A Probabilistic Approach to Parking

Beneﬁts of Routing Instead of Spotting

Gabor Feher, Balazs Andras Lajtha and Akos Lovasz

Dept. of Telecommunication and Media Informatics,

Budapest University of Technology and Economics, Budapest, Hungary

Keywords:

Smart City, Parking, Parking Route, Parking Probability.

Abstract:

Urban parking is an important issue in all modern countries. Technological advances, with in-car sensors

and always connected smartphones have already paved the way to an ICT solution for this problem. However,

every attempt - including that of such a big companies, as Google - has failed to provide a suitable solution. So

far, the appeared solutions were centered around the notion of free parking spots. This approach does not take

into account the dynamics of the trafﬁc and the drivers outside of the system. Here we propose a fundamentally

different approach based on parking probabilities and parking routes. Our solution can truly reduce the time,

resource and environmental damage wasted on parking place hunting, while keeping the operational costs low

and the users satisﬁed.

1 INTRODUCTION

In cities of the developed countries vehicle owner-

ship per household is close to and may reach 1, and

decreases only slowly (Goodwin, 2012). In the big

cities, the cars cause urbanization problems, most sig-

niﬁcantly trafﬁc jams and parking. Diseases con-

nected to air pollution and the stress caused by the

transportation have severe impact on all other area

of human life. While shifting to the environment

friendly, green transportation, trafﬁc jams and related

issues seem to persist or even worsen due to speed

limits and reduction of road surface in favor of other

uses like urban vegetation or bicycle lanes. However,

the advances of the Information and Communication

Technology (ICT) in smart cities can create a cure for

the biggest problems.

One of the big problems of individual transporta-

tion is the problem of parking in frequented areas. In

those places, a great share of the trafﬁc is caused by

drivers seeking a parking spot. A survey from 2005

(Arnott et al., 2005) claims that in big cities of the

U.S., in every moment 30 percent of the drivers are

looking for parking spots. Each single car spends 7.8

minutes to ﬁnd a parking place in average. According

to a more recent survey (Dohler et al., 2011) the aver-

age parking time is 15 minutes in cities over 1 million

population in Europe. The average parking time is

13 minutes in Madrid, 15 minutes in Barcelona and

26 minutes in Granada. This also means that these

cars searching for parking place, produce 2300 tons

of CO2 per day.

2 RELATED WORKS

In the topic of parking in smart cities, there are al-

ready numerous research papers and application pub-

lished. We had a focus on Parking Guidance and

Information (PGI) systems. These systems aim to

solve the parking problem by providing information

to users about the amount of available parking places.

PGI systems are used for both parking lots and on-

street parking, while there are some signiﬁcant differ-

ences, the same basic concepts apply.

Every PGI system handles information in the form

of available parking spots. The information about

parking spots can be aggregated assigning a positive

integer to a parking lot or a street segment, or it can

be a ﬂag associated to each individual parking spot,

indicating it’s current state. Parking spots are well

deﬁned in parking lots and in some cities where in-

dividual parking meters or sensors are deployed for

each spot. However in many European cities park-

ing spots are organic, only the parking style (parallel,

perpendicular or angled) is regulated.

Feher G., Andras Lajtha B. and Lovasz A..

A Probabilistic Approach to Parking - Beneﬁts of Routing Instead of Spotting.

DOI: 10.5220/0005495400950100

In Proceedings of the 4th International Conference on Smart Cities and Green ICT Systems (SMARTGREENS-2015), pages 95-100

ISBN: 978-989-758-105-2

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

2.1 Information Collection

There are two ways to collect information about park-

ing spot availability. Either through infrastructure, or

through crowd sourcing.

Existing infrastructure can be used such as park-

ing meters (Caliskan et al., 2007) (Nawaz et al., 2013)

However using parking meters does not provide accu-

rate results, as in the case of the prepaid meters, usu-

ally the meters are overpaid and indicate occupancy

even when the car has left. On the other hand a mo-

bile phone based parking payment system can signal

the start and the end of the parking really accurately,

but lacks information about the position of the park-

ing car. Furthermore local residents may be entitled

to free parking, hence their parking events are not reg-

istered by any parking meters.

More accurate are the dedicated devices, like sen-

sors built into the road (Kessler, 2011), (Dohler et al.,

2011), or ultrasonic sensors in parking lots. These

devices provide exact measurements at a high instal-

lation and maintenance cost, an investment that local

authorities often choose not to make.

The other approach is to leverage user’s resources

and crowdsource the task of free spot detection.

