NIST Technical Note 1722 

Simple Estimates of Combined 

Stairwell / Elevator Egress in 

Buildings 

Paul A. Reneke 

Piotr Tofilo 

Richard D. Peacock 

Bryan L. Hoskins 

http://dx.doi.org/10.6028/NIST.TN.1722 
 

 

 

 

 

 

 

 

 

 

 

NIST Technical Note 1722 

Simple Estimates of Combined 

Stairwell / Elevator Egress in 

Buildings 

Paul A. Reneke 

Piotr Tofilo 

Richard D. Peacock 

Bryan L. Hoskins 

Fire Research Division 

Engineering Laboratory 

http://dx.doi.org/10.6028/NIST.TN.1722 

February 2013 

U.S. Department of Commerce 

Rebecca Blank, Acting Secretary 

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
 

 

 

 

 

Certain commercial entities, equipment, or materials may be identified in this 

document in order to describe an experimental procedure or concept adequately. 

Such identification is not intended to imply recommendation or endorsement by the 

National Institute of Standards and Technology, nor is it intended to imply that the 

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1722 

Natl. Inst. Stand. Technol. Tech. Note 1722, 44 pages (February 2013) 

http://dx.doi.org/10.6028/NIST.TN.1722 

CODEN: NTNOEF 
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iii 
 

 

 

 

 

 

 

 

Figures and Tables 

Figure 1. Evacuee speed on stairwells as a function of stairwell angle. Data from Table 1 

taken from reference [6]. .............................................................................................7

Figure 2. Estimated egress time in an arbitrary building configuration for different 

building heights and solver time steps.........................................................................9

Figure 3. Stair 8 North data with the prediction of Egress Estimator and twice the 

prediction. Uncertainty is ± 1 s..................................................................................31

Figure 4. Comparison of Stair 8 South data and Egress Estimator prediction and twice 

prediction. Uncertainty is ± 1 s..................................................................................32

Figure 5. Comparison of Stair 8 South data and Egress Estimator prediction and twice 

prediction. Uncertainty is ± 1 s..................................................................................33

Figure 6. Comparison of Stair 5 A and Egress Estimator prediction and twice prediction. 

Uncertainty is ± 1 s ....................................................................................................34

Figure 7. Comparison of Stair 4 B data and Egress Estimator prediction and twice 

prediction. Uncertainty is ± 1 s..................................................................................35

Figure 8. Normalized data from all stairs as compared to predictions of Egress Estimator. 

Uncertainty is less than ± 0.004.................................................................................36

Table 1. Constants for equation (8) for a range of geometries. Data from reference [6]. ...6

Table 2. Summary of comparison of egress data with Egress Estimator predictions .......35

iv 
 

 

 

 

 

 

 

 

 

Simple Estimates of Combined Stairwell / Elevator
 

Egress in Buildings
 

Paul A. Reneke, Richard D. Peacock, and Bryan L. Hoskins
 

Engineering Laboratory
 

National Institute of Standards and Technology
 

1 Introduction 

The U.S. General Service Administration (GSA) manages thousands of federal 

properties, the design and construction of new buildings and the renovation of existing 

ones. One aspect of this mission is determining what fire safety and life safety systems to 

include in construction or renovation projects. While GSA generally meets or exceeds 

local building standards in a cost-effective way, the lack of quality research data makes it 

very difficult to determine the performance of current or new systems. To address this 

problem the GSA has funded the Engineering Laboratory (EL) of the National Institute of 

Standards and Technology (NIST) to develop performance requirements and data suitable 

to support the design and acceptance of cost-effective elevator and stairwell systems that 

provide for efficient and timely evacuation of occupants including those with disabilities, 

and that facilitate more efficient fire department operations. 

Approximately $63 billion annually is spent on fire protection features in building 

construction with life safety being a primary concern [1]. A major component of life 

safety of a building is the ability to evacuate part or all of a building when an emergency 

occurs. Historically, requirements for fire safety in general and for stairwell egress in 

particular have evolved in response to large loss fire incidents. Currently, egress systems 

are designed around an antiquated concept of providing stair capacity for the largest 

occupant load floor in the building with little or no consideration of occupant behavior, 

needs of emergency responders, or evolving technologies. NIST has had a leading role in 

providing a scientific basis for code requirements since the early 1900s. For example, 

design requirements for stairs, along with the now-ubiquitous 1.2 m (44 in) stair width, 

were documented in 1935 by the National Bureau of Standards (NBS, now NIST) report 

Design and Construction of Building Exits [2]. The landmark 1935 NBS report 

substantiates recommendations for exit system design based on surveys distributed to 

practicing architects, field inspections, citations to previous investigations as far back as 

1909, as well as simple observations of exits and exit component usage during rush-hour 

and fire drill evacuation conditions for contemporary building designs. These 

recommendations constitute the primary basis for current egress requirements, though 

modifications have resulted from large-loss incidents, as well as subsequent research. 

Science-based egress designs have significant potential to mitigate the growing costs of 

fire protection features in building construction. Further, about one-fourth of fire victims 

perish during evacuation, which suggests that there are opportunities to save lives 

through egress design improvements. Adoption of efficient egress designs and advanced 

egress technologies can therefore have an impact the life loss due to fire. For example, 

1
 
 

 

 

 

 

improvements in signage, markings, and lighting led to great reductions in egress time 

from One World Trade Center on September 11, 2001 compared to the 1993 bombing of 

the same building. On September 11, 2001, the use of elevators in World Trade Center 

Building Two (before it was struck by an airplane) led to thousands of lives being saved. 

Interest in estimating occupant movement during evacuation is not new. The 1935 NBS 

report [2] included empirical correlations for movement speed based on stairwell 

configuration. Over the years, numerous researchers have developed other correlations 

based on experimental data to predict movement speeds during building evacuations [3 – 

7] and others have developed computer-based evacuation models that vary widely in 

application and complexity [8]. All of these are intended to provide building designers 

and engineers with the ability to develop efficient egress designs to meet building code 

requirements. 

Like stairwell provisions, the use of elevators during fire emergencies was considered as 

well. As early as 1914, properly protected elevators were seen as essential in taller 

buildings, but automatic elevators were deemed unsuitable in the 1935 NBS report [2]. 

More recently, there has been considerable attention to the use of elevators to speed up 

building evacuation. This included studies of the feasibility of elevator evacuation, 

human behavior, and the use of elevator lobbies as areas of refuge [9]. Protection from 

heat, flame, smoke, water, overheating of machinery, and loss of electrical power were 

seen as important to elevator design [9]. Using model calculations for example buildings, 

elevator evacuation was estimated to speed evacuation by 16 % to 25 % compared to 

evacuation by stairs alone; the taller the building the greater the impact. 

This report describes a simple tool that combines estimates of stairwell and elevator 

egress timing to provide an overall estimate of evacuation from buildings. It is based on 

methods developed in the Society for Fire Protection Engineers (SFPE) Handbook [6] for 

egress using stairwells and the work of Klote and Alvord [10] on modeling elevator 

evacuations. First, the theory underlying the use of stairs and elevators will be described. 

Next, a description of how to use the model will be given. Finally, some results of the 

model will be examined and compared to available experimental data. 

2
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2 Overview of the Egress Estimator Model 

In examining the calculations in the Egress Estimator, it is important to understand the 

problem being solved. The Egress Estimator is envisioned as a screening tool that would 

be used early as part of the design process to help establish broad design criteria for a 

building design rather than for a detailed analysis of the performance of a final design. 

The Egress Estimator calculates a reference time that can be thought of as an expected 

time to complete evacuation. While it is becoming increasingly clear that the evacuation 

of a building is best described with a distribution of times [11] in determining the impact 

of changes in design criteria a single value such as average time or median are often 

easier to work with. 

The Egress Estimator consists of two sub-models: a model for evacuation using stairs and 

one for evacuation via elevators. Egress times for the two models are calculated 

separately but synchronized in simulation time and the maximum of the two times is 

taken as the overall egress time. 

The two models are described in the following sections. First the model of stairwell 

evacuation will be discussed, including theory and implementation. Then the elevator 

model will be detailed, including a brief review of the Klote model [10] and its 

implementation. 

