![Distribution of times between shutting off tape recorder and making a phone call using data from Nober et al. [27].](https://www.researchgate.net/profile/Ruggiero-Lovreglio/publication/351449785/figure/fig1/AS:1021842395496448@1620637620230/Distribution-of-times-between-shutting-off-tape-recorder-and-making-a-phone-call-using_Q320.jpg)
Content uploaded by Ruggiero Lovreglio
Author content
All content in this area was uploaded by Ruggiero Lovreglio on May 10, 2021
Content may be subject to copyright.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
1
The Response of Sleeping Adults to Smoke Alarm Signals in the
Evacuation Decision Model
M Spearpoint1, R Lovreglio2, S Gwynne3,4
1 OFR Consultants, Manchester, UK
2 School of Built Environment, Massey University, New Zealand
3 Movement Strategies, London, UK
4 Lund University, Sweden
ABSTRACT
Simulating evacuation behaviour in fire emergencies is an increasingly important method for assessing
design to mitigate the likelihood of life losses. To date, several approaches have been used to predict
the pre-evacuation time (i.e. time between the first alarm or other initial cue until the moment an evacuee
starts moving toward a safe place) using distribution functions or evacuation decision models. In this
work a modified version of the Evacuation Decision Model (EDM) is developed and incorporated into
an agent-based egress simulation tool. The paper identifies input distributions for the characteristic time
to reach an investigating state when an agent receives an alarm alert using waking time measurements
from the literature. The results from EDM simulations are compared to the New Zealand verification
method (C/VM2) pre-travel activity times. Exceedance probabilities are identified for scenarios in
which occupants are sleeping in a familiar building and exposed to a ‘standard’ alarm or sleeping in an
unfamiliar building and exposed to a ‘standard’ or voice alarm. A corresponding pre-evacuation time
for a scenario in which occupants are sleeping, familiar with the building and exposed to a voice alarm
signal is forecast using EDM.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
2
1 INTRODUCTION
In order to calculate the time for people to evacuate a building in the event of a fire it is necessary to
determine several component factors. Typically, these are the pre-evacuation time, travel time, queuing
time etc. Pre-evacuation time (sometimes referred to as pre-movement or pre-travel time) can defined
as the “time between the first alarm or other initial cue until the population starts evacuating” [1].
Prior to a fire and the onset of the initial cue (i.e. enhancing situational awareness), building occupants
can be in various states whether that be asleep, awake, focussed on a particular activity etc., which may
affect their pre-evacuation time [2], [3]. For sleeping occupants, part of their pre-evacuation time is the
time it takes for them to wake up when subject to a fire cue. Cues could include the sound of an alarm
(or other sounds such as glass breaking, a noise from an animal or person, etc.), or the presence of fire
products (heat and/or smoke). Clearly, waking time constitutes only one element of pre-evacuation and
time is also likely to be spent getting out of bed, dressing, investigating, notifying other people etc. [4].
There is also a relationship between waking time and the sleep stage (light or deep), for example, as
noted in the work by Nakano and Hagiwara [5], in which longer waking times are associated with
deeper sleep.
In a design context, pre-evacuation times are often taken to be constant values that effectively
incorporate a set of reaction and preparatory actions (waking, notification, investigating times, etc.).
Such design values are selected to give a sufficiently large safety margin to account for the difficulty in
achieving efficient evacuations [6]. Documents such as INSTA 950 [7], the recently released annex to
the Australian Fire Safety Verification Method [8] and the New Zealand the C/VM2 verification method
[9] all provide pre-evacuation times. However, for a performance-based design approach the use of
fixed, conservative times is less desirable as this is one of the factors that does not account for the
behavioural uncertainty affecting the evacuation process [10], [11]. Research [12], [13], [14], [15]
shows that pre-evacuation times typically follow a skewed distribution such as log-normal or Weibull
distribution. One approach to model the pre-evacuation period is to directly use previously measured
pre-evacuation times as part of a performance-based analysis through the imposition of a distribution
to reflect the initial delay experienced by each individual. Unfortunately, such data is fairly sparse and
is somewhat limited to the original situation from which the measurements were taken. For example,
BS PD 7974-6 [6] lists pre-evacuation times from 21 actual fires and evacuation exercises across several
occupancy types including hotels, offices, department stores and apartment buildings in which the data
was obtained from questionnaires and/or video recordings. The application of a distribution assigns pre-
evacuation times independent of many underlying factors that influences the individual delays
experienced.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
3
Instead of assigning a pre-evacuation time from a distribution, it would be advantageous to predict them
from an underlying set of characteristics that could be applied to a range of egress scenarios. To address
this issue, different pre-evacuation decision models have been proposed in the literature. Reneke [1]
developed a model which estimates the pre-evacuation times depending on the cues to which occupants
have been exposed. This model has been expanded and calibrated using both discrete choice models
(by Lovreglio et al. [16], [17]) and machine learning (by Zhao et al. [18]). However, full implementation
of predictive pre-evacuation models in agent-based simulation tools have not been reported in the
existing literature.
