Agile Urban Parking Recommendation Service for ... - IEEE Xplore

Agile Urban Parking Recommendation Service for Intelligent Vehicular Guiding System Eric Hsiao-Kuang Wu and Chi-Yun Liu Dept. of Computer Science and Information Engineering, National Central University, JhongLi, Taiwan E-mails: [email protected], [email protected]

Jagruti Sahoo

Dept. of Electrical and Computer Engineering, University of Sherbrooke, Sherbrooke, Canada E-mail: [email protected]

Ming-Hui Jin and Shu-Hui Lin

Networks & Multimedia Institute line, Institute for Information Industry, Taipei, Taiwan E-mails: [email protected], [email protected]

© wikimedia commons

Abstract—Nowadays, Intelligent Transportation Systems (ITS) technologies are exploring a wide range of services such as freeway management, crash prevention & safety, driver assistance, and infotainment of drivers and/or passengers. In this paper, an agile urban parking recommendation service for vehicular intelligent guiding system is designed to facilitate city citizens with fully efficient, real-time and precise parking lot guiding suggestions for the sustainability of the future green city. The system offers drivers a friendly parking lot recommendation sequence and saves drivers’ time circling around by the accurate prediction of the successful parking probability in each parking lot. The proposed cost model constructs an optimal recommendation sequence considering successful parking probability and time to reach the parking lot. Through the collection and analysis of realistic records from parking lots in Taipei city, a prediction algorithm is developed to estimate the successful parking Digital Object Identifier 10.1109/MITS.2013.2268549 Date of publication: 21 January 2014

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probability by using current available space counts. Extensive experiments are conducted to demonstrate the effectiveness of the prediction algorithm.

I. Introduction

I

n recent years, smart living has been the trend of future life where human beings are expected to live in an agile environment saturated with sensing and computing capability [1]. With the rapid advances of wireless technologies, customers can access and enjoy a wide range of key information or innovative services at the right time and in the right place. The development of Intelligent Transportation Systems (ITS) creates vehicular scenarios where vehicles equipped with wireless devices enable drivers to access the mass information available on Internet. Such information is truly in demand because of its usefulness [2, 3]. The major objective of ITS has been clearly to address transportation problems like traffic congestion, driving safety, transport efficiency and environmental conservation [4]. Furthermore, urban citizens in the future smart green city require not only driving safety but also a convenient and comfortable driving experience. With the advanced wireless technologies, new driver assistance systems based on inter-vehicle communication and opportunistic traffic navigation are highly expected. In 2003, the Federal Communications Commission (FCC) adopted the licensed 5.9 GHz band or Dedicated ShortRange Communication (DSRC) for ITS to develop ubiquitous and agile applications. More recently, the 802.11p standard was proposed to motivate standardized communications over the allotted spectrum. DSRC channels might suffer from scarcity of spectrum due to high vehicle density. A novel system such as cognitive radio (CR) solves this issue and achieves ubiquitous communications by exploiting spatially and temporally available spectrum [5–7] in an opportunistic way. For drivers, an efficient vehicle navigation service is clearly important for optimizing journeys, which is a rather complex task. Global Positioning System (GPS), as the major member of Global Navigation Satellite System (GNSS), has been widely adopted in the civilian applications. The ongoing development in positioning and navigation technologies [8–10] could be classified into two categories [11]. One category offers specific GPS-based devices produced by original equipment manufacturers (OEM) and third-party systems which not only provides location and route guidance information, but also render highly critical traffic condition information such as traffic congestion and accidents for advanced driver assistance and safety applications. The second category covers the advanced downloaded applications on handheld personal navigation devices. GPS-based vehicle navigation offers drivers basic route guidance functions such as current location of the vehicle on the map and visual and audio notification of the way to reach the destination.

Emerging navigation systems employing sensing technologies and intelligent image pattern processing also make modern driving safer, more efficient and more environmentfriendly. In a nutshell, navigation systems enhance transport efficiency and reduce driving stress by offering guiding tips all the way from the origin to the destination. Unlike road routing, the parking problem in urban areas draws another significant attention for urban drivers. As the city modernization progresses and the number of vehicles grows rapidly, the parking supply may be perceived as inadequate given the uncertainty in the demand of parking. The consequence of cars circling around street blocks to find parking spaces not only wastes time and fuel, but also produces extra exhaust gas that deteriorates the greenhouse effect. Although researchers keep finding an alternative energy resource, gasoline is still the predominant energy for vehicles. The fundamental concern for the green eco-city is transportation emission which is one of the major contributors of air pollution in Taipei City. A survey of private transportation usage [13] indicates that the average time spent to find a parking space is up to 16 minutes and about 16.6 percent drivers in Taipei City might spend over 30 minutes. For the average driving speed in urban area being 50 km/h and the gasoline mileage being 22.7 km/L [14], the 16 minutes journey circling around for a parking space could travel 13.33 kilometers which consumes 0.592 L extra gasoline, and will keep consuming 0.037 L for every additional minute. Moreover, the carbon dioxide emission [15] per liter gasoline can reach to 2.32 kilograms. Considering all kinds of transportations, the great quantity of carbon dioxide emission caused by journey cruising for a parking spot produces the air pollution in city and may cause unpredictable and unnecessary consequences. Being aware of the challenge, a number of traffic systems start to deal with the parking problem in different aspects. Seong-eun et al. [16] implemented the parking guidance system leading vehicles to appropriate parking lots where sensor network is deployed to detect the parking space availability in parking lots. A wireless-sensor network-based navigation [17] uses WiMAX multi-hop relay networks as the inter-vehicle communications to meet the demands of an optimal routing path for achieving the least travel time, which in turn reduces gasoline consumption. The environmental conservation factor is considered in this scheme so that the user chooses less air polluted route with higher priority. Rongxing et al. proposed [18] a multifunction system containing auto theft prevention, realtime parking navigation, and friendly parking information dissemination in vehicular ad hoc network (VANETs). The developed parking algorithm relies on a complex queuing model to estimate the blocking probability in a parking lot. Their design requires the entry/exit gate in the parking lots to obtain the arrival and departure time of every single

