Accounting for Emergency Response in 

Building Evacuation: Modeling 

Differential Egress Capacity Solutions

Jason D. Averill 

Weiguo Song

NISTIR 7425
 

NISTIR 7425

Accounting for Emergency Response 

in Building Evacuation: Modeling 

Differential Egress Capacity Solutions

Jason D. Averill 

Building and Fire Research Laboratory

Weiguo Song, Ph.D. 

Guest Researcher 

Building and Fire Research Laboratory

and 

State Key Laboratory of Fire Science, USTC, China

April 2007

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary 

Technology Administration 

Robert Cresanti, Under Secretary of Commerce for Technology 

National Institute of Standards and Technology 
 

Accounting for Emergency Response in Building Evacuation: 

Modeling Differential Egress Capacity Solutions 

Abstract: The impact of firefighter response on the progress of the building evacuation is 

not typically considered. Responders use of the stairs while occupants are evacuating can 

significantly increase total building evacuation time. To account for emergency 

response, this analysis considered whether adding capacity through extra stairwell width 

was equivalent to providing the same total egress capacity through an additional 

stairwell. An egress simulation with a counterflow submodel was calibrated against 

recent fire-drill experimental results to demonstrate the capability of the model to 

produce meaningful evacuation results. The model was then applied to a hypothetical 

50 story office building with 350 occupants per floor. When comparing equivalent total 

width, additional stairwells outperform wider stairwells from the perspective of 

evacuation performance, as well as firefighter ascent times. A third stairwell can 

completely mitigate the effect of firefighter response or even improve the building 

evacuation time compared to two stairwells with no firefighter response. 

Background: The ICC Terrorism Resistant Buildings (TRB) Committee has proposed a 

change to Section 403 of the International Building Code (IBC), which would require one 

additional stairwell (one greater than otherwise required) for all high-rise buildings (other 

than R-2) taller than 420 ft (128 m). The proposal would provide greater egress capacity 

than currently required, recognizing that one stairwell may become unusable during 

evacuation due to the introduction of smoke and heat and blockage by fire hoses once 

suppression operations begin. 

Objective: Perform computer egress modeling to provide quantitative comparisons of 

different stairwell configurations with and without emergency response interaction. 

Model Description

The computer model is a modified form of a biased random walk model without back 

step.1

 The model is defined in a two-dimensional grid, of which each site can be occupied 

by a pedestrian or be empty. Each pedestrian can move to a neighboring site with certain 

probabilities. Usually, every pedestrian has a drift to move to the preferential site. All the 

possible configurations of downward walkers are demonstrated in Figure 1. The 

movement probabilities can be calculated with Equation 1. 
 

(a) (b) (c) 

(d) (e) (f) 

(g) (h) 

Figure 1: Basic Movement Rules 

Pf is the probability of moving forward; Pl is the probability moving leftward; Pr is the 

probability of moving rightward; and Ps is the probability of stopping. The values of 

probabilities corresponding to Figure 1 are as follows: 

(a) Pf=0.8 Pl=0.05 Pr=0.15 Ps=0.0 

(b) Pf=0.8 Pl=0.05 Pr=0.0 Ps=0.1 

(c) Pf=0.8 Pl=0.0 Pr=0.15 Ps=0.05 

(d) Pf=0.8 Pl=0.0 Pr=0.0 Ps=0.2 

(e) Pf=0.0 Pl=0.05 Pr=0.15 Ps=0.8 

(f) Pf=0.0 Pl=0.0 Pr=0.15 Ps=0.85 

(g) Pf=0.0 Pl=0.05 Pr=0.0 Ps=0.95 

(h) Pf=0.0 Pl=0.0 Pr=0.0 Py=1.0 

Note that all of the probabilities sum to 1.0, as shown in 

(Eq. 1.) 

Pf +Pl +Pr +Ps = 1.0 (Eq. 1) 

Stairwell evacuation also has its own characteristics, including right-side walking 

tendency and firefighter avoidance. People in a stairwell have a right-side walking 

tendency. There are three reasons for a right-side walking requirement in the model. First, 

right-side walking is consistent with the traffic rules in the U.S. with which people are 

familiar. Second, the staircase descends and rotates in clockwise direction, so right-side 

walking is inner-side walking, which results in shorter walking distance relative to leftside walking. Third, for firefighters, adopting a right-side walking strategy will avoid 

collisions with occupants. So both pedestrians and fire fighters walk with a right-side 
 

tendency. Fire fighters walk on the left side or middle only if the right side of the stair is 

blocked by occupants. Firefighter avoidance means occupants make room for firefighters 

when they encounter each other. That is a significant difference from the traditional 

definition of counterflow where pedestrians with opposite walking direction compete 

with each other for the walking opportunities. 