This paper presents an implementation of Reneke’s [1] Evacuation Decision Model (EDM) into an
agent-based network egress simulation software tool (Evacuationz [19]), to investigate the waking
effectiveness of an alarm and its impact on pre-evacuation time. Firstly, through an optimization process
the paper generates a consistent set of inputs to EDM that best match waking time measurements
reported in the literature. The paper then uses the calibrated version of EDM to assess the likelihood of
the C/VM2 [9] pre-travel activity times (referred to as the C/VM2 pre-evacuation time in this paper)
being met through an exceedance probability analysis. The key outcome of this paper is that it presents
a method that can predict the impact of different cues on the pre-evacuation times of evacuees. The
calibrated version of EDM is used to determine a pre-evacuation time for a scenario that is currently
not covered in C/VM2, namely where occupants are to respond to a voice alarm where they are familiar
with the building. The relationship between previous research and the four steps presented in the current
study is shown in Figure 1.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
4
Figure 1. Relationship between current study and previous work.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
5
2 EVACUATION DECISION MODEL
The mathematical formulation of the Evacuation Decision Model (EDM) was originally proposed by
Reneke [1] based on the earlier findings of Gwynne [20] and Kuligowski [21]. Subsequently, Retana
Rodriguez and Spearpoint [22] modified EDM and incorporated it into the Evacuationz network egress
model. Work has also been carried out by Lovreglio et al. [16], [17], [18] as an extension of Reneke’s
approach that includes a case study of the evacuation of people from a cinema.
EDM represents the decision-making process to take protective action based on a measure of risk
perception (𝑅(𝑡)). A change in risk perception depends on the agent’s previous experience and
environmental cues to which the agent is exposed. The time difference between the first cue the agent
receives and the start of the evacuating state is the pre-evacuation time. The risk perception in EDM is
defined by three states:
Normal state (N): Agent is assessing whether there is any threat.
Investigating state (I): Agent is seeking additional information to decide whether protective action
is required.
Evacuating state (E): Agent has decided to take protective action and evacuate the building.
The model considers that the cues received by the agent could be an alarm, smoke and/or by social
influence. The total increase in the perceived risk caused by these cues is proportional to their intensity
and the timing of different cues received by the agent i. This model was formulated by Reneke using
the following differential equation:
𝑅
̇
(
𝑡
)
=
d
𝑅
(
𝑡
)
dt
=
(
𝑘
+
𝑞
+
𝑞
+
𝑠
)
𝑅
(
𝑡
)
(1)
where
𝑘 is the prior knowledge constant for agent i;
𝑞 is the impact of an alarm cue on the risk perception;
𝑞 is the impact of the smoke on the risk perception;
𝑠 is the impact of social influence cue on the risk perception;
Equation 1 shows that the risk perception keeps increasing with the exposure to cues. As such, the agent
i will pass from Normal to Investigate state when 𝑅(𝑡) reaches 𝑅 (i.e. the minimum level of perceived
risk for an agent to be in its investigating state) at time 𝑡. If the risk perception keeps increasing, the
agent i will pass to its Evacuation state once 𝑅(𝑡) reaches 𝑅 at time 𝑡.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
6
Retana Rodriguez and Spearpoint [22] adapted the equations that are described in Reneke’s version of
EDM to incorporate them into the Evacuationz agent-based network egress simulation software tool.
More details regarding the agent movement and route selection algorithms can be found elsewhere [19]
though these capabilities are not required for the work described in this paper. As part of their work
Retana Rodriguez and Spearpoint specifically examined the C/VM2 pre-evacuation times to determine
whether it was possible to identify a set of input parameters to EDM that showed consistency with
C/VM2, and this paper builds on that previous work.
C/VM2 specifies pre-evacuation times for a range of different scenarios including where the occupants
are awake or asleep; familiar or unfamiliar with the building; in the same enclosure as the fire or remote
from it and in some scenarios whether a ‘standard’ (bell or tone) or voice alarm is present. As discussed
in the commentary to C/VM2 [23], the times were based on those published in the 2004 edition of
BS PD 7974-6 (whereas the latest edition of BS PD 7974-6 was published in 2019 [6]) but modified to
account for a culture of prompt evacuations due to the regulatory requirements for evacuation schemes
in most public non-residential buildings. For occupants who are asleep / familiar with the building and
not in the same enclosure as the fire C/VM2 gives a pre-evacuation of 300 s when a standard alarm is
present. For the corresponding asleep / unfamiliar scenario, the pre-evacuation is 600 s. When a voice
alarm signal is present in the unfamiliar scenario the pre-evacuation time is 300 s (i.e. 50% of the
standard alarm case) but C/VM2 does not give a time if a voice alarm is present in the familiar scenario.
In addition, C/VM2 makes no distinction as to the alarm sound level and frequency or the age
distribution of the design population. Using an optimization process analogous with that described later
in this paper, it has been found using an that setting 𝑅= 1, 𝑅=2.5 and 𝑅= 7 allows EDM to
match C/VM2 pre-evacuation times. EDM also defines a prior knowledge parameter and in the work
by Retana Rodriguez and Spearpoint this parameter was used to assign C/VM2 familiarity and defined
by fixed constant values for the ‘familiar’ and ‘unfamiliar’ scenarios. As a result, for the asleep / familiar
/ remote scenario the implementation of EDM obtains 300 s for the C/VM2 pre-evacuation time with a
standard alarm signal. For the asleep / unfamiliar / remote scenario EDM obtains 602 s with a standard
alarm signal and 302 s with a voice alarm signal.
The parameters within the EDM equations represent the interplay between the familiarity of the building
to the occupants, the types of cues that occupants may respond to in terms of alarm types and the
visibility of smoke, and whether occupants are awake or asleep. Since this paper addresses the effect of
an alarm signal on the pre-evacuation of agents, only the relevant EDM equations and equivalent
parameters from Retana Rodriguez and Spearpoint [22] that have been incorporated into Evacuationz
are presented here.
