A Review of Building Evacuation Models - NIST Virtual Library

not gained, and this is labeled as a negative instance. The probabilities of acquiring or not
acquiring information are shown here as Equations (A.6):
+
−
+ n
− n
p =
p =
(A.6)
+ −
+ −
n + n
n + n
In these equations, n + is the number of positive instances and n - refers to the negative instances.
The total entropy of the system is given by Equation (A.7):
+
+ −
−
H = −( p )log
2
p − ( p ) log
2
p
(A.7)
Assumptions used in the model are the following:
• Evacuees do not have previous knowledge of the building
• Each evacuee is treated as the only occupant in the building, ignoring influence of other
occupants
• Multiple exits from any compartment are equally likely
• No signage is used throughout the building
• Evacuees do not experience panic
• All evacuees are able-bodied
• All networks are trees
• A backtrack path is equivalent to one positive and one negative instance
• A forward path resembles a positive instance.
• Each evacuee has a path memory.
• An example of the steps taken for the most basic model is shown here. This example
involves a single floor, single exit and the steps that the model takes to reach an output of
entropy and complexity are listed:
• Selection of a node on the network which is not an exit
• For the arcs on the path that lead directly from the node to the exit, a single-headed arrow is
drawn in the direction of the exit
• On all other remaining arcs, a double headed arrow is drawn.
• Count the number of double-headed arrows and this is the value for n -
• Count the number of single-headed arrows and this is the value for n +
• Substitute the values in for n - and n + to calculate the entropy value for that node
• Repeat steps 1-6 for each non-exit node
• Average all nodal entropy values together
This results in the average entropy value for each node or the overall complexity value.
The suggested improvements to the model, such as occupants with disabilities, buildings with
greater than one exit, simulation of locked doors, etc. were listed but not explained as to how
these would alter the simulation and results.
Output: The output from the model is an average entropy value for each node, which is the
overall complexity value for each floor.
Use of fire data: None.
A-76