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spaces through intelligent parking suggestions. Based on individual driver’s need, a cost model is proposed in this study. The cost model is based on parameters such as successful parking probability, and distance from the current location. Since the successful parking probability varies with time, we propose a probability estimation method by using remaining available space count. The experiments and validations were cooperated and conducted with the Institute for Information Industry to build an intelligent vehicle guiding system. The architecture of the system is shown in Figure 1(a), whereas the snapshots of the parking guidance and recommendation are shown in Figure 1 (b) and Figure 1(c) respectively. The client side of the system offers a well adopted web interface and Android client deployed on mobile devices and

car. This implies a significant communication overhead. On the contrary, the parking data collected by the Parking Management and Development Office of Taipei City does not contain the information regarding arrival and departure events. As a result, applying the queuing model to estimate the parking probability is not feasible and scalable in current stage. In the current system, the parking database maintains the number of remaining available parking spaces of various parking lots and is updated every 3 minutes. We, therefore, intend to adopt the history parking data as the most cost-effective way to conduct our analysis and then the result is used to develop the prediction algorithm. To alleviate the driver’s inconvenience in city environment, we design an effective parking guidance system which will assist eco-city drivers to reserve parking

Client Available Parking Space Query Service

Parking Resource Real-Time Data

Parking Lot Recommendation Service

Parking Statistics

Parking Space Reservation Service

Parking Service Transaction Record

Parking Management System (a)

(b) Search

My Location Reservations

Park 24 105, Dunhua North Road, 150 Empty: 7, 24 in Total $25 NT Per 30 Minutes Reservation: YES Park 24 105, Dunhua North Road, 240 Empty: 9, 37 in Total $25 NT Per 30 Minutes Reservation: YES Zhon Xiao Public Parking Lot Empty: 47, 189 in Total $30 NT Per Hour Reservation: YES

(c) Fig 1 (a) System architecture. (b) Vehicular guiding system. (c) Parking recommendation system. IEEE Intelligent transportation systems magazine •

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on vehicles. The vehicular guiding system provides parking space query service, parking lot recommendation service, and parking space reservation service as illustrated in Figure 1(a). The service modules and the parking database are maintained by the traffic control center in Taipei city. The parking management system collects real-time data from all parking lots and sends periodic (e.g. 3 minutes) updates to the database in traffic control center. The driver uses its smart phone or any mobile device to request the traffic control center by specifying details such as the ID of parking lot. The traffic control center retrieves the parking data from its database and sends the available parking space in real-time. The real-time communication between the client (i.e. the smart phone of the driver) and the traffic control center is achieved through cellular networks. Similarly, a driver can ask for intelligent parking suggestions through the parking lot recommendation service. The remainder of this paper is organized as follows: Section II presents a cost model for the parking recommendation system. Section III covers a summary of existing parking models as well as parking information systems. In section IV, we present the Parking Probability Estimation and the Shift Prediction algorithms. We performed evaluation by extensive experiments in Section V. Finally, section VI concludes the paper with some remarks for future development.

II. The Parking Recommendation Problem Parking is a critical problem in urban areas, particularly near tourist attractions and business centers. The irritating traffic jams and excessive emission caused by the waiting queue of parking cars debase the quality of life in many ways. During the past years, a number of researchers and institutes have proposed systems to work on this challenge. Initially, the Parking Management and Development Office of Taipei City have built a Parking Information Guiding System that provides drivers the current remaining

PL2, L2, T0,2, P(T0,2) D0,2 D1,2

D1,3

C, L0

D3,4

PL3, L3, T0,3, P(T0,3) PL4, L4, T0,4, P(T0,4) PL1, L1, T0,1, P(T0,1)

Fig 2 Parking sequence.

available parking space count in a parking lot. Enhanced guiding systems further provide parking billing information as well with surrounding map. Apparently, these solutions only respond to the instant query issued by the driver based on the remaining available parking space count in each parking area. However, a realistic approach is to take the arrival time at the destination into consideration. In other words, while the drivers can select an ideal parking lot with shortest distance and reasonable price in the existing system, they might not find the available parking space given the uncertainty of arriving after a period of time in the preferred parking lot, especially in peak hours. Without a systematic statistics of history parking information, in the existing parking information systems, it may be difficult to determine the availability of a parking lot in the near future. If a systematic statistics is included in parking available space count information, the system will be able to exploit the current data as well as history data to predict the availability in the future. As the case mentioned earlier, a driver at the distance of fifteen minutes away from the destination can reckon in history information to decide whether to select the parking lot or not. Consider the situation of a single car searching for an appropriate parking lot in a given range containing several parking lot candidates as illustrated in Figure 2. The vehicles are assumed to be location-aware and can obtain their geographical location from a GPS receiver. The possible parking lot candidates can be responded by mobile client applications by retrieving the parking database. As shown in Figure 2, the parking lots are first filtered by a fixed range centered at the car’s current location. Let " PL 1, PL 2 f, PL n , be the n parking lots filtered in this range and t 0 be denoted as the time at which the driver requests for the parking recommendation service. This study makes the following notations and definitions for modeling the parking recommendation problem. A1) T he location of parking lots PL i is L i for 1 # i # n, and L 0 is the location of the car C . A2) The time consumed from L i to L j is t i, j . A3) T he probability that PL i has available parking space at time t is Pi (t) . A4) r is a permutation of the set " 1, 2, f, n , A5) The sequence 1 PL r (1), PL r (2), f, PL r (n) 2 represents the parking recommendation sequence based on the permutation r . This means driver will look for parking space in PL r (1) first, and if there is no available parking space in PL r (1), then goes to PL r (2), to try, and so on. Given a permutation r, the car C first goes to parking lot PL r (1) . If there is no parking space in parking lot PL r (1), then car C goes to the parking lot PL r (2), and so on. The probability to park successfully at parking lot PL r (i) is described as follows:

PR (r, i) = e % ^ 1 - Pr (j) (Tr (j )) ho # Pr (i) (Tr (i )), (1) i -1

j =1


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where

m

Tr (m) = t 0 + / t r (k - 1), r (k) .(2) k =1

In equation (1), the first expression represents the probability to park unsuccessfully in former parking lots assuming that the driver follows the parking recommendation based on permutation r . The optimal result is to spend minimum time on parking in an ideal parking lot. In Figure 2, the expected value of consumed driving time from current car location, L 0 , to the parking lots in given range is the summation of the prospective parking time in each parking lot. The expected value to park at PL r (i) is PR (r, i) # (Tr (i) - t 0) . Therefore, the expected time for the car C following the parking recommendation based on permutation r is

n

PT (C, r) = / PR (r, i) # (Tr (i) - t 0) .(3) i =1

Applying equations (1), (2) and (3), the parking recommendation problem can be formally stated as follows: For the car C which accepts the parking lots " PL 1, PL 2, f, PL n ,, find a permutation r to minimize the value of PT ^C, π h . The parking recommendation problem is one kind of Traveling Salesman Problem (TSP). A number of feasible proposed algorithms can efficiently bring high quality solutions. In the above cost model, all parameters except the value of probability Pi ^ t h can be easily inferred through the help of the navigation system. Therefore, estimating the value of the probability Pi ^ t h becomes essential for the parking recommendation service. This paper presents an algorithm by referring the historical statistics to calculate the predicted value of probability Pi ^ t h that there are available parking spaces at parking lot PL i on time t .

III. Related Works The main objective of parking guiding systems is to find the appropriate way to secure a parking space for achieving the least travel time and exhausted gasoline in urban areas. Three representative categories of parking guiding systems have been developed and deployed. The first one applies the queuing model into the parking behavior, analyzes the cars’ arriving event and departure event and uses the blocking rate to obtain the success/failure probability of parking. The second one includes vehicle detection systems which handle flow of vehicles. The third one builds a complete urban planning which gathers all parking information from the parking lots and disseminates the recommendation via road signs or road electric billboard.

A. Queuing Model Rongxing et al. [18] proposed an intelligent privacy-preserving parking scheme through vehicular communications. By exchanging message between roadside units and

onboard devices in cars, the system provides real-time parking navigation, anti-theft protection, and propagation of parking information. The parking information dissemination function applies the M/G/c/c queuing model into the parking behavior and forwards the parking lot’s capacity and blocking probability to the vehicles. The queuing model uses Poisson process for the vehicle arrivals and considers a fixed mean parking time. They simulated the blocking rate results by different arriving rates m, mean parking time E ^ t h, and parking lot capacity c . With the prediction of blocking probability, the service of parking guiding can be achieved. Arif et al. [31] analyzes the probability distribution of parking lot occupancy as a function of time using Poisson arrivals and departures. Gongjun et al. [19] proposed a secure and intelligent parking system by using secured wireless network and sensor networks. The system provides an interface for drivers to view and reserve the parking space, and for parking lot proprietors to predict the revenue by a birth-death stochastic process analysis. The birth event corresponds to the event of vehicle entering and occupying a spot for a time period. The death event stands for the event of vehicle leaving which means parking spot becoming vacant. In order to obtain birth rate and death rate of the vehicles in parking lots, the system assumed the city to be provided with traffic detection systems, laser scanner and video camera which detect the traffic flow and store the information for the other ITS application usage [20]. The simulation shows probability of occupied parking spaces for different birth/ death rates. Both systems [18, 19] apply the queuing model to simulate the parking behavior. However, acquiring the arriving rate and the parking time would take additional cost like the construction of traffic detection infrastructure in cities or video cameras in parking lots, which can be expensive.

B. Vehicle Detection System Vehicle detection systems are widely used in parking management systems since traffic data is one of the key factors in many ITS applications [21]. The vehicle detection systems can be classified into two types: in-roadway and over-roadway. The in-roadway systems indicate detectors that are embedded in the pavement, taped to the surface of the roadway, including inductive loops, pneumatic road tubes, and capacitive sensors. For the usage on the roadway in urban areas, these detectors collect data of vehicle presence, speed and density. When it comes to over-roadway, detectors are placed above the surface of roadway, like video cameras, acoustic signal processors, radar, or ultrasonic and infrared sensors. Relative to the in-roadway detectors, over-roadway detectors do not disrupt traffic flow during installation and maintenance. The traffic data is collected into the traffic control center for the later usage in ITS applications. These researches aid the parking lot


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proprietor to manage the resource of parking spaces efficiently. The devices inside the parking lot or on the streets provide the information of parking occupancy of each parking space. As soon as drivers arrive at the parking lot, the management system can guide them to vacant parking spaces which can efficiently reduce the time of driving around for an empty parking space.