Once 𝑡≥𝑡 (i.e. the time when the alarm first alerts agent 𝑖), the perceived risk of an agent is updated
at each simulation time step, ∆𝑡:
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
7
𝑅
𝑡
=
𝑅
𝑡
+
𝑅
̇
𝑡
∆
𝑡
(2)
When 𝑅(𝑡)<𝑅 (i.e. the agent has yet to reach its investigating state), then
𝑅
̇
(
𝑡
)
=
𝑙𝑛
(
𝑅
)
𝜏
,
∙
(
𝑘
+
𝑞
+
𝑞
+
𝑠
)
∙
𝑅
(
𝑡
)
(3)
where 𝜏, is the characteristic time for agent 𝑖 to reach investigating state on receipt of an alarm alert.
Finally, when 𝑅<𝑅(𝑡)≤𝑅 (i.e. the agent is in its investigating state), then
𝑅
̇
(
𝑡
)
=
𝑙𝑛
(
𝐶
)
∆
𝑡
∙
𝑅
(
𝑡
)
(4)
where
∆𝑡=𝑡∙𝑙𝑛(𝐶𝐸)
𝑙𝑛(𝑅)+1∙1
(𝑘+𝑞+𝑞+𝑠)−1
and 𝐶 =𝑅/𝑅
Incorporating the EDM algorithm into Evacuationz (Figure 2), along with appropriate parameter values,
allows for the prediction of pre-evacuation times for different scenarios as part of an overall evacuation
simulation analysis. However, it is outside to scope of this paper to investigate the impact of the pre-
evacuation times on the overall evacuation time, as presented by Spearpoint [24] for example.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
8
Figure 2. Flow diagram of the EDM algorithm implemented in Evacuationz.
In this paper, the EDM implementation and C/VM2 baseline parameters of Retana Rodriguez and
Spearpoint have been updated (Step 1 in Figure 1) where necessary using a similar optimization process
as before. This current work considers agents independently in which there is no social influence and
thus 𝑠
=0. For an ‘unfamiliar’ scenario k
i
= 0 and for a ‘familiar’ scenario k
i
= 0.425. The variable 𝑎
is the alarm factor which represents the alarm type (standard alarm, 𝑎
= 0.5; voice alarm, 𝑎
= 1.0) and
𝑎
is the alarm time constant from which the characteristic time is found from 𝜏
,
=𝑎
×𝑎
. To
correspond to the C/VM2 pre-evacuation times 𝑎
needs to be set to 57 if the agent is awake and 283
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
9
if the agent is asleep, as previously determined by Retana Rodriguez and Spearpoint. The alarm cue
variable, 𝑞 is set to 0.5 and the smoke cue variable, 𝑞 is also set to 0.5.
3 MEASURED TIMES
There are many potential behaviours that building occupants may exhibit during the pre-evacuation
phase which may include waking-up, getting dressed, warning others, etc. each of which will have times
associated with them. In order to obtain the variability in awakening times in response to an alarm signal
the EDM predicted times for an agent to reach its investigating state (RI) on hearing an alarm sound are
calibrated in Section 4 to waking data from the literature for the familiar and unfamiliar scenario cases.
This section summarises the literature used to provide waking times and also some other data relevant
to this study.
When considering the ability of an alarm to wake a sleeping person there are a number of factors that
can be taken into account [25]. These factors include the
characteristics of the alarm in terms of its sound level, frequency spectrum and whether a voice
is part of the signal.
distance of the alarm from the person,
any intervening barriers and the presence of background noise which interacts with the signal
received by the person
characteristics of the person, e.g. hearing capability (in which age and long-term exposure to
noise can be important factors); familiarity of the alarm sound; whether the person is under the
influence of alcohol, medication, recreational drugs; whether the person is a heavy or light
sleeper and their sleep stage.
Several research studies, briefly summarised below, have been conducted to assess the waking
effectiveness of alarms and the influence of individual person characteristics. In some cases, researchers
have carried out experiments in a specifically designed sleep laboratory setting whereas others have
conducted their measurements in people’s own homes. Most of the research referred to in this paper has
considered the effect of sound level on the waking effectiveness of an alarm. It is also noted that in
some of the previous research several of the participants did not respond to the alarm signal and these
cases are not included in the analysis presented herein.
3.1 Vistnes et al. [26]
Vistnes et al. [26] suggest that a log-normal distribution with a mean and standard deviation of 60 ±
18 s can account for the time it takes a previously sleeping person to get dressed. Whether a person is
asleep or awake another delay component will occur if they make a telephone call to the fire service or
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
10
to other people. Vistnes et al. suggest telephone calls have a log-normal distribution with a mean and
standard deviation of 30 ± 9 s.
3.2 Nober et al. [27]
Nober et al. [27] measured the time it took participants, aged 19 – 29 yr, in their own home to shut off
a tape recorder playing a smoke alarm sound and then to make a specified phone call to the local fire
department. The sound level was arranged to give 55 dBA, 70 dBA or 85 dBA such that there were 10
time delays at each sound level, i.e. a total of 30 measurements.
