Millgrove Evacuation Study

IBM Research Technical Report:
Millgrove Evacuation Study
May 4, 2013
Anton Beloglazov, Juerg von Kaenel, Jan Richter, Kent Steer and Ziyuan Wang∗
∗ In
alphabetical order.
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Abstract
In this research report we present a recent study undertaken by IBM Research Australia into the dynamics of an
evacuation of residents from the Victorian country town of Millgrove. The primary objective was to explore and
understand the difference, in terms of traffic conditions, between the establishment of a single fire-safe refuge, or
the establishment of two such refuges.
The study utilised a set of evacuation planning tools that are currently under development by IBM Research
Australia that should be considered a research prototype level.
NOTE: readers should carefully study the assumptions and simplifications that have been made, and described
herein, to fully understand to what level the findings may be applicable. IBM makes no warranties as to the
applicability or usability of the results in this research study.
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Introduction
The township of Millgrove is located 61 km east of Melbourne (Australia) and is home to around 2700 people. It
lies on the edge of the Yarra Ranges National Park, which creates an idyllic setting, but also presents a significant
bushfire risk. Local authorities are planning to establish either one or two refuges within the township where locals
can seek refuge in the event of a fire. Two candidate sites have been chosen: (1) a school on Cavanagh Road,
and (2) a soon-to-be disused fire station on the southern side of the Warburton Highway (see Figure 1).
IBM Research Australia has used these plans to test our evacuation simulation prototype by carrying out a study
of the traffic conditions induced by an evacuation under the two refuge options. Points of concern include the
single bridge across the river that the majority of residents will need to use, and two intersections on the
Warburton Highway where evacuees must negotiate oncoming traffic before reaching the designated refuges. IBM
Research’s evacuation planning tools provide detailed insights into the location and extent of congestion under a
variety of scenarios and assumptions, which may enable planning authorities to make more informed decisions.
In particular, the impact of the following three factors has been studied:
1. The number of fire refuges: one refuge at the school on Cavanagh Road, or two refuges with an extra site at
the fire station on the southern side of the Warburton Highway.
2. The percentage of evacuee vehicles leaving to refuge destinations: 40%, 60%, or 80%.
3. The volume of highway background traffic: 100, 500, or 1000 cars per hour, much of which may be caused
by evacuees from neighbouring towns trying to leave the area.
A
D
B
C
De
F
d
Roa
E
Cavana
M cKenzie Kin
g Dr
iv
d
oa
eR
r
Rive
e
N
gh Road
B1
H3
1
H4
2
H1
War
bu
r to n H
ig h w a y
m
M
to
e lb
ne
our
61
k
H5
G
H2
Figure 1: Map of the Millgrove area showing: regions A through G; road segments B1 and H1 through H5; and,
two refuges sites under consideration, labelled nodes 1 and 2.
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Evacuation planning toolchain (IBM Research Australia)
Input data:
• Road network
• Demographics
SCENARIO
MODELLER
TRAFFIC
SIMULATION
ANALYTICS
Output
• Behaviour
Megaffic
(IBM Research Tokyo)
Figure 2: The evacuation modelling workflow. Boxes represent functional components. The Scenario modeller,
Traffic simulation, and Analytics components compose an evacuation modelling toolchain developed at IBM Research Australia. This toolchain utilises Megaffic, an agent-based traffic simulator developed at IBM Research
Tokyo.
Figure 2 is a high level schematic of the evacuation planning workflow. We use Megaffic1 as our traffic simulation
component in this study. Megaffic is an agent-based simulator developed by IBM Research Tokyo. It is capable of
representing millions of vehicles and their interactions in large-scale traffic networks, and is well suited to major
road infrastructure planning. As we demonstrate here, it can also be used to simulate traffic under evacuation
conditions by carefully constructing an appropriate input scenario.
The analytics component performs post-processing on the simulation results to produce views of the data that
support evacuation planning.
1 Osogami
et al., “IBM Mega Traffic Simulator”: http://domino.research.ibm.com/library/cyberdig.nsf/papers
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Experiment design
Data
The models developed during this study are based on information obtained from public data sources and input
from subject matter experts. The following public data sets have been used:
• The road network model used in this study is based on data obtained from the OpenStreetMap (OSM)
project2 . The project creates and distributes free and open geographic data, licensed under the Open Data
Commons Open Database License (ODbL)3 . Since maps provided by the project are a work-in-progress,
and anyone is allowed to edit the data, OpenStreetMap is not a complete or accurate map of the world. This
study utilises the OpenStreetMap road network data current for April 2013.
