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A Parking Slot Allocation Framework Based on
Virtual Voting and Adaptive Pricing Algorithm
Vikas Hassija, Vikas Saxena, Vinay Chamola, and F. Richard Yu, Fellow, IEEE
Abstract—Parking lot allocation problem has received much
attention in recent years. There have been various works in
the literature that target the parking slot allocation problem.
However, most of these works use algorithms that run on cen-
tralized servers and are based on some predictions on historical
data. Due to the dynamic nature of vehicular networks, the
accuracy of such prediction models is not high which ends up
in a chaotic situation for the parking lot owners as well as the
vehicle owners. Therefore, a distributed Parking slot Allocation
Framework based on Adaptive Pricing Algorithm and Virtual
Voting is proposed in this paper. The proposed model is based
on virtual voting and hashgraph consensus algorithm. Using the
model, all users and parking lot owners can easily come to
consensus finality about the allocation of a parking slot with
the use of minimal bandwidth. The proposed model provides
a fair, fast and cost-optimal parking slot allocation method.
The perfect ordering of allocation requests is also maintained
based on consensus timestamp. Further, an adaptive pricing
model is proposed to enhance the overall revenue of the parking
lot owners and comfort of the users. The proposed model is
deterministic and can reduce the average parking cost and
time. Performance evaluations reveal that the proposed model
outperforms its counterparts in terms of accurate parking slot
allocation, reduced cost and parking lot resource utilization.
Index Terms—Directed Acyclic Graph, parking lot, parking
allocation, distributed applications, consensus finality, smart
parking, blockchain
I. INTRODUCTION
The number of motor vehicles is rapidly increasing world-
wide and therefore the parking problem is attracting a lot of
attention. It becomes very difficult to find a vacant parking
slot in a densely populated area especially during peak hours.
Drivers keep on circling the complete parking lot to find a
single empty slot. Leaving the vehicle in an unauthorized space
has its own security and legal issues. At times people avoid
travelling by their private vehicles and prefer the discomfort of
traveling by public vehicles just to avoid the problems faced in
Manuscript received July 14, 2019; revised Sep 24, 2019; revised Nov 28,
2019, accepted Feb 24, 2020. This work was supported in part by the Natural
Sciences and Engineering Research Council of Canada (NSERC). The review
of this article was coordinated by Dr Zhanyu Ma. (Corresponding Author: F.
Richard Yu
Vikas Hassija, and Vikas Saxena are with the Department of Computer
Science and IT, JIIT, Noida, India 201304 (e-mail: vikas.hassija@jiit.ac.in,
vikas.saxena@jiit.ac.in).
Vinay Chamola is with the Department of Electrical and Electron-
ics Engineering, BITS-Pilani, Pilani Campus, India 333031 (e-mail:
vinay.chamola@pilani.bits-pilani.ac.in).
F. Richard Yu, Fellow, IEEE is with the Department of Systems and
Computer Engineering, Carleton University, Ottawa, ON K1S 5B6, Canada
(e-mail: richard yu@carleton.ca).
Digital Object Identifier: XXXXXXXXXXXX
parking their vehicles [1]. Different centralized agencies take
charge of the parking lots and charge heavily in order to allot
a parking slot to the users. Here centralized agency refers to
some third party contractors that are given charge of parking
slot allocation to the users.
There have been various works in recent years to improve
the problem of parking slot allocation. However, most of
these works are based on the predictions on historical data.
With the increase of the number of vehicles, the nature of
vehicular network is also getting highly dynamic, and therefore
the prediction models fail to give high accuracy most of the
times. The dynamic nature of vehicular network refers to the
difficulty of predicting the number of parking requests in a
particular area at a particular time.
There are various Internet of Things (IoT) applications being
developed in order to direct the vehicles towards an empty
parking slot [2]. Although such applications appear to solve
the problem to some extent, they involve a lot of infrastructure
changes, sensor deployments, data collection, etc., which ends
up in enormous expenditures. The expenditures are in the form
of installation expenditure and various maintenance related
expenditures. Furthermore, these applications are limited to the
parking lot premises where these are installed [3]. For instance,
there is no provisioning to inform or warn an approaching
vehicle about the saturation of parking slots in a particular
zone and redirecting the user to another parking zone. All
these solutions are limited to the particular area and do not
provide an end-to-end parking allotment solution to the users.
Some recent works have suggested the use of vehicular
adhoc networks (VANETs) to connect the vehicles together
to solve the parking problem. Vehicles can communicate with
each other about the status of parking lot saturation. Vehicles
can also act as hops and can further transmit the information
to other vehicles. Although theoretically such a model may
appear to solve the problem, it is not feasible to practically
implement it. Firstly, there is no motivation for the vehicles
to share the information with other vehicles. Secondly, the
information shared is always very probabilistic and there is no
consensus mechanism that can be trusted upon for the shared
information.
Due to the centralized nature of parking slot allocation,
there is no provision for small garages or open parking spaces
to get registered and be used for parking vehicles by other
people [4]. The distributed platform proposed in this paper can
help anyone register a space to be used for parking through
which he can earn monetary benefits [5]. The users looking for
parking space can also choose the nearest available space and
will not have to drive far from the required destination just to
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park the vehicle. The system will eventually be cost-optimal
both for the users and the parking lot owners. This will also
reduce the monopoly of few big parking lot owners and will
prevent them from charging high price for parking vehicles.
A. Motivation
This work is motivated with the need of having a platform
or a framework that can help people easily book a slot to park
their vehicle before they actually reach the destination. They
do not have to search for a slot in a big parking zone and can
directly move to the allotted slot and park their vehicle at the
allotted price.
According to the recent IRNIX 2018 Global Traffic Score-
card (GTS), the average loss of time in finding a parking slot
per driver is 44 hours annually in United Kingdom (UK) [6].