C. Parking Guidance and Information System PGIS is defined as one of the components in ITS, which informs drivers of parking locations and parking availability. The main function of PGIS is to reduce the travel time, improve existing parking area utilization rates, and to reduce the traffic caused by searching for a parking space. The system emphasizes on collecting the parking data to the central computer system, building the adaptable message sign, and disseminating the parking information through routing nodes between central computer system and variable message signs on the roadway. The parking information is displayed at major intersections or important business points to reduce drivers’ journey to vacant parking space. Mo and Su [22] propose a PGIS system in which dynamic variable message signs infrastructure is designed according to the objectives of the target city. Mei et al. [26] proposes a parking reliability model for PGIS systems. The parking guiding is less reliable when the display information is inconsistent with the actual usable parking spaces. In such a case, drivers do not trust on the message sign boards. As a result, the benefits of PGIS system are decreased. The authors define the parking reliability as the ratio of parking flow that is guided by the real-time parking information to the total parking flow. Parking choice behavior of drivers and parking arrival flow is used to determine an algorithm to calculate the guiding parking reliability. The results of the paper show that guiding reliability is mostly influenced by quantitative change in number of available parking spaces and display conditions on message signs. It is observed that parking guiding information can achieve highest reliability when the parking capacity is close to the demand.

D. Parking Reservation and Pricing Strategies An intelligent parking reservation system is proposed in [29] in which fuzzy logic is used to make decisions such as accepting or rejecting a driver’s request for reserving parking space. In addition, different tariff classes are considered to maximize the revenue for car parking operators. In [25], important aspects of parking management systems such as optimal parking capacity determination, pricing strategies, etc. are discussed. A parking cash-out strategy proposed in [28] aims at reducing vehicle trips by giving employees the cash equivalent of the price of the parking. The strategy has many benefits such as giving commuters more choices, economic advantage, attract more workers,

reduce environmental concerns by less amount of gasoline emission. By redistributing parking space in a fair way the cash-out strategy is able to reduce vehicle congestion in peak hours. A parking model based on Markov birth/death process is designed in [30]. The model describes the behavior of patrolling drivers searching for inexpensive on-street parking. The objective is to reduce urban road congestion which is achieved by a pricing strategy that encourages impatient drivers to opt for off-street parking (i.e. in parking lots). Sfpark [27] is a pilot parking project implanted in San Francisco. Its major goals are to provide drivers realtime parking information, offer demand-responsive pricing, reduce congestion, improve traffic flow, render a pollution free environment and finally to increase economic vitality.

E. Shortcomings of the Existing Schemes The above existing solutions for the urban parking problem have several shortcomings in practice. The systems applying queuing model on the parking behavior may not be pragmatic and affordable since they require arriving time as well as departing time of every vehicle. Again, to obtain the arrival rates, they need to rely on traffic detection system which is not always available in every city and takes a considerable construction cost. On the other hand, systems utilizing complicated or wireless sensor systems tend to deploy the detecting devices in each parking lot, some at each parking space, in advance. The systems with sensors are not easy to maintain since the sensors are distributed at different locations. It is difficult to maintain the hardware equipment one by one. A cost-effective, practical, and flexible system is, therefore, more appropriate for developed cities to append the parking guiding system to the original traffic system. This paper presents a parking guiding system that employs counting equipment which exists in most of parking lots. The parking resource information are collected in each parking lot and then stored in the database for later use. No additional equipment is needed in parking lots. Our system provides web page and handheld device application for drivers to access the service. Since the main service is based on software, the maintenance is much easier than the maintenance of other hardware systems. Moreover, with the mobile network of drivers’ handheld device, both instant and easy access of real-time parking availability information and parking statistics information can be achieved.

IV. Algorithm Design for Parking Probability Estimation A. Data Observation and Available Space Count Regularity The parking space information used in this study is obtained from the database in parking management and development office, Taipei city. The database provides remaining parking space counts of various parking lots and is refreshed every 3–5 minutes. To determine the