• Demographic data were obtained from the Australian Bureau of Statistics (ABS)4 . In particular, the data are
a subset of the data collected during the Census of Population and Housing conducted by the ABS on 9
August 2011, which was Australia’s sixteenth national Census5 . This study uses the data on population size
and household counts per Statistical Area Level 1 (SA1); SA1s are the smallest areas for which these types
of Census data are released. SA1s have been designed to contain an average population of approximately
400 people. There are about 55,000 SA1s covering Australia. The provided data sets are of the highest
quality available on the demographics of Australia. Prior to being released, the data pass through a
confidentiality process, which results in small introduced errors; however, the information value of the data
set as a whole is not affected.
The input from subject matter experts (SMEs) defined the evacuation area and destinations, as well as the road
segments of interest displayed in Figure 1. SMEs also provided guidance on the distribution of the number of
vehicles utilised by each household type, shown in Table 1. This information, in conjunction with the ABS data,
enabled the calculation of the number of vehicles originating from each SA1 listed in Table 2.
Table 1: Distribution of vehicles per household type
0 vehicles
1 vehicle
2 vehicles
3 vehicles
Singles
Families without children
Families with children
0%
100%
0%
0%
0%
90%
10%
0%
0%
50%
50%
0%
Table 2: Number of vehicles per SA1
SA1
Vehicle number
A
B
C
D
E
F
G
49
137
254
271
311
200
189
2 OpenStreetMap.
http://openstreetmap.org/
Copyright and License. http://openstreetmap.org/copyright
4 Australian Bureau of Statistics. http://abs.gov.au/
5 Australian Census of Population and Housing. http://abs.gov.au/websitedbs/censushome.nsf/home/census
3 OpenStreetMap:
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Scenario modelling
The modelling approach undertaken in this study was to design a base scenario and determine a set of variables,
whose value combinations would define a number of scenarios. In the base scenario, the evacuation starts at
10:10 am. We allow a 10 minute buffer at the beginning of each simulation to reach steady traffic conditions on the
Warburton Highway prior to the evacuation (i.e., the simulation itself begins at 10:00 am). Vehicles from each
origin area travel to one of the available destinations: fire refuges, or towards Melbourne. When entering the
highway, vehicles merge with the background traffic formed by vehicles travelling towards the Melbourne from
other suburbs, and vehicles travelling in the opposite direction.
A number of scenarios have been derived from the base scenario by varying three major variables, as listed in
Table 3. The first variable directly follows from the aim of the study, i.e., the number of refuges serving as
destinations for the evacuees. One option is to construct a single fire refuge based at a school on Cavanagh Road
with the capacity of 500 people. The other option is to establish two refuges: a school on Cavanagh Road and
another refuge at a fire station on the southern side of the Warburton Highway.
Table 3: Scenario variables and their values
Variable
Set of values
Number of fire refuges
Refuge participation rate
Volume of the highway traffic (cars per hour)
1 refuge, 2 refuges
40%, 60%, 80%
100, 500, 1000
Another variable in defining the scenarios is the percentage of vehicles from the evacuation area that leave to one
of the refuge destinations, which is referred to as the refuge participation rate. Three participation rates have been
selected to construct scenarios: 40%, 60%, and 80%. The fraction of evacuee vehicles heading towards the city is
fixed at 20% for all the scenarios. The scenarios with the 80% refuge participation rate can be considered the
worst cases as they assume 100% of people will leave the evacuation area.
The third variable investigated is the volume of background traffic on the highway, which has been set to 100, 500,
and 1000 vehicles per hour. The arrival times of the background traffic vehicles are calculated based on time
intervals between vehicle arrivals sampled from an exponential distribution with the specified rate parameter.
All the combinations of the described variable values have been used to construct simulation scenarios giving in a
total of 18 scenarios. Using the modelling tools, the input for each scenario has been converted into a trip design
for the traffic simulator. A trip design is an input data format required by Megaffic to initiate traffic simulation. The
input contains a list of tuples of origin and destination road network nodes, departure time, and the number of
vehicles following the trip. According to the received trip design, Megaffic calculates a route for each vehicle based
on a given driver or route selection model. In this study, we use the shortest path route selection criterion.
