ANALYSIS DESIGN AND SIMULATION OF ADVANCED PARKING MANAGEMENT SYSTEMS By ZHIBIN CHEN A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 201 7
201 7 Zhibin Chen
To my parents and my wife
4 ACKNOWLEDGMENTS First of all, I would like to express my sincere gratitude to my advisor, Dr. Yafeng Yin. As an advisor, his profound knowledge professional attitude, and rich creativity have impressed and enlighten ed me Without his individualized guidance, constant support, encouragement, and patience, I would not have finished this dissertatio n. I find myself extremely fortunate to be one of his Ph.D. student s I would like to thank Dr s Lily Elefteriadou Scott Washburn, Sivaramakrishman Srinivasan, and Yongpei Guan for serving as my committee members, providing valuable suggestions on my dis sertation and offering inspiring courses, which have and will continue to play an important role on my research I also would like to thank many faculties and staffs such as Ines Aviles Spadoni, Dr. Guanghui L an Dr. Sojung Kim and Dr. Siriphong Lawphon gpanich for t heir precious support Furthermore, I am very grateful to my colleagues and friends for their company and friendship. Last ly but most importantly, I would like to thank my parents Guanjin Chen and Xiunong Xiao, and my wife, Fangfang Yuan, fo r their selfless and u biquitous love, which supports me all the time.
5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 8 ABSTRACT ................................ ................................ ................................ ................................ ... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 12 1.1 Background ................................ ................................ ................................ ....................... 12 1.2 Problem Statement and Dissertation Objective ................................ ................................ 16 1.2.1 Analysis of Advanced Management of Curbside Parking ................................ ..... 16 1.2.2 Smartphone based Parking Reservation System ................................ .................... 16 1.2.3 Smartphone based Parking Navigation System ................................ ..................... 17 1.2.4 Microscopic Parking Simulation ................................ ................................ ............ 17 1.3 Dissertation Outline ................................ ................................ ................................ .......... 18 2 LITERATURE REVIEW ................................ ................................ ................................ ....... 19 2.1 Analysis and Design of Advanced Parking Management Systems ................................ .. 19 2.1.1 Parking Reservation System ................................ ................................ ................... 19 2.1.2 Parking Navigation System ................................ ................................ .................... 25 2.2 Parking Simulation ................................ ................................ ................................ ........... 30 3 ANALYSIS OF ADVANCED MANAGEMENT OF CURBSIDE PARKING ................... 35 3.1 Analytical Models ................................ ................................ ................................ ............. 35 3.1.1 Steady State of Status Quo ................................ ................................ ..................... 36 3.1.2 Stea dy State with Parking Information ................................ ................................ ... 39 3.1.3 Steady State with Parking Reservation ................................ ................................ ... 43 3.2 Verification ................................ ................................ ................................ ....................... 44 3.3 Comparison ................................ ................................ ................................ ....................... 46 3.4 Summary ................................ ................................ ................................ ........................... 51 4 PARKING RESERVATION FOR MANAGING DOWNTOWN CURBSIDE PA RKING ................................ ................................ ................................ ............................... 58 4.1 Parking Reservation with Perfect Information ................................ ................................ 59 4.1.1 Static Scheme Design ................................ ................................ ............................. 59 4.1.2 Dynamic Scheme Design ................................ ................................ ....................... 60 4.2 Parking Reservation with Private Information ................................ ................................ 61
6 4.2.1 Incentive to Lie ................................ ................................ ................................ ....... 61 4.2.2 Static Scheme Design ................................ ................................ ............................. 62 4.2.3 Dynamic Scheme Design ................................ ................................ ....................... 65 4.3 Numerical Example ................................ ................................ ................................ .......... 67 4.4 Revenue Redistribution ................................ ................................ ................................ .... 68 4.5 Summary ................................ ................................ ................................ ........................... 69 5 AN ADVANCED PARKING NAVIGATION SYSTEM FOR DOWNTOWN PARKING ................................ ................................ ................................ ............................... 74 5.1 Parking Navigation System ................................ ................................ .............................. 75 5.2 Matching Mechani sm Design ................................ ................................ ........................... 75 5.2.1 Two Sided Match ................................ ................................ ................................ ... 75 5.2.2 Distributed Stable Match ................................ ................................ ........................ 80 5.3 Simulation Experiment ................................ ................................ ................................ ..... 82 5.4 Summary ................................ ................................ ................................ ........................... 86 6 MICROSCOPIC PARKING SIMULATION ................................ ................................ ......... 93 6.1 Parking Simulation Model ................................ ................................ ................................ 93 6.1.1 Transportation Network ................................ ................................ .......................... 94 6.1.2 Parking Behavior of Drivers ................................ ................................ ................... 94 6.2 Simulation Experiment ................................ ................................ ................................ ..... 96 6.2.1 Simulation Setting ................................ ................................ ................................ .. 96 6.2.2 Simu lation Result ................................ ................................ ................................ ... 96 6.3 Summary ................................ ................................ ................................ ........................... 98 7 CONCLUSION ................................ ................................ ................................ ..................... 106 LIST OF REFEREN CES ................................ ................................ ................................ ............. 109 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 115
7 LIST OF TABLES Table page 3 1 Walking times and ex pected walking times at various starting spaces ............................. 53 4 1 Parking costs and request sequences ................................ ................................ .................. 71 4 2 Parking costs at system opti mum ................................ ................................ ....................... 71 4 3 Untruthful parking costs ................................ ................................ ................................ .... 71 4 4 Experimental results ................................ ................................ ................................ ........... 71 5 1 Preference list of three drivers and three spaces ................................ ................................ 88 5 2 Simulation setting for the basic scenario ................................ ................................ ........... 88 5 3 Simulation result ................................ ................................ ................................ ................ 88 6 1 Average driving time and walking time in different scenarios ................................ .......... 99 6 2 Average driving time and walking time in st atus quo scenarios with different cruising roads ................................ ................................ ................................ ..................... 99
8 LIST OF FIGURES Figure page 2 1 Route choice for drivers ................................ ................................ ................................ ..... 33 2 2 The probability to continue driving towards the destination ................................ ............. 33 2 3 Simulation procedure in SUSTAPARK ................................ ................................ ............ 34 3 1 An abstract setting of curbside parking at a one way street ................................ .............. 54 3 2 Probability of being available in the status quo scenario ................................ .................. 54 3 3 Probability of being available with information ................................ ................................ 54 3 4 The relation between parking with real time information and reservation service ........... 54 3 5 Probability of being available ................................ ................................ ............................ 54 3 6 Expected walking times from analytical model and simulation ................................ ........ 55 3 7 Results of fitting index vs. parking spaces in different scenarios ................................ ...... 56 3 8 Results from analytical model in different scenarios ................................ ......................... 56 3 9 Flow charts of and ................................ ................................ .................... 57 4 1 Parking reservation scenario ................................ ................................ .............................. 72 4 2 Parking reservation scenario with misreported destination ................................ ............... 72 4 3 Percentage of revenue redistributed to drivers ................................ ................................ ... 73 4 4 Individual parking fee and re bate of every driver in a selected scenario ........................... 73 5 1 Architecture of parking navigation system ................................ ................................ ........ 89 5 2 Procedure of parking navigat ion system ................................ ................................ ............ 89 5 3 Screenshot of the parking simulation ................................ ................................ ................. 90 5 4 Effects of arrival rate on different system performance measures ................................ .... 91 5 5 Effects of market penetration on different system performance measures ........................ 92 6 1 Components in the Road Traffic Library ................................ ................................ ........... 99 6 2 A small road network representation ................................ ................................ ............... 100