Since Nober et al. [27] measured the time to shut off the smoke alarm sound on the tape recorder and
then make a phone call, this data can be used to estimate a component part of the pre-evacuation time
rather than just the waking time. Using Nober et al.’s data, times to shut of the sound are subtracted
from the times to make the phone call and a triangular distribution shows a good fit, as shown in Figure
3. Rounded up to the nearest second, the distribution has a minimum value of 5 s, a most likely value
of 20 s and a maximum of 105 s. In comparison with the distribution suggested by Vistnes et al., if a
log-normal distribution is fitted to the Nober et al. data then the mean and standard deviation are 42 ±
24 s.
Figure 3. Distribution of times between shutting off tape recorder and making a phone
call using data from Nober et al. [27].
0
10
20
30
40
50
60
70
80
90
100
1
1
0
0.000
0.005
0.010
0.015
0.020
0.025
Time (s)
P
r
o
b
a
b
i
l
i
t
y
d
e
n
s
i
t
y
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
11
3.3 Kahn [28]
Kahn [28] conducted two series of experiments on 24 male participants aged between around 19 – 25 yr.
The experiments were carried out in a sleep laboratory designed to have a ‘homelike’ environment. In
one series sleeping participants were exposed to alarm signals at three sound levels (44, 54 and 78 dBA)
at the head position by locating the smoke alarm in different places within the laboratory. The smoke
alarm had a bi-periodic signal that peaked at 2000 and 4000 Hz when placed in the 78 dBA location. In
the second series participants were exposed to an odour and heat so as to represent other fire cues as
well as a 54 dBA alarm signal. In both series each cue was presented separately in a random order. The
25 responses to the alarm signal examined by Kahn in his analysis (96 ± 200 s with a maximum time
of 857 s) are used in this paper and are treated as a C/VM2-equivalent ‘unfamiliar’ scenario.
3.4 Bruck and Horasan [29]
Bruck and Horasan [29] conducted a set of waking experiments on 24 young adults (aged 18 – 24 yr)
in a sleep laboratory. In their standard protocol participants were twice exposed to a 10 min alarm signal
at 60 dBA (in the range 55 – 65 dBA) at the pillow with a frequency from approximately 2000 to
4000 Hz. The study measured the time to awaken during different sleep stages. Five subjects were not
awoken in one or more cases where some repeated alarm presentations were made to further examine
arousal outside of the standard two-alarm presentation protocol. Consistent with Bruck and Horasan,
the participant awaking times in this analysis have been collated together irrespective of sleep stage.
Bruck and Horasan report that four participants had waking times of greater than 120 s but since exact
times are not given these data have not been included here.
3.5 Bruck [30]
Bruck [30] conducted a waking time study on adults and children in their own homes exposed to a 3 min
alarm signal at 60 ± 3 dBA at the pillow. Participants were exposed to the alarm on two nights over a
four-night period. The study included 16 adults (8 male and 8 female), aged 30 – 59 yr. For practical
purposes waking time measurements were recorded to the nearest 16 s; however, the only information
given by Bruck is that all of the adults woke within 32 s of alarm. Thus, for the purpose of this paper
the 42 adult waking times are evenly distributed at 16, 24 and 32 s as an estimate of the variation in
waking times.
3.6 Duncan [31]
Experiments conducted by Duncan [31] in forty different family homes involved 128 people aged
between 1 to 79 yr of which 61 were female and 67 male. The experiments resulted in 101 events in
which people were present that provided 229 alarm exposure measurements to range of sound levels
from around 60 dBA to just over 90 dBA. As before, this paper only considers cases where people
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
12
responded to the alarm signal. Duncan’s experiments resulted in an average response time of 22 s and
times of up to 100 s but also found no correlation between waking time and sound level.
4 ANALYSIS PROCEDURE
4.1 Application of alarm response data
The second step (as shown in Figure 1) is to develop a consistent set of inputs for alarm type, familiarity
and wakefulness to EDM that best match the waking time measurements in the literature. In order to
achieve this, the published data discussed in Section 3 is adapted to fit the scope of the analysis. Bruck
and Horasan [29], Nober et al. [27] and Duncan [31] noted that gender difference was not significant in
their data and so males and females are treated as the same population. The effect of sound level has
not been considered herein since there are insufficient measurements to group the data and still carry
out an appropriate analysis as well as some studies, such as Duncan’s [31], that were not always
conclusive as to the benefit of having a higher level. Finally, this paper only uses the data in which
participants awoke to the sound of the alarm. Although from a wider performance-based design
perspective, it would be straight-forward to include a probability that the agent responds to an alarm
and only then a waking time be applied, this aspect is not within the scope of this paper.
As discussed in Section 4.3, the collated waking time measurements are used to calibrate EDM so as to
generate a probability distribution for the waking time of occupants subject to the adaptations to the
data discussed above. In the context of C/VM2, this paper assembles the various data into distributions
that distinguish between ‘familiar’ and ‘unfamiliar’ scenarios. As such it is considered that experiments
in a laboratory equate to the C/VM2 ‘unfamiliar’ building scenarios whereas those in people’s homes
are considered to be ‘familiar’ surroundings. Almost all of the experiments that are referred to exclude
the presence of fire cues such as heat or smoke when assessing the participant’s waking time and
therefore the experiments represent a C/VM2 ‘remote’ scenario. Some researchers [30], [31], [32] have
investigated the capability of alarms to wake children and adults. Since C/VM2 does not account for
age, although research has shown there is a difference, this paper only considers those data that have
been obtained for adults.