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The stairwell evacuation sub-model uses a simplified egress calculation based on 

algorithms published in Chapter 3-14 of the SFPE Handbook [6]. The population 

assigned to a particular stairwell starts in a single room. This compartment is connected 

to a single corridor of a given length (the Handbook uses the maximum path length, 

which ends at the door to the stairwell). Every floor connects to the stairwell, which leads 

down an exit corridor and finally an exit door. The next three sections describe the logic 

for the model used, the theoretical development and implementation. 

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Since the model is to serve as a screening tool rather than validating a final design, it is 

appropriate to include as input averages to account for specific evacuee traits. Individual 

and group dynamics such as individual occupant speeds and behaviors, individual or 

group decisions, and the impact of environmental conditions are not included in this 

simple tool. 

It is also clear from observations of actual evacuations, that movement in corridors and 

stairways is limited primarily by physical rather than behavioral constraints (in crowded 

situations at exit doors or in the stairwell when capacity reaches maximum). Since this 

model is meant as a screening tool, the building population is assumed to have a single, 

“average,” set of behavioral characteristics (such as a delay in beginning to evacuate, 

speed in corridors and on stairs, and merging behavior entering the stairwells) so that 

differences in evacuation times are based on the design parameters of the building and 

their impact on the averaged occupant characteristics. 

3
 
 

 

 

 

 

 

 

 

 

 

 

!

This “average” behavior is modeled as a fluid using two state variables, density and 

speed, to track the evacuation. The density equation accounts for physical constraints in 

the evacuation and the tracking of evacuees. Conversely, the speed equation represents 

the human behavior aspect of the problem. In such a simple model, human behavior is 

limited. Each evacuee is assumed to begin to evacuate at the same time, an individual 

slows down or speeds up as the people ahead slow down or speed up, and finally if the 

space ahead of an occupant is full, the speed goes to zero. 

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The stairwell evacuation is modeled as a 1D problem with two state variables, D for 

density and s for speed. Density and speed are assumed to be the same throughout a cell 

with area W!x, where W is width of the cell and !x is the length of the cell. Note that 

depending on the dimensions of W and !x a cell can hold more than one person. 

To find the partial differential equation for density start with the equation for a change in 

the number of people in a cell, which is simply 

"P = Pin # Pout (1) 

where !P is the change in the number of people, Pin is the number of people that enter the 

cell and Pout is the number of people that exit the cell. We can redefine the number of 

people so that 

!P = !DW!x

Pi = fi!t (2)

fi = Disiwi

where !D is the change in density, f is the flow, !t is the change in time and the subscript 

i = in or out. Substituting into the first equation gives 

!DW!x = fin!t " fout!t (3) 

Dividing both sides by !W!x!t and group gives 

!D fin " fout 1 !f = = " !t W!x W !x (4) 

!f = fout " fin

Taking the limit as !D, !f, !t and !x go to 0 gives the partial differential equation 

1 ! f D! = ! (5) W !x

4
 
5

Because fi = Disiwi we can simplify the derivative even further to an equation only 

dependent on that state variables

D! = ! w

W

s

"D

"x

+ D "s

"x

+

Ds

w

"w

"x

#

$

% &

'

( (6)

If the width of the entry and exit of a cell are the same and equal to the width of the cell 

the equation further simplifies to

D! = !(s

"D

"x

+ D "s

"x

) (7)

In stairs, the width of the cell is defined as the full width of the stairs less a boundary 

layer on each side to account for handrails and the fact that evacuees leave space near the 

sides of the stairs. On stairs and landings, this boundary layer is taken to be 0.15 m [6]. 

According to Hoskins et al [7], it is important to include only the space evacuees actually 

use in calculation of landing density. The egress estimator calculates landing density with 

the following method from [7]. The path length is given by

ll = !ws

2

2

+lg

(8)

where ll is the travel length on the landing, ws is the width of the stair and lg is the length 

of the gap between the two stairs. The path assumes that evacuees travel in an arc and use

a semi-circle plus the length of the gap, which is assumed to be 0.1 m.

The area on the landing that is used by the evacuees is calculated assuming the same arc 

path and is essentially half a doughnut with the hole defined by the boundary layer, bs. 

The equation for the area, Al, is given by 

Al = !

2 (ws ! bs )

1

2 ! bs

" 2

#$ %&'+lg (ws ! 2bs )

(9)

The effective width used for the landing cells is simply the area divided by the travel path 

given as

wl = Al

ll (10)

where wl is the effective width of the landing area.

There is one other issue with the geometry used in the Egress Estimator. In previous 

estimates [12] stair density is calculated using only horizontal stair tread depth. Other 

publications do not indicate how the calculation is made. The ratio between travel 

distance and length used for density on a flight of stairs is
6

ns(ws ! 2bs )r(lt

2 +lr2

)

1

2 = ns(ws ! 2bs )lt

r = lt

2

lt

2 +lr2

"

#

$ %

&

'

1

2

(11)

where ns is the number of stairs, lt is the depth of the tread and lr is the height of the riser. 

The egress estimator uses the ratio to adjust the area and speed used in the density 

equation. The ratio is used wherever the density on the stairs multiplies a unit of length in 

the direction of travel on the stairs. Consider the case of the cell at a top of a flight of 

stairs where the flow of evacuees is coming from the landing. The equation would be

D! = ! Di

siwi ! Dorsowo

Wor"x

(12)

where the i subscript designates values from the landing cell and the o subscript is for 

values coming from the cell at the top of the flight of stairs. Note that this only impacts 

the density equation for the cell at the top of a flight of stairs and the first cell of the 

landing at the bottom of a flight of stairs; the ratio cancels out for interior stair cells.

The SFPE Handbook gives the following equation relating speed (m/s) to density 

(person/m2) for density D greater than 0.54 people/m2.

ssfpe (D) = k ! akD (13)

with a = 0.266 and k (m/s) given in Table 1.

Table 1. Constants for equation (8) for a range of geometries. Data from reference [6].

Exit route element K

(m/s)

ssfpe(0.54)

(m/s)

Corridor, isle, ramp or doorway 1.40 1.20

Stairs, Riser (in) Stairs, Tread (in)

7.5 10 1.00 0.86

7.0 11 1.08 0.92

6.5 12 1.16 0.99

6.5 13 1.23 1.05

For density, D, less than 0.54 people/m2, the speed, s, is equal to ssfpe(0.54) as shown in 

Table 1.

We will assume that people’s speed doesn’t change instantly but approaches the ideal 

speed given by the Handbook equation. Furthermore we assume that people don’t adjust 

their speed based on the conditions around them but just based on the conditions ahead of 

them. This gives the equation
7

s!j = a ssfpe (Dj+1)! s ( j) (14)

where a is a parameter determining how quickly speed changes, sj is the speed in the jth

cell and Dj+1 is the density in the next cell in the direction of egress. 

The SFPE Handbook [6] includes values for four stair configurations and a flat surface

(see Table 1). To be more general, it is desirable to allow a continuous range of stair 

configurations. The first step is to determine a method for calculating the maximum 

speed (or k, since one defines the other) for a general configuration. 

The following plot shows the speeds given in the SFPE Handbook against the angle of 

the stairs. It also shows two fits to the data. One is a linear fit and the other uses a 

quadratic. Clearly the quadratic fit represents the data and has the better R2. The Egress 

Estimator determines the maximum speed for a given stair configuration using this 

quadratic equation. 

Figure 1. Evacuee speed on stairwells as a function of stairwell angle. Data from Table 1

taken from reference [6].

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In order to find k used for a given maximum speed, we first reorganize ssfpe(D) so that it is 

more easily interpreted physically

ssfpe (D) = (1! aD)k

ssfpe (D) = Dmax ! D

Dmax

sˆ

max

(15)

where ! ! ! is the pseudo maximum speed. If speed continued to increase for D < 0.54 

then at D = 0 the speed would be !. Solving for ! gives

sˆ

max = Dmaxsmax

Dmax ! Dmin

(16)

where Dmin=0.54. Substituting into ssfpe(D) and (11) yields

s!j =

a(smax ! sj) for D " Dmin = 0.54

a

Dmax ! Dj+1

Dmax ! Dmin

smax ! sj

#

$

% &

'

( for D > Dmin

#

$

%

%

%

%

(17)

Equations (5) and (12) are the time derivatives for density and speed used in the model.