Model Validation 

The model was calibrated against data collected from an unannounced evacuation drill 

observed in a six-story office building.2

 During the evacuation, two stairwells (designated 

“Stairwell A” and “Stairwell B”) were observed. The stairwells were in separate, 

neighboring wings. The floor areas serving the stairs were nominally identical, with the 

same number of elevators, stairwells, and exterior exit doors. The stairwells in each wing 

were equally accessible from all rooms and floors. Both stairwells deposited occupants 

into a lobby through a set of double doors, where they subsequently made their way 

outside. 

Figure 2 shows the geometry of the stairwell and tread. The stairwell had a width of 

3.25 m and a length of 7.09 m. Occupants exited the stairwell through a 1.73 m wide 

double exit door. In other floors, occupants entered the stairwell through a 0.91 m wide 

exit door and merge with those from upper floors. In both Stairwells there were eight 

steps per flight. The only exception was in Stairwell B between floor 2 and floor 1. From 

floor 2 to floor 1.5 there were six steps, and from floor 1.5 and floor 1 there were 10 

steps; this averaged out to eight steps for each flight. The steps in both stairwells had the 

same tread and depth dimensions. The rise of each stair was 0.2 m (8 in), and the tread 

was 0.28 m (11.1 in). The diagonal distance of each stair was 0.35 m (13.7 in). 

There was no firefighter counterflow in Stairwell A. The walking speed of occupants 

was determined by Figure 4, where the average speed is plotted against different 

occupant density. The free walking speed, or maximum walking speed, is the speed of an 

occupant when there is no obstacle nor occupants surrounding him. In fact, it is the speed 

when occupant density is close to 0. In both Stairwell A and Stairwell B, the average 

walking speed shows an approximately monotonic decrease with the increase of occupant 

density. It is possible to obtain the free walking speed with the measured relation between 

walking speed and occupant density. 
 

0.28m 

0.20m 

0.35m 

Down 

3.25m 

1.52m 3.13m 2.44m 

0.91m 

3.25m 

1.93m 

1.73m 

(a) 

(b) 

(c) 

 (a) stairwell over second floor (b) first floor (c)tread geometry 

Figure 2: Floor and Tread Geometry 

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

0.3

0.4

0.5

0.6

0.7

0.8

0.9

average speed (m/s)

density (p/m2)

 Wing A

 Wing B

Figure 3: Occupant Speed Versus Density 

The drill was conducted in 2005 on a sunny, warm, and clear day. DV-cameras were 

used to record the egress process. The timeline of the egress drill was as follows. 

• At t = 0 s, the fire alarm was activated. 

• At t = 80 s, the first group of firefighters was sent into Stairwell B. 
 

• At t = 149 s, the second group of firefighters was sent into Stairwell B. 

• The egress drill was completed after all people went out. 

0 200 400

-5

0

5

10

15

20

25

30

35

40

45

50

55

Occupant number inside

Time /s

 Egress Drill

 Model (average of 10 runs)

(a) Stairwell A (no counterflow) 

-50 0 50 100 150 200 250 300 350 400

-10

0

10

20

30

40

50

60

70

80

Occupants Number inside

Time /s

 Egress drill

 Model Run (average of 10 runs)

(b) Stairwell B (with counterflow) 

Figure 4: Change of occupant number inside stairwell with time 

Figure 4 shows the change in the number of occupants inside the stairwell as a function 

of time for both stairwells. The entrance time for an individual occupant to the stairwell 

was an input condition to the model. The occupant movement speeds, interactions with 

other occupants and responders (if any) were calculated using the model. The differences 
 

in occupant density between Stairwells A and B due to the firefighter counterflow were 

well captured by the model. 