The Evacuationz software has the ability to use probabilistic simulation methods by the user applying
distributions to various input parameters. Distribution shapes can be normal, lognormal, uniform,
triangular or Weibull. Consistent with Cleary [4] (who fitted separate log-normal distributions to Nober
et al.’s and Duncan’s data), log-normal distributions can reasonably fit the collated data used in this
paper. Figure 4(a) shows the fit (mean 21 s, standard deviation 12 s) for the ‘familiar’ data consisting
of measurements from Nober et al. [27], Bruck [30] and Duncan [31]. Figure 4(b) shows the fit (mean
46 s, standard deviation 66 s) for the ‘unfamiliar’ data consisting of measurements from Kahn [28] and
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
13
Bruck & Horasan [29]. Thus, for the calibration of the EDM alarm time constant 𝑎 a log-normal
distribution is assumed in the Evacuationz implementation.
(a)
(b)
Figure 4. Best fit log-normal distributions for the measured waking time data (a)
‘familiar’ scenario, (b) ‘unfamiliar’ scenario.
Time (s)
8880726456484032241680
Probability density
0.52
0.48
0.44
0.4
0.36
0.32
0.28
0.24
0.2
0.16
0.12
0.08
0.04
0
Time (s)
800720640560480400320240160800
Probability density
0.88
0.8
0.72
0.64
0.56
0.48
0.4
0.32
0.24
0.16
0.08
0
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
14
4.2 Simulation set-up
A simple egress scenario is simulated in which a single agent is placed in an arbitrary space with a floor
area of 1.0 m by 1.0 m and allowed to exit through a single 1.0 m wide door to a ‘safe’ location. In this
context, the evacuation time is not considered as the primary result, but it is the predicted time for the
agent to reach the investigation and evacuation states. To simplify the presentation, the evacuation times
are not reported as the agent movement is not affected by the model development outlined here.
However, the simulations were still run to completion taking 300 simulations until the results converged
such that new time for the agent to reach the ‘safe’ location varied from the existing average by less
than 0.05%. 5000 simulations were run to get an extended set of results to better determine the relevant
output distribution shapes.
4.3 Alarm time constant configuration
In this section an appropriate input for the EDM alarm time constant 𝑎 to match with the published
‘familiar’ and ‘unfamiliar’ waking time datasets for a standard alarm signal is determined. Here it is
assumed that when an agent reaches their investigation state (i.e. 𝑅=2.5) then they are awake. Pairs
of mean and standard deviation values for the alarm time have been trialled for the ‘familiar’ and
‘unfamiliar’ scenarios to find the minimum least-squared error between the data (Figure 4) and the
simulations. The resulting mean and standard deviation pair for the two scenarios where then weighted
using the method given by Lovreglio et al. [14] to obtain a combined best-fit mean and standard
deviation pair with the optimized log-normal distribution for 𝑎 found to have a mean of 14 s and a
standard deviation of 13 s as indicated in Figure 5.
Figure 5. Optimization of the mean and standard deviation pair for the characteristic alarm time.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
15
Figure 6 shows the cumulative densities for the collated data and the resultant output curves from the
simulations. For the ‘familiar’ scenario the mean and standard deviation measured waking time is 21 ±
14 s against 15 ± 14 s from the EDM implementation simulated in Evacuationz. The cumulative density
for the collated data and the resultant output curve from the simulations for the ‘unfamiliar’ scenario
are only plotted up to 330 s although there is data that extends out to 857 s (from Kahn [28], as shown
in Figure 4b). It shows that EDM under-predicts the proportion of occupants that would wake prior to
around 45 s but thereafter over-predicts. The mean measured waking time is 52 ± 133 s against 28 ±
28 s from the simulations.
(a)
(b)
Figure 6. Calibrated simulation results shown as a cumulative density function against
collated data for (a) the familiar scenario with a standard alarm, (b) the unfamiliar
scenario with a standard alarm.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
16
4.4 Application of additional pre-evacuation components
As discussed in Section 3, the pre-evacuation time of an occupant is likely to be a combination of the
identified component times. Therefore, predictions using the EDM implementation are shown here to
account for these additional pre-evacuation components by summing predicted waking times using the
alarm time constant 𝑎
input log-normal distribution with a sampling of the triangular distribution for
the time difference between waking and making the telephone call given in Figure 3.
Figure 7 compares the times that Nober et al.’s participants made the phone calls with the predictions
for the start of the agent investigation state. As expected, the simulations exhibit overall longer times
since the selection of distribution parameters includes cases in which tail-end values for both the waking
time and the delay to make the telephone call. However, the simulation results show a general match
with the data in which Nober et al.’s measurements have a mean and standard deviation of 52 ± 24 s
whereas the EDM implementation in Evacuation gives 59 ± 26 s.
Figure 7. Predicted pre-evacuation times from waking and phone distribution inputs against Nober et
al.’s [27] participant times to make phone call ( symbols).
Similarly, the distribution given by Vistnes et al. [26] for time to get dressed can be implemented as an
additional component although no data has been found in the literature to serve as a comparison.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
17
5 COMPARISON WITH C/VM2 VALUES
The work described above completes Step 2 shown in Figure 1 in which inputs to the implementation
of EDM in Evacuationz have been calibrated against measurements from the literature both for waking
times and also pre-evacuation times that combine the time to awaken with the time to make a phone
call.