9 6 3 Properties of parking lot ................................ ................................ ................................ ... 100 6 4 Parking simulation flowchart of different scenarios ................................ ........................ 101 6 5 Parking simulation process of different scenarios in AnyLogic ................................ ...... 102 6 6 Parking simulation network topology ................................ ................................ .............. 10 3 6 7 A screenshot of the parking simulation ................................ ................................ ........... 104 6 8 Number of differen t types of vehicles in the network at different simulation times ....... 105
10 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for t he Degree of Doctor of Philosophy ANALYSIS DESIGN, AND SIMULATION OF ADVANCED PARKING MANAGEMENT SYSTEMS By Zhibin Chen May 201 7 Chair: Yafeng Yin Major: Civil Engineering Due to the increasing car ownership, parking has become a major problem in many large cities and downtown areas all over the world. Cruising for parking is time consuming and frustrating for driver s and further makes traffic congestion more severe by slowing down through vehicle s and increasing traffic volume on road s Advanced par king management services, including parking information, reservation and navigation, aim to help drivers find parking spaces quickly. Although the latter two are still in their infancy t he proliferation of advanced smartphones and the development of sensi ng and wireless communication technologies provide tremendous opportunity for advanced parking management This dissertation devotes to analyzing the impacts and implications of those emerging parking management services, and providing guidance on their de velopment and deployment. Specifically we first establish analytical models in a highly stylized and abstract setting to understand how real time parking information and reservation services change the spatial distribution of parking activities. Results show that, compared with the status quo, the reservation service can improve the performance of the parking system, while providing information may not. In light of the finding, we proceed to design a smartphone based parking
11 reservation system that manage s a finite number of curbside parking spaces in a downtown area in a way to minimize the social cost of parking information (e.g., destination) on the parking cost In the following, as the reservation service ma y result in the waste of public resource (e.g., some spaces may be reserved to someone that will be absent), we develop a parking navigation system to manage the public parking spaces in downtown areas. P articular ly a two sided matching model is adopted t o allocate the parking resource so that each driver will be guided to her most appropriate space (if any) and each open space will be assigned to at most one driver Lastly as it is rather difficult to develop analytical models to explore the local impac ts of different parking management services on a general network, we propose to establish a microscopic parking simulation that can be of help to government agencies for deployment planning of parking services
12 CHAPTER 1 INTRODUCTION 1.1 Background Parki ng is a growing problem in many downtown areas around the world. The time spent on searching for a desirable parking space often constitutes a substantial portion of travel cost of individual drivers. Shoup ( 2006 ) reviewed empirical studies conducted in th e U.S. and found that the average time to search for a curbside parking space ranged between 3.5 and 14 minutes. Using a more conservative estimate of three minute search time, Shoup calculated that the cruising for a curbside parking yields 1,825 vehicle miles each year. For a city like Chicago with over 35,000 curbside parking spaces ( Ayala et al., 2011 ), this translates into approximately 64 million vehicle miles travelled, 3 million gallons of gasoline consumed and 30 thousand tons of CO 2 emitted every year On top of these, the cruising yields additional traffic demand to the downtown road network, making already congested streets even more congested. Shoup (2006) pointed out that the share of traffic cruising for parking spaces in some major city (e.g. Detroit, Freiburg, Cambridge) can reach to more than 30%. A study conducted in the district of Schwabing, Munich estimated that the proportion of traffic searching for free parking spaces amounts to 44% of the entire traffic ( Caliskan et al., 2006 ). Adva nced parking management services, including parking pricing (e.g., Glazer, 1992; Ayala et al., 2012 b ; Fosgerau and de Palma, 2013 ; He et al., 2015 ), information (see, e.g., Caicedo, 2010; Kokolaki et al., 2013) reservation (e.g., Teodorovic and Lucic, 200 6; Delot et al., 2009 ) and navigation (e.g., Shin and Jun, 2014; Ayala et al., 2012a,c; Idris et al., 2009) aim to help drivers find parking spaces quickly and reduce the deadweight loss associated with the cruising for parking The pricing service manag es parking spaces via imposing parking fees on drivers for using parking spaces; information service provides real time availability and prices of
