return of Evacuees. As the disaster subsides or the evacuation order is lifted, evacuees start returning to their homes or the affected areas. This stage represents the influx of traffic as people make their way back, potentially causing fluctuations and challenges in traffic flow;
* Stage 4: Regained Normal Traffic Flow. This final stage indicates the restoration of normal traffic conditions, where the road network recovers from the impact of the disaster, and traffic flow returns to pre-disaster levels. Apart from the volatile traffic trend during the evacuation, the regular traffic data often shows a daily seasonality scenario.