Figure 3 shows the vehicle numbers generated based on the trip design per area and destination for the one and
two refuge scenarios. In order to provide similar conditions, the total number of vehicles travelling to refuge
destinations has been set equal for each participation rate for one and two refuge scenarios. This allowed us to
isolate the effect of the addition of a second refuge on the southern side of the Warburton highway.
The output generated by Megaffic contains statistical information for each road segment, such as the average
speed or the number of passed cars in a certain time interval. We use the average speed for 10 minute time
intervals.
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Participation: 40%
Participation: 60%
Participation: 80%
250
Vehicles
200
Target
150
City Direction
100
Millgrove School
50
0
A
B
C
D
E
G
A
B
C
D
E
G
A
B
C
D
E
G
Area
(a) One refuge
Participation: 40%
Participation: 60%
Participation: 80%
150
Vehicles
Target
100
City Direction
Fire Station
Millgrove School
50
0
A
B
C
D
E
G
A
B
C
D
E
G
A
B
C
D
E
G
Area
(b) Two refuges
Figure 3: Vehicle numbers for both scenarios per area and destination, for each of the three participation levels
studied (40%, 60% and 80%).
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Assumptions and simplifications
The scenarios presented are not necessarily representative of all possible scenarios and care should be taken
when attempting to generalise from any findings. Furthermore, the following assumptions need to be taken into
account when interpreting the results:
• Evacuee departure times (also called mobilisation times) follow a Rayleigh distribution with a mode of 30
minutes. This distribution has been found to closely match data provided by subject matter experts (see
Tweedie et al.6 ). The Rayleigh cumulative distribution function with a mode of σ can be expressed as:
F (t) = 1 − exp(−t2 /2σ 2 ).
• The version of the traffic simulator used in this study incorporates a simplified vehicle interaction model.
Specifically, merging of two streams of traffic into one is based on equal priority and vehicles moving along
crossed paths are assumed to have no interaction. To mimic the influence of priority, merging and egress
factors, we modify the speed limit on certain segments: the bridge immediately before the highway; and
segments connecting the highway and outgoing roads.
• To simulate the car parking behaviour, the speed limits on the road segments immediately preceding the
refuge destinations have been reduced to 20 km/h.
• Vehicle numbers are derived from residential data. This will tend to over-estimate the number of people in
the area, particularly during the day when many people may be away from their homes.
• Route selection is static; drivers do not change their route even when encountering significant delays.
6 Tweedie, Stephen W., et al. “A methodology for estimating emergency evacuation times,” The Social Science Journal, Volume
23, Issue 2, Summer 1986, 189-204.
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Results
The figures presented in this section have been designed to show the difference between the one and two refuge
options under a variety of scenarios. As such, within each figure we always show both options (among other
variables) and indicate the one refuge option with a solid line, and the two refuge option with a dashed line. In
general, the difference can be seen by comparing two lines of the same colour.
Each figure corresponds to one direction of one road segment. We have focussed on six segments in total
(Table 4): five from the Melbourne direction of the Warburton Highway as it passes through Millgrove (labelled H1
through H5 in Figure 1), and one for the bridge connecting properties north of the river to the Warburton Highway
(labelled B1 in Figure 1). For each segment we show the direction that will be most significantly affected by a large
volume of traffic moving from residences to the refuges. For the Warburton Highway this also shows the traffic
moving from Warburton towards Melbourne.
Table 4: Road segment groups and labels
Road segment group
Melbourne direction of the Warburton Highway
Bridge from the north Millgrove area to the Warburton Highway
Labels
H1, H2, H3, H4 and H5
B1
Figures 4-7 all show the average speed of vehicles travelling over the aforementioned segments. These averages
are calculated for every 10 minute interval of time, and thus represent a discrete time series. For example, a data
point at time 10:30 am represents the average speed of all vehicles travelling along the given segment between
10:20 am and 10:30 am. If no vehicle passes a segment during that interval of time, then no value is plotted (e.g.,
Figure 5c after 12:10 pm.) These averages are presented with respect to time so that we can see how the average
speed of a segment changes over the period of simulation. The figures are broken into those which show variation
in participation rate (Figures 4 and 5) and those which show variation in highway traffic volume (Figures 6 and 7).
