Modeling of fire spread through probabilistic networks

Abstract The postflashover fire spread from room to room is treated in a stochastic analysis beginning with the development of a probabilistic network, and followed by a method of solving the network for discrete probability distributions. The first step in this analysis is the construction of a graph representing a space in which the rooms are nodes, and the walls and other fire barriers are links between the nodes. The space network graph is then transformed into a probabilistic network by introducing one node for representing the preflashover state and another node for representing the postflashover state of each room with the link between them representing the probability of flashover and the time characteristic to flashover. Each link between a flashed-over room and an adjacent space has a probability of the barrier being breached and a characteristic time of fire resistance. The probabilistic network is then solved by creating an “equivalent network” which has multiple links between the nodes to represent the uncertainty intrinsic to fire spread. For instance, a door may be open or closed. This would be represented by two links, one with the probability of the door being open with a characteristic time of zero, and the other with the probability of the door being closed with the time associated with the fire resistance of the door. The analysis of the possible flow through equivalent networks is discussed and the probability of a source node connecting with the sink node as well as the expected shortest travel time are calculated. Finally a numerical example is solved in which the source node is the room of origin of a fire, and the sink node is a section of the corridor which is critical to the escape of the occupants in nearby rooms Two cases are developed, one with “5-minute” doors and the other with “20-minute” doors and automatic closures. A different fire scenario is shown to be represented by each path through the equivalent network, and the probability and characteristic time for each of these scenarios is also calculated. The consequence of the changing to a 20-minute door is presented in quantitative terms and the probability of the door being open is used as a sensitivity parameter.