1
Geosimulation of Parking
in the City
Itzhak Benenson1, Karel Martens2
1Department of Geography and Human Environment, 2Institute for Management Research,
Radboud University Nijmegen, the Netherlands
2
Parking zones in Tel Aviv - Yaffo
Start of project:Tel Aviv in search of new parking policy
3
Starting points
• Many unanswered questions:
– Maintain existing system of parking zones?
– Parking permissions/restrictions for various driver categories (local citizens, workers, visitors, etc.)?
– Level of on-street and off-street parking fees?
– Level of control and enforcement?
– Political consequences of current/proposed policy?
• Limited knowledge base, especially at zone/area level:
– Level of demand?
– What is the supply, including privately-owned parking?
– What is the economically justified parking fee for citizens or visitors?
– What is the parking fee citizens or visitors are willing to pay?
– What level of control is necessary to avoid illegal parking?
4
In a metropolitan center like Tel Aviv, demand for parking will always exceed parking supply, unless appropriate parking policies are designed, implemented and enforced. The policy challenge is to find the appropriate design.
Geosimulation of the parking process in Tel-Aviv
Payment for on-street parking
towing…
5
Starting points
of the parking model
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The goals
Dreams for the driver:
To find parking quickly and close to the destination, if necessary against a small, fair, fee.
Dreams for the municipality:
To guarantee car drivers a safe and convenient access to the city.To guarantee citizens and visitors an overall pleasant urban
environment. To book high overall revenues from parking fees.
Meta-goal for the municipality:
To increase the chances of re-election for current major and city council…
7
Spatial determinants of parking supply and demand
Tel Aviv municipal GIS
• Street network that
includes traffic directions
and turns, thus enabling
estimation of the process of
driving to the destination
• Parking permissions
along the streets, off-
street parking places and
lots, thus enabling
estimation of parking space
supply
• Residential buildings,
public buildings, offices
and businesses, thus
enabling estimating of the
numbers of the drivers that
want to park
8
בן יהודה
אבן גבירול
גוריון -בן
זמנגוף
חניון בזל
דיזנגוף
סוקולוב
Non-spatial determinants of parking demand
• Duration of parking for the residents and visitors of different types• Willingness-to-pay of the residents and visitors of different types
The way of estimating:
Surveys at various locations throughout the city
The surveyors marked the cars on high-resolution map and recorded plate numbers.
These data were further analyzed
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• Short-time parking along the main streets and long-time parking within residential areas:
– Parking in the daytime that lasts less than 30 minutes: on arterial roads -
70% of drivers, collector roads - 50%, local streets – 10-15%
– The duration of parking when it takes more than half an hour distributed
uniformly (each survey lasts 6 or 8 hours)
• Majority of drivers are ready to pay a fair fee for on-street parking:– about 5 NIS for short-term parking (< 30 minutes)
– about 10-12 NIS for long-term parking (2 hours and longer)
• Majority of residents: more than 5-minutes walk between overnight parking place and residence
• Fraction of visitors parking within residential areas− at night – about 5% (only!)
− in the daytime – about 20%
•Fraction of the empty parking spaces within residential areas− at night – 0%
− in the daytime – about 20%
Summary of the survey results
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One of two unexpected result of the surveys:
How far from the destination are we ready to park?
We estimated this distance for drivers who succeeded to park on-street for a night.
The surveys was carried out on two sequential weekdays, between 5:30 – 6:30h.
About 800 car plates were recorded and related to the file that contains the plate
number and address of the owner. This database is maintained by the Ministry of
Transport and is available in LAMAS.
About 20% of the cars parking in the area are registered at a distances of 1km and further…
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The same surveys, data at a distance of 1 km or less selected…
Do the drivers who park far from their registered address really live there?
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The drivers, whose addresses are far from the parking place do not live there!
154 of 447 cars registered Tel-Aviv addresses were recorded twice.
