## 5 Evacuation Modeling
### Queue Model and Evacuation Process  
In this study, the people evacuation process was investigated by considering four types of burning vehicles (characterized by a HRR equal respectively to 8, 30, 50, and 100 MW) located at five different longitudinal positions from portal A (145, 280, 420, 570, and 710 m). In the case of bi-directional traffic within the tunnel tube (according to the driving direction from portal B to A) the estimation of the number of vehicles in the queue downstream of the fire is based on the following assumptions: (i) queued vehicles stop without going over the burning vehicle; (ii) vehicles queue up filling one lane; (iii) the first vehicle of the queue stops at 10 m from the burning vehicle; (iv) each vehicle maintains a certain distance from the preceding vehicle in the queue (i.e., 1 m during the daily peak-hours in which the traffic volume is equal to capacity (i.e., 1600 vehicles/hour per lane), and 10 m overnight due to the lowest traffic volumes (i.e., 200 vehicles/hour per lane)).  
Based on the above assumptions, the number of vehicles queued downstream of the fire for each of the five locations of the burning vehicle (i.e., 145, 280, 420, 570, and 710 m from portal A) is equal to 98, 79, 59, 37, and 17 in the daily-peak hours, respectively. By assuming an average number of people present in each vehicle equal to 2, we estimated the corresponding number of people escaping downstream of the fire: 196, 158, 118, 74, and 34. It was considered, when the burning vehicle is located at 145 or 280 m from portal A, that users evacuate both from the emergency exit (located in the middle of the tunnel length) and portal B. The initial position of each escaping user is assumed to be next to his own vehicle.  
During each of the eight night-hours and for the aforementioned five positions of the burning vehicle, we estimated a number of vehicles queued equal to 33, 33, 25, 16, and 7, respectively; and as a result the corresponding number of escaping users was found to be 66, 66, 50, 32, and 14. It is to be mentioned that the number of vehicles in the queue downstream of the fire was the same for the location of the vehicle burning at both 145 and 280 m from the portal A. This is due to fact that after a time of 10 min from the fire start, the bi-directional tube is assumed to be closed to traffic by tunnel operators (i.e., overnight the maximum number of vehicles entering the bi-directional tube within 10 min is equal to 33).  
Figure 2a,b show the layout of queued vehicles downstream of the burning vehicle for bi-directional traffic in both the daily peak-hours and overnight, respectively. Table 1 reports the number of people escaping from the emergency exit and portal B for the different fire locations along the tunnel.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Number of People Escaping from:**} \\ \cline{2-5}
**Fire Location** & \multicolumn{2}{c}{**Day**} & \multicolumn{2}{c}{**Night**} \\ \cline{2-5}
**(Distance from Portal A)** & **Emergency Exit** & **Portal B** & **Emergency Exit** & **Portal B** \\ \hline
145 m & 102 & 94 & 45 & 21 \\
280 m & 64 & 94 & 28 & 38 \\
420 m & – & 118 & – & 50 \\
570 m & – & 74 & – & 32 \\
710 m & – & 34 & – & 14 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Number of people downstream of the fire escaping from the emergency exit and/or portal B.  
A further extension of the present paper might be that to perform a queue formation model in the event of fire in a one-way tunnel used for bi-directional traffic under emergency circumstances.