In terms of monetary losses the figures come out to be 33
billion USD per year in 2018 in the U.S.A [6]. 95.7 billion
USD were spent in 2018 in the form of fines for parking the
vehicles in unauthorized places in the U.S.A [7]. Apart from
the losses related to time and money, there are various other
non-economic and health related loses reported in the IRNIX
2018 survey report for UK and US [6]. 69% of female drivers
in UK have reported stress and anxiety issues due to not being
able to find a suitable parking slot [7]. 40% of the people in
UK have reported the issue of missing an important meeting or
an appointment with a doctor due to parking issues [7]. There
also have been cases of fight and arguments with fellow drivers
due to frustration caused by lack of suitable parking space.
These statistics show that with the increase in the number of
vehicles, parking problem is becoming more intense in terms
of time, money, environment, health and social relationships.
Therefore, it is highly imperative to improve the basic
architecture of the parking system and to make is completely
distributed, fair, secure and cost-optimal. The main contribu-
tions of this work are as follows:
1. A framework for distributed parking slot allocation sys-
tem based on directed acyclic graph is proposed.
2. The framework gives cost-optimal parking slot allocation
to the users based on the current demand of parking in a
particular area.
3. It gives monetary opportunity for small garages and open
parking spaces to get registered and to be used by other
users for parking vehicles.
4. It gives the user facility to reserve parking slot before
reaching the destination with consensus finality, thereby
preventing any unwanted fights or arguments among the
drivers.
5. Pre-notification to the users is case of parking zone
saturation is incorporated to avoid unwanted jamming or
queues outside the parking zones.
B. Organization
The rest of this paper is organized as follows. The recent
works related to smart parking and parking slot scheduling
are presented in Section II. Some background information
about the distributed ledger technologies (DLTs) and directed
acyclic graph (DAG) technology is presented in Section III.
Section IV presents the network and system model for the
proposed framework. The adaptive pricing algorithm for price
formulation strategy for a parking slot is discussed in section
V. Section VI presents the assignment model for final parking
slot allocation to the user. In Section VII the simulation results
are presented and are compared with the existing models for
parking allocation. Section VIII finally concludes the paper.
II. RE LATE D WOR KS
In this section we present all the existing works in the
direction of parking lot scheduling and allocation. For a better
classification of all the related work, the following sub-sections
explain the works that use different strategies and technologies
to solve the parking problem. We also present the basic
algorithms used in these works, their advantages as well as
their limitations. Table I summarizes the main contributions
of the previous works in terms of improving the system of
parking scheduling and allocation.
A. Related work based on IoT
Authors of [8] have added a parking agent in the smart
parking system. The agent is responsible to analyze the traffic
data and allot parking slots to different users accordingly.
Various works make use of extensive IoT data from IoT
sensors deployed in parking zones and analyze the data to
provide parking information to users [9].
Wei Shao et al. [10] and Jae Kyu Suhr et al. [11] have
proposed ways to manage parking violation issues using sensor
data. Sensors are used to send the data of the vehicles violating
the parking rules to the concerned authorities. The problem
with IoT data based approaches is that, the data is extensive
and the computation latency in response time would end up
into misreporting of the data. Also, the get high accuracy, a
lot of infrastructure changes is required especially in terms of
sensor installations.
B. Related work based on Machine-Learning
Various machine learning based approaches have been ex-
plored to make the parking scheduling system better [16], [13].
The predictive algorithms do not support the dynamic nature
of vehicular networks. Authors of [19] have also proposed the
use of Around-view Monitoring (AVM) algorithm to search for
the free slots in a parking zone. Tooraj Rajabioun et al. [20]
have proposed the use of multivariate auto regressive model
to study the nature of the parking availability data in a big
city. The model takes into account both temporal and spatial
correlations of parking availability.
Lin Zhang et al. [21] have proposed a deep convolu-
tional neural network (DCNN)-based parking-slot detection
approach. The empty parking slots are identified based on
image processing techniques. These techniques depend on
historical data and the predictions are made based on the data.
As discussed, the parking slot should be allocated to a user
with high probability and depending on the predictions from
historical data is not appropriate. A Smart Parking Algorithm
(SPA) is proposed in [17] that predicts the estimated parking
3
TABLE I: Related Work on Parking Lot Allocation
Year Author Contributions
2016 Xueshi Hou et al. [12] Fog computing based solutions to compute the parking data at the sensor level to reduce latency.
2017 Ching-Chun Huang et al. [13] Vacant Parking Space Detection Based on a Multi layer Inference Framework
2017 Ricard Garra et al. [14] Pay-by-phone parking system in a privacy-preserving way to prevent leakage and misuse of user data.
2018 Samy Faddel et al. [15] Formulation of a bilayer Pareto optimization problem to optimally allocate and size an EV parking garage.
2018 Cristian Roman et al. [16] Machile learning model for detecting on-street parking spaces in smart cities.
2018 Wei shao et al. [10] Methods to manage parking violation issues using sensor data.
2019 Jiazao Lin et al. [17] Smart Parking Algorithm Based on Driver Behavior and Parking Traffic Predictions.
2019 Nir Fulman et al. [18] Dynamic pricing model for parking slots based on demand supply ratio for autonomous vehicles.
traffic in different areas and different times of the day based
on driver behavior. Based on the prediction outcomes, the
users are directed to different parking slots. The limitation with
the machine-learning based approaches is that, most of these
approaches depend on the predictions from the historical data.
Due to the dynamic nature of vehicular networks, the accuracy
of such prediction models is not high in real life scenarios.
C. Related work based on slot reservation
A privacy-preserving reservation based scheme for parking
autonomous vehicles is presented in [22]. The security and
privacy issues in automated parking systems are addressed
to prevent double-reservation attacks. The concept of zero-
knowledge proof and proxy re-signature is used to secure the
identity of the users. Authors of [14] have introduced a pay-by-
phone parking system in a privacy-preserving way. The system
proposed by them prevents the user’s data from getting leaked
and misused.
FU Jiabin et al. [23] and Yanfeng Geng et al. [24] have
presented a reservation based parking lot allocation model.
The issue with reservation based models is that the empty
space cannot be used by other drivers as it has been reserved
for a user who may or may not come. Sensor based data and
a parking management system is used to allocate parking lot
to the users.