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The Egress Estimator is a 1-dimensional partial differential equation set that uses an 

explicit Runga-Kutta solver. To implement the model, the simulation is first broken into 

different elements: corridors, flights of stairs or landings. Each element has its own 

parameters including width, length, maximum speed and maximum density. Elements are 

discretized into cells with widths equal to the element’s width and approximately 1 m in 

length. There are at least two cells in each element. Because elements can be of any 

length, for example a corridor could be 43.2 m in length, the cells are not exactly 1 m but 

the program determines the number of cells so the length is as close to 1 m as possible. 

One important issue of an explicit solver is the length of the time step. The longer the 

time step the faster the model runs but the more error can accumulate reducing the 

accuracy of the solution. The shorter the time step the less error accumulates but the 

longer each run of the model takes. In order to establish the time step to use for the 

model, the estimated egress time for four cases (that differed only in the number of floors 

in the building) was calculated using time steps 0.05 s, 0.1 s, 0.2 s, 0.3 s, 0.4 s and 0.5 s. 

Figure 2 shows the percent difference between each run and the run using a time step of 

0.2 s. 
9

For time steps greater than 0.2 s, solver error seems to accumulate, but even the largest 

error is less than 1.6 %. A time step of 0.2 s was chosen to balance both speed of 

calculation and limiting accumulating error.

Figure 2. Estimated egress time in an arbitrary building configuration for different 

building heights and solver time steps.

The density equation used in the model is Eq. (5) rather than (6) since it is operationally 

simpler. When the entry and exit are the same width as the cell (6) takes only 4 

multiplications or divisions it takes 3 additions or subtractions. Eq. (5) takes 5 

multiplications or division but only 1 subtraction. However, when the entry or exit width 

is different from the cell width or the flow of two cells are merging into one cell the 

implementation of (6) is significantly more difficult than (5). 

Because doors can constrain flow not only because of the width, but also due to the use of 

automatic door closers, which are not considered in the model, the model allows the user 

to specify a maximum flow rate in order to capture additional effects, if appropriate.

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The GSA has been interested in the use of elevators in emergency evacuations for many 

years. In 1992, with GSA support, Klote and Alvord [10] published a model of elevator 

evacuation, ELVAC. This model serves as the basis for the elevator model included in 

the current model and so the following sections will review the ELVAC model.

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The ELVAC model starts off with a basic equation that describes the total evacuation 

time for elevator evacuation

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E! E#$! E#"! E#/! E#4! E#J! E#H!

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te = ta + to +

1+!

J

tr, j

j=1

mr

!r=2

R

! (18)

where te is the total time for evacuation, ta is the time for elevator cars to be recalled to 

the first floor, to is the evacuation time for the 1st floor elevator lobby, J is the number of 

elevators, R is the number of floors being evacuated, mr is the number of trips it takes to 

evacuate the rth floor, tr,j is the total trip time for the jth trip to the rth floor and (1 + ") is 

the trip inefficiency.

The start up time, ta, is a user specified time when all the elevator cars are in the lobby 

ready to start the evacuation. The evacuation time of the first floor lobby, to, is also a user 

specified time and represents the amount of time from when the last car unloads in the 

lobby till everyone has evacuated the building. 

The trip time is calculated in the following equation

tr, j = 2tt,r + ti + tu + 2td (19)

where tt,r is the time it takes to go from the lobby to floor r or vice versa, ti is the time it 

takes to load the elevator, tu is the time it takes to unload the car and td is the time it takes 

to open or close the car doors. As can be seen in the equation for trip time the model 

makes heavy use of symmetry. Each term in the trip time equation will be discussed 

separately.

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As a car travels from one floor to another, it can go through as many as 5 phases of 

acceleration depending on the distance: constant acceleration, transitional acceleration, 

constant speed or no acceleration, transitional deceleration and constant deceleration. The 

duration and distance travel in the constant acceleration and deceleration phases are equal 

as well as in the transitional acceleration and deceleration phases. 

The acceleration/deceleration phase ends when a car reaches a certain fraction, f, of the 

normal maximum travel speed, vmax. Using Newton’s equations of motion for a constant 

acceleration to find the duration of constant acceleration, t1 gives

fvmax = at

1

t

1 = fvmax

a

(20)

with t1, the distance traveled, as

s1 = 1

2at

1

2

s1 = f 2

vmax

2

2a (21)
11

Remembering that it takes the same amount of time and distance to decelerate as 

accelerate, if the height of r

th floor, sr, is less then the distance required to complete the 

acceleration/deceleration phase, 2s1, the car never leaves the constant 

acceleration/deceleration phase. The total time, te, is twice the acceleration time, since at 

the half way point the car starts to decelerate, which gives

sr

2 = atr

2

2

tr = sr

a

te = 2tr + t! = 2 sr

a

+ t!

(22)

If sr >2s1 then the car enters the transitional acceleration phase. The transitional 

acceleration phase is not derived directly but the distance traveled and duration are 

approximated. The time it takes to go from constant acceleration to constant velocity, 

delta t2, and the total time, t2, are given by

!t2 = vmax

2 " v12

2v1a

t2 = !t2 + t

1

(23)

The distance traveled in the transitional acceleration phase and the total distance traveled 

after the transitional acceleration phase are given by

!s2 = 1

3a

vmax

3

v1

" v1

2 #

$

% &

'

(

s2 = !s2 + s1

(24)

If s1 < sr < s2 then the velocity, vr, at the end of transitional acceleration when transitional 

deceleration would start is 

vr = v1

3 +3av1

sr

2 ! s1

"

#

$ %

&

' (

)

* +

,

-

1

3

(25)

The time in the transitional acceleration/deceleration phase and the total time of the trip, 

tr, are given by 
12

!tr = vr

2 " v12

2av1

tr = !tr + t

1

te = 2tr + t!

(26)

If sr > s2 then the car travels a certain distance, delta s3 = sr – s2, at the constant speed, 

vmax. The time the car travels at constant speed and the total time the car travels are

!t3 = sT " 2s2

vmax

te = !t3 + 2t2 + t!

(27)

where tl is the leveling time. The leveling time is the time the car takes to make final 

adjustments to line up with the arrival floor and it is assumed to be 0.5 s. [9]

!"!"#"! >,+.&-.?)/-5'

The standing time, ts, is the time it takes to load passengers on the evacuation floor, ti,

and unload them on the exit floor, tu, plus the time it takes to open and close the doors 

twice, td. The equation is

ts = (ti + tu + 2td )(1+μ) (28)

where , μ, is the transfer inefficiency, which is defined as

μ =! +" +# (29)

where # is basic transfer inefficiency taken here as 0.1, $ takes into account populations 

that have significant mobility challenges. In this model, $ is 0.0, representative of a 

normally mobile population, and % which is the variance from a standard 1200 mm (48 

in) door. Values for gamma come from table 1 of the Appendix of Klote [10]. Opening 

and closing times are taken from the same table.

Loading and unloading times have the same form but differ in coefficients. There is a 

minimum time that the elevator doors are open. This is the time it takes to load 2 people. 

For more than 2 people there is a rate, which is different for loading and unloading. The 

equation is 

ts = tdw for N ! 2

tdw + tin/out (N " 2) for N > 2

#

$

%

&

% (30)
13

where tdw is the dwell time or minimum time the door remains open and is 4.0 s, tin/out is 

the rate that people load or unload a car with the loading rate equal to 1.0 person/s and 

the unloading rate equal to 0.6 person/s.

!"!"! @<<A56,-%.<)+.&)456('5'.,+,-%.

The above description is of the model of elevator evacuation that has been previously 

developed in ELVAC [10]. There is one significant difference between the original 

ELVAC model and the one included in the Egress Estimator. Instead of using assuming a 

trip inefficiency as in Eq. (18), the current model implements a simple elevator control 

algorithm to allow more flexibility. This was done for two reasons. The first was so that 

elevator evacuation could be tracked along with the stair evacuation for output. The 

second is that including an elevator control algorithm makes it possible to test alternative 

algorithms and layouts of elevators not included in the original ELVAC model. For 

example, the original ELVAC model assumed that evacuation proceeded in a single bank 

of elevators operating in unison beginning at the highest occupied floor in the building.