Crowdsourcing can either rely on user input, or smart-

phone sensors (Chen et al., 2013). When drivers and

pedestrians are tasked to report parking spots, user

motivation becomes an important aspect. Compensat-

ing users for their input may lead to falsely reported

spots. On the other hand not providing external in-

centives results in freeriding that will reduce the per-

formance of the system. (Lan and Wang, 2013)

Cameras and radars can detect parking spots pass-

ing by them, but require special mounts or external

equipment. They also have a high error rate. Activity

sensors are more accurate, but can only detect parking

actions performed by the participating users (Lan and

Shih, 2014). Many solutions are based on different

types of sensors from gyroscopes through GPS posi-

tioning to WiFi signal strength analysis (Nawaz et al.,

2013), but all suffer from the same problem: when

application penetration is low, data about free parking

spaces will be sparse, and usability will be limited.

2.2 Information Processing

Information about an individual parking spot’s avail-

ability has a short expiration date. In frequented areas

parking spots do not last a minute, systems can only

work if future openings are predicted. The only accu-

rate way of predicting the opening of a parking spot

so far is through tracking the driver (Lan and Shih,

2014). When parking spot information is aggregated,

predictions can be made with more certainty from his-

torical measurements.

2.3 Information Dissemination

Information can be displayed to the users publicly or

personally. Moreover, personalized information can

be free or for sale.

In traditional Parking Information Systems (PIS)

roadside boards display the number of free spaces in

the parking lot or area. These systems have been ex-

tended with mobile applications that deliver the same

information to every user.

Many research work have the conclusion that PIS

are not effective, moreover in areas where there is a

shortage in parking spots, they cause severe trafﬁc

jams, when drivers try to get to the last places. This

realization focused research efforts on matching users

to parking spots, displaying the information of only a

single parking spot to each user. Wang, using simula-

tion (Wang and He, 2011) proves that the time needed

to park is shorter in the case of reserved parking than

it is with PGI systems.

Besides the great amount of research work there

are several smart phone applications aiming to solve

the parking problem. Most of these applications

failed and are already discontinued. Open Spot form

Google (Kincaid, 2010) is an often mentioned exam-

ple. While supported by Google, Open Spot ended

up closing because the users were not collaborative

enough and did not help others with signaling of the

free parking spots. The TakeMySpot application fol-

lowed the same path and suffered the same fate.

Despite the failures, newer and newer applica-

tions arise trying to establish themselves in the mar-

ket. Many have simpler functionality, just displaying

prices, zones, parking lots and not providing guidance

or real time information. Such applications are Best-

Parking or Parkopedia, covering many cities world-

wide.

3 THE ParkingRoutes SOLUTION

Investigating the recent works in the ﬁeld shows that

the current solutions are all based on the concept of

acquiring information of open spots. This information

is than either displayed publicly, or delivered to the

most suitable or highest bidding user. These works

address many aspects of the problem, starting from

the sensing of free spots to handling freeriding and

predicting the effect of low application penetration.

Even the deﬁnition of a parking spot raises research

questions.

SMARTGREENS2015-4thInternationalConferenceonSmartCitiesandGreenICTSystems

But this approach has many drawbacks. The col-

lection of free and busy information about given park-

ing spot is difﬁcult or costly. The most reliable sensor

based solutions requires large investments, while the

maintenance could be expensive as well.

In crowded areas in rush hour parking spots open

and get taken literally in seconds. A system signaling

free parking spots is useless: the driver cannot get to

the spot in time and ends up driving more than she

would have without the application.

In highly frequented areas, aggregated parking in-

formation will be misleading. The amount of avail-

able parking spots will oscillate between zero and

one, and the drivers would be discouraged, however

he could have had good chance to take a freshly

opened spot.

Instead of focusing on the quantity of discrete

parking spots, we base our solution on a probabilis-

tic nature of parking. We came up with an idea, to use

parking routes. This novel approach creates a work-

ing solution without the previously identiﬁed draw-

backs.

3.1 Parking Probabilities

Instead of focusing on the state of individual parking

spot, we introduce the notion of parking probability.

We assign parking probability to street segments: a

part of the street delimited by two intersections. Seg-

ments have directions, meaning that parking probabil-

ity might be different on the same street for cars trav-

eling in the opposite direction. Parking probability is

metric that indicates the probability of being able to

ﬁnd a parking spot on that segment. This metric is

much closer to how we perceive parking availability,

than a list of free parking spots.

The beneﬁt of using parking probability is that

while probability varies in time, it shows periodicity

as opposed to the availability of a single parking spot,

which is stochastic. Parking probability can be fore-

casted based on historical data supplemented by pas-

sive measurements. We will detail our proposed algo-

rithm for determining parking probability after intro-

ducing our implemented service.