D. Related work based on Fog Computing
Authors of [12] have proposed fog computing based so-
lutions to compute the parking data at the sensor itself and
to avoid latency in response time. Rongxing Lu et al. [25]
present a Vehicular ad hoc Network (VANET) based vehicular
communication model to search for a vacant parking lot in a
large zone. The vehicles communicate with each other using
fog nodes to inform about the availability of a parking space.
In such schemes different drivers get information about the
same parking space. Only the driver who reaches the parking
lot first gets the space and others have to choose for another
space.
E. Related work based on Dynamic-pricing
The Authors of [18] propose dynamic pricing model for
parking slot allotment for autonomous and human-driven
vehicles, based on supply and demand. The limitation of the
model is that it is focusing only on the limited set of suppliers
i.e., parking lots. There is no provision for the small garages
or open spaces to participate in the model. Furthermore, the
model is running on a centralized server having its own
limitations in terms of scalability and throughput.
F. Highlights of proposed model
Although there are several works in this direction, they are
mostly based on either historical data prediction or information
from sensor data. Furthermore, all these algorithms run on
centralized servers. Sensor data based approaches are quite
expensive and prediction based approaches are probabilistic.
Over and above, there is no method where the small garages
and open parking spaces can register themselves to be used by
the drivers. This calls the need for a distributed framework for
parking system that is cost-optimal, fair, secure, fast and ac-
curate. This paper proposes an end-to-end distributed parking
application that aims at maximizing the comfort level for the
end user and revenue of the parking lot owners simultaneously.
III. DIS TR IBUTED PARKING LOT SCHEDULING
Current parking lot allocation or scheduling majorly relies
on handful of centralized private agencies or the third party
contractors. The allocation algorithm is mainly the blind search
process, where the drivers are fed into a huge parking zone and
are left free to blindly search for a free slot. The centralized
agencies have created a monopoly in the parking industry and
charge heavy prices even for a small duration of parking. All
the more, the small garages or open free spaces have no way
to be used as a parking zone by the common public.
Using distributed parking lot scheduling algorithm, all users,
parking lot owners, small garages, free open parking space
owners, etc., can be the part of a same distributed network. The
users can securely request for a reservation of a parking slot
by submitting a transaction on a directed acyclic graph (DAG)
and the owners can submit the best possible slots available for
the users. DLTs are the distributed ledgers that keep record of
all the transactions taking place in the network. There is no
centralized authority involved and the users in the network
maintain the network. The task of trust development in the
network is carried out using different consensus algorithms.
Bitcoin is the first DLT that was introduced in 2008 and is run-
ning securely since then. There have been various consensus
algorithms proposed in the literature to improve the efficiency,
consensus time and throughput of the transactions. Some of the
famous consensus algorithms include proof of work (PoW),
proof of stake (poS), proof of burn (PoB), hashgrpah, etc.
Various smart contract can be further deployed on these DLTs
to make them more reliable and robust. Smart contracts are
4
the sort of self executable lines of code that act as agreements
between the parties involved in transactions.
The adaptive pricing model, that is deployed on the hash-
graph DLT as a smart contract can further help in deciding
the appropriate price for the parking lot based on the demand
supply ratio. This would help in maximizing the profit of both
the users and the parking lot (PL) owners. A smart agent
is introduced in the form of a smart contract, that does the
task of analysis and provides the user with the set of best
parking solution, rather than flooding the user with all the
owner responses.
A. Digital Identity
A distributed network of drivers, Parking lot owners and
other small garage owners or free space owners is proposed
in this work. As soon as a user wishes to enter the network,
a set of private and public key is generated for the user using
an elliptic curve digital signature application (ECDSA) [26],
[27]. A random number generator is used to create a large
random number to be used as the private key d. The public
key is computed using the random private key using equation
Q(X, y) = d×G(X, y)through point multiplication. Here
Q(x, y)acts as the public key of the user and G(x, y)is
the domain parameter. The set of keys are used for all the
transactions or communication taking place between different
nodes in the network. The issuing party needs to digitally sign
the transaction using the private key and all other intended
nodes can verify the transaction using the public key of the
signing authority [28]. This prevents the problem of non
repudiation and thereby solves the uncertainty of actually
getting the allotted parking slot.
Once the user gets the set of keys, he can request for a
parking lot by filling the basic details including area, duration
of parking, time to reach and maximum price that the user is
willing to pay. The above mentioned details will be packed
in a transaction container and will be flooded in the network
of users in the form of a gossip event. The event architecture
is presented in Fig. 1. The users will “gossip the gossip” and
the event will reach all the network nodes exponentially. The
gossip protocol is used here for communication as it requires
very less bandwidth to gossip the DAG created as compared
to sending the signed transaction to all the nodes. The detailed
process of parking lot allocation and scheduling using gossip
protocol is explained in the next section.
B. Consensus Algorithm
The major part of any distributed ledger technology (DLT)
or a distributed application (Dapp) is the consensus algorithms
[29], [30]. In a distributed application there is no centralized
agency to bring all the involved parties to a single agreement.
The consensus algorithms play an important role in Dapps
to bring a level of trust among the untrusted parties in the
network. Various commonly used consensus algorithms for a
closed group of member nodes like Raft and Paxos, make use
of an appointed leader to reach a consensus. These algorithms
are highly vulnerable to DOS attacks and infinite delays, even
if one node in the network is infected by an attacker [31].
Fig. 1: Architecture of event created in DAG.
The POW (proof-of-work) algorithm used in bitcoin tries
to overcome all these above-mentioned issues to reach a
consensus in an open distributed network [32], [33]. In POW
the node that is able to solve a random mathematical puzzle
in minimum time is allowed to add the blocks [2]. Although,
the POW process avoids the issue of a node being byzantine,
still there are various issues involved with the generic POW
algorithm. The first issue is that the algorithm involves solving
mathematical puzzles that introduces an extra latency in block
addition and increases the power consumption of the entire
process [34]. Secondly, the POW algorithm doesn’t ensure
consensus finality, and as a result, the transaction added to
a block today may get pruned in future due to being the
fork in the chain. Over and above that, the POW algorithm
doesn’t consider or maintain the perfect ordering of the
transactions. There is no relation between the order in which
the transactions enter the network and the order in which they
are executed. In a system like bitcoin the perfect ordering of
transactions might not be required [35], [36]. However, in a
parking allocation and scheduling system, the perfect ordering
needs to be maintained. The parking slots are limited and the
users are much more than the slots. Therefore, it is imperative
to consider the order in which the requests arrive and to allot
the slots accordingly.