The elevator control algorithm is simple and based on call signals from occupied floors. 

At the beginning of the evacuation the cars are given an initial order with the first car 

going to the highest floor, the next car to the next highest floor, and so on. When a car on 

the ground floor is assigned a destination floor, that floor’s call signal is stopped so that 

the next available car will not go to that floor until the originally assigned car has loaded 

and left the floor. If any occupants remain on the floor, another call is activated and the 

process starts anew. Once a car has returned to the ground floor and unloaded its 

passengers, it is assigned the highest floor that has a call signal and repeats the process. 

Towards the end of an evacuation the situation can arise that there are more elevator cars 

than occupied floors. When this happens, a car can be on the ground floor and finished 

unloading but all the occupied floors have cars assigned to them. The car then waits at the 

ground floor until an occupied floor call is activated. While this is typical of Phase I 

recall requirements in the model codes, other more sophisticated algorithms are certainly 

possible.

The model assumes that everyone that is using the elevators is in the elevator lobby when 

the elevators start the evacuation mode. The second assumption is that once an elevator 

car has loaded and left a floor, any remaining people will press the call button to get the 

next available car.

The implementation is straightforward. A single round trip is made up of four events: 

traveling to the call floor, loading passengers and closing the doors, traveling to the 

ground floor, and unloading passengers. For each car, the time until the next event is 

calculated and put in its appropriate position in an ordered queue. The queue is ordered so 

that the first event off the queue is the next event (a first-in, first-out queue). The next 

event is then taken off the queue and when the simulation reaches that time, the event is 

said to be complete and the time to the next event is calculated. 
14

3 Use of the Model

1"# 23%(0456%'03

This section describes the user interface and required inputs. The program uses a single 

window (below) for both inputs and calculated egress time output. This software tool is 

intended to help the user estimate the time that would be required for building evacuation 

by stairs, elevators, or a combination of both. While the tool considers occupant loading, 

the capacity and number of stairs and elevators in a building, the details of occupant 

behavior, environmental effects, or damage due to an emergency event, and other 

potentially important events are not included. If more detailed analyses are needed, other 

simulation tools should be employed (for examples see [13]).

The program input is divided into several areas that allow the user to define details of 

building occupants, stairwells, elevators, and exits.

1"! 7'+*-8*35

At the top of the window the Egress Estimator has a single menu item, File. Clicking on 

File drops down three sub menu items: New, Open, and Save. Clicking on New resets all 

the fields to the default conditions. Open allows the user to select an Egress Estimator 

output file or saved file to set the initial conditions. Save allows the user to save the 

current initial conditions to a file without having to run a full simulation.

1"1 95'+4'3:-&34-;0<5+&%'03
15

For the estimates in this tool, the building is defined by the number of floors in the 

building, the number of occupants on each floor of the building, and the fraction of 

building occupants who use the elevators during evacuation.

Number of Floors: Input the number of floors in the building, including the exit floor. 

For the simple estimates in this tool, all floors of the building are assumed to be occupied. 

If the building includes unoccupied floors with mechanical or other equipment, these 

would normally not be included in the input. The number or height of stairs in each flight 

can be adjusted upward to account for the additional height of the unoccupied floors.

Number of Occupants on Each Floor: The average number of occupants on each floor 

of the building. For the simple estimates in this tool, all floors are assumed to have the 

same number of occupants.

Fraction of Occupants that Use Elevators: Input the fraction of occupants on each 

floor that use elevators for evacuation. The remaining population are spread evenly 

among the stairwells.

Use building data file: If checked, the software will prompt for a comma-delimited 

spreadsheet file containing floor-specific information. Each line of the spreadsheet 

specifies the following information for one or more floors:

Starting floor: the lowest floor (inclusive) in the group of floors being specified

Ending floor: the highest floor (inclusive) in the group of floors being specified

Population: the number occupants on each floor in the group of floors

Fraction using elevators: the fraction of occupant on each floor in the group of 

floors that use elevators for evacuation.

Starting time for stairwell evacuation: delay time from beginning of evacuation 

when occupants begin to travel towards the stairwells for evacuation.

Starting time for elevator evacuation: delay time from beginning of evacuation 

when occupants begin to travel towards the elevators for evacuation.

A sample building data file is shown below. Note that you only need to include floor 

data that is different from the values already specified in the main input page for Egress 

Estimator. All other values and floors use the values specified on the main input page.

Start floor

(inclusive)

End floor

(inclusive)

Population on

floor

Fraction using 

elevator

Start of stair

evacuation

Start of elevator

evacuation

2 2 100 0 0 0

10 15 30 1 0 0

End

The first cell of the row after all input is made has to have the word “End” and the 

program is case sensitive. All information in cells on that row or subsequent rows will be 

ignored.
16

1"= $%&'()*++-23<5%,

For stairwell evacuation, occupant travel is comprised of travel from a single 

compartment, from the compartment to a stairwell in a corridor, and down a stairway.

Maximum Travel Distance (m): As a conservative estimate, input the longest distance 

occupants would have to travel from their starting point to a stairwell for evacuation. For 

this tool, all corridors (and stairwells) are assumed to be of identical size and 

configuration.

Hall Width: Input the width of the corridor occupants use to travel from their starting 

point to the stairwell for evacuation.

Maximum Rate Occupants Can Enter Hallway (people/s): A typical value for flow 

through a single doorway is 1 person/s [6]. If there are multiple doorways opening onto 

the corridor or obstructions to entering the corridor, this value may be increased or 

decreased as appropriate. The SPFE handbook [6] includes additional information on 

movement speed as a function of width and occupant density.

Number of Stairwells: The number of stairwells in the building that are used for 

occupant egress. For this tool, all stairwells are identical and are assumed to serve all 

floors of the building.

Occupants on First Floor Use Stairwells: Check this box if occupants on the exit floor 

typically use the same egress path as occupant on the stairwells. When checked, 

occupants from the exit floor merge with occupants from higher floors (see merging 

options below) as part of the egress calculation. 

Stair Width (m): Input the full width of the stairwell.
17

Flights of Stairs Per Floor: Input the typical number of flights of stairs from (landing to 

landing) between floors. For this tool, all flights of stairs are assumed to be identical 

throughout the building.

Number of Stairs Per Flight: Input the number of stairs in each flight of stairs. For this 

tool, the number of stairs in each flight is assumed to be the same throughout the 

building.

Stair Riser Height (mm): Input the height of each stair measured from tread to tread.

Stair Tread Depth (mm): Input the size from front to back of each stair tread.

Maximum Rate Occupants Can Enter Stairwell (people/s): Gwynne et al found that 

the typical flow rate through a door with a closer is 0.92 people/(m s) [14]. If there are 

multiple doorways opening onto the stairwell or obstructions to entering the corridor, this 

value may be increased or decreased as appropriate. The SPFE Handbook [6] includes 

additional information on movement speed as a function of width and occupant density.

Maximum Rate Occupants Can Leave Stairwell (people/s): Gwynne et al found that 

the typical flow rate through a door with a closer is 0.92 people/(m s) [14]. If there are 

multiple doorways opening from the stairwell or obstructions when leaving the corridor, 

this value may be increased or decreased as appropriate. The SPFE handbook [6] 

includes additional information on movement speed as a function of width and occupant 

density.

Distance to Exit Discharge (m): Input the length of the exit corridor from the stairs to 

the building exit or another point of safety.

Exit Width (m): Input the width of the exit from the stairs.

Maximum Rate Occupants Can Leave Exit Discharge (people/s): A typical value for 

flow through a single doorway is 1 person/s. If there are multiple doorways opening onto 

the corridor or obstructions to entering the corridor, this value may be increased or 

decreased as appropriate. The SPFE handbook [6] includes additional information on 

movement speed as a function of width and occupant density.
18

1"> .+*/&%0(-23<5%,

For elevator evacuation, occupant travel is defined by the capacity of the elevators and 

the travel speed of the elevator. For this tool, elevator evacuation is assumed to proceed 

as follows: Elevators initially travel to the discharge floor. Once the elevators reach the 

discharge floor, evacuation begins with the highest occupied floor. Once the highest 

floor is completely evacuated to the discharge floor, evacuation proceeds with the next 

highest occupied floor and continues until the entire occupant population is evacuated. It 

is assumed that the same fraction of occupants on all floors use the elevator for 

evacuation. In practice, it is likely that some occupants on the lower floors will use the 

stairs. If a more detailed analysis is required, more complex evacuation models are 

available [13].