13 parking spaces; the reservation service allows drivers to reserve a parking space before departure or on the go, while the navigation service guides them to an open space ( FHWA, 2007 ) Although the former two ha ve been implemented in a number of cities (e.g., San Francisco New York, and Chicago ) the latter two are still in their infancy. However, the proliferat ion of advanced smartphones and the development of sensing and wireless communication technologies provide tremendous opportunity for advanced parking management. The number of smartphone users has been rising steadily and forecasts suggest that by 2019, the number could reach 236 million in the U.S. ( Statista, 2016 a ) and 2 659 million worldwide (Statista, 2016b) S ensors that enable to measure occupancy, turnover, and parking duration for each parking space, have been installed for around 1 7,000 parking spaces in San Francisco and Los Angeles and the real time information can be distributed to the public through Internet (Djuric et al., 2016) We envision in the near future a widespread adoption of smartphone based advanced parking management systems, wh ich allow motorists to use smartphone applications to view the real time availability and prices of parking spaces as well as to further select and reserve the spaces. The applications may also guide motorists to an open or reserved parking space. From the perspective of parking management authorities, the systems can be designed to better manage parking demand so as to reduce traffic congestion and emission or increase parking revenue For example, Teodorovic and Lucic (2006) proposed a parking reservatio n system for revenue management, which makes Mackowski et al. (2015) designed a dynamic parking pricing system to manage parking demand in a way to balance parking occupanc y as well as to reduce traffic congestion. Besides these theoretical frameworks w e further note that the smartphone based parking applications have begun to
14 emerge, e.g., ParkMe and SFpark for parking information, SpotHero and ParkingPanda for parking res ervation. It is of critical importance and also intriguing to understand the impacts and implications of th e se emerging parking management services, and provide guidance on their development and deployment. Although the pace of parking research has increas ed markedly in recent years (see, e.g. Inci, 2015; Cao and Menendez, 2015; and Boyles et al., 2015, for recent reviews), many focus on pricing policies (e.g., He et al., 2015; Mackowski et al., 2015; Qian et al., 2012 ; Qian and Rajagopal 2014 ; Zakharenko 2016 ; Liu and Geroliminis, 2016 ), and analytical studies of other advanced parking manag ement services, i.e., information, reservation and navigation are still limited. Among a few exceptions, Arnott and Rowse ( 1999 ) discussed the value of a particular parking management system where each driver is informed of the available parking space closest to her destination and if she decides to drive, the space will be reserved to her. They pointed out that the system is welfare improving when the parking occupan cy is high without the system. Liu et al. ( 2014a,b ) explored parking permit scheme s and reservation strateg ies the social welfare. On the other hand, in order to analyze advanced parking manageme nt services, it is vital to capture Generally, this type of models can be classified into analytic al approaches and simulation based approaches ( Boyles et al. 2015). Among the former, Arnott and his collaborato rs ( 1999 ; 2006 ; 20 10 ) proposed a parking search strategy that a driver decides where to start cruising for parking, and parks immediately if a parking space is available; otherwise, she will keep cruising around her destination. Leurent and Boujnah ( 2014 ) explored herself to other lots according to a matrix of transition probabilities determined by their
15 Some other related studies can be referred to Guo et al. (2013), Tang et al. ( 2014 ) Boyles et al. ( 2015 ) and Cao and Menendez (2015). For the latter, s imulation based approaches including PARKAGENT (Benenson et al., 2008) and SUSTAPARK (Dieussaer et al., 2009) ar e developed to imitate the parking search process in the city by designing behavioral rules for drivers. Although great efforts have been made on designing advanced parking management services and analyzing their impacts, a) none literature has been propo sed to compare the impacts of different parking management services; b) the existing reservation services are either in efficient regarding improving social welfare as they simply adopt the first come first served (FCFS) basis, or unpractical due to strong assumptions such that parking requests are made at the same time, and drivers will truthfully report their p rivate information (e.g., destination), which is closely related to the parking cost ; c) the proposed navigation systems may intensify the parking competition, as more than one driver will be guided to the same space. Furthermore, most of these systems need to disclos e which may lead to the public antipathy ; d) the established parking simulation tools can neither captur e sophisticated car following and lane changing behaviors, nor be applicable to intricate networks e.g., networks with signal control. To fill the gap s t his dissertation aims at a) establishing analytical models to compare the impacts of parking informat ion and reservation services on the spatial distribution of parking activities ; b) developing a smartphone based parking reservation system to manage curbside parking spaces in a downtown area in a way to maximize the social welfare taking account of the impacts of on the parking cost ; c) proposing a novel parking navigation system for downtown parking so as to guide drivers to their most appropriate spaces (if any) without disclosing their private information and intensifying the parking