Considering all the above mentioned issues related to
generic consensus algorithm, a DAG based consensus algo-
rithm is proposed [37], [38]. The proposed algorithm provides
all the benefits of blockchain [39], [40] and at the same time
can be very fast, deterministic and avoids any valid block
from becoming a fork [41]. Every miner can mine new blocks
without spending high computational power and all the blocks
5
mined are added to the main chain [42]. In the proposed
algorithm, the concept of virtual voting is used [43]. This
avoids sending any vote or message over the network, and
hence there are no overhead messages.
C. Gossip Protocol and Virtual Voting
We use a gossip protocol to spread the information between
the members of the network. Every member tells everything
that is known to him to all other members, and therefore in
very less time, everyone in the network comes to know about
any information known to anyone in the network. Gossip sync
is a state where every participating member is aware of the
information shared between two members. We store the history
of all these events as a Directed Acyclic Graph (DAG) that
grows with time. Each member of the network has a copy of
the DAG locally, and it goes on updating it as more events
are created. The local copies of all the members are always
consistent [44], [45].
We make use of the concept of virtual voting to reach a
secure consensus among the member nodes for the ordering
of the parking slot allocation. Although voting is the most
effective method to reach a consensus in a distributed envi-
ronment and to identify the byzantine nodes, it involves the
overhead of bandwidth required to send votes. Using virtual
voting, we achieve the benefits of voting mechanism, without
using any extra bandwidth for voting. There is no physical
message transfer for votes. Every member calculates a virtual
vote for other members by applying a predefined virtual voting
algorithm on the local copy of DAG. Apart from saving
bandwidth, virtual voting is more secure than physical voting,
because, the votes are calculated based on an algorithm [46].
Even if a node becomes faulty, still the vote calculated for
that node by other nodes will not be faulty. The byzantine
agreement is guaranteed with the virtual voting algorithm.
Virtual voting happens in following 3 steps namely divide
round, decide fame, and find order [47]. Figure. 2 shows the
process of round division based on the gossip protocol between
four network nodes.
IV. NET WO RK MO DE L AN D PROP OS ED FRAMEWORK
We design a network model with multiple number of users,
parking lot owners and small garages or free parking space
owners. The network nodes are basically divided into two
categories i.e., users and parking lot providers. The set of users
is denoted by ΓU= (Ui|i∈N),N={0,1,2, . . . , N }). The
set of service providers is denoted by ΓS= (Sj|j∈M),M=
{0,1,2, . . . , M }while the number of parking slots is denoted
by ΓP= (Pk|k∈Z),Z={0,1,2, . . . , Z}.
Any user can become a part of the network and can add
a request for a parking lot giving the basic information. The
user is required to submit the destination, expected duration
of parking and time of arrival. Let dlat and dlon be the
latitude and longitude of the user’s destination, Edur be the
expected duration for which the user plans to park the vehicle
and Atbe the arrival time. In order to prevent the issues
related to unused reserved parking slots, we allot a parking
slot to a user with a constraint of At< Ct+ 30, where Ct
B6
D4
C3
B3 D3
C2
B2
D6
C1B1A1
A3
A3
1
2
34
D1
D2
Time
Fig. 2: Dividing all the Gossip Messages into Rounds.
is the current time. If the user does not arrive the parking
lot within 30 minutes of reservation, then the reservation is
held cancelled and the slot is allotted to another user. This
also prevents unwanted or extra slot reservations by the users.
Users will only choose the appropriate slot and will try to
reach the slot in time. Using DAG technique, users are having
the consensus finality that they will surely get the booked
slot and therefore there is no motivation to book extra slots.
The lot selection decision is optimized by the smart contract
and the final optimized lot or a list of final optimized slots
is presented to the user. Smart contract is a self executable
lines of code that runs on a distributed ledger. This prevents
the user getting flooded with the unwanted requests from the
PL owners [48]. The PL owners can submit their proposal
to the smart contract, but only the appropriate proposals that
meet the user’s expectations are forwarded to the user. Users
can set the weight for the preferences as filters and based on
that the suitable slots can be recommended. Some users might
prefer a lower cost over the distance of parking lot from their
destination and some might be ready to pay a little higher price
to get a parking slot nearest to their destination. Some users
6
Fig. 3: Steps involved in the proposed model for parking slot allocation.
might also be sensitive to the total capacity of the parking lot
and might prefer a lot with more number of total slots. Let
Wd,Wtand Wpbe the weight for the distance of lot from
the destination, total number of slots and the price offered
for parking respectively. Changing the values of these weights
will change the priority of the optimal solution presented to
the user.
The model does not keep the parking prices to be fixed
[49]. The prices are dynamic and are kept within the allowed
range by the government authorities in an area [50], [51].
The dynamic nature of price depends on various factors
such as number of free slots left in a parking lot, expected
duration of parking by the user, day of the week, time of
the day and festival or non-festival day [52]. The adaptive
pricing algorithm explained in next section takes care of all
these parameters and calculates an optimal price for parking
lot [53]. Once an optimal price is calculated for all the
neighbouring parking lots, to find out the best-suited parking
lot for a particular user, we make use of the Hungarian
algorithm [54], [55]. There are various users, parking lots and
specific requirements of the users. Mapping multiple number
of users to the appropriate parking lot requires an assignment
model. Hungarian algorithm solves the assignment problem
in polynomial time [56]. Most of the existing literature used
Hungarian model to solve the assignment model [57]. The
proposed model takes care that only one slot is assigned to
each user and the overall cost of parking is minimized. Figure.
3 shows the steps involved in the adaptive price calculation
and parking slot allocation to a user. The details of the steps
followed in the figure can be summarized as follows.
1. A hashgraph network is created on hedera platform and
all the parking requests from the users are recorded on it.
The requests include all the required parameters such as
destination, expected duration of parking, time of arrival,
cost weight, distance weight etc.