Modeling Scenario: The objective of this study was to understand the differences, if any, 

between two commonly discussed strategies for increasing egress capacity: adding 

additional width to existing stairs, or adding an additional stair. Therefore, a challenging 

evacuation scenario was developed in order to clearly demonstrate any differences in 

evacuation times. The modeling scenario selected was a high-rise office building with a 

relatively high occupant load per floor. The model building was a 50 story high-rise 

office building with 350 persons per floor. The evacuation mode was full-building 

evacuation and input parameters were chosen to emphasize the effect of the primary 

variable (stair width) on evacuation time. It was assumed that: (a) there were no 

occupant evacuation initiation delays, (b) there were no mobility impaired occupants, and 

(c) that occupants left by the nearest available exit. 

A baseline scenario, where firefighters do not use the stairwells until the building is 

evacuated, was calculated to quantify the impact of the emergency response on the 

evacuation time. Subsequently, evacuation times were calculated varying three basic 

parameters: stair width, response scenario, and location of the fire in the building. 

Additionally, the ascent time for the firefighters is calculated. Note that ascent time does 

not include the time that it would take to stage and mount an attack on the fire floor, nor 

the physical impact that the ascent has on the overall ability of the firefighter to 

subsequently fight the fire. 

Evacuation times were calculated for two stair width configurations: (a) a two person 

wide stair (roughly 1100 mm (44 in) clear width); and (b) a three person wide stair 

(roughly 1700 mm (66 in) clear width). The results were also calculated for two fire 

department response conditions. In the first scenario, referred to as the ‘counterflow’ 

scenario, firefighters ascend the stairs against the flow of the descending occupants until 

they reach the fire floor, when the stairwell is taken out of service for use by occupants 

above the fire floor. Occupants above the fire floor in the counterflow stairwell are 

assumed to immediately exit the stairwell and transfer to the nearest available stairwell. 

The counterflow scenario assumes that a new group of four firefighters enters the 

stairwell every 5 min and begins to climb the stairs. Every 20 floors, the firefighters stop 

and rest for 5 min (not in the stairwell) before resuming their climb to the fire floor.†

 In 

the second scenario, referred to as the “closed stairwell’ scenario, firefighters close one 

stairwell to occupant use after 10 min in order to maintain a dedicated attack stairwell. 

Again, occupants are assumed to immediately exit the attack stairwell and enter the 

nearest available stairwell. The firefighter ascent times are determined by the time when 

the first firefighter reaches the fire floor. Finally, three different fire locations were 

selected within the building. The fire high in the building was located on floor 50. The 

fire in the middle of the building was located on floor 25. The fire low in the building 

was located on floor 5. 

 

†

 This estimate was based on reports from the NIST WTC Investigation. See NCSTAR 1-8 “The 

Emergency Response Operations” pp. 89 – 91, available at http://wtc.nist.gov. Individual firefighter climb 

rates may vary and resting may or may not be necessary. 
 

Results:

Table 1 shows the results of the baseline evacuation modeling scenarios. National model 

codes would currently require two 1100 mm (44 in) stairwells in a 50 story office 

building with an occupant load of 350 persons per floor (unless travel distance 

requirements required an additional stair). Under ideal evacuation circumstances 

(described above) and assuming that the fire service did not utilize the stairways during 

the occupant evacuation time period, the building would evacuate in approximately 

179 min (three hours). In the event that one of the two stairwells was out of service, the 

evacuation time would approximately double (although this scenario was not modeled). 

Next, the benefits of requiring additional egress capacity were evaluated. Two stairs 

providing three flow lanes each (approximately 1700 mm (66 in) clear width) would 

decrease the building evacuation time by approximately 40 min, or 22 %, compared to 

two stairs each providing two flow lanes. Alternatively, three stairs, each providing two 

lanes of flow (approximately 1100 mm (44 in) clear width), would decrease the building 

evacuation time by 61 min, or 34 %. 

Table 1: No fire in the building, full building evacuation (baseline) 

Scenario Occupant Evacuation Time (min) 

Two 44 in stairs 179 

Two 66 in stairs 141 

Three 44 in stairs 119 

The results in Table 1 do not account for the impact of the emergency response on the 

building evacuation time. Assuming that the firefighters do not use the elevators, they 

are likely to employ one of two strategies in order to initiate suppression activities: 

walking up the stairs against the flow of descending occupants (counterflow) and closing 

the attack stair when reaching the fire floor; alternatively, the fire service may close one 

of the stairwells to occupant use upon arrival (assumed to be 10 min). The impact of the 

two fire service strategies, along with the fire location (high, medium, and low in the 

building) and the two stairway configurations, on the overall evacuation time is 

summarized in Table 2. Figure 5Figure 7 show the same information graphically. 
 