3.2 Collecting Parking Probability

As every other solution, ours is also based on the sens-

ing of parking activity. While our implementation is

based on crowdsensing, it can utilize the data from

deployed sensory networks too.

3.3 Parking Route

We observed the way drivers search for parking

spaces and conducted personal interviews on the sub-

ject to ﬁnd patterns. People choose different strate-

gies for different scenarios. When going home, the

walking distance is very important: they are willing

to trade a couple of minutes in the evening to have the

car nearby when running late in the morning. They

end up circling the block for half an hour. Should they

have known it in advance they would have chosen dif-

ferently, and still they perform the same search each

day. When going to a regular event (play sports, go

to work) people devise a parking plan. They scout ar-

eas that they expect to be less crowded, maybe further

from the target, but with higher chance of an avail-

able parking spot. When people go to a target in an

unknown area, they usually pass by their destination,

and start looking for a parking spot afterwards. But

instead of making tight loops as in the ﬁrst scenario,

they tend to map the area, widening the search un-

til a suitable spot is found. Parking strategies involve

a utility function that trades time spent cruising for

a parking space for walking distance from the park-

ing spot to the destination and some knowledge about

parking availability.

While showing the parking probability might help

the user to make better navigating decisions, evaluat-

ing the utility function for different possible routes is

tricky, especially when users have to deal with proba-

bilities. Our solution not only provides the map of es-

timated parking probabilities, but also advises a route

for parking.

For each parking segment s, a walking cost c

calculated to the target. Than based on parking prob-

abilities q

, the location of the user and her target,

our system recommends a parking route. A park-

ing route is a continuous path p composed of park-

ing segments each with an indication for parking or

for travel. Travel is indicating a segment that the

user should pass in order to reach areas more suit-

able for parking. When driving through a segment

labeled for parking the user has to take advantage

of the ﬁrst parking opportunity. Only segments in

walking

vicinity of the target can be marked for park-

ing: (c

< B

walking

p = (s

, s

, . . . , s

l(p)

) (1)

Each parking route guaranties that the probabil-

ity of ﬁnding a parking spot on the route is greater

than 1 − ε, and parking route’s total length is below

driving

AProbabilisticApproachtoParking-BenefitsofRoutingInsteadofSpotting

∑

s∈p

≤ B

driving

(2)

∏

s∈p

(1 − q

) ≤ ε (3)

It is important to note that the parking route is

not the shortest path to a good parking space or area.

While strange at ﬁrst, it is common that a parking

route does not reach the user’s destination.

There might be no parking route for the given tar-

get and location, or there might be many. When mul-

tiple parking routes are present, they are ranked based

on the cost function w(p) provided by the user. For

the sake of simplicity, we used the linear combina-

tion of walking distance and driving distance, with the

user preference, a being the coefﬁcient for walking.

w(p) =

l(p)

∑

i=1

i−1

∏

j=1



1 − q



+ a

∑

j=1

(4)

When searching for the best route, we are mini-

mizing this cost function.

min

p ∈ P

w(p) (5)

When searching for the best parking route, we as-

sume that we know the actual parking probability for

every street segment of the target area.

The search for suitable routes consists of two

phases. In the ﬁrst phase maximal routes are enu-

merated. A maximal route is a route that’s length is

driving

and the parking probability along the route is

more than 1 − ε. A maximal route can contain the

same segments several times. To ﬁnd all maximal

routes, we use a breadth ﬁrst search.

When a route is found a second search is per-

formed to ﬁnd the segments marked for parking and

for travel. Each combination is considered and the

parking probability is evaluated. If the parking prob-

ability for the combination is above 1 − ε, the cost

function is evaluated.

It is easy to see that even the number of possi-

ble routes increases exponentially with B

driving

, with

an exponent between two and three depending on the

topology of the given area, and the parking / travel

segment determination has is exponential in length

too.

As many path had similar cost, it is not crucial

to ﬁnd the optimal solution. For the second prob-

lem: ﬁnding the parking and traveling segments of a

given route a greedy algorithm produced good results.

Adding the segments in order of their evaluated cost

until the desired overall probability is reached proved

to a good approximation.

To reduce the number of routes to evaluate saving

memory and runtime, we implemented a naive heuris-

tic to restrict the search ﬁeld. We assigned weights to

each segment, depending on their distance to the des-

tination and parking probability. The longer the route

was the less likely the algorithm chose a segment with

small weight. This reduced the exponent, keeping the

problem space smaller.