2. The hashgraph consensus algorithm is run for the created
hashgraph. The output of the algorithm gives the consen-
sus timestamp that is agreed upon by all the nodes in the
network. Nodes here refer to the users and parking lot
owners.
3. The smart contract is deployed on the hashgraph. The
smart contract consists of the details of the adaptive
pricing algorithm discussed in next section.
4. The smart contract assigns the adaptive prices to different
users from different parking lots. The distance of the
parking lots from user destination is also calculated.
5. The best suited parking lot is suggested back to the
user. The details of cost to be charged and distance from
destination are also shared.
6. The parking payment is charged using hbar cryptocur-
rency and the number of empty slots with that particular
parking lot is reduced by 1.
7. Re-run steps 3-6 for the next parking request in consensus
order.
Now, we present an adaptive pricing algorithm and the assign-
ment problem formulation in the next section.
V. ADAPTIVE PRICING ALGORITHM
In this section we propose an algorithm using which the
adaptive price offered for the parking lot is calculated. The
price offered depends on various constraints associated with
the parking lot’s capacity and the demand factor [58]. We
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TABLE II: Notation Summary
Notations Meaning
WdWeight for the distance of lot from destination
WtWeight for the total number of slots
WpWeight for the minimum price offered
BmMaximum base price for parking lot
BnMinimum base price for parking lot
ψik Price offered by kth PL owner to ith user
DmMaximum distance of PL from destination
ϕ1latitude of the user destination
ϕ2latitude of the parking lot
∆ϕdifference between the respective latitudes
∆λdifference between the respective longitudes
δDistance between user destination and PL
γik Inflated price due to distance parameter
θik Inflated price due to traffic density
λik Inflated price due to parking time duration
βik inflated price due to pending free slots
assume that the prices are decided for every hour of the day
and the complete life cycle of a slot is considered to be 24
hours. To maintain the generality of the model we assume Bm
and Bnas the maximum and minimum base price authorized
by the regulating authorities in a particular area. Based on the
variations in the above discussed parameters the final prices
for different users by different parking lots are calculated using
adaptive pricing and are updated in the cost matrix shown in
Table III. The adaptive price calculation is done in a smart
contract and therefore the price monopoly is prevented. The
adaptive pricing model enhances the revenue of all the PL
owners and at the same time improves the Quality of Service
(QoS) and cost for the individual users. The detailed steps in
calculation of the adaptive price based on different parameters
under consideration are shown in Algorithm 1.
Here ψik refers to the price offered by kth PL owner
to ith user. The initial value of all ψik is kept as Bnand
the value continues to get updated based on the adaptive
pricing parameters. The final price ψik cannot be less than the
minimum base price and cannot be more than the maximum
base price.
Bn≤ψik ≤ Bm(1)
A. Price Variation due to Distance Parameter
We can safely assume that every user or driver would
prefer to park the vehicle as close as possible to the desired
destination. The parking lot that is closest to the desired
destination of the user can safely increase the parking price
over the minimum base price and can still expect to be chosen
by the user due to close proximity. The parking lots that are
little far away from the desired destination can also increase
their probability of getting chosen by the user by keeping the
price near to the minimum base price. In this way the proposed
model ends up into increasing the probability of winning the
user for all the neighbouring PL owners. The parking lots that
are more than a maximum distance Dmsubmitted by the user
are not allowed to participate in the process for that particular
TABLE III: Cost Matrix for Prices Offered by k PL owners
to i users
Parking Lots
Users
ψ11 ψ12 ... ψ1k
ψ21 ψ22 ... ψ2k
... ... ... ...
ψi1ψi2... ψik
user. Among the parking lots that are allowed to participate in
the selection process for a user, the parking lot with minimum
distance from user’s destination is allowed to increase the price
by a value αik. The variation in price due to distance parameter
is shown in Algorithm 1 in steps 3 to 6.
γik =Bn+αik,∀ Bn≤γik ≤ Bm(2)
Where γik is the inflated price due to distance parameter and,
αik =Bn∗ Wd(3)
We use Haversine formula to calculate the shortest and accu-
rate distance between the user destination and the parking lots
based on the respective latitudes and longitudes [59].
ξ= sin2(∆ϕ/2) + cos ϕ1·cos ϕ2·sin2(∆λ/2) (4)
Here, ϕ1iand ϕ2kare the latitudes of the ith user destination
and kth parking lot. ∆ϕand ∆λrefer to the difference
between the respective latitudes and longitudes of user des-
tination and parking lot. The calculated value of a is used in
next equation to finally calculate the distance δbetween the
two points.
C= 2 ·atan 2(pξ , p(1 −ξ)) (5)
δ=R·C (6)
Here, δis the final distance and Ris the radius of the earth,
which is taken as 3961 miles.
B. Price Variation due to Remaining Free Slots
It can be safely assumed that the PL owners want to
maximize their revenue and they always expect to have a low
number of free slots. If the number of free slots is higher
than a pre-defined percentage of total slots, then the owners
would not increase the price to attract more users. On the other
hand, if the number of free slots is lower than the pre-defined
percentage of total slots, then the PL owners can afford to
increase the price by a unit value and can still have most of
the slots filled. Let mbe the minimum pre-defined percentage
of free slots. Whenever a user applies to reserve a parking slot
in the network, all the PL owners check the pending number
of free slots and if the number of free slots is less then m
percent of their total slots, then they decide to inflate the price
by unit value. Let Ube the unit value increase in the prices
for all PL owners. The variation in price due to remaining free
slots is shown in Algorithm 1 in steps 8 to 10.
8
Let βik be the inflated price due to free slot parameter.
βik =γik +Wt∗ U,∀ Bn≤βik ≤ Bm(7)
For all price inflation the inflated price should never be more
than the maximum base price Bm.
Algorithm 1 Adaptive Pricing Algorithm
Input: The latitude ϕ1iand longitude λ1position of iuser’s
destination.
ϕ1=ϕ11, ϕ12, ..., ϕ1i
λ1=λ11, λ12, ..., λ1i
Output: The cost matrix for prices ψik given by the kparking
lots owners to iusers.