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remaining space count, the parking management system uses a counter which is controlled by a counting equipment placed at the entry/exit gate of the parking lot. When a vehicle enters the lot, the counter is decremented by one. Similarly, the counter is incremented by one on detecting a vehicle exiting the lot. When the counter is equal to zero, the parking system will prohibit vehicles from accessing the parking facility. Once the counter becomes greater than zero, the prohibition is lifted. The system uploads the parking lot ID and the current value of the counter to the parking database every 3–5 minutes. The accuracy of the space count is affected by the arrival as well as departure rates. Inaccuracy usually occurs in case of large arrival rate and small departure rate, or small arrival rate and large departure rate. However, when arrival rate and departure rate are both large or both small, the rate of change of the counter will be not high. As a result, the counter accurately reflects the number of parking space. In fact, the proposed parking probability prediction algorithm is designed for parking lots that exhibit high vehicle arrival rates as well as high departure rates. In the current parking management system, it is not feasible to obtain arrival rate and departure rate. Instead, the system provides the result of arrival rate less departure rate. Parking records are collected from parking lots in Taipei city, Kaohsiung city, and Taoyuan county in Taiwan by sampling the remaining available space count for each given time slot. A time slot is defined to be a five-minutes-period according to the specification of the parking information systems in the three cities in Taiwan. For each day, the parking records are measured from 00:00 to 23:59 where the first time slot being from 00:00 to 00:04, the second time slot being from 00:05 to 00:09, and so on. Hence, in the system, there are 288 time slots in each day. The sample period of this study is set to two months. For the available space count value, the mean and standard deviation can roughly describe its variation behavior over time in a single day. Figure 3 shows available space count during weekdays of a cinema parking lot from 2010/11/29 to 2010/12/28. Based on the observations, this study makes the following notations and assumptions for describing the regularity of the available space count of individual parking lot. A6) 1 T1, T2 f Tm 2 is the sequence of all the time slots in a day. In the data collected by this study, m = 288 and T1 = 60: 00, 0: 05 h, T2 = 60.05, 0: 10 h, and so on. A7) For each time slot Ti and each parking lot PL k, the available space count is a random variable ASC i, k . The mean and standard deviation of ASC i, k are n i, k and v i, k, respectively. A8) Given a specific time t dTi, we define ASC k (t) to be the number of available space count at time t in the parking lot PL k . Since the time slots are short enough, this study assumes that, for each k, Pk ^ t h is equally likely to the probability of the event ASC i, k 2 0.

A9) To estimate the probability of the event ASC i, k 2 0, this study assumes that ASC i, k are skellam random variables. A10) Given two specific time t dTi and t’ dT j, if t–t’ is small enough, then this study assumes that, for each k, ASC k ^ t h – ASC k ^t’ h is closed to be the value n i, k - n j, k . A11) Given two specific time t dTi and t’ dT j, with t’ < t and given the value of ASC k ^t’ h with ASC k ^t’ h ! n j, k, this study assumes that the mean value of the random variable ASC k ^ t h will tend to n i, k as the value of t - t’ increases. In order to derive assumption A9, we express the available space count in time slot Ti +1 as ASC i + 1, k = ASC i, k + X i –Yi, where X i and Yi represent the number of cars arrived and departed respectively in time interval Ti . Since, X i and Yi can be modeled by a Poisson distribution, X i – Yi becomes a skellam random variable [23]. Addition of two skellam random variable is also skellam distributed. Therefore, it is deduced that available space count in a time slot is a skellam random variable. Assumptions A10 and A11 are based on the correlations between the random variables ASC i, k and ASC j, k, which belong to time slots Ti and T j respectively. The Autocorrelation coefficient provides an efficient way to explore the correlation between available space count in any two time slots in the time sequence of a day. As stated in A6, the time sequence consists of m time slots. The sample autocorrelation coefficient of available space count between consecutive time slots is given by:

/ ^ A i - A- (1)h^ A i +1 - A- (2)h

m -1

r1 =

i =1 m -1

2 = / ^ A i - A (1)h i =1

/ ^ A j +1 - A- (2)h2G

m -1 j =1

Where, A i represents the observed available space count at time slot Ti . A (1) and A (2) represent the mean of first m - 1 and last m - 1 observations in a day. The generalized expression for autocorrelation coefficient between two space counts n time slots apart is given by:

/ ^ A i - A- (1)h^ A i +n - A- (2)h

m -n

rn =

i =1 m -n

2 = / ^ A i - A (1)h i =1

m

/

j = n +1

^ A j - A (2) h2G

(4)

-

Where, n is called the time lag. The value of rn ranges between -1 and +1. The closer is rn to +1 or -1 the higher is the correlation between the two variables. If rn = 0, there is no relationship between the variables. Figure 4 shows the autocorrelation coefficient at different time lags for four parking lots described in Section-V-A. It is noticed that, space counts one time slot apart are highly correlated. However, as time lag increases, the correlation decreases. Although, the correlation amount differs from one parking


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Time Slot Fig 3 The available space count distributions of weekdays of one parking lot.

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Available Space Count

23:40 23:20 23:00 22:40 22:20 22:00 21:40 21:20 21:00 20:40 20:20 20:00 19:40 19:20 19:00 18:40 18:20 18:00 17:40 17:20 17:00 16:40 16:20 16:00 15:40 15:20 15:00 14:40 14:20 14:00 13:40 13:20 13:00 12:40 12:20 12:00 11:40 11:20 11:00 10:40 10:20 10:00 09:40 09:20 09:00 08:40 08:20 08:00 07:40 07:20 07:00 06:40 06:20 06:00 05:40 05:20 05:00 04:40 04:20 04:00 03:40 03:20 03:00 02:40 02:20 02:00 01:40 01:20 01:00 00:40 00:20 00:00

lot to another, the above fact is observed for all four parking lots. The objective of this study is to predict the value of ASC k ^ t h when ASC k ^t’ h is known, where t’ < t. Figure 3 shows that space count data exhibits a regular behavior. Then, the space count at time Ti +1 can be represented as Ap = A i ) a + b. Using mean square error, we have

mean (A i +1 - A p) 2 = mean (A i +1 - a ) A i - b) 2 .(5)

To minimize error, optimal values of a and b need to be determined. Since, A i and A i +1 represent space counts in any two time slots in the time sequence of a day, solution of (5) results in the following expression: A p - A i + 1 = rn

vi + 1 (A i - A i) (6) vi

Where A i + 1, A i, v i +1, v i represent the mean and standard deviation computed from sample space count data. Substituting rn = 0 in (6), we get A p = A i + 1 i.e. space count is best predicted by the history mean. Similarly, substituting rn = 1 in (6), we find A p = A i + 1 - A i + A i . The above discussion provides basis for assumptions A10 and A11.