It is interesting to see that the use of the second refuge (the fire station) does not significantly change the traffic
conditions on the Warburton highway when the departure times of all vehicles are distributed. On the highway
segments H1 and H2 (Figures 4a, 4b, 6a, and 6b) before and after the intersection with bridge B1 the average
speed for the two scenarios (one and two refuges) is almost identical across different highway traffic and
participation rates. Although the average speed on road segments H3 and H4 (Figures 4c, 5a, 6c, and 7a)
reduces in some cases for two refuges, the difference is only significant for a 60% participation rate and highway
traffic with 500 cars/h. On the other hand, Segment H5 (Figures 5b and 7b) shows no difference. Figures 5c and
7c demonstrate that bridge B1 acts as a bottleneck since it is the only direct connecting road to the residential
area across the river. The speed drops below 10 km/h for a longer period of time where most cars leave to the
refuges. As expected, the duration of the congestion depends primarily on the participation rate (Figure 5c)
whereas the congestion on the bridge eases only if traffic on the highway is very low (100 cars/h, Figure 7c).
In general, the participation rate of vehicles leaving significantly affects the traffic conditions on and near the
bridge B1, especially segments H1 and H2. As shown in Figures 4a and 4b, lower rates reduce the average speed
to a shorter period of time. The other segments—H3, H4 and H5—are not significantly affected. Similarly, highway
traffic rates mostly affect segments H1 and H2 (Figures 6a and 6b) with a pronounced effect on segment H1 due
to the merging traffic from the bridge. Increasing traffic rates lowers the average speed on H1, whereas on H2
lower rates result in an earlier return to a higher average speed.
Tables 5 and 6 show an overview of the minimum and maximum average speed on the studied road segments and
variables over all 10 minute time intervals during the simulation. Table 7 provides an overview of the duration the
average speed was below a certain threshold on the road segments. We can see that the minimum and maximum
speeds on the segments around the bridge are most affected, especially by the rate of highway traffic. Due to the
bridge being the only road where traffic flows into the highway it has the lowest maximum speed throughout the
simulation. Also, the values in the tables are similar for both refuge scenarios in most cases.
It should be noted that the similarity of the one and two refuge cases were observed when the departure
behaviour of all vehicles is distributed over time (in this study we used the Rayleigh distribution with a mode of 30
minutes). Such departure distributions typically represent the evacuation behaviour more realistically. The
difference in average speed for one and two refuges may increase, however, when departure times of vehicles are
less distributed, or, in the extreme case, are simultaneous. This scenario is presented in the appendix.
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60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H1
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H2
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment H3
Figure 4: The effect of participation rate (highway rate is fixed at 500 cars per hour, distributed departure times)
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60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H4
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H5
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment B1
Figure 5: The effect of participation rate (highway rate is fixed at 500 cars per hour, distributed departure times)
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60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H1
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H2
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment H3
Figure 6: The effect of highway rate (participation rate is fixed at 60%, distributed departure times)
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60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H4
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H5
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment B1
Figure 7: The effect of highway rate (participation rate is fixed at 60%, distributed departure times)
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Table 5: Minimum average speed in km/h (1 refuge / 2 refuges)
Hwy
traffic
(cars/h)
Part.
rate
(%)
H1
H2
H3
H4
H5
B1
100
40
60
80
52.3 / 52.3
52.3 / 52.3
52.3 / 52.3
33.3 / 33.0
32.3 / 33.0
33.1 / 29.8
44.9 / 44.8
43.5 / 44.1
44.6 / 44.4
45.2 / 42.3
46.4 / 42.0
44.9 / 41.3
37.3 / 36.9
37.5 / 36.8
37.2 / 36.7
0.0 / 0.0
0.0 / 0.0
0.0 / 0.0
500
40
60
80
29.1 / 28.4
24.4 / 18.6
14.6 / 15.0
31.2 / 30.9
31.3 / 31.1
30.9 / 30.8
43.6 / 37.7
40.3 / 34.3
40.3 / 34.3
46.9 / 39.2
45.2 / 34.2
47.6 / 39.4
37.5 / 36.3
37.3 / 35.6
37.6 / 36.3
0.0 / 0.0
0.0 / 0.0
0.0 / 0.0
1000
40
60
80
2.4 / 2.4
2.4 / 2.4
2.4 / 2.4
30.1 / 30.8
31.1 / 30.9
30.5 / 30.9
41.4 / 34.7
39.8 / 39.7
41.9 / 30.1
45.8 / 43.4
46.7 / 38.2
45.6 / 42.0
37.3 / 36.8
37.3 / 36.2
37.4 / 36.2
0.0 / 0.0
0.0 / 0.0
0.0 / 0.0
Table 6: Maximum average speed in km/h (1 refuge / 2 refuges)
Hwy
traffic
(cars/h)
Part.