1: for i=1:ido
2: for k=1:kdo
3: Price Variation due to Distance Parameter:
4: if δik =min(δ)then
5: αik =Bn∗ Wd
6: γik =Bn+αik
7: end if
8: Price Variation due to Remaining Free Slots:
9: if TotalSlots ≤(FreeSlots ∗(m/100)) then
10: βik =γik +Wt∗ U
11: end if
12: Price Variation due to Traffic Density:
13: if 10AM ≤t < 3PM then
14: θik =βik +U
15: end if
16: if 5AM ≤t < 10AM then
17: θik =βik + 2 ∗ U
18: end if
19: if 3PM ≤t < 8PM then
20: θik =βik + 2 ∗ U
21: end if
22: θ∗
ik =θik +U
23: Price Variation due to Parking Duration:
24: if 8Hours ≤Duration <16Hours then
25: λik =θik +U
26: end if
27: if 16Hours ≤Duration <24Hours then
28: λik =θik + 2 ∗ U
29: end if
30: The price ψik by kth PL owner to ith user:
31: ψik =γik +θik +λik +βik
32: end for
33: end for
C. Price Variation due to Traffic Density
Traffic density is one of the major deciding parameter for
the price variation in parking lot allotment. We have analyzed
the hourly road traffic in different areas of New Jersey and the
analysis results are shown in Section VII. The major factors
deciding the price variation due to traffic density are listed as
follows:
•Time of the day tfor parking slot reservation.
•Day of the week dfor parking slot reservation.
•Date of the year ffor parking slot reservation i.e., festival
or non festival day.
The traffic density is calculated based on these parameters and
the prices are increased or reduced based on the results. The
data analysis show that the traffic density in most of the areas
is low from mid-night till 5 AM. The density starts growing
and is high from 5 AM to 10 AM. Traffic density is seen
to be in normal range from 10 AM to 3 PM and again rises
from 3 PM to 8 PM. After 8 PM the density is again low till
mid-night. Based on these observations the parking prices can
be varied depending on the time of the day for parking slot
reservation.
Let θik be the inflated price due to traffic density. If the
time of slot reservation is in the range of high traffic density
then the prices can be inflated accordingly. We keep different
price inflation for normal and high traffic density as shown
below.
•Normal traffic density scenario
θik =βik +U,∀ Bn≤θik ≤ Bm(8)
•High traffic density scenario
θik =βik + 2 ∗ U,∀ Bn≤θik ≤ Bm(9)
The traffic data analysis shows that the density also varies
according to the day of the week apart from the time of the
day. The traffic is found to be lower in the most areas of New
Jersey on the weekends as compared to the weekdays. The PL
owners can afford to inflate the price for the weekdays and
reduce it for the weekends. Similarly, the density is higher on
the festivals as compared to the normal days. Let θ∗
ik be the
inflated price due to the day and date parameter. If the day is
weekday and the date is a festival date, then the prices can be
adjusted accordingly, within the allowed range. The variation
in price due to traffic density is shown in Algorithm 1 in steps
12 to 22.
θ∗
ik =θik +U,∀ Bn≤θ∗
ik ≤ Bm(10)
D. Price Variation due to Parking Duration
Parking duration is the only parameter that is considered by
all the parking lot owners to adjust the parking prices. Some
of the local garages or free spaces allow for a free first hour
parking to attract users and charge heavily or a little extension
of time. The proposed model follows the price shifting model
after every 8 hours of parking duration. The prices are not
increased for the first 8 hours of parking. For 8 to 16 hours the
prices are increased by unit value and by twice the unit value
for 24 hours. The variation in price due to parking duration is
shown in Algorithm 1 in steps 23 to 29.
λik =θik +U,∀ Bn≤λik ≤ Bm(11)
λik =θik + 2 ∗ U,∀ Bn≤λik ≤ Bm(12)
ψik =γik +θik +λik +βik,∀ Bn≤ψik ≤ Bm(13)
9
Fig. 4: Parking Lots and User Destination on Real Map of
New Jersey.
Equations (11) and (12) show the price inflation for 8 to 16
hour and 16 to 24 hour parking duration respectively. Once all
the price variation parameters are calculated and the prices are
adjusted, the final prices ψik for each user by each available
parking lot are stored in the final cost matrix as discussed in
Section V and shown in (13). The final price variation due
to the cumulative effect of all the above discussed parameters
is shown in Algorithm 1 in steps 30 to 31. The Hungarian
assignment model is used to finally map each user to the best
suitable PL in a cost-optimal manner. The assignment model
is explained in the next section.
VI. ASSIGNMENT MO DE L
Hungarian assignment model is used to assign a single
parking lot to a single user in a cost-optimal way and in
polynomial time. The final prices after all the considerations
are calculated and stored in the cost matrix as discussed in
Table III. Now we have the final prices offered to different
users by different parking lots based on their constraints and
traffic data. Let Xki denote the assignment of the kth parking
lot to the ith user.
Xki =0,if the kth parking lot is not assigned to ith user,
1,if the kth parking lot is assigned to ith user.
(14)
The problem formulation for the assignment problem can be
expressed as follows.
Minimize: Z=
k
X
k=1
i
X
i=1
ψkiXk i (15)
Subject to following constraints:
k
X
k=1
Xki = 1, k = 1,2,3, . . . , k (16)
Xki = 0 or 1(17)
The Hungarian algorithm works on solving the assignment
problem in a cost-optimal manner and in polynomial time.
TABLE IV: Latitudes and Longitudes of locations considered
in simulation.
Parking Lot Latitude Longitude
Westfield garden plaza 40.9206 -74.0722
Rochelle Park 40.9073 -74.0754
Bergen Town Center 40.9155 -74.0592
Arcola Country Club 40.9296 -74.0875
Paramas High School 40.9283 -74.0613
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
200
400
600
800
1000
1200
Hours of The Day
Number of Cars Near Parking Zones
Parking Lot 1
Parking Lot 2
Parking Lot 3
Parking Lot 4
Parking Lot 5
Fig. 5: Flow of Traffic Recorded Near Different Parking Zones
on Weekend.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
200
400
600
800
1000
1200
1400
1600
1800
Hours of The Day
Number of Cars Near Parking Zones
Parking Lot 1
Parking Lot 2
Parking Lot 3
Parking Lot 4
Parking Lot 5
Fig. 6: Flow of Traffic Recorded Near Different Parking Zones
on Weekday.
