## 3 Materials and Methods  
### Description of the Tunnel and the Corresponding Road Network  
An existing twin-tube tunnel located along an Italian motorway was investigated. Each tube is characterized by two lanes and unidirectional traffic in ordinary conditions of functionality, and with a length of 850 m. It has a horseshoe-shaped cross-section of 55.2 m\({}^{2}\), with a maximum height of 6.8 m and a total width of 9.5 m (i.e., two lanes of 3.5 m, and two sidewalks). Each tube is straight, and flat without an emergency lane. Figure 1 shows the cross-section of the investigated twin-tube motorway tunnel.  
Figure 1: Cross-section of the twin-tube motorway tunnel investigated.  
Figure 1 also indicates the occurrence of a disruptive event (i.e., a traffic crash or fire) within the tube which is characterized by the transit traffic towards the north direction (namely, the north tube).  
The occurrence of an incident within the aforementioned tube was assumed to lead to different possible scenarios causing the partial or complete closure of the tube, with consequences (i.e., delay times) affecting the vehicular transit both on the motorway as well as on the nearby road network connected by means of the motorway junctions.  
Several preliminary macro-simulations were performed in order to define an appropriate area of study (i.e., a portion of the road network within which the major effects on traffic due to an incident occurred in the mentioned tunnel tube might be confined). In this respect, we found that the consequences on traffic caused by the disruptive event affected an area of about 25 km long and 8 km wide, which is schematically represented in Figure 2.  
In particular, Figure 2 shows: (i) the motorway section containing the investigated twin-tube tunnel; (ii) the tunnel tube that might be interested by a disruptive event (e.g., a crash or fire in the tube characterized in ordinary conditions by unidirectional traffic towards the north direction (i.e., from the Nodes A to D)); (iii) the undisruptive tube (i.e., the tube characterized in normal operating conditions by unidirectional traffic towards the south direction (i.e., from the Nodes D to A)); (iv) the major rural road, which is characterized by bi-directional traffic (i.e., E-I road section), that might be used due to the presence of the two motorway junctions (i.e., B and C) as an alternative itinerary in the case of the complete closure of the north tube of the tunnel (e.g., by using the links B-E and C-L-I); (v) several minor rural roads (i.e., F-M, G-N, H-O, I-L, and L-P) characterized by bi-directional traffic that are connected by means of certain intersections with the aforementioned major rural road (i.e., F, G, H, and I intersections); (vi) two traffic by-passes at the twin-tube tunnel portals that can be used in order to reorganize the traffic flow (e.g., by utilizing the adjacent tube for bi-directional traffic in the event of the complete closure of the other tube (i.e., the north tube in our case)); (vii) the sea that delimits the study area to the east.  
Figure 2: Schematic representation of the study area affected by a traffic accident or fire occurring in the north tube of the twin-tube motorway tunnel investigated (the image is not to scale).