3.4 Estimating Parking Probability

The practical interpretation of parking probability is

the ratio of successful parking attempts on a segment,

divided by the number of vehicles traveling through

that segment with the intent of ﬁnding a parking spot.

Hence to determine the parking probability on a given

segment at a given time, these two numbers have to be

measured or estimated.

When we propose a parking route to a driver, it

is expected that she follows the route and attempts to

park on the suggested segments. So a driver follow-

ing the parking route can be considered a driver look-

ing for a parking spot. If the driver parks on a seg-

ment, she will increase the number successful parking

events. Hence we can measure parking probability by

observing our users. Higher the application’s penetra-

tion, the higher the accuracy of this measurement.

The paradox of this approach is that not the open-

ing but the taking of a parking spot will increase park-

ing probability on the segment.

It is also important to consider the temporal prop-

erties of parking probability. In different zones - res-

idential, industrial, commercial - we observed differ-

ent ﬂuctuations of the probability, ranging from mul-

tiple vacant spots to full load with several cars cir-

cling for parking. On the other hand parking proba-

bility seems to be a periodic function, with daily and

weekly cycles. Hence it is often better to estimate

parking probability based on historical measurements

than on recent ones. To handle this phenomenon we

divided time to 15 minute long segments. We register

measurements for these segments.

As the periodic nature for each segment may be

different, the weight in the prediction of the recent

measurement and the daily, weekly, monthly and

yearly periods should be determined by examining the

correlation between measured values. Also as current

measurements accumulate, the effect of past measure-

ments should be decreased.

3.5 Implementation

Our implementation consists of a database containing

the parking probabilities, an event database, a predic-

SMARTGREENS2015-4thInternationalConferenceonSmartCitiesandGreenICTSystems

Smartphone ParkingRoute service

Display

Parking

sensor

module

Route

planner

Event

database

Probability

database

Prediction

engine

Sensed

events

Street section

probabilities

Historical data

Figure 1: ParkingRoutes architecture.

tion service and a mobile client. Their connections

are shown on Figure 1.

In order to get the required topology of the cities,

we process the Open Street Map topology, and derive

an oriented graph consisting of segments.

The mobile client is responsible for capturing

parking events. Parking data is collected in the event

database, and periodically processed by the prediction

service to update the probability database. When the

user wants to park, the mobile client queries the prob-

ability database for actual information. Than the route

search is done on the mobile device, and the result is

presented to the user.

Screenshots with navigations can be seen on Fig-

ure 2. The red car icon shows the actual position of

the car, the orange target icon is the desired parking

location and the dashed line is the parking route. The

dashed line can have different sections with differ-

ent colors. The dark blue section is a shortest route

navigation to the parking zone. We do not plan any

parking on this route. At the end of this section, the

car enters to the area where the smartphone made the

parking route from the entry point to the destination.

It is also possible, that parking is not recommended on

some sections of the parking route, as there are better

sections for the stop. These street sections are colored

to light blue.

Besides displaying the parking route, the parking

probabilities for the street sections around the desired

parking location are also displayed. The color key:

green, yellow, orange and red shows the parking prob-

ability for the given section. Street sections in green

color have high parking probabilities, while the red

color means hardly any chance for parking. This gives

the user the ability to evaluate the suggested route and

in turn increase trust in the system.

The parking events, when the car is stopped at a

place or when the car leaves the parking spot is sig-

naled to the ParkingRoutes server together with the

GPS position of the spot. On the server side the park-

ing probabilities are adjusted based on these events.

3.6 Feasibility Studies

Since all the parking route computations are running

on the smartphone, we investigated the resource de-

mand of the routing algorithms, whether it is suitable

for smartphones or not.

We made test in two different scenarios. The

downtown scenario is a scenario where the streets are

full of parking cars, and the parking probability is

very low. In contrast, the other tested scenario is the

suburb scenario, which has plenty of spaces on the

streets, so the parking probability is generally high.

In the two scenarios the radius of the parking

search area was set to 1000 meter, the parking route

calculation worked with those street sections that

were within this area. The maximum parking route

length was set to 1000 meter.

Figure 2 displays the two scenarios, and the se-

lected parking locations. The position of the car and

the position of the desired parking place were ﬁxed

during the measurements.

Figure 2: The inner city and the suburb test scenarios.

We measured two metrics. The memory consump-

tion and the running time of the algorithm. For the

test we used a mid range Nexus 4 device with An-

droid 4.1 operating system. The memory consump-

tion was calculated by the algorithm itself. When the

parking route search algorithm initiated a new recur-

sive search from the given state, we allocated a mem-

ory block for that. The metric counted the maximum

number of these blocks, which existed at the same

time, and not the total number of allocations. With

the runtime metric we measured the total execution

time of the parking route planning algorithm, exclud-

ing the street section data downloading.