Sun Mon Tue Wed Thur Fri Sat
0
200
400
600
800
1000
1200
Days of the Week
Average Daily Traffic
Parking Lot 1
Parking Lot 2
Parking Lot 3
Parking Lot 4
Parking Lot 5
Fig. 7: Average Daily Traffic in New Jersey based on Days of
the Week.
VII. NUMERICAL ANALYSIS
In this section, simulations are conducted to show the
efficiency and performance of our proposed algorithm for the
10
Request 1 Request 2 Request 3 Request 4 Request 5
hashgraph
allocation 1
hashgraph
allocation 2
hashgraph
allocation 3
hashgraph
allocation 4
hashgraph
allocation 5
Blockchain
allocation 4
Blockchain
allocation 2
Blockchain
allocation 1
Blockchain
allocation 3
Time (miniutes)
01 3 4 5 6 7 8 9 10 11 12 13 14 152
Fig. 8: Comparison of blockchain and hashgraph in terms of timestamp order of parking request.
1 2 3 4 5
90
100
110
120
130
140
150
160
170
Plarking Lots with Different Capacity
Parking Price Offered
User 1
User 2
User 3
User 4
Fig. 9: Variation of Prices to Different Users by Different
Parking Lots on a Non-Festival day.
1 2 3 4 5
130
140
150
160
170
180
190
200
Plarking Lots with Different Capacity
Parking Price Offered
User 1
User 2
User 3
User 4
Fig. 10: Variation of Prices to Different Users by Different
Parking Lots on a Festival day.
parking lot allocation.
A. Simulation Settings
To validate the performance and efficiency of the proposed
model, the traffic data of five separate locations in New Jersey
has been analyzed. Fig. 4 shows the selected locations on real
map of New Jersey. The respective latitudes and longitudes of
the selected locations are shown in Table IV. Each location
is a parking slot with different number of total parking slots.
Any of the selected locations or any other nearby location can
be the user destination. The distance of all the parking slots
from the user destination is calculated using the Haversine
formula discussed in Section V. Hourly traffic data from UCI
library for all hours of each day for 2018 has been analyzed
to prove the compatibility of the proposed model with real
data. Fig. 5 shows the traffic flow for 10th June 2018 near the
selected parking slots based on latitude and longitude. It can
be observed from the figure that the traffic density is uniformly
increasing or decreasing for all the zones. Initially the density
is low till 5 AM and it gradually increases till 3 PM and
again drops from 4 PM to midnight. Similar trend is seen for
a weekday day i.e., 13th June 2018 in Fig. 6. Although, the
trend of traffic density is similar on weekday and weekend,
the traffic density is observed to be much more on weekday
as compared to weekend. It can be observed that the peak
number of vehicles is less than 1000 in Fig. 5 as compared
to 1800 vehicles during park hours in Fig. 6. The analysis of
the traffic density for different days of the week from 10th to
16th June 2018 is shown in Fig. 7. It can be observed from
the figure that the average traffic density is much lower on the
weekends as compared to the weekdays. For the purpose of
simulation, we have taken the minimum base price for parking
slot i.e., Bnto be 50 cents and the maximum price for parking
slot i.e., Bmto be 250 cents.
11
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hours of The Day
Resource Utilization Rate
Parking Lot 1
Parking Lot 2
Parking Lot 3
Parking Lot 4
Parking Lot 5
(a)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Hours of The Day
Resource Utilization Rate
Parking Lot 1
Parking Lot 2
Parking Lot 3
Parking Lot 4
Parking Lot 5
(b)
Fig. 11: (a) Rate of Resource Utilization for different PLs Without Proposed Model and (b) Rate of Resource Utilization for
different PLs With Proposed Model.
1 2 3 4
0
50
100
150
200
Users
Parking Price Offered
Proposed Model
Fixed price
Greedy
Fig. 12: Comparison of Prices to Different Users by Proposed,
fixed price and Greedy schemes on festival day.
1 2 3 4
0
20
40
60
80
100
120
140
160
180
200
220
Users
Parking Price Offered
Proposed Model
Fixed price
Greedy
Fig. 13: Comparison of Prices to Different Users by Proposed,
fixed price and Greedy schemes on Non festival day.
B. Performance Evaluation
Fig. 8 shows the comparison of blockchain and proposed
model in terms of timestamp order of parking request. It can
be seen that the proposed model allocates the parking slot
exactly in the order in which the requests were generated.
The order of processing is random in case of blockchain. It
is not mandatory that the request that was submitted first gets
executed first.
Fig. 9 shows the variations in the parking prices offered to
different users by different PL owners. Different users might
wish to reserve a parking slot for different destinations. We
assume that user 1 wishes to reserve a slot for destination to be
same as parking lot 1 and user 2 reserves a slot for destination
as parking lot 2. It can observed from the figure that as the
distance of the parking lot from the user destination increases
the price offered by the PL owner decreases. Less the distance
from the destination more is the price. A similar trend is seen
in Fig. 10, where the parking day is a weekday and a festival.
It can be observed that the prices asked for the festival days
are higher for all the parking lots as compared to the prices
on normal days.
Fig. 12 and Fig. 13 show the comparison of the proposed
model with the greedy parking slot allocation and fixed price
slot allocation model where there is no peer-to-peer network of
users and the PL owners. To clearly distinguish the improved
features of the proposed model, we assume that even in greedy
setting the PL owners are aware of the traffic flow trend and
try to set the prices accordingly. The only difference is that
there is no peer-to-peer network and no consensus algorithm to
order the request arrival. All the PL owners uniformly increase
the prices on festival days and weekdays irrespective of the
number of requests and distance of user destination from the
slot. No PL owner is aware of the complete picture of the
parking requests in different zones. The prices are increased
without knowing the complete picture thereby reducing the
overall revenue of the PL owners and creating a situation
of chaos and jam in the parking zones. It can be observed
in Fig. 12 that on a festival day in greedy approach all the
PLs uniformly increase the price for the same user, whereas
in proposed model the prices are increased based on above
discussed parameters. The prices offered in the proposed
model by all the PL owners are less as compared to the prices
offered in greedy approach. The proposed model keeps into
account of the overall revenue of the PL as well. It can be
observed from Fig. 12 that on festival days the prices offered
by proposed model are higher than the fixed prices. Therefore,
12
the proposed scheme collaboratively enhances the experience
of the users and the overall revenue of the PL owner.