rate
(%)
H1
H2
H3
H4
H5
B1
100
40
60
80
52.3 / 52.3
52.3 / 52.3
52.3 / 52.3
53.0 / 53.0
53.0 / 53.0
53.0 / 53.0
48.3 / 48.3
48.3 / 48.3
48.3 / 48.3
52.3 / 53.2
53.1 / 52.4
53.5 / 53.2
38.4 / 38.5
38.5 / 38.5
38.6 / 38.5
16.2 / 16.7
16.4 / 16.3
16.1 / 16.0
500
40
60
80
52.3 / 52.3
52.3 / 52.3
52.3 / 52.3
53.0 / 53.0
53.0 / 53.0
53.0 / 53.0
48.3 / 48.4
48.3 / 48.3
48.3 / 48.3
52.9 / 52.2
52.9 / 52.6
52.3 / 53.3
38.5 / 38.4
38.5 / 38.4
38.4 / 38.5
16.1 / 16.1
12.5 / 15.9
9.9 / 11.9
1000
40
60
80
52.3 / 51.9
52.2 / 52.3
52.3 / 51.8
51.9 / 52.9
52.9 / 53.0
53.0 / 53.0
48.2 / 48.3
48.3 / 48.3
48.3 / 48.4
52.1 / 52.0
52.1 / 52.1
52.0 / 52.2
38.4 / 38.3
38.4 / 38.4
38.4 / 38.4
16.1 / 16.3
15.7 / 16.0
12.2 / 13.8
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Table 7: Duration of decreased speed period in minutes (1 refuge / 2 refuges)
Speed
below
Highway
traffic
(cars/h
Part.
rate
(%)
H1
H2
H3
H4
H5
B1
< 50 km/h
100
40
60
80
0/0
0/0
0/0
120 / 110
100 / 110
130 / 110
180 / 180
180 / 180
180 / 180
60 / 50
30 / 70
20 / 60
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
500
40
60
80
50 / 60
90 / 100
120 / 120
90 / 90
110 / 110
140 / 140
180 / 180
180 / 180
180 / 180
60 / 70
30 / 70
50 / 70
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
1000
40
60
80
170 / 170
170 / 170
170 / 170
170 / 170
170 / 170
170 / 170
180 / 180
180 / 180
180 / 180
50 / 70
50 / 60
40 / 160
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
100
40
60
80
0/0
0/0
0/0
0/0
0/0
0 / 10
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
500
40
60
80
10 / 20
40 / 40
70 / 70
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
1000
40
60
80
160 / 160
160 / 160
160 / 160
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
100
40
60
80
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
500
40
60
80
0/0
0 / 10
40 / 20
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
1000
40
60
80
150 / 160
160 / 160
160 / 160
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
< 30 km/h
< 20 km/h
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Summary
Figure 8 summarises the difference between the one and two refuge options in terms of the average speed over
the whole simulation. Positive values indicate the one refuge option produced, on average, better traffic flow.
Based on the results presented here, we make the following observations:
• There is not a major difference between traffic conditions between the one and two refuge options in most
situations.
• The bottleneck at the bridge reduces the influence of departure behaviour.
Participation: 40%
Participation: 60%
Participation: 80%
B1 H1 H2 H3 H4 H5
B1 H1 H2 H3 H4 H5
B1 H1 H2 H3 H4 H5
10.0
Highway: 100 Cars/h
7.5
2.5
0.0
10.0
Highway: 500 Cars/h
7.5
5.0
2.5
0.0
10.0
Highway: 1000 Cars/h
Avg. speed difference between 1 and 2 refuges
5.0
7.5
5.0
2.5
0.0
Segment
Figure 8: The average speed difference between one and two refuges for each of the variables being studied.
Positive values indicate that the average speed for the one refuge option was greater than for the two refuge option.