30% of 154 twice
recorder cars parked
farther than 250 m from
their registered address
We thus conclude that drivers
consistently search for a parking place
located not farther than 250 m (air)
distance from the destination (~5
minutes walk at 4-5 km/hour speed)
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Building the model
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Model starting point: driver/agent perspective
“Where” and “when” is critical for the driver we have to
characterize the parking situation for a specific area and a specific time interval
Given the area and time:
• All drivers want to find parking place as close as possible to their destination the distribution of distance between my parking
place and destination should have mean and STD as close to zero as possible
• All drivers want to find parking place quickly the distribution of
my search time should have mean and STD as close to zero as possible
• All drivers want to pay as less as possible the distribution of
my payment should have mean and STD as close to zero as possible
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Point theory of parking (search time only)
Cars arrive to a specific area at arrival rate a(t) (cars/time unit),
Already parked cars leave at an egress rate e(t) (cars/time unit). Let us also assume that the maximal driver's search time is n time units, and then the driver leaves the area.
Let us estimate the probability that the car arriving at t would fail to find a parking place until t + n.
Below we consider the process as starting with all parking places occupied at t = 0.
Let C(t) is the overall number of cars in the system, N(t, t - k) the number of cars that entered the system at t - k and are still searching for the parking place at t,
p(t) the fraction of cars that fail to find a free parking place between t and t + 1,
F(t) the number of cars that leave the system at t. Note that we are interested in F(t).
The following simple system of equations represent the dynamics of N(t, t - k), C(t), and p(t):
C(t + 1) = C(t ) + (a(t) – e(t)) - F(t)
The fraction of cars that found a parking place during [t, t + 1] is e(t)/C(t), The fraction of the cars that failed to find a parking place as
p(t , t + 1) = 1 – e(t)/C(t)
The number of cars which entered the system 0, 1, 2, ..., (n – 1) time units before t and still searching for parking can be easily calculated
as
N(t + 1, 0) = a(t),
N(t + 1, -1) = N(t, 0)*p(t)
N(t + 1, -2) = N(t, -1)*p(t)…
N(t + 1, -n) = N(t, -(n-1))*p(t)
The cars searching for parking for n time intervals leave the system, i.e. F(t + 1) = N(t, -n)
Note that the number of cars that fail to find a parking place in a real city is always higher than F(t), as we do not account for the distance
between the car searching for parking and the parking place that becomes free and assume that the latter is occupied immediately by one of the cars searching for parking at that moment.
I dare to say that bugs are too often in simulation programs… To believe in results I’d prefer some analytic explanation of the major effects…
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Figure 4 presents the dynamics of the C(t), F(t)/a and the accumulated number of cars that failed to find a
parking place for the constant and linearly decreasing arrival and egress rates during the time interval
17:00-21:00h.
We assume that the time unit = 1 min and that the maximal search time is 10 minutes and base overall
arrivals and egresses as obtained for the Basel neighborhood.
According to Table 1, about 5,000 cars are arriving to the neighborhood during four evening hours and
about 4,000 visitors' cars leave.
This results in an average arrival rate am 5000/(4*60) 20.8 cars/min and an average egress rate em
4000/(4*60) 16.7 cars/min.
We imitate the evening decay in arrivals and egresses by assuming that a(t) and e(t) decrease linearly
from 17:00h till 21:00h as follows:
a(17:00) = am + 120*da, a(21:00) = am - 120*da,
e(17:00) = em + 120*de, e(21:00) = em - 120*de,
where da(cars/min2) and de(cars/min2) are the decay rates of arrival and egress respectively.
We present four curves for da = 0.00 and 0.05 and de = 0.00 and 0.05. Note that we assume in the
theoretical calculations that there are no free parking places at 17:00h and the number of cars searching
for parking at 17:00h is zero.
The results show that the probability not to find a parking place changes over time and is highly dependent
on the decay rates of arrivals and egresses. Over the whole time interval, the average probability not to
find a parking place within 10 minutes is ~ 24%, irrespective of the decay rates. Note that, since we do not
account for space in this theoretical model, this is the lowest possible probability given the real -life access
and egress rates for the Basel neighborhood.
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The dynamics of the (a) overall number of cars searching for a parking place C(t); (b) fraction of cars that fail to find a parking place F(t)/a; (c) accumulated number of cars that failed to find a parking place for da = 0.00, 0.05 and de = 0.00, 0.05. The time interval is 17:00-21:00h.
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2000 drivers appluing for 1000 parking places that are left during two hours.
Fraction of drivers who did not find a parking place during 10 mins
0.5
0.6
0.7
0.8
0.9
1.0
0 50 100 150 200 250 300 350 400 450
Number of additional parking places
Fracti
on
of
driv
ers w
ho
failed
to
fin
d a
parkin
g
pla
ce
/
.