Fig. 11 (a) and (b) show the parking lot resource utilization
rate without and with the proposed model respectively. It can
be clearly observed that without a peer-to-peer connection
between the users and PL owners all the users are naturally
attracted to the biggest PL in the region, thereby flooding the
lot and ending up into a chaotic situation. On the other hand,
the other PLs are not being utilized to the best of their ability,
even in the peak hours. The users end up paying a higher
price and spend extra time in searching for a single empty
slot in the huge parking zone. The proposed model could
easily recommend another empty slot in neighbouring location
with less price and less wastage of time and resources. The
proposed model, therefore proves to be beneficial both for the
users as well as the PL owners. The users can get the best
possible parking solution and the PLs can also be utilized to
their best. Fig. 11 (b) shows that with the proposed model the
resource utilization for the biggest PL remains similar, whereas
the resource utilization for the other four PLs in the vicinity
is significantly improved.
VIII. CONCLUSION
In this paper, a Distributed Ledger Technology (DLT) and
Directed Acyclic Graph (DAG) based parking lot allocation
model is discussed. The DLT technique helps in creating a
secure peer-to-peer network of the users, parking lot owners,
garages and free spaces. Any one with a free parking slot can
register in the network and can securely utilize the resources
for monetary benefits. The hashgraph or DAG technique used
for network and transaction creation gives a unique consensus
timestamp for all the parking reservation requests, thereby
ensuring the best possible service to the users in a cost-optimal
way. An adaptive pricing model is discussed to generate
a unique price for each parking request based on multiple
parameters. The pricing model proves to be equally beneficial
both for the users and the PL owners. The users get the best
available parking slot in less time and less cost, whereas,
the PL owners get the best utilization for their resources
at the best possible prices. Simulation results show that the
proposed model is highly beneficial for saving user’s time
in searching free parking slots, jam prevention and optimal
resource utilization.
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Vikas Hassija received the B.Tech. degree from
Maharshi Dayanand University, Rohtak, India, in
2010, and the M.S. degree in telecommunications
and software engineering from the Birla Institute
of Technology and Science (BITS), Pilani, India, in
2014. He is currently pursuing the Ph.D. degree in
IoT security and blockchain with the Jaypee Institute
of Information and Technology (JIIT), Noida, where
he is currently an Assistant Professor. He has eight
years of industrial experience and has worked with
various telecommunication companies, such as Tech
Mahindra and Accenture. His research interests include the IoT security,
network security, blockchain, and distributed computing.
Vikas Saxena is currently Professor and head of
computer science and information technology de-
partment at Jaypee Institute of Information and
Technology, Noida, India. He received his B.tech de-
gree from IET, MJP Rohilkhand University, Breilly,
india in 2000, the M.E degree from VJTI, Mumbai,
India, in 2002, and the Ph.D. degree in CSE from
Jaypee Institute of Information and Technology, in
2009. He is having more than 17 years of experi-
ence of teaching and research. His research interests
include image processing, blockchain, computer vi-
sion, software engineering and multimedia. Dr. Vikas served as Publicity Co-
Chair in the International Conference IC3-2008, India conducted by JIIT and
University of Florida, USA.
Vinay Chamola received the B.E. degree in elec-
trical and electronics engineering and master’s de-
gree in communication engineering from the Birla
Institute of Technology and Science, Pilani, India, in
2010 and 2013, respectively, and the Ph.D. degree
in electrical and computer engineering from the Na-
tional University of Singapore, Singapore, in 2016.
In 2015, he was a Visiting Researcher with the Au-
tonomous Networks Research Group, University of
Southern California, Los Angeles, CA, USA. He is
currently an Assistant Professor with the Department
of Electrical and Electronics Engineering, BITS-Pilani, Pilani Campus. His
research interests include Green communications and networking, 5G network
management, Internet of Things and Blockchain.
F. Richard Yu (S00-M04-SM08-F18) received the
PhD degree in electrical engineering from the Uni-
versity of British Columbia (UBC) in 2003. From
2002 to 2006, he was with Ericsson (in Lund, Swe-
den) and a start-up in California, USA. He joined
Carleton University in 2007, where he is currently a
Professor. He received the IEEE Outstanding Service
Award in 2016, IEEE Outstanding Leadership Award
in 2013, Carleton Research Achievement Award in
2012, the Ontario Early Researcher Award (formerly
Premiers Research Excellence Award) in 2011, the
Excellent Contribution Award at IEEE/IFIP TrustCom 2010, the Leadership
Opportunity Fund Award from Canada Foundation of Innovation in 2009 and
the Best Paper Awards at IEEE ICNC 2018, VTC 2017 Spring, ICC 2014,
Globecom 2012, IEEE/IFIP TrustCom 2009 and Intl Conference on Net-
working 2005. His research interests include wireless cyber-physical systems,
connected/autonomous vehicles, security, distributed ledger technology, and
deep learning. He serves on the editorial boards of several journals, including
Co-Editorin-Chief for Ad Hoc Sensor Wireless Networks, Lead Series
Editor for IEEE Transactions on Vehicular Technology, IEEE Transactions on
Green Communications and Networking, and IEEE Communications Surveys
Tutorials. He has served as the Technical Program Committee (TPC) CoChair
of numerous conferences. Dr. Yu is a registered Professional Engineer in the
province of Ontario, Canada, a Fellow of the Institution of Engineering and
Technology (IET), and a Fellow of the IEEE. He is a Distinguished Lecturer,
the Vice President (Membership), and an elected member of the Board of
Governors (BoG) of the IEEE Vehicular Technology Society.