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be trademarks or services marks of IBM or others. A current list of IBM trademarks is available on the Web at “Copyright and trademark information” at www.ibm.com/legal/copytrade.shtml. © Copyright IBM
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Appendix
The remaining pages present the results for the scenarios in which all vehicles depart their homes at the same
time. In this set of scenarios the difference between the one or two refuges is more pronounced for higher
participation and highway traffic rates on the highway segments after the bridge, especially H2 and H3 (Figures
11b, 11c, 9b, and 9c). The observed average speed was lower in most of these cases for the two refuge scenario.
Similar to the previous case with distributed departures the bridge B1 acts as a bottleneck causing prolonged
congestion times. As a result, the average speed on bridge B1 is very low for a longer time period than in the
previous case, and recovers only once the area above the river is cleared (Figures 10c and 12c).
As in the scenario with distributed departures the highway segments H1 to H3 are most affected during the
evacuation, and the strongest change in average speed could be observed at different rates of highway traffic. As
most of the traffic caused by the simultaneous evacuation flows into the highway, at least on segment H2, the
participation rate also strongly influences the highway traffic conditions, but to a lesser degree than the traffic on
the highway itself. The minimum and maximum average speed in Tables 8 and 9 as well as the duration for
various speed thresholds in Table 10) further demonstrates this finding.
It should be noted that although there is a significant difference between the two refuge scenarios for larger
highway traffic and participation rates (Figure 13) the simultaneous departure of all vehicles is very unrealistic.
This is even more so for a higher participation rate. Lower participation and highway traffic rates as well as
distributed departure behaviour show no significant difference in traffic conditions for one or two refuges.
Table 8: Minimum average speed in km/h (1 refuge / 2 refuges) for simultaneous departure
Hwy
traffic
(cars/h)
Part.
rate
(%)
H1
H2
H3
H4
H5
B1
100
40
60
80
52.3 / 52.3
52.3 / 52.3
52.3 / 52.3
33.1 / 31.7
32.6 / 32.7
32.7 / 32.8
45.5 / 44.1
43.1 / 37.3
43.6 / 34.5
36.4 / 27.9
37.1 / 26.5
40.0 / 25.4
36.1 / 34.8
36.2 / 34.6
36.5 / 34.4
0.0 / 0.0
0.0 / 0.0
0.0 / 0.0
500
40
60
80
17.3 / 18.4
14.5 / 14.4
14.4 / 12.9
30.9 / 31.0
31.1 / 11.8
31.2 / 11.9
34.5 / 34.6
26.8 / 29.2
43.0 / 28.7
34.7 / 25.1
35.4 / 25.1
33.7 / 24.9
35.7 / 34.3
35.6 / 34.4
35.7 / 34.3
0.0 / 0.0
0.0 / 0.0
0.0 / 0.0
1000
40
60
80
2.4 / 2.4
2.4 / 2.4
2.4 / 2.3
31.0 / 29.0
27.6 / 12.2
30.4 / 11.9
34.4 / 28.4
35.1 / 28.8
33.7 / 21.3
29.0 / 25.2
30.2 / 25.0
30.0 / 25.0
34.9 / 34.4
34.9 / 34.3
35.1 / 34.4
0.0 / 0.0
0.0 / 0.0
0.0 / 0.0
Table 9: Maximum average speed in km/h (1 refuge / 2 refuges) for simultaneous departure
Hwy
traffic
(cars/h)
Part.