2000 cars applying for 1000 places during two hours
Mean search time for those who succeeded to find a parking place dependening on the
number of additional parking places (for maximal search time = 10)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 50 100 150 200 250 300 350 400 450
The number of additional parking places
Mean
search
tim
e
/
The history of arrival and egress
Probability to find a parking place at a moment t
?
Q: Why do we need the agent-based simulation of
parking search process?
A: In order to estimate the
probability to find a parking place for a given: area, time interval, arrival and egress
processes, etc
Real curve
2000 cars applying for 1000 places during two hours. Mean search time for those who succeeded to park
2000 cars applying for 1000 places during two hours. Fraction of those who failed (10-min search)
Mean field curve
Real curve
Mean field curve
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Some commonsensical observations - daily dynamics of arrival and egress rates
As every queuing process, the process of parking is inherently non-stationary. That is, either every driver who enters an area quickly finds a parking place, or the average search time and number of failures grows in time. The arrival and egress rates essentially vary in time, the parking time and parking preferences, including willingness to pay, essentially depends on the type of the driver.
Agent-Based Model enables direct estimating of distributions of search time, distance to destination, payment, etc, for various regimes of arrivals and egress, characteristics of the area, drivers’ behavior, levels of enforcement.
6:00 10:00 14:00 18:00 22:00 02:00
Typical dynamics of the arrival and egress rates
within residential area
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To investigate parking problem from the driver’s point of view - distributions of search time, distance to destination, and fees we need:
high-resolution,
spatially explicit
agent-based
model of parking in the city
The model is developed as an
ArcGIS application, and can work with practically unlimited
number of drivers
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• Parking
places –
intervals of 4
m length -
along the
street
Attributes:
permissions,
fees
• Dedicated
parking
places
Attributes:
permissions
• Parking lots
Attributes:
capacity, fees
Geosimulation of parking in the city: Objects
• Street segments
Attributes: traffic directions, parking permissions
• Destinations: Houses and Public places
Attributes: capacity, working hours
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Geosimulation of parking in the city: Agents
Drivers belonging to one of four categories:
• Residents
• Guests
with residential buildings as their destination, and
• Employees
• Customers
with public places as their destination.
Agents characteristics:
Destination, willingness-to-pay, arrival time, duration of stay.
Agents’ states:
(1) Drives to destination (2) Drives to destination and estimates the state of parking
in the area, (2) Searches for on-street parking, (3) Parks on-street or off-street,
(4) Drives out of the system.
Agents’ behavioral rules:
(1) Try to park close to the destination; (2) If failed, search for parking at some
reasonable distance during some reasonable time; (3) If failed, park for money
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Destination
Distance between the current junction and the
destination
This junction is closest to the destination
The chosen turn
Geosimulation of parking in the city: Agents Behavior
1. Drive to a junction which is the closest to the destination
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Geosimulation of parking in the city: Agents Behavior
2.a. Driver’s parking behavior before passing the destination:
• Stage 0:
Enter the system at a point at an air distance of ~300 m from its destination
• Stage 1: (300m -100 m)
Estimate parking situation while driving towards destination
• Stage 2: (100 m – destination)
Search for parking and park if possible on the way to destination
Dawareness
Dparking
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Some details of driver’s behavior at Stage 1 and Stage 2
• Stage 1: (300 m – 100 m) Estimate expected fraction of free parking places as
pfree = Nfree/(Nfree + Nocc)
• Stage 2: (100 m – destination) estimate expected number of free parking places on the way
to destination
Fexp = pfree*D/length of the parking place
Where D is the air distance from current position to destination.