B. Algorithm Design If we consider only the assumptions A8 and A9, then, for each t dTi and parking lot PL k, the value of Pk ^ t h can be estimated. In order to compute Pk ^ t h, the skellam distribution requires mean arrival rate ^m x, i h and mean departure rate ^m y,i h . of vehicles for time interval Ti . Since, the current parking system does not provide information regarding arrivals and departures; it is difficult to estimate the probability. Apparently, for large values of m x, i and m y, i, the skellam distribution is approximated by normal distribution [24]. Hence Pk ^ t h is estimated by the following equation. Pk (t) =

1 v i, k 2r

#0 3 e -

(x - n i,k) 2 2

2v i,k

dx (7)

Autocorrelation Coefficient

1

PL1 PL2 PL3 PL4

0.8 0.6 0.4

Algorithm 1. Shift_Prediction (k, t j , Tt, D) . Input: Parking lot k, current time t j , driving duration Tt, current date D Output: The mean value of the available space count A i on time t j + Tt

0.2 0

Where, the expected number of available space count in the parking lot PL k at time t dTi is n i, k with standard deviation v i, k . However, if the system knows that, at time t’ dT j with t’ 1 t, the number of available space count in the parking lot PL k is not n j, k, then, according to the assumption A10, equation (7) brings inaccurate value of Pk ^ t h unless the value of t – t’ is large enough. This introduces two problem issues. The first one is how to estimate the value of Pk ^ t h given the value ASC k ^t’ h is known. According to the assumption A11, if the value of t – t’ is large enough, we should apply equation (7) to estimate the value of Pk ^ t h . This means that, for each value t’ and k, there exists a value D ^t’, k h satisfying t – t’ 2 D ^t’, k h . Thus, the second problem issue is, given the value of k, t’dT j and ASC k ^t’ h, how to calculate the value D ^t’, k h . This study proposed a Shift Prediction Algorithm (SPA) to address the first problem issue. Given the value ASC k ^t’ h is known and t 2 t’ with t dTi, the SPA shifts the distribution of ASC k ^ t h by replacing the random variable ASC k ^ t h as ASC k ^ t h - n j, k + ASC k ^t’ h . Thus, the mean and standard deviation of the new random variable becomes n i, k - n j, k + ASC k ^ t’ h and v i, k, respectively. By using new parameters in equation (7), the system can get more accurate probability estimation. Based on this concept, Algorithm 1 presents the pseudo code for the Shift Prediction Algorithm. Among the input parameters, k denotes the identifier of parking lot, t j denotes the current time, Tt is the estimated driving duration to destination, and D is the current date. First of all, the time slot of current time t j and target time tj + Tt is determined for the purpose of querying historical data from database. The function Mean ^k, Slqt j, D h provides the mean of available space count for time slot Slot j using history data. The enquired mean values as well as current value are used to perform the prediction. Summation A i is the available space count determined by Shift Prediction algorithm. It should be noted that the output of Algorithm 1 is the mean parameter to be used in (7). According to the assumptions A10 and A11, with shorter driving duration the system could apply the Shift Prediction Algorithm, while with longer driving duration, the history mean value should be used as the predicted remaining available space count. The later method is referred as Historical

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Time Lag Fig 4 Autocorrelation coefficient of available space count.

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Slot j = findSlot ^ t j h Slot i = findSlot (t j + Tt ) A j is the available space count on time t j , date D . n j = Mean ^k, Slot j , D h n i = Mean ^k, Slot i , D h Ai = ni - nj + Aj


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Algorithm 2. Threshold_Estimation( k, t j , ∆t, Test_Days). Input: Parking lot k, current time t j , driving duration Tt, Testing data set Test_Days Output: Switching threshold DT 1 Slot j = findSlot ^ t j h 2 while period is 5 to MAX_PERIOD then 3 while D x ! Test_Days then 4 a is the actual available space count on time t j + Dt 5 M x = Abs ^a - Mean ^k, Slqt j , D x hh 6 S x = Abs ^a - Shift_Predictiqn ^k, t j , Tt, D x hh 7 End 8 n m = mean ^M x h 9 n s = mean ^S x h 10 if n m 1 n s then return period end end

Algorithm 3. Probability_Estimation( k, t j , Tt, D, Test_Days). Input: Parking lot k, current time t j , driving duration Tt, current date D, Test data period Test_Days Output: Parking Probability Pk ^t j + Dt h 1 Slot j = findSlot (t j + Tt ) 2 v i = Stdev ^k, Slot i , D h 3 DT = Threshold_Estimation ^k, t j , Dt, Test_Days h 4 if Dt 1 DT then 5 Count = Shift_Prediction ^k, t j , Dt, D h 6 else 7 Count = Mean ^k, Slot j , D h end 8 Pk ^t j + Dt h = Norm_Prob ^Count, v i h

Mean method. The system alters the prediction method from Shift Prediction Algorithm to Historical Mean method when the estimated driving duration exceeds a threshold value. The threshold value is obtained by an iterative process comparing the accuracy of prediction result by Shift Prediction with Historical Mean. The driving duration for which Historical Mean outperforms Shift Prediction for the first time is considered as the threshold value. The pseudo code to obtain the threshold value of driving time is described in Algorithm 2. Algorithm 3 is used to estimate the parking probability at time t j + Tt. The standard deviation parameter is obtained by the function Stdev( k, Slot i, D ) which queries the history data. For each given parking lot PL k and each time slot Slot j, this study applies the Threshold Estimation Algorithm to derive the threshold value D ^t’, k h for all time t’ d Slot j by analyzing the previous available space count data of Test_Days days recorded in the parking information database. Once, the mean and standard deviation parameters are determined, the function Norm_Prob(Count, v i ) evaluates equation (7) to estimate the probability Pk ^t + Tt h . Note that the two methods used to estimate probability differs in

the way that one (Shift Prediction) uses history as well as current data whereas the other one (Historical Mean) only uses history data. Based on the threshold, the appropriate method is selected by algorithm 3.