In order to be able to compare the results to other

values, we measured a shortest path algorithm as

well. This algorithm creates the shortest route from

the car position to the target. This is not a parking

AProbabilisticApproachtoParking-BenefitsofRoutingInsteadofSpotting

route.

As neither the car and target positions, nor the

street section probability database was changed dur-

ing the tests, therefore subsequent runs on the given

scenario produced always the same results.

Figure 3 displays the measurement results for the

downtown and the suburb scenario. As it can be seen

the optimal solution is slow and resource demanding

compared to the other two algorithms. However, the

worst case 273 ms running time and the 70k allocated

memory blocks still makes this algorithm a feasible

choice for the users. The simple heuristic algorithm

created 62 memory blocks and ended within 50 ms

in the challenging downtown scenario. As it was

expected, the algorithms are faster and require less

memory allocations in the suburb area, as the park-

ing possibility is high enough on shorter routes. The

optimal algorithm runs for 46 ms, and allocates 5537

memory blocks, while the simple heuristic algorithm

takes 17 ms and 47 memory blocks.

Figure 3: Resource allocation at the downtown and suburb

scenario.

From the measurements we can see, that parking

route searching in a reasonable sized areas, with a rea-

sonable sized parking routes is feasible even with the

slowest and most resource hungry optimal algorithm.

The search is longer in areas where the parking possi-

bility is low. Using the simple heuristic approach, the

search is faster and requires less memory. For old de-

vices with limited CPU and memory capabilities, this

searching algorithm suits better than the optimal one.

4 CONCLUSION

The dawn of the smartphones brought new opportuni-

ties to solving the parking problem. Many proposed

applications failed in early stages, and til this day

there is no working solution for urban parking. The

parking spot based approach taken by others cannot

cope with low usage, as drivers outside of the sys-

tem render the sparse available information obsolete

by the time it is advertised.

We took a new approach that is not based on park-

ing spot availability, but rather on the probability of

parking on a given street segment. Parking probabil-

ity is fundamentally different from individual parking

spots, and as such we had to rethink and redesign ev-

ery step of the parking guidance, from the deﬁnition

of the information through data collection and data

processing to the way information is presented to the

user.

We answered all the design questions and imple-

mented a system that demonstrates the feasibility of

our idea. We run simulations to validate our solution.

The initial results look promising, however more thor-

ough trafﬁc simulations are needed.

REFERENCES

Arnott, R., Rave, T., and Schb, R. (2005). Alleviating Urban

Trafﬁc Congestion, volume 1 of MIT Press Books. The

MIT Press.

Caliskan, M., Barthels, A., Scheuermann, B., and Mauve,

M. (2007). Predicting parking lot occupancy in ve-

hicular ad hoc networks. In Vehicular Technology

Conference, 2007. VTC2007-Spring. IEEE 65th, page

277281.

Chen, X., Santos-Neto, E., and Ripeanu, M. (2013). Smart

parking by the COIN. In Proceedings of the Third

ACM International Symposium on Design and Anal-

ysis of Intelligent Vehicular Networks and Applica-

tions, DIVANet ’13, page 109114, New York, NY,

USA. ACM.

Dohler, M., Vilajosana, I., Vilajosana, X., and LLosa, J.

(2011). Smart cities: An action plan. In Proceedings

of Barcelona Smart Cities Congress.

Goodwin, P. (2012). Peak travel, peak car and the future of

mobility.

Kessler, S. (2011). How Smarter Parking Technology Will

Reduce Trafﬁc Congestion.

Kincaid, J. (2010). Googles open spot makes parking a

breeze, assuming everyone turns into a good samar-

itan.

Lan, K.-C. and Shih, W.-Y. (2014). An intelligent driver lo-

cation system for smart parking. Expert Systems with

Applications, 41(5):2443–2456.

Lan, K. C. and Wang, H. Y. (2013). On providing incen-

tives to collect road trafﬁc information. In Interna-

tional wireless communications & mobile computing

conference (IWCMC13).

Nawaz, S., Efstratiou, C., and Mascolo, C. (2013). Park-

Sense: a smartphone based sensing system for on-

street parking. In Proceedings of the 19th annual in-

ternational conference on Mobile computing & net-

working, page 7586.

Wang, H. and He, W. (2011). A reservation-based smart

parking system. In Computer Communications Work-

shops (INFOCOM WKSHPS), 2011 IEEE Conference

on, page 690695.

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