Decide whether to park or to continue driving towards destination based on the following
dependence:
1
0
Probability to continue driving towards destination
F1 ~ 1 F2 ~ 3
Continuously update pfree while driving within the zone appropriate for parking
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Geosimulation of parking in the city: Agents Behavior
2.b Driver’s parking behavior after the destination is missed:
• Stage 3: If the destination is missed, extend the search area and park at any reasonable
place. Search area grows linearly in time, 30 m/min. Next junction is randomly selected from
the set of junctions within the search area
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The model output: driver’s view
Over the given Area, during given Time Interval
Distribution of the search time
02468
101214161820
10
40
70
100
130
160
190
220
250
280
310
340
370
400
430
460
490
520
550
580
Search Time (s)
Dri
verC
ou
nt
Distribution of the distance to destination
0
5
10
15
20
25
30
10
40
70
100
130
160
190
220
250
280
310
340
370
400
430
460
490
520
550
580
Distance to target (m)
Dri
verC
ou
nt
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The model output: planner’s viewNumber of drivers searchig for parking place
0
100
200
300
400
500
600
700
17:3
0
17:3
2
17:3
4
17:3
6
17:3
8
17:4
0
17:4
2
17:4
4
17:4
6
17:4
8
17:5
0
17:5
2
17:5
4
17:5
6
17:5
8
18:0
0
18:0
2
18:0
4
18:0
6
18:0
8
18:1
0
18:1
2
18:1
4
18:1
6
18:1
8
18:2
0
18:2
2
18:2
4
18:2
6
18:2
8
18:3
0
18:3
2
18:3
4
18:3
6
18:3
8
18:4
0
18:4
2
18:4
4
18:4
6
18:4
8
18:5
0
18:5
2
18:5
4
18:5
6
18:5
8
Model run time
No
of
dri
vers
.
Number of free parking places
0
5
10
15
20
25
30
35
17
:30
17
:34
17
:38
17
:42
17
:46
17
:50
17
:54
17
:58
18
:02
18
:06
18
:10
18
:14
18
:18
18
:22
18
:26
18
:30
18
:34
18
:38
18
:42
18
:46
18
:50
18
:54
18
:58
Model running time
No o
f fr
ee p
ark
ing p
laces
.
Over the given Area, during given Time Interval
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The model output: municipality’s view
Illegal parking
Revenues from legal parking
Type of parking Revenue/hour
On-street 1154
Parking Lot N 1353 2027
Parking Lot N 1401 632
Parking Lot N 1481 3014
Over a given Area, during a given Time Interval
Type of illegal parkingNumber of
cars
Overall places of a
given type
Fraction occupied
illegally
Red-White 232 240 0.967
Blue-White, no regional label 120 1400 0.086
Other illegal 25 28 0.893
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Cinema scenario (common destination) first and second arrival
Testing the model – minimal casesO
ccupation r
ate
Distance from common destination
Occupation r
ate
Abstract versus real-world road network
Distance from common destination
Occupation r
ate
1. The model properly simulates
theoretically simple cases
2. The outcomes of the abstract and
real cases do not differ significantly
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Real-world planning application (local change):
new parking lot in the Basel neighborhood
1300 m
680 m
Additional parking facility, dedicated to local residents, is provided within a neighborhood where parking demand exceeds supply.
Estimate the consequences of this intervention, if existent, taking into account the facility’s capacity.
32
1300 m
680 m
The scenario’s background:
At 17:00h 8700 places are occupied, 60% is occupied by residents and 20% by daytime visitors. The remaining 2200 parking places are free.
Between 17:00-21:00h, 1600 parking places are freed, while 5,100 residents and 550 visitors enter the area.
NBH2NBH1
Residents’ overnight (O) and end-of-day (E) demand for, and supply of, on-street parking places in NBH1, and NBH2
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Even 200 new parking facilities do not influence essentially parking search time
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Even 200 new parking facilities do not influence essentially the distance between the parking place and destination
35
The percentage of drivers who aim at destinations within NBH1 and
NBH2, and search for parking place for more than 10 minutes
0
10
20
30
40
50
60
0 50 100 150 200 250
Number of parking places (pp) at a new lot
Percen
tag
e o
f d
riv
ers
.
NBH1, changes within NBH1 NBH2, changes within NBH1
New parking facilities essentially influence the fraction of the long-searchers (more than 10 minutes)
36
From one large lot of 1000 parking places comparing to
four small lots of 250 parking places
1300 m
680 m
1300 m
680 m
400 - 450 250 - 300
Number of drivers who search for parking more than 10 minutes
37
1. One parking lot of the maximal possible capacity of 250 cars cannot essentially influence the parking situation in the area
2. The addition of the lots of half of this size at every 500x500m square
(about 500 parking places per km2) will essentially improve parking conditions of the residents.
3. The effectiveness of adding large parking lots of 500+ places is low. The majority of the residents will not consider them as improving the state of
the parking in “their” area.
Policy conclusions of the “local change” scenario
38
We consider the above results as the test of the model concept.
The results of current study seem much less predictable.
They aim at:
– Establishing the level of on-street pricing that
prevents cruising
– Optimization of enforcement measures
39
Questions?