Table 2: Summary of Modeled Evacuation and Ascent Times 

Firefighter Ascent Time 

(min) 

Occupant Descent Time 

(min) Scenario 

Counterflow Closed 

Stairwell Counterflow Closed Stairwell 

Two 66 in stairs 129 41 161 274 

Fire on 

Floor 50 

Three 44 in stairs 108 41 136 174 

Two 66 in stairs 67 25 221 274 

Fire on 

Floor 25 

Three 44 in stairs 61 25 156 174 

Two 66 in stairs 12 11 N/A 274 

Fire on 

Floor 5 

Three 44 in stairs 12 11 N/A 174 
 

Figure 5: Evacuation and Response Times for Fire at Floor 50 

Occupant - 

Baseline Evac 

Time

Occupant - 

Counterflow Evac 

Time

Occupant - Close 

Stairwell Evac 

Time

Firefighter - 

Counterflow 

Ascent Time

Firefighter - Close 

Stairwell Ascent 

Time

0

50

100

150

200

250

300

Time (minutes)

Two 66 inch stairs

Three 44 inch stairs

Two 44 inch stairs

baseline occupant

evacuation

No Emergency Response Occupant Evacuation Time with Emergency Response Firefighter Ascent Time

Figure 6: Evacuation and Response Times for Fire at Floor 25 

Occupant - 

Baseline Evac 

Time

Occupant - 

Counterflow Evac 

Time

Occupant - Close 

Stairwell Evac 

Time

Firefighter - 

Counterflow 

Ascent Time

Firefighter - Close 

Stairwell Ascent 

Time

0

50

100

150

200

250

300

Time (minutes)

Two 66 inch stairs

Three 44 inch stairs

Two 44 inch stairs

baseline occupant

evacuation

No Emergency Response Occupant Evacuation Time with Emergency Response Firefighter Ascent Time

Figure 7: Evacuation and Response Times for Fire at Floor 5 

Occupant - 

Baseline Evac 

Time

Occupant - 

Counterflow Evac 

Time

Occupant - Close 

Stairwell Evac 

Time

Firefighter - 

Counterflow 

Ascent Time

Firefighter - Close 

Stairwell Ascent 

Time

0

50

100

150

200

250

300

Time (minutes)

Two 66 inch stairs

Three 44 inch stairs

Two 44 inch stairs

baseline occupant

evacuation

No Emergency Response Occupant Evacuation Time with Emergency Response Firefighter Ascent Time

N/A
 

The impact of counterflow on total evacuation time is dependent upon the location of the 

fire and the configuration of the stairwell. The reason that the fire low in the building has 

a more significant impact on the building evacuation time than a fire higher in the 

building is due to the fact that the firefighters close the stairwell for use above the fire 

floor once they arrive at the fire floor. 

Table 3: Impact of Emergency Response on Evacuation Time* 

Difference in Evacuation Time 

Comparing Same Stair 

Configuration With and Without 

Emergency Response 

Difference in Evacuation Time 

Comparing Alternative Stair 

Configuration With Emergency 

Response to Two 44 in Stairs 

Without Emergency Response 

Scenario 

Counterflow Closed 

Stairwell Counterflow Closed Stairwell 

Two 66 in 

stairs 14 % 94 % -11 % 52% 

Fire on 

Floor 50 

Three 44 in 

stairs 14 % 46 % -24 % -3 % 

Two 66 in 

stairs 57 % 94 % 23% 52 % 

Fire on 

Floor 25 

Three 44 in 

stairs 31 % 46 % -13% -3 % 

Two 66 in 

stairs N/A 94 % N/A 52 % 

Fire on Floor 5 

Three 44 in 

stairs N/A 46 % N/A -3 % 

* Positive indicates longer evacuation times and negative indicates shorter evacuation times. 

Accounting for emergency response in high-rise buildings may significantly increase the 

expected building evacuation time. Table 3 shows percent increase in total building 

evacuation time when the impact of emergency response is calculated compared to 

building evacuation time when the emergency response is neglected. Closing a stairwell 

after 10 min has the effect of proportionally increasing the evacuation time: removing 

one of the two stairwells nearly doubles the evacuation time (94% increase). For a 

building with three stairwells, removing one-third of the stairwells increases the 

evacuation time by 46%. 