The final part of this work is for the calibrated version of the EDM to be used to determine the
exceedance probabilities of the corresponding C/VM2 scenarios. The input distributions described in
the previous sections for the waking times, time to get dressed from Vistnes et al. [26] and time to make
a phone call from Nober et al. [27] are combined in the implementation of EDM in Evacuationz to
generate pre-evacuation delay times that correspond to the waking time plus the additional delay time
that might represent other activities. Cumulative density curves are generated from the predicted times
that agents reach their evacuating state. The exceedance probability thresholds that correspond to the
currently defined C/VM2 pre-travel times for the familiar and unfamiliar scenarios with the standard
alarm signal, and the unfamiliar scenario with the voice alarm are determined (Step 3, Figure 1). These
thresholds are then used to assess what would be likely C/VM2-eqivalent time for the familiar scenario
with the voice alarm signal (Step 4, Figure 1) and also pre-evacuation times are determined for the
C/VM2 scenarios for the 90%, 95% and 99% exceedance cases.
For each of the scenarios simulated in this section 10,000 iterations have been undertaken in which the
Halton method is used to preferentially sample extreme limits of the input distributions, as per the earlier
work of Lovreglio et al. [33].
5.1 Standard alarm signal scenarios
When the characteristic alarm time (𝑎), input distribution function is applied to the EDM
implementation in Evacuationz for the familiar, standard alarm signal scenario the probability of being
within the C/VM2 pre-evacuation time of 300 s is 99.40% (Figure 8a). For the unfamiliar, standard
alarm signal scenario the probability of being within the C/VM2 pre-evacuation time of 600 s is 98.55%
(Figure 8b).
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
18
(a)
(b)
Figure 8. Distribution for the C/VM2-equivalent standard alarm signal for the (a)
familiar scenario; (b) unfamiliar scenario.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
19
For consistency the probabilities of being within the C/VM2 pre-evacuation times would ideally be
similar for both the familiar and unfamiliar scenarios but this is not the case. If the 98.55% threshold
identified from the unfamiliar scenario is applied to the familiar scenario distribution, then the
corresponding pre-evacuation time is 260 s (i.e. 40 s less than the C/VM2 value of 300 s). Similarly, if
the 99.40% familiar scenario threshold is applied to the unfamiliar scenario then the pre-evacuation
time is 710 s (i.e. 110 s greater than the C/VM2 value of 600 s).
Clearly, the small percentage of simulations that exceed the C/VM2 times might suggest that the C/VM2
values are conservative or the approach of combining Nober et al.’s and Vistnes et al.’s delays might
not account for all of the activities that may occur before occupants decide to evacuate where they may
investigate, warn others etc.
5.2 Unfamiliar, voice alarm signal scenario
Using the alarm time constant (𝑎), input distribution function with the knowledge parameter
previously identified by Retana Rodriguez and Spearpoint and halving for the use of a voice alarm
signal (as discussed in Section 2) the EDM implementation gives the distribution shown in Figure 9
which has a mean and standard deviation of 162 ± 65 s. C/VM2 gives a value for the pre-evacuation
time of 300 s for this scenario which corresponds to a threshold probability of 96.82%.
If the threshold percentage for the C/VM2-equivalent pre-evacuation time of 600 s for the unfamiliar,
standard alarm signal scenario of 98.55% is applied to the distribution then a pre-evacuation delay time
of 360 s is obtained. The result is therefore consistent with C/VM2 in that for the unfamiliar / standard
alarm signal scenario the pre-evacuation time is 600 s and a shorter delay of 360 s is obtained for the
corresponding voice alarm signal scenario.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
20
Figure 9. Distribution for the C/VM2-equivalent unfamiliar scenario with a voice alarm
signal.
5.3 Familiar, voice alarm signal scenario
The current version of C/VM2 does not stipulate a pre-evacuation time for the asleep / familiar / remote
scenario with a voice alarm signal. Given C/VM2 halves the pre-evacuation time to 300 s when a voice
alarm is used in the unfamiliar scenario compared with 600 s standard alarm signal scenario, a consistent
approach would be to halve the C/VM2 the pre-evacuation time of 300 s for the unfamiliar, voice alarm
scenario to 150 s for the familiar, voice scenario.
Here the EDM implementation is extended to the familiar, voice alarm signal scenario to propose a time
that is consistent with the other C/VM2 exceedance probabilities already identified in the previous
sections of this paper. By applying the alarm time constant input distribution, familiar prior knowledge
and the voice alarm factors, EDM gives mean and standard deviation of 122 ± 34 s (Figure 10) which
has a mean of ~40 s earlier than the unfamiliar / voice alarm signal case. If the unfamiliar / voice alarm
signal threshold probability of 96.82% is used to forecast times for C/VM2 then a pre-evacuation time
of ~188 s is obtained. This therefore suggests that a C/VM2-equivalent pre-evacuation time for the
familiar, voice alarm signal scenario would be 190 s (rather than 150 s) compared with the 300 s value
prescribed for the unfamiliar / voice alarm scenario.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
21
Figure 10. Derived distribution for the C/VM2-equivalent familiar scenario with a voice
alarm signal.
5.4 Pre-evacuation time summary
Table 1 gives a summary of the C/VM2-equivalent pre-evacuation time exceedance probabilities
determined above. It has also been possible to find the times for any given threshold probability and
therefore Table 1 gives these times for the 90%, 95% and 99% percentile cases, noting that BS PD
7974-6 [6] gives a 99
th
percentile upper bound for its suggested pre-evacuation times for different design
behavioural scenario categories. Comparing the pre-evacuation times for the standard and voice alarm
cases suggests that the benefit of a voice alarm does not halve that of the standard alarm case for the
same familiarity situation.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
22
Table 1. Summary of pre-evacuation times and exceedance probabilities.