C. Discussion Despite the parking probability prediction algorithm’s advantages, it does have some limitations. First, parking behavior of customers on holidays is unique. The space count of each parking lot seriously limits the algorithm’s usefulness in parking probability prediction. Particularly challenging is the parking behavior on junction day between regular day and holiday as parking behavior of customers on holiday can be very different from regular days. Secondly, due to use of normal approximation for skellam random variable which models the remaining available parking space, the suitability of the algorithm is limited to certain conditions such as large number of vehicles arriving in and departing out of the parking lots or large value of sum of arrivals and departures. The accuracy of the prediction algorithm is higher for parking lots which exhibit these characteristics.

IV. Experiment Result A. Experiment Setup The parking information database maintains the history data for more than 260 parking lots. However, this study presents the experimental results of only four representative parking lots. For each parking lot, the history data are divided into learning data and testing data according to the time. The learning data are used to estimate the mean and standard deviation of the available space count for each time slot. Figure 5 presents the mean and standard deviation of the available space count for the four parking lots. For each time slot, the threshold for applying the Shift Prediction Algorithm is determined by the Threshold Estimation Algorithm. The testing data are used to evaluate the result of our proposed methods. Information of holidays are not included in our experiment since the parking behavior on holidays is not the same as weekday and this study does not collect enough sample size for studying parking behavior on holidays. A maximum driving duration is set to the maximum value of iteratively attaining the switching threshold. We implement simple java program to perform the statistics and database operations. The settings are shown in Table 1. In order to validate the proposed methods, we used Moving Average method [32] which is widely adopted to analyze time series data.

B. Experiment Result Since A10 and A11 are the key assumptions for proposing the shift prediction algorithm, the first experiment is designed to simply test whether the real data validates the two assumptions. The experimental results are shown in


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Fig 5 Mean and standard deviation of available space count (a) Parking lot PL 1 in a cinema, with parking space capacity 511. (b) Parking lot PL 2 in a residential area, with parking space capacity 256. (c) Parking lot PL 3 in a suburban area, with parking space capacity 62. (d) Parking lot PL 4 near the Kaohsiung International Airport, with parking space capacity 20.

Figure 6. In this experiment, all parking lots are investigated considering driving duration of 5 minutes to maximum driving duration of 330 minutes. In Figure 6 (a), the absolute difference of Shift Prediction in parking lot PL 1 for 10 minutes driving duration is the lowest with average value of 5.26. Prediction for 60 minutes produces higher absolute difference with mean value 12.64. Highest absolute difference in PL1 is observed for 110 minutes. Figure 6 (b) displays the result of Shift Prediction in parking lot PL 2 . Although the outcome is better than that of PL 1, the impact of driving duration on the absolute difference remains same in both parking lots. It is also noticed that parking lots with less capacity experience small absolute difference. The result can also be verified in Figure 6 (c) and (d). The comparison verifies the accuracy of Shift Prediction, shown by the absolute difference between the predicted value and the actual value of remaining available space count. The results demonstrate that the Shift Prediction performed better when the driving duration is less. On the other hand, it performed worse as the predicting time period becomes longer. For different parking lots from larger capacity in PL 1 to less capacity in PL 4, a consistent experimental results support the assumption A10 and A11. In this paper, we propose the Shift Prediction Algorithm to improve the probability estimation accuracy in short driving

duration. To verify this proposal, the second experiment compares the accuracy of the Shift Prediction Algorithm with the accuracy of Historical Mean method which applies equation (7) directly without considering the current situation. Besides, we also portrayed the accuracy of Moving Average method and discuss the performance comparisons with Shift Prediction and Historical Mean methods. Since the frequency of the event that available space count becomes 0 decreases with increase in parking space capacity, the second experiment only includes the parking lot PL 3 and PL 4 . As shown in Figure 7(a), for parking lot PL 3, the prediction accuracy of Historical Mean is worse than Shift Prediction significantly. The mean of absolute difference between the Table 1. Experiment settings. Learning data

2010/11/23 – 2011/1/25

Testing data

2011/1/26 – 2011/3/28

Holiday data

Not included

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330 minutes

Parking lots

4 parking lots

Real-time data inquiry

Every 5 minutes


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Fig 6 Comparison of absolute difference shown in parking lots when driving duration is 10, 60, and 110 minutes. (a) PL 1, capacity = 511, (b) PL 2, capacity = 256, (c) PL 3, capacity = 62, and (d) PL 4, capacity = 20.