rate
(%)
H1
H2
H3
H4
H5
B1
100
40
60
80
52.3 / 52.3
52.3 / 52.3
52.3 / 52.3
53.0 / 53.0
53.0 / 53.0
53.0 / 53.0
48.3 / 48.3
48.3 / 48.3
48.3 / 48.3
53.2 / 52.9
53.2 / 52.4
53.2 / 52.9
38.5 / 38.5
38.5 / 38.5
38.5 / 38.5
4.2 / 4.3
4.4 / 4.2
4.3 / 4.4
500
40
60
80
52.3 / 52.3
52.3 / 52.3
52.3 / 52.3
53.0 / 53.0
53.0 / 53.0
53.0 / 53.0
48.3 / 48.3
48.3 / 48.4
48.3 / 48.4
52.7 / 52.7
52.5 / 52.3
52.7 / 53.3
38.5 / 38.5
38.5 / 38.4
38.5 / 38.5
4.1 / 4.1
4.1 / 4.0
4.2 / 4.2
1000
40
60
80
52.3 / 52.3
52.3 / 52.2
52.3 / 51.8
53.0 / 53.0
53.0 / 53.0
53.0 / 53.0
48.3 / 48.3
48.3 / 48.4
48.3 / 48.3
52.2 / 52.0
52.2 / 52.8
52.5 / 51.9
38.4 / 38.4
38.4 / 38.5
38.4 / 38.4
3.6 / 3.7
3.7 / 3.7
3.8 / 3.7
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IBMNCA0620
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H1
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H2
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment H3
Figure 9: The effect of participation rate (highway rate is fixed at 500 cars per hour)
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be trademarks or services marks of IBM or others. A current list of IBM trademarks is available on the Web at “Copyright and trademark information” at www.ibm.com/legal/copytrade.shtml. © Copyright IBM
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60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H4
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H5
60
Participation
40 %
40
30
20
60 %
Evac. begins
Average speed (km/h)
50
80 %
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment B1
Figure 10: The effect of participation rate (highway rate is fixed at 500 cars per hour)
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be trademarks or services marks of IBM or others. A current list of IBM trademarks is available on the Web at “Copyright and trademark information” at www.ibm.com/legal/copytrade.shtml. © Copyright IBM
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60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H1
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H2
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment H3
Figure 11: The effect of highway rate (participation rate is fixed at 60%)
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60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(a) Segment H4
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(b) Segment H5
60
Highway traffic
100 cars/h
40
30
20
500 cars/h
Evac. begins
Average speed (km/h)
50
1000 cars/h
Shelters
1
2
10
0
10:00
10:30
11:00
11:30
12:00
12:30
13:00
Time
(c) Segment B1
Figure 12: The effect of highway rate (participation rate is fixed at 60%)
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Participation: 40%
Participation: 60%
Participation: 80%
B1 H1 H2 H3 H4 H5
B1 H1 H2 H3 H4 H5
B1 H1 H2 H3 H4 H5
Highway: 100 Cars/h
15
5
0
15
Highway: 500 Cars/h
10
5
0
15
Highway: 1000 Cars/h
Avg. speed difference between 1 and 2 refuges
10
10
5
0
Segment
Figure 13: Average speed difference between one and two refuges for each of the studied variables in the case of
simultaneous departure times of vehicles (Positive values indicate that the average speed for the one refuge option
was greater than for the two refuge option).
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be trademarks or services marks of IBM or others. A current list of IBM trademarks is available on the Web at “Copyright and trademark information” at www.ibm.com/legal/copytrade.shtml. © Copyright IBM
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Table 10: Duration of decreased speed period in minutes (1 refuge / 2 refuges) for simultaneous departure
Speed
below
Highway
traffic
(cars/h
Part.
rate
(%)
H1
H2
H3
H4
H5
B1
< 50 km/h
100
40
60
80
0/0
0/0
0/0
60 / 60
80 / 80
100 / 100
180 / 180
180 / 180
180 / 180
10 / 10
10 / 10
10 / 10
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
500
40
60
80
80 / 80
100 / 100
130 / 130
80 / 80
110 / 110
130 / 140
180 / 180
180 / 180
180 / 180
10 / 20
10 / 20
10 / 140
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
1000
40
60
80
170 / 170
170 / 170
170 / 170
170 / 170
170 / 170
170 / 170
180 / 180
180 / 180
180 / 180
10 / 170
10 / 170
10 / 170
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
180 / 180
100
40
60
80
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0 / 10
0 / 10
0 / 10
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
500
40
60
80
70 / 70
90 / 90
110 / 120
0/0
0 / 110
0 / 130
0/0
100 / 20
0 / 130
0 / 10
0 / 10
0 / 10
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
1000
40
60
80
160 / 170
170 / 170
170 / 170
0 / 10
10 / 170
0 / 170
0 / 170
0 / 170
0 / 170
10 / 10
0 / 10
10 / 10
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
100
40
60
80
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
500
40
60
80
10 / 20
20 / 30
60 / 60
0/0
0 / 100
0 / 130
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
1000
40
60
80
160 / 160
160 / 160
160 / 160
0/0
0 / 170
0 / 170
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
0/0
180 / 180
180 / 180
180 / 180
< 30 km/h
< 20 km/h
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be trademarks or services marks of IBM or others. A current list of IBM trademarks is available on the Web at “Copyright and trademark information” at www.ibm.com/legal/copytrade.shtml. © Copyright IBM
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