Familiarity
Alarm
type
Pre-evacuation time (s)
C/VM2 with
threshold percentile
in brackets
EDM simulation result at designated
percentile threshold
90% 95% 99%
Familiar Standard 300
(99.40%) 192 215 274
Voice Not applicable 164 180 212
Unfamiliar Standard 600
(96.82%) 347 422 648
Voice 300
(98.55%) 231 270 385
6 CONCLUSION
The formulation of the EDM proposed by Reneke [1] has been modified and incorporated into the
Evacuationz egress software and a set of input parameters to EDM have been previously proposed by
Retana Rodriguez and Spearpoint [22] to match the pre-evacuation times given in C/VM2. Building on
that earlier work, this paper has determined a log-normal distribution for the alarm time constant
(defined in EDM by the parameter 𝑎) through calibration against waking time measurements for
adults in familiar and unfamiliar building situations.
Predicted waking time distributions using the Evacuationz implementation of EDM have been
compared against the C/VM2 pre-evacuation times to identify the equivalent probability exceedance
thresholds. The study illustrates how the methodology can be extended to other C/VM2 scenarios where
currently values are not specified. The analysis suggests that for the C/VM2 familiar, voice alarm
scenario a pre-travel activity of 190 s is reasonable to correspond to the threshold for the C/VM2
unfamiliar / voice alarm scenario. The predictions from EDM have also been used to derive pre-
evacuations time for designated percentile thresholds.
This paper illustrates how EDM can be used to provide a probabilistic calculation for the waking times
of people when exposed to an alarm signal that could be used as part of a performance-based design
procedure. EDM can also be used to determine likely waking times for situations where there is no data
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
23
available. The waking time can be coupled with an assessment of the additional factors that cause a
delay to the start of evacuation to give an overall prediction of the pre-evacuation delay.
The work is only a first step in applying EDM and identifying calibrated values for its parameters using
data from the literature. The procedure described in this paper could be used to suggest C/VM2-
equivalent pre-evacuation times for other population groups such as children or the elderly etc. Waking
time data for children is already available in the literature although currently there is no expectation that
C/VM2 will be modified to distinguish between adults and children. Similarly, the analysis present in
this work could be used to assess the effect on waking times due to the sound level of an alarm, however
as already noted, data is sparse and not always consistent. It would be useful to examine how the parallel
work by Lovreglio et al. [16] could be allied with this study and to identify characteristic input
distributions to EDM for situations where agents are awake. Finally, EDM could be used to assess the
pre-evacuation times that are given in other documents similar to C/VM2 such as INSTA 950 [7] and
the Australian Fire Safety Verification Method [8].
7 REFERENCES
[1] P. A. Reneke, ‘Evacuation Decision Model’, National Institute of Standards and
Technology, Gaithersburg, MD, NISTIR 7914, 2013.
[2] S. Gwynne and K. Boyce, ‘Engineering data’, in SFPE Handbook of Fire Protection
Engineering, 5th Edition., Springer, 2016, pp. 2429–2551.
[3] D. A. Purser and M. Bensilum, ‘Quantification of behaviour for engineering design
standards and escape time calculations’, Saf. Sci., vol. 38, no. 2, pp. 157–182, Jul. 2001,
doi: 10.1016/S0925-7535(00)00066-7.
[4] T. G. Cleary, ‘An analysis of the performance of smoke alarms’, Fire Saf. Sci., vol. 10, pp.
823–836, 2011.
[5] M. Nakano and I. Hagiwara, ‘Experimental study on starting time of evacuation in sleeping
condition’, in Fire Safety Science, 2000, vol. 4, pp. 263–274, Accessed: Jun. 05, 2020.
[Online].
[6] BSI, ‘PD 7974-6:2019 Application of fire safety engineering principles to the design of
buildings. Human factors. Life safety strategies. Occupant evacuation, behaviour and
condition (Sub-system 6)’, BSI, London, 2019.
[7] ‘Fire safety engineering – Comparative method to verify fire safety design in buildings’,
INSTA TS 950, 2014.
[8] ‘Fire Safety Verification Method data sheets: Handbook annex’, Australian Building Codes
Board, Canberra, ACT, version 1.1, 2020.
[9] Ministry of Business, Innovation & Employment, ‘C/VM2, verification method:
framework for fire safety design, for New Zealand Building Code clauses C1-C6 protection
from fire’, New Zealand Government, Amendment 5, 2017.
[10] E. Ronchi, P. A. Reneke, and R. D. Peacock, ‘A method for the analysis of behavioural
uncertainty in evacuation modelling’, Fire Technol., vol. 50, no. 6, pp. 1545–1571, Nov.
2014, doi: 10.1007/s10694-013-0352-7.
[11] R. Lovreglio, E. Ronchi, and D. Borri, ‘The validation of evacuation simulation models
through the analysis of behavioural uncertainty’, Reliab. Eng. Syst. Saf., vol. 131, pp. 166–
174, Nov. 2014, doi: 10.1016/j.ress.2014.07.007.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
24
[12] M. Bensilum and D. A. Purser, ‘Grid Flow: An object-oriented building evacuation
model combining pre-movement and movement behaviours for performance-based
design’, Fire Saf. Sci., vol. 7, pp. 941–952, 2003.