Number of Elevators: Input the number of elevators used for occupant evacuation. For 

this tool, all elevators in the building are assumed to be identical and operate as a group 

during evacuation. This assumption will tend to slightly overestimate the time required 

for elevator evacuation.

Elevator Capacity (kg/people): Input the maximum number of people that can use each

elevator car.

Door Type: Select from a range of elevator door types and widths. This input impacts the 

door opening and closing times for each elevator car at the beginning and end of each 

trip.

Normal Operating Velocity (m/s): Input the normal full operating velocity of the 

elevator car. The default in the model uses is a typical value of 3.0 m/s [10].

Elevator Acceleration (m/s2): Elevator motion starts with constant acceleration, 

followed by a transitional acceleration until constant velocity motion at the normal 

operating velocity is attained. Input the constant acceleration. Transitional acceleration is 

calculated by the software. The default value the model uses is 3.0 m/s2 [10].

Elevator Startup Time (s): The time from activation of the alarms (for example) to the 

start of the round trips that evacuate people. Input the time spent before the actual 
19

evacuation by elevator cars begins. Most typically, it is computed to be the time required 

to bring a fully loaded elevator car from the most distant floor to the discharge floor. If 

this is not satisfactory, a larger or smaller value may be used. 

If the elevators are operated automatically during evacuation, one starts the elevator 

evacuation after all of the elevators have been moved to the discharge floor and anyone in 

the elevators have left the elevators. In the case of manual elevator operation, the time 

for elevator operators to reach the cars must be included. 

1"? ;(0:(&@-A5%<5%,

Once appropriate inputs for the building are input to the software, the “Estimate” button 

begins calculation of occupant egress from the building. The user is prompted for a 

filename and location to store the results of the calculation (as a comma delimited file 

that can be read into most spreadsheet programs for further analysis or display.

During the simulation, the number of occupants evacuated and the evacuation time is 

displayed. When the calculation is complete, the total number of occupants and total 

evacuation time is shown. 

Detailed information on occupant location throughout the evacuation is available in the 

comma-separated spreadsheet file created during the simulation.
20

1"B C3&+D,',-0E-%F*-05%<5%

As the Egress Estimator produces extensive sets of data an additional prototype tool was 

developed to facilitate the analysis and visualization of the output data. This tool was 

created as a VBA enhanced Microsoft Excel 2007 Workbook. It is available together with 

Egress Estimator and the file is named EgressVisualization.xlsm. As the 

EgressVisualization is currently utilizing the VBA macro technology it is necessary to 

enable macros upon opening the workbook. Unfortunately the tool will most probably not 

work properly on earlier versions of Excel due to smaller number of columns allowed in 

previous versions.

EgressVisualization consists of two main screens allowing for a quick overview of output 

data without the need to manually process the output CSV files. 

The first screen allows for interactive time based visualization of egress progress. This 

can happen after pressing the button at the top of the screen “Load file to visualize 

egress” and loading up the selected CSV file using the standard file dialog. After loading 

the output file, the user can track the egress progress in the simulated building by using 

the egress time scroll bar at the top of the screen. The time based egress situation is 

presented on the five graphs depicting respectively: approximate position of elevators at a 

given time, number of people still in the elevator lobbies, number of people in each stair, 

hall/corridor and initial room (numbers of people are represented by green bars). The 

colors of bars representing the number of people in the stairs can additionally adjusted to 

represent flow density according to the width of the stair (the stair width has to be 

adjusted manually at the top of the screen). The last graph presents the overall egress 

history in the building and the indication of the current time represented by a purple 

vertical line. By interactively changing the time, the user has the ability to observe the 

elevator and stair system operation and to establish times when a given egress component 

(elevator lobby, stair, hall/corridor or room) is empty. With reasonable computing power, 
21

dragging the scroll bar or pressing and holding the buttons at either end of the scroll can 

reproduce the dynamics of the egress system quite smoothly. 

The following pictures present screenshots from the EgressVisualization after loading 

output data from EgressEstimator for an example test case that was run for a 30-floor 

building. First screenshot shows initial situation at time = 0 and the second screen shows 

the situation at an arbitrary time selected by the user with the slider on the time scroll.
22

The second screen of the EgressVisualization tool is accessed by pressing the button 

"Analyse Output". This screen is designed to distill more useful information from the 

Egress Estimator output. Then, by pressing the button "Select files for analysis" the user 

can load up one or multiple files (by pressing CTRL during file selection) to observe or

compare the progress of egress in the selected output files. This may allow for closer 

observation of the effects of varying building designs and for testing and comparing 

egress strategies using stairs and elevators. The output is presented on five graphs. The 

two leftmost depict the times when each elevator lobby, room or corridor/hall is 

evacuated. The next graph provides the user with information on how long people are 

assumed to wait for an elevator. The evacuation of halls/corridors provides information 

as to when people from a given floor are all within an exit stair, which is considered to be 

a place of relative safety. The time to leave rooms or halls/corridors can be regarded as 

the Required Safe Egress Floor (RSET) for a given floor (assuming that elevator lobbies 

are also considered as a place of relative safety if designed properly). The three other 

graphs depict the history of egress process in three configurations: total building egress 

i.e. number of people who remain in the building, total number of people who remain in 

elevator lobbies on all floors, and the total number of people who remain in stairs and 

floors (i.e. stairs, halls/corridors and rooms). 

The following picture presents a screenshot from the EgressVisualization after loading 

output data files from EgressEstimator that was run for a 30-floor building in two 

different design configurations. In this case, there was a different number of elevator cars 

in the two scenarios. The user can observe effects in total egress total lobby egress times, 

but the total stair egress remains the same. On the leftmost graph it can be noted that due 

to different number of elevator cars in one case the lobbies are evacuated sooner than the 

other case, which also means that the waiting times for people were shorter. The 

evacuation time of halls/corridors show no difference as there was no difference in stair 

system design.
23

4 Results

Egress Estimator was tested for qualitative and/or quantitative agreement with reference 

sources in addition to comparisons with available experimental evacuation drill data. 

First, some test cases from International Maritime Organization (IMO) [15] were run to 

verify that the model was behaving in a reasonable manner for the given parameters. 

Second, test cases from the SFPE Handbook [6] for stair movement and from a paper by 

Klote and Alvord [10] for elevator movement were examined to verify that the results 

were comparable to established methods. Finally, a comparison was made to a set of 

evacuation drill data previously collected by NIST [16].

="# 28A-G('%*('&

The IMO regulations include qualification criteria for software used to estimate 

evacuation times from passenger vessels. While not a true validation of a model, these 

provide both a qualitative and quantitative assessment of the predictive capability of a 

model. The criteria were originally designed for agent based evacuation models but they 

are relevant for all evacuation models. The results of the IMO tests are as follows:

• 5%M!$N A!7(2>&.!-.!->&)+,-&.!-.!+!O&22-'&2!:+)P-.Q!+,!$#E!6R>!>1&B)'!,2+9()!

4E 6 -.!4E>#

o 5.!?Q2(>>!?>,-6+,&2!>7(('>!'&!.&,!O1+.Q(!-.!+!O)(+2!O&22-'&2#!01(!;-2>,!

7(2>&.!-.!+!>-6B)+,('!2B.!6((,>!,1->!O2-,(2-&.#
24

• 5%M!"!+.'!5%M!/N A!7(2>&.!-.!->&)+,-&.!+>O(.'-.Q!S&2!'(>O(.'-.QT!>,+-2>!+,!

$#E!6R>!>1&B)'!,2+9()!$E!6!-.!$E!>#

o 5.!?Q2(>>!?>,-6+,&2U!>,+-2>!+2(!>+6(!+>!O&22-'&2>!(FO(7,!;&2!,1(!

6+F-6B6 >7(('#!!V1(.!,1(!>7(('!&;!+.!&OOB7+.,!-.!->&)+,-&.!->!

$#E 6R>U!,1(3!:-))!,2+9()!$E!6!-.!$E!>#

• 5%M!4N 5.!+!2&&6!:-,1!$EE!7(2>&.>!+.'!+!$#E!6!'&&2U!,1(!;)&:!2+,(!>1&B)'!.&,!

