## 5 Evacuation Modeling
### Queue Formation and Evacuation Process  
Evac simulations were carried out for each position occupied by the five investigated burning vehicles (characterized by a HRR\({}_{\text{max}}\) of 8, 15, 30, 50, and 100 MW) along the tunnel length (145, 280, 420, 570, and 710 m from portal A). The same was done with reference to the aforementioned modified fire curves of the HRR\({}_{\text{max}}\) of 30, 15, and 8 MW in order to show the effects of using the micronized water system. However, in all the investigated cases, the number of vehicles queued upstream of the fire source was computed according to the following assumptions: (i) queued vehicles stop without going beyond the burning vehicle; (ii) vehicles queue up filling both lanes; (iii) the distance between the burning vehicle and the first queued vehicle is 10 m; (iv) the distance between the queued vehicles is 1 m.  
The frequency per time unit with which vehicles enter the tunnel was assumed to be stationary. This means that the arrival time of the first vehicle upstream of the fire source is computed to be 3.6, 2.4, and 1.8 s from the fire's start for the three investigated peak hour volumes (VHPs) of 1000, 1500, and 2000 vehicles/hour per lane, respectively. Therefore, the last user who leaves the tunnel in the event of a fire, walking towards a safe place, will be affected by a delay of 1.2 or 1.8 s when the VHP is equal to 1000 vehicles/hour per lane compared to the case in which VHP is of 1500 or 2000 vehicles/hour per lane, respectively.  
The users' pre-movement time (i.e., the sum of the detection and reaction time) for leaving their own queued vehicle upstream of the fire was assumed to be 1.5 min when HRR\({}_{\text{max}}\) equal to 8, 15, 50, and 100 MW; while it increased by 1 min (i.e., 2.5 min in total) in the event of a fire with HRR\({}_{\text{max}}\) equal to 30 MW by considering the additional time required to get off the bus ([PERSON] et al., 2017).  
The analysis of the consequences on users was made after 10 min from the fire's start, which means that after this period the longitudinal part of the tunnel upstream of the fire is full of vehicles in all the aforementioned three conditions of traffic volumes (i.e., VHPs), and with a distance between the vehicles queued of 1 m only.  
According to the mentioned assumptions, the number of vehicles in the queue upstream of the burning vehicle is the same with reference to the three VHPs and is equal to 36, 74, 114, 158, and 198 when the fire source is at 145, 280, 420, 570, and 710 m from portal A, respectively. The corresponding number of users potentially at risk was computed by considering that on average there are 2 people in each equivalent vehicle in the queue (for more details see [PERSON] et al. (2016), in which we assumed that the occupancy rate of cars,HGVs, and buses were equal to 1.7, 1, and 30 people, respectively). As a result, the number of people escaping upstream of the fire is 72, 148, 228, 316, and 396 when the fire source is at 145, 280, 420, 570, and 710 m from portal A, respectively.  
Figure 5 shows a schematic layout of vehicles in the queue upstream of the fire source for the investigated unidirectional road tunnel. It is to be remembered that the two sidewalks and the emergency exit are assumed to be still under construction. Consequently, each user, initially positioned next to his/her own vehicle, is forced to walk on the road carriageway by using the physical space between the two queues of stopped vehicles or the space between each queue of stopped vehicles and the safety barrier for reaching a safe place, which, in the circumstances examined, is represented by the traffic entrance portal only (i.e., portal A). The presence of these queued vehicles acts as an obstacle for the movement of evacuees, reducing their walking speed to a value assumed to be on average of 0.3 m/s.