[13] E. R. Galea, S. J. Deere, C. G. Hopkin, and H. Xie, ‘Evacuation response behaviour of
occupants in a large theatre during a live performance’, Fire Mater., vol. 41, no. 5, pp.
467–492, 2017, doi: 10.1002/fam.2424.
[14] R. Lovreglio, E. Kuligowski, S. Gwynne, and K. Boyce, ‘A pre-evacuation database
for use in egress simulations’, Fire Saf. J., vol. 105, pp. 107–128, Apr. 2019, doi:
10.1016/j.firesaf.2018.12.009.
[15] M. Forssberg, J. Kjellström, H. Frantzich, A. Mossberg, and D. Nilsson, ‘The variation
of pre-movement time in building evacuation’, Fire Technol., vol. 55, no. 6, pp. 2491–
2513, Nov. 2019, doi: 10.1007/s10694-019-00881-1.
[16] R. Lovreglio, E. Ronchi, and D. Nilsson, ‘A model of the decision-making process
during pre-evacuation’, Fire Saf. J., vol. 78, pp. 168–179, Nov. 2015, doi:
10.1016/j.firesaf.2015.07.001.
[17] R. Lovreglio, E. Ronchi, and D. Nilsson, ‘An Evacuation Decision Model based on
perceived risk, social influence and behavioural uncertainty’, Simul. Model. Pract. Theory,
vol. 66, pp. 226–242, Aug. 2016, doi: 10.1016/j.simpat.2016.03.006.
[18] X. Zhao, R. Lovreglio, and D. Nilsson, ‘Modelling and interpreting pre-evacuation
decision-making using machine learning’, Autom. Constr., vol. 113, p. 103140, May 2020,
doi: 10.1016/j.autcon.2020.103140.
[19] M. J. Spearpoint, ‘Comparative verification exercises on a probabilistic network model
for building evacuation’, J. Fire Sci., Jun. 2009, doi: 10.1177/0734904109105373.
[20] S. M. Gwynne, ‘Translating behavioral theory of human response into modeling
practice’, National Institute of Standards and Technology, Gaithersburg, MD, NISTGCR
12-972, Nov. 2012. Accessed: Mar. 20, 2020. [Online]. Available:
https://www.nist.gov/publications/translating-behavioral-theory-human-response-
modeling-practice-nistgcr-12-972.
[21] E. Kuligowski, ‘Predicting human behavior during fires’, Fire Technol., vol. 49, no. 1,
pp. 101–120, Jan. 2013, doi: 10.1007/s10694-011-0245-6.
[22] E. Retana Rodriguez and M. Spearpoint, ‘Assessment of the New Zealand verification
method pre-travel scenarios using the evacuation decision model’, presented at the 6th
International Symposium on Human Behaviour in Fire, Cambridge, UK, Sep. 2015.
[23] Ministry of Business, Innovation & Employment, ‘Commentary for Building Code
Clauses C1–C6 and Verification Method C/VM2’, Wellington, New Zealand, Dec. 2013.
[24] M. Spearpoint, ‘The effect of pre-evacuation on evacuation times in the Simulex
model’, J. Fire Prot. Eng., vol. 14, no. 1, pp. 33–53, Feb. 2004, doi:
10.1177/1042391504034742.
[25] D. Bruck, ‘The who, what, where and why of waking to fire alarms: a review’, Fire Saf.
J., vol. 36, no. 7, pp. 623–639, Oct. 2001, doi: 10.1016/S0379-7112(01)00025-X.
[26] J. Vistnes, S. J. Grubits, and Y. He, ‘A stochastic approach to occupant pre-movement
in fires’, Fire Saf. Sci., vol. 8, pp. 531–542, 2005.
[27] E. Nober, H. Peirce, A. Well, C. C. Johnson, and C. Clifton, ‘Waking effectiveness of
household smoke and fire detection device’, National Bureau of Standards, Gaithersburg,
MD, NBS-GCR-80-284, 1980.
[28] M. J. Kahn, ‘Detection times to fire-related stimuli by sleeping subjects’, National
Bureau of Standards, Gaithersburg, MD, NBS-GCR-83-435, 1983.
[29] D. Bruck and M. Horasan, ‘Non-arousal and non-action of normal sleepers in response
to a smoke detector alarm’, Fire Saf. J., vol. 25, no. 2, pp. 125–139, Sep. 1995, doi:
10.1016/0379-7112(95)00041-0.
Pre-print of manuscript accepted for publication in Fire Safety Journal, 2021
25
[30] D. Bruck, ‘Non-awakening in children in response to a smoke detector alarm’, Fire Saf.
J., vol. 32, no. 4, pp. 369–376, Jun. 1999, doi: 10.1016/S0379-7112(98)00035-6.
[31] C. R. Duncan, ‘The effectiveness of the domestic smoke alarm signal’, University of
Canterbury, Christchurch, New Zealand, Fire Engineering Research Report 99/5, 1999.
[32] D. Bruck and A. Bliss, ‘Sleeping children and smoke alarms’, Fire Saf. Sci., vol. 4, pp.
603–612, 2000.
[33] R. Lovreglio, M. Spearpoint, and M. Girault, ‘The impact of sampling methods on
evacuation model convergence and egress time’, Reliab. Eng. Syst. Saf., vol. 185, pp. 24–
34, May 2019, doi: 10.1016/j.ress.2018.12.015.