(FO(('!$#//!7(2>&.>R>

o 5.!?Q2(>>!?>,-6+,&2U!;)&:!2+,(>!+2(!B>(2!>7(O-;-('#!V1(.!,1(!;)&:!2+,(!

->!>(,!,&!$#//!7(2>&.>R>!&2!)(>>U!,1->!O2-,(2-&. ->!6(,#

• 5%M!JN W(2-;3!,1+,!1B6+.>!X(Q-.!,&!6&9(!X+>('!&.!+!B.-;&26!2(+O,-&.!,-6(!

'->,2-XB,-&.#

o 5.!?Q2(>>!?>,-6+,&2U!+))!&OOB7+.,>!X(Q-.!,&!6&9(!>-6B),+.(&B>)3 :-,1!

+!B>(2D>7(O-;-('!72(D(9+OB+,-&.!,-6(#!!Y(Q-..-.Q!&;!6&9(6(.,!->!.&,!

X+>('!&.!+!B.-;&26!'->,2-XB,-&.#

• 5%M!H!A!7(2>&.!+772&+O1-.Q!+!O&2.(2!:+)P>!+2&B.'!,1(!&X>,2BO,-&.!2+,1(2!

,1+.!7(.(,2+,-.Q!-,#

o 5.!?Q2(>>!?>,-6+,&2U!,1(2(!+2(!.&!O&2.(2> '(;-.('!X(O+B>(!-,!->!+!>(6-D

&.(D'-6(.>-&.+) 6&'()#

• 5%M!KN Z->,2-XB,(!,1(!:+)P-.Q!>7(('!&9(2!JE!7(2>&.>!+.'!>1&:!,1+,!,1(!

:+)P-.Q!>7(('>!+2(!O&.>->,(.,!:-,1!,1(!>7(O-;-('!-.7B,#

o ?Q2(>>!?>,-6+,&2!'&(>!.&,!B>(!+!:+)P-.Q!>7(('!'->,2-XB,-&.#

• 5%M!8!+.'!5%M!@N W(2-;3!,1+,!,1(!(;;(O,>!;2&6!>6&P(!O+)OB)+,('!X3!,1(!6&'()!

6+,O1!,1(!(F7(O,('!9+)B(>#

o ?Q2(>>!?>,-6+,&2!'&(>!.&,!O&.>-'(2!,1(!(;;(O,>!&;!>6&P(#

="! G0@<&(',03-)'%F-*@<'('6&+-60((*+&%'03,-E0(-,%&'(-@0/*@*3%

Stair movement correlations have been developed long time ago and they are considered 

to be well grounded in fire engineering discipline. A good source of these is SFPE Fire 

Engineering Handbook e.g. in Chapter 14 Emergency Movement by Nelson and Mowrer 

in the 3rd edition.

The Handbook offers fundamental equations for speed depending on density and the 

specific flow depending on density. These are empirically derived correlations that are 

widely accepted in fire engineering field and they form a basis for Egress Estimator. It 

does not mean that they are not questioned as the curve fit through which they are 

obtained involves large scatter. Other sources e.g. Russian data suggest that the flow 

often continues behind the density limit of 4.0 persons per square meter. Nevertheless in 

fire engineering calculations the SFPE correlations are considered conservative, easy to 
25

apply and safe to use for simple calculations. Apart from the fundamental speed/density 

and specific flow/density correlations Handbook offers simple correlations to estimate the 

egress time from tall buildings (Chapter Movement of People: Evacuation Timing by 

Proulx). These correlations are given below. 

T = 0.68 + 0.081p0.73 [min] (31)

T = 2.0 + 0.0117p [min] (32)

T = 0.7 + 0.0133p [min] (33)

According to the Handbook Eq. X should be used for buildings up to 15 stories high. 

Equations Y and Z are recommended for buildings with respectively below or above 800 

occupants per meter of effective stair width. 

A comparison study was performed to see how these correlations compare with the 

Egress Estimator predictions. The table below contains data corresponding to 9 runs of 

Egress Estimator for a single stair 30 story building and 50 occupants per floor and 

varying stair width. The correlations Y and Z were used in accordance with the 

abovementioned limit of 800 persons per meter of effective stair width.

!"#$%&'$(")&*+, -./ -.0 -.1 -.2 -.3 0./ 0.0 0.1 0.2

45567"$86&9$(")&*+, /.: /.; -.- -.< -.= -.: -.; 0.- 0.<

>?@AB#"$?C&@6%&+6"6%&?5&65567"$86&'$(") 0/:- -2-- -<-3 ---= ;2: 3=< :2< 2;/ 2</

D$+6&@%6($7"6(&EF&!G>4&7?%%6B#"$?CH&*H, -=:1 -0=- -/1= ;/< :;; :-; 2=- =;< =1=

D$+6&#H&$C($7#"6(&EF&4I%6HH&4H"$+#"?%&*H, 0<:0 -20/ -<</ --<< ;;0 330 :;2 :0: 2:0

The figures above show that the simple engineering correlations recommended by the 

SFPE Handbook result in somewhat smaller egress times. The differences are 

E!

JEE!

$EEE!

$JEE!

"EEE!

"JEE!

E#E! $#E! "#E! /#E!

R&$8:+45%066+R*70++S6T

<$8*%+U*'$3+S7T

[\]?!O&22()+,-&.>!

?Q2(>>!?>,-6+,&2!

E!

JEE!

$EEE!

$JEE!

"EEE!

"JEE!

E! $EEE! "EEE!

45%066+R*70+86+VG+45%066+46$*78$&%+S6T

45%066+R*70+86+VG+<WA4+J&%%0:8$*+S6T
26

proportionally bigger for cases of smaller stair width or bigger population per meter of 

effective stair width. This effect is explained below.

The transformation of equation 32 and 33 to the format where all terms are in seconds 

rather than minutes reveals that both formulas involve implicit specific flow rates i.e. the 

flow per meter of effective stair width. 

T = 120 + p/1.425 [s] (34)

T = 41 + p/1.253 [s] (35)

These specific flows are noticeably bigger than the maximum specific flows that 

consequently result from the fundamental speed/density correlation and which are 

specified in the figure and table from the SFPE Handbook reproduced below.

The bigger specific flow rates result in faster egress times predicted by the SFPE tall 

building egress time correlations. This difference in specific flow rates seems to be 

related to the conservative nature of the fundamental speed/density correlation. The 

experimental data from unannounced evacuation drills implies bigger values of specific 

flow rate. As the Egress Estimator is based on this fundamental correlation it can be 

expected that the emerging specific flows will be closer to the maximum specific flows 

resulting from the fundamental speed/density correlation. Further analysis of Egress 

Estimator predictions is continued below.

First a qualitative view is presented to discuss the characteristics of the flow in the 

stairwell and the distribution of occupants across the height of the building. Results from 

the previously mentioned study of a single stair 30 story building with varying stair width 

is used.

The effects of changing the stair width are clearly seen in the distribution of occupants in 

the stairwell. In the graphical example below there are no restrictions on flow rate from 

each floor and at the bottom of the stair so there are no additional influences on the flow 

apart from the stair itself. Despite the same interval after the initiation of the evacuation 

each picture represents slightly different phase of egress in terms of flow uniformity 

across the floors. This depends on whether the floors are already empty or not. If not, the 
27

lowest point of flow convergence defines a height from which the density decreases 

gradually. This effect of flow decompression could be expected in reality. If the flow is 

not slowed down due to flow convergence it tends to be more uniform in terms of density 

across the floors.

Fig. X. Distribution of occupants in the stairwell across the height of the 30 story

building taken 5 minutes after the initiation of evacuation. Four cases represent four stair 

widths: 1.2, 1.6, 2.0 and 2.4 m. 

Density 0.0-0.5 0.5-1.0 1.0-1.5 1.5-2.0 2.0-2.5 2.5-3.0 3.0-3.5 3.5-4.0

Occupants Occupants Occupants Occupants
28

It can be noted that the wider the stair the more people can enter the stairwell, and the 

less time is needed for egress. Consequently, the end of the flow is located visibly lower. 

As the standing area of landings and flights increases, the density decreases. 