The building evacuation time for a fire very low in the building in the counterflow 

scenario will asymptote to the ‘closed stairwell’ scenario since the ascent time 

approaches zero. The percentage impact of counterflow on occupant evacuation time for 

a fire high in the building (where no occupants are forced to change stairwells) is similar 

for both stairwell configurations (two 1700 mm (66 in) and three 1100 mm (44 in) stairs) 

at 14 %; however, as the baseline occupant evacuation time for the three stair 
 

configuration is shorter than the baseline occupant evacuation time for the two stair 

configuration (119 min versus 141 min), the total impact is less for the three stair 

configuration. 

Therefore, the rightmost two columns in Table 3 show the impact of emergency response 

when the calculations are normalized on a common basis (in this case, 179 min for two 

1100 mm (44 in) stairs with no emergency response). Three 1100 mm (44 in) stairwells 

with emergency responders will result in faster occupant evacuation times than two 1100 

mm (44 in) stairs without emergency responders (as shown by the negative values for 

evacuation times for three 1100 mm (44 in) stair rows in Table 3). Two 1700 mm (66 in) 

stairs with emergency responders will result in longer evacuation times than two 1100 

mm (44 in) stairs without emergency responders, with the exception of the fire high in the 

building and firefighter counterflow scenario because there are no occupants above the 

fire floor when the firefighters arrive. 

Emergency response strategy is a trade-off between minimizing the arrival time of the 

firefighters to the fire floor in order to conduct rescue and suppression activities and 

minimizing the occupant evacuation time. The strategy of closing a stairwell upon arrival 

of the fire department will approximately double the evacuation time if only two 

stairways are otherwise available (141 min with both 1700 mm (66 in) stairs available 

compared to 274 min if one stairwell is removed from occupant service after 10 min). If 

three stairways are available, the strategy of closing a stairwell will increase the occupant 

evacuation time by 46 % (119 min with three 1100 mm (44 in) stairs available compared 

to 174 min if one stairwell is removed from occupant service after 10 min). On the other 

hand, closing one stairwell can dramatically reduce the response time for the emergency 

responders for fires higher in the building; for a response to a fire on floor 50, it would 

take firefighters 129 min to reach the fire floor for a 1700 mm (66 in) stairway with 

counterflow versus 41 min for an open 66 in (1700 mm) stairway; 108 min for a 1100 

mm (44 in) stairway with counterflow versus 41 min for an open 1100 mm (44 in) 

stairway. 

If the counterflow strategy is employed by the firefighters, the impact of the occupants on 

firefighter response time is dependent upon the location of the fire in the building. For 

fires high in the building (floor 50), two 1700 mm (66 in) stairs require 19 % longer 

evacuation time (129 min versus 108 min) than three 1100 mm (44 in) stairs. For fires in 

the middle of the building (floor 25), two 1700 mm (66 in) stairs require 10 % greater 

evacuation time (67 versus 61 min) than three 1100 mm (44 in) stairs. For a fire on floor 

5, no simulation was performed. 

Conclusions:

Subject to the assumptions and limitations of this simplified analysis, it is apparent that if 

the fire department uses a stairwell (either by removing it from occupant use or walking 

upward against the flow of the occupants) for emergency response prior to completion of 

the evacuation, an additional stairwell restores all or more of the capacity lost to fire 

department suppression operations. Further, when comparing equivalent total width, 
 

additional stairwells outperform wider stairwells from the perspective of evacuation 

performance. No cost analysis was performed for this study. 

Acknowledgments: The authors wish to acknowledge the contributions of Jessica 

Kratchman, Erica Kuligowski, and Richard Peacock, NIST. 

 

1

 “Evacuation behaviors at exit in CA model with force essentials: A comparison with social force model.” 

Song, W., Yu, Y., Wang, B., and Fan, W. Physica A, Vol. 371 (2006) pp. 658-666. 

2

 “Emergency Responder Counterflow in Stairwells.” Averill, J. and Kratchman, J. Partners for 

Protection: Fire Protection Engineers and the Fire Service. Oct. 17 and 18, 2006, Ellicott City, Md.