prediction of Shift Prediction and real data is 1.05, while the mean of absolute difference in case of Historical Mean is 3.62. Moving Average outperforms Historical Mean. This is because, in Moving Average method, the parking space availability at a given time slot is predicted based on the availability in previous time slots. Therefore, the average value of a number of accumulated predicted values provides better prediction than Historical Mean. However, the absolute difference of moving average is much larger than that of shift prediction. The rationale behind this fact is that Shift Prediction takes into consideration the correlation between observations small duration apart and thus predicts with higher accuracy. Figure 7 (b) shows outcomes for driving duration 150 minutes in PL 3 . It is observed that the prediction result of Historical Mean is still worse than Shift Prediction. But, the difference between performances of both methods is insignificant. On the other hand, the performance of Moving Average is now closer to shift prediction. In Figure 7 (c), with longer driving duration (i.e 300 minutes), the Historical Mean remains better than Shift Prediction most of the time. Figure 7 (d), (e), and (f) show similar observations for parking lot PL 4 . The observations in Figure 7 verify

the fact that when the driving duration is short, the Shift Prediction produces the most satisfactory result because it combines the history statistics as well as current information. However, its accuracy decreases with driving duration. The current information is less likely to be related with space count after a long period and hence it usually causes inaccurate prediction. On the contrary, the Historical Mean produces worse result with short driving duration, but its outcome holds a stable trend. As the predicting duration becomes longer, we can alter the predicting function from Shift Prediction to Historical Mean according to the value of driving duration threshold. Finally, Figure 8 shows the value of driving duration threshold for parking lots PL 1, PL 2, PL 3 and PL 4 . The absolute difference is calculated as mean of the difference between predicted value and actual value for every time slot in each day of the test days. Figure 8 (a) shows the absolute difference for PL 1 . The historical mean attains values from 25.36 to 27.1. Shift Prediction performs well up to driving duration 365 minutes after which it provides less accuracy than Historical Mean. Thus 365 minutes can be set as the driving duration threshold for parking lot PL 1 . The


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Fig 7 Performances of shift prediction, historical mean and moving average. (a) PL 3, driving duration 5 minutes, (b) PL 3, driving duration 150 minutes, (c) PL 3, driving duration 300 minutes, (d) PL 4, driving duration 5 minutes, (e) PL 4, driving duration 150 minutes, and (f) PL 4, driving duration 300 minutes.

absolute difference for parking lot PL 2 is demonstrated in Figure 8 (b). It is noticed that driving duration threshold of 390 minutes can be used to decide the appropriate prediction algorithm. As shown in Figure. 8(c), in case of parking lot PL 3, the accuracy of Historical Mean remains almost

stable by having value from 3.6 to 4.1. The accuracy of Shift Prediction is outstanding at the beginning when the driving duration is very small. As the driving duration increases, the accuracy gets reduced. The Historical Mean outperforms Shift Prediction when the driving duration is higher


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than 250 minutes. This experiment shows that, in most time slots, the proposed probability estimation algorithm can consider a driving duration threshold of 250 minutes to switch the prediction method from Shift Prediction to Historical Mean in order to enhance the prediction accuracy in parking lot PL 3 . Similarly, Figure 8 (d) shows that the Historical Mean provides higher accuracy than Shift Prediction when the driving duration is greater than 275 minutes. Thus, 275 minutes can be used as the driving duration threshold in the probability estimation algorithm for parking lot PL 4 .

V. Conclusion and Future Works The finding of this research leads to a parking probability prediction algorithm along with a cost model which will allow us to implement a recommendation sequence of parking lots. In general, the parking probability prediction algorithm will be useful to improve prediction of parking space after a short driving duration as well as after a long driving duration. On a more specific basis, this method could serve to reinforce the result of prediction by evaluating the proposed algorithm and obtain a threshold to

switch between two proposed methods in order to achieve the optimal prediction result. Future research should include designing an algorithm that determines and distributes the exact location of available parking space to drivers on the way. Besides saving time and fuel, this research initiative would relive drivers from the frustrating experience of looking for an empty slot especially in big and busy parking lots. Aside from using mean and standard deviation of history data, the short-period prediction can be unpredictable. Due to this characteristic, we would like to apply the concept of Brownian motion to simulate the uncertainty of the variation of remaining available space count.

About the Authors


Eric Hsiao-Kuang Wu received his B.S. degree in computer science and information engineering from National Taiwan University in 1989. He received his Master and Ph.D. in computer science from University of California, Los Angeles (UCLA) in 1993 and 1997. 48

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He is a Professor of Computer Science and Information Engineering at National Central University, Taiwan. His primary research interests include Wireless Networks, Mobile Computing and Broadband Networks. He is a member of IICM (Institute of Information and Computing Machinery) and IEEE. Chi-Yun Liu graduated from National Central University with B.S. and M.S. degree in Computer Science and Information Engineering. Her research interests include Queuing Theory, Wireless Network, and Smart Phone Application Development. Jagruti Sahoo received the M.Tech. degree in Computer science from Utkal University, Bhubaneshwar, India, in 2006, and her PhD degree in Computer Science and Information Engineering from Natioanal Central University, Taiwan in Jan., 2013. She is currently working as a Post-Doctoral Fellow in the Department of Electrical and Computer Engineering, University of Sherbrooke, Canada. Her research interest includes vehicular ad hoc networks and wireless sensor networks. Ming-Hui Jin received his B.S. degree in mathematics from National Central University in 1995. He received his Ph.D. in computer science from National Central University in 2003. He is now a principal engineer in the Institute for Information Industry. His primary research interests include Location-based Services, Telematics, Medical Information System, Computer Vision, Wireless Sensor Networks, Mobile Computing, Queuing Theory, Scheduling, Data Mining and Database System. Shu-Hui Lin received MBA degree in National Taiwan University of Science and Technology. Now she is an associate planner in the Institute for Information Industry. Her primary research interests include Telematics, The Internet of Thing, and Radio Technology.

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