Interestingly, the density at the bottom of the stair is similar in all cases. This suggests 

that the characteristic flow at the critical section of the stair is probably similar regardless 

of the stair width. This is confirmed in further analysis.

The occupant flow at the bottom of the stair in 9 cases was analyzed excluding the period 

when the occupants have not yet reached the bottom of the stair. This leaves very linear 

flow histories in all cases which can be easily trendlined and the slope can be established. 

The slope is the flow out of the stairwell in persons per second. All estimator runs are 

presented in the figure below with corresponding trendline function and R2 value.

Linear slope coefficients obtained at this stage are then plotted against the stair width 

which can be seen on the next figure. This gives two series of data points for full width 

and effective width that turn out to fit linear functions very closely. The line 

corresponding to the effective appears to be more useful as it crosses the 0,0 point which 

suggests that the characteristic flow measured in persons/s/m is similarly proportional to 

the effective widths in all cases. The slope of the curve fitted function for the effective 

width is 0.97. Characteristic flow derived in such way corresponds quite closely with the 

maximum specific flow for this stair configuration (7 inch riser, 11 inch tread) as given 

by the SFPE Fire Engineering Handbook and reproduced in this section. This suggests 

that the flow conditions generated by the Egress Estimator are emerging as close to the 

optimal maximum flows for a given stair width. The consistent value of specific flow

also allows for quick and simple prediction of the Egress Estimator output for simple 

cases of simultaneous egress of buildings with uniform distribution of population on all 
29

floors. It may not to be consistent with cases of tall buildings and small populations per 

floor as the flow may be much smaller.

The above study confirms robustness of estimations made by Egress Estimator and its 

consistency with the fundamental SFPE egress speed/density correlation. It opens up a 

question however of whether this correlation is not overly conservative and of what 

should be the recommended correlation for egress modeling using computer models in 

cases when the realism of results is the object of the study. 

="1 G0@<&(',03-)'%F-.HICG-G&+65+&%'03,

Next the elevator portion of Egress Estimator was compared to a published sample 

problem. ELVAC [10] calculated the time required for five 1600 kg (3500 lbs) elevators 

with 1.2 m-wide, center-opening door to evacuate 90 persons per floor from the top 11 

floors of a 21 floor building and 3 persons per floor from the lower floors in the building. 

The floors were 3.2 m high. Each car had a maximum capacity of 16 passengers, 

maximum velocity of 3.0 m/s, and acceleration of 1.2 m/s2. For this problem, Klote 

calculates a time of 1258 s. Using Klote’s calculation method, the time required to 

evacuate 90 persons from all floors would be 1842 s. Using the same assumptions, 

Egress Estimator calculated an evacuation time of 1835 s. Egress Estimator is within 1 % 

of the time calculated by ELVAC.
30

="= G0@<&(',03-)'%F-./&65&%'03-J('++-J&%&

While there is a lack of data on elevator evacuations, NIST has an ongoing project to 

collect stair movement data during fire drill evacuations [16]. In the study, fire drill 

evacuations were monitored by positioning video cameras out of the way of building 

occupants to record an overhead view of occupant movement in an exit stair during the 

evacuation. In most buildings, unless specified, the video cameras were placed on every 

other floor to capture a view of that floor’s main landing, the door into the stair at that 

level, and 2 steps to 3 steps on each side of the main landing (leading to and from the 

main landing). This camera placement captured the times in which the occupant was seen 

moving past a particular floor landing as well as the time when he/she was seen moving 

into the stairs.

After video data was taken from each building evacuation drill, NIST transcribed specific 

data from the videos into a spreadsheet format for each stair monitored during the drill. 

For each stair recorded, data were collected 1) for each occupant evacuating in that stair 

and 2) for each time during the evacuation drill that the occupant was seen at a specific 

floor in the stair (a camera position), typically both entering and exiting the camera view.

The data is recorded to the nearest 0.01 s with a maximum estimated uncertainty of less 

than ± 0.5 s. All data is rounded to the nearest second because higher precision serves no 

purpose. Including rounding error the maximum uncertainty is ± 1.0 s. Model data is 

given to 0.2 s to emphasize that it is a model calculation using time steps of exactly 0.2 s 

giving high precision but possibly low accuracy.

Data from a total of four stairwells in three different buildings are used to compare 

against predictions made by the Egress Estimator.

Building 8 is a 31-story office building on the East Coast of the United States. The 

building has two stairs (North and South) that both exit on the 2nd floor onto the street 

level. The two stairs are 1.38 m (54.3 in) wide, 1.26 m (49.8 in) between the handrails. 

There are two flights of 9 steps separated by a landing between each floor with the 

individual steps measuring 0.18 m (7.0 in) for the rise and 0.27 m (10.8 in) for the tread 

depth. For the Egress Estimator calculation, transfer corridors and additional steps 

leading to the discharge level were excluded resulting in a decreased travel distance. The

exit door in the South stair is approximately 0.88 m wide (34.8 in) and the North exit 

door is about 1.02 m wide (40.0 in) both with door closers. Assuming a flow of 0.92 

people/meter of width that gives a maximum flow of 0.81 people/s out of the South stair

and a maximum flow of 0.94 people/s out of the North stair.

The North stair of Building 8 had 652 persons above the second floor evacuate during the 

first 1072 s ± 1 s of the drill. For this scenario, Egress Estimator used 667 people to 

evenly distribute people in the building. The calculated total evacuation time was 887 s. 

This prediction has an error of 17.2% than the actual experiment. The graph in Figure 3
31

shows the cumulative number of people that have evacuated for the experimental data 

including stragglers, the Egress Estimator prediction, and two times the prediction to 

bracket the experimental data.

Figure 3. Stair 8 North data with the prediction of Egress Estimator and twice the 

prediction. Uncertainty is ± 1 s.

The south stair has 525 people who evacuate but the last 74 follow an evacuee who had

significant difficulties with the stairs. A total of 522 were used divided evenly among all 

the floors in the Egress Estimator simulation. The predicted time to evacuate was 708 s 

while the actual egress time was 1002 s ± 1 s for an error of 29.3%. Figure 4 shows all 

the evacuation data bracketed by the Egress Estimator calculation and twice the 

calculation as in the graph of the North stair data in Figure 3.

Notice that the data has the evacuation broken into two groups. The larger one is first and 

the Egress Estimator does a much better job predicting the egress time and a second 

smaller group that comes down significantly later. The second group followed an evacuee 

that had significant physical difficulties negotiating the stairs and so everyone was 

slowed following him/her.
32

Figure 4. Comparison of Stair 8 South data and Egress Estimator prediction and twice 

prediction. Uncertainty is ± 1 s.

Because the Egress Estimator is a screening tool it doesn’t attempt to account for 

evacuees that are significantly slower than the average person. For applicability of the 

data, the analysis of the south stair is done with the first 451 people. The Egress 

Estimator used 464 people evenly divided among all the floors. In the evacuation the first 

451 people left the building in about 761 s ± 1 s. The Egress Estimator calculated a time 

of 636 s for an error of 16.4% faster than the drill. Figure 5 shows Stair 8 South egress 

data and the Egress Estimators prediction of the first 464 people as well as twice the 

calculation.
33

Figure 5. Comparison of Stair 8 South data and Egress Estimator prediction and twice 

prediction. Uncertainty is ± 1 s.

The third example is a West Coast Building designated as Building 5. Two stairs were 

monitored, however, only stair A is used in this analysis since counterflow (not account 

for in the model) took place in stair B. Building 5 has 10 stories and the stair A exit on 

the first floor. Between each floor are two flights of 11 steps with a landing in between. 

The steps are 1.27 m (50 in) wide, 1.22 m (48 in) between the handrails with the risers 

and treads measuring 0.18 m (7 in) by 0.28 m (11 in). On the first floor, the stairs lead 

into a 1.37 m (54 in) wide hallway that took evacuees outside. The actual exit door is not 

observed, so a maximum flow rate of 1.26 people/s is used in the model run.

A total of 432 people used stair A with three individuals following well behind the main 

mass of evacuees. The Egress Estimator used 432 people in its prediction. The Egress 

Estimator calculated an egress time of 533 s while the actual evacuation took about 

628 s ± 1 s for an error of 15.1 % faster than the drill. The cumulative plot of the data and 

the bracketing estimates from the Egress Estimator are shown in Figure 6.
34

Figure 6. Comparison of Stair 5 A and Egress Estimator prediction and twice prediction.

Uncertainty is ± 1 s

The last comparison example used is a 24 story West Coast office building designated as 

Building 4. Again two stairs were monitored but in one stair firefighters entered during

the evacuation. Stair B, used in this example, exited directly outside on the first floor. 

The width of Stair B is 1.12 m (44 in) wide, measuring 1.02 m (40 in) between the 

handrails, and had 0.18 m (7 in) risers and 0.28 m (11 in) treads. Between each floor were 

two flights of stairs with 10 steps each with a landing in the middle. The exit is 1.09 m

(43 in) wide giving a maximum flow of 1.0 person/s. 

The 348 people in the main mass in Stair B completed their evacuation in about 650 s ± 1

s. The 345 people used in the Egress Estimator completed the evacuation in 511 s for an 

error of 21.4 % faster. The cumulative graph of evacuation data and prediction are shown 

in Figure 7.
35

Figure 7. Comparison of Stair 4 B data and Egress Estimator prediction and twice 

prediction. Uncertainty is ± 1 s.

Table 2. Summary of comparison of egress data with Egress Estimator predictions

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Table 2 summarizes the results. Included in the table is the population used in the Egress 

Estimator, the population from the evacuation and the percentage difference. Notice that 

the percentage error in the calculation compared to that actual evacuation is less than the 

percentage difference in the populations. This implies the model is predicting movement 

a bit fast even if the populations matched perfectly.

Another thing to note from the table is that Stair 4 B and Stair 8 South are the worst 

prediction and significantly different compared to the other predictions. The reason for 

the difference in Stair 8 South has already been discussed. The significant difference 

between Stair 4 B and the other stairs is that there were very few instances of people 
36

passing other people or of the population forming two lanes on the stairs. [17] In the 

other evacuations there was significant number of instances of both behaviors. 

In order to gain a better understanding of how the Egress Estimators calculations look 

overall it would be helpful to compare the four cases. Normalizing each of the plots using 

the time and number of evacuees used in each case, the graphs can be combined. The 

results are in Figure 8.

Figure 8. Normalized data from all stairs as compared to predictions of Egress Estimator. 

Uncertainty is less than ± 0.004.

As can be seen the main mass of all the evacuations are actually completed within 125% 

of the time calculated by the Egress Estimator. Even including all the stragglers everyone 

evacuates in less than twice the time predicted by the Egress Estimator. As a screening 

tool this provides a reasonable first estimate of the evacuation time of a building. 

4.5 H'@'%&%'03,

It is important to keep in mind what the Egress Estimator is and is not. It is a simple 

screening tool to help in the design of multi-story buildings. The purpose is to establish 

broad design parameters based on some simple calculations.

The model assumes a simplified design on the building’s stair and elevator egress 

systems. It makes assumptions about how individual behaviors average out to the 

population’s behavior. 
37

There are a number of limitations to keep in mind when using the Egress Estimator. The 

first is the limited amount of validation work that has been done so far. The stair model 

has only been validated against a small set of data. Because of a lack of data, the elevator 

model hasn’t been validated.

The Egress Estimator is not the tool for final validation analysis of a design. It doesn’t 

handle a number of phenomena that would be important to consider in a final design 

including but not limited to:

• Mobility challenged evacuees

• Counter flow

• Uneven distribution of the population among floors

• Different demographic distributions of the population

• Stairs with differing designs in the same building

• The effects of smoke and/or fire

• The effects of building damage.
38

5 Conclusion

A computer model for estimation of egress time for combined stairwell and elevator 

evacuation is described. The model is intended as a screening tool to make simple 

estimates of the impact of some of the parameters in an egress system design. The model 

allows for the inclusion of both elevators and stairs in the egress system. 

The model uses a one-dimensional partial differential equation sub-model to estimate the 

flow of people down stairs based on the SFPE Handbook. The elevator model is based on 

the model ELVAC but differs in the use of an explicit elevator control model. 

When the Egress Estimator is compared to the models that serve as the basis of the 

Egress Estimator the results show a good agreement. The Egress Estimator comes within 

1 % of the example given by Klote and Alvord for ELVAC.

Comparing the stairs model to model to collected fire drill data the few individuals with 

significantly longer egress times, also known as stragglers, were excluded. When the 

flow model in the Egress Estimator was compared against fire drill evacuation data, it 

was found that the model’s predicted total egress time was within 15 % of the measured 

time for the range of experiments studied. To account for stragglers when evaluating 

designs appropriate design margins should be considered.
39

6 References

1 NIST. “Strategic Roadmap for Fire Risk Reduction in Buildings and Communities” 

Natl. Inst. Stand. Technol., Special Publication (2011).

2 NBS. Design and Construction of Building Exits. National Bureau of Standards 

Miscellaneous Publication M151. National Bureau of Standards. Washington, 

DC. October 10, 1935. Document can be found at: 

http://www.nist.gov/el/fire_research/egress.cfm.

3 Fruin, J. J., Pedestrian Planning and Design, Metropolitan Association of Urban 

Designers and Environmental Planners, Inc., New York, NY, 1971.

4 Fruin, J.J. Pedestrian Planning and Design, Revised Edition). ElevatorWorld, Inc., 

Mobile, AL, 1987.

5 G. Proulx. “Movement of People: The Evacuation Timing.” Chapter 3-13, pages 3-341 

– 3-366. In The SFPE Handbook of Fire Protection Engineering. Society of Fire 

Protection Engineers, Bethesda, MD, third edition, 2002.

6 Nelson, H. E. and F. W. Mowrer, “Emergency Movement,” Chapter 3-14 in SFPE 

Handbook for Fire Protection Engineering, 3rd Ed., National Fire Protection 

Association and Society of Fire Protection Engineering (2002).

7 Hoskins, B. L., “The Effects of Individual Characteristics and Group Dynamics on 

Egress on Stairs.” PhD Thesis, University of Maryland, College Park, 2011.

8 Kuligowski, E. D., Peacock, R. D., and Hoskins, B. L., “A Review of Building 

Evacuation Models, 2nd Edition,” Natl. Inst. Stand. Technol., Technical Note 

1680 (2010).

9 Klote, J.H., An Overview of Elevator Use for Emergency Evacuation. CIB-CTBUH 

Conference on Tall Buildings. Proceedings. Task Group on Tall Buildings: CIB 

TG50. CIB Publication No. 290. October 20-23, 2003, Kuala Lumpur, Malaysia, 

Shafii, F.; Bukowski, R.; Klemencic, R., Editors, 175-185 pp., 2003.

10 Klote, J. H., “Method for Calculation of Elevator Evacuation Time,” J. of Fire 

Protection Engineering, Vol. 5, No. 3, 86-96 (1993).

11 Lord, J., B. Meacham, A. Moore, R. Fahy, and G. Proulx, “Guide for Evaluating the 

Predictive Capability of Computer Egress Models,” Natl. Inst. Stand. Technol., 

Grant Report, NIST GCR 06-886 (2005)

12 Pauls, J. L., Evacuation Drill Held in the BC Hydro Building 26 June 1969, National 

Research Council of Canada, Building Research Report 80, 1971.

13 Kuligowski, E. D. and R. D. Peacock, “Review of Building Evacuation Models,” Natl. 

Inst. Stand. Technol., Technical Note 1471 (2005).

14 Gwynne, S.M.V, Kuligowski, E.D., Kratchman, J., Milke, J.A., “Questioning the 

Linear Relationship Between Doorway Width and Achievable Flow Rate,” Fire 

Safety Journal, 44 (2009) 80-87.

15 IMO, “Interim guidelines for evacuation analyses for new and existing passenger 

ships”, MSC/Circ.1033, International Maritime Organization, London, (2002).

16 Kuligowski, E. D. and Peacock, R. D., "Building Occupant Egress Data," Report of 

Test FR 4024, Natl. Inst. Stand. Technol., Gaithersburg, MD (2010).
40

17 Hoskins, B.L., “The Effects of Individual Characteristics and Group Dynamics on 

Egress on Stairs.” PhD Thesis, University of Maryland, College Park, 2011.