16 competition ; d) designing a microscopic parking simulation model, which is capable to capture the local impact of parking search behavior in complicated networks and serve as a tool for decision makers to analyz e different parking policies. 1.2 Problem Statement and Dissertation Objective 1.2. 1 Analysis of Advanced Management of Curbside Parking U nderstand ing the impacts and implications of various emerging parking management services can provide guidance on their development and deployment In this dissertation, interest is restricted to analytically explor e how real time parking information and reservation change the spatial distribution of parking activ ities. W e analyze stylized setting where an attrac tion (destination) is located on a long one way street and on street parking spaces are scattered around the destination; drivers are assumed to find a space to park to minimize their walking time to the destination. Analytical models are established to de scribe the search outcomes and compare the impacts of parking information and reservation services. An agent based simulation experiment is then conducted to verify the results draw n from the analytical models. 1.2.2 Smart p hone based Parking Reservation System Parking reservation service holds great promise to be an efficient approach to eliminate or reduce the parking cruising time, we thus consider a smartphone based parking reservation system that manages a finite number of curbside parking spaces loca ted at different places in a downtown area. We first illustrate the need for designing a reservation scheme to minimize the total parking cost. Given that the parking cost is closely related to a private information of drivers, i.e., their final destinatio ns, we show that drivers have incentive to misreport the information, and thus lead to undesired system output. We then apply a mechanism to ensure all drivers to provide truthful information and allocate parking spaces optimally.
17 1.2. 3 Smart p hone based Pa rking Navigation System Although parking reservation systems are of efficiency with respect to reduce parking cost, in practice, they are seldom applicable to managing public parking space s. One reason is that reservation services may lead to the waste of the public resource For example, some parking spaces may be reserved to someone who will be absent Also, to guarantee parking space s for driver s with reservation, the reserved parking space s cannot be utilized by any other driver even if they are current ly vacant In light of such a limitation providing parking navigation for public parking spaces seems more favorable to the public as these public resources can be fully exploited However, most of the current navigation systems are not ready for practic al implementation, due to expensive computation, strong assumptions or the need for disclosing open space, which intensifies the parking competition. Consequently, the a doption of navigation system in reality is still limited. T o cope with the above shortcomings we adopt a stable matching algorithm to design a navigation system which manages a finite number of parking spaces in a downtown area. Via this system, drivers w ill be guided to their most appropriate spaces (if any) at all times without disclosing their private information and each open space will be assigned to at most one driver Simulation experiments are then conducted to demonstrate the performance of the p roposed navigation system compared with other navigation systems. 1.2.4 Microscopic Parking Simulation It is rather difficult, if not impossible, to develop analytic al model s to explore the impacts of different parking management services on a general net work due to the difficulty of modeling the sophisticated parking search behavior of drivers Furthermore, parking management services are normally app lied to address parking problem in particular areas, such as a downtown area, instead of a whole city, so it is vital to capture the local impact due to the parking search
18 behavior within these relative small areas. In a nutshell it is necessary to develop a microscopic parking simulation which is capable to subtly mimic the parking search behavior consider ing car following and lane changing behaviors, as well as different traffic control measures e.g., signal control under different types of parking management services To this end, we consider AnyLogic ( http://www. anylogic.com/ ) to construct an agent based microscopic parking simulation model that can be of help to government agencies for deployment planning of parking services T hree scenarios, including status quo, with information provision, and with reservation service, will be conducted as application examples. 1.3 Dissertation Outline The dissertation is organized as follows Chapter 2 provides an overview of related studies, including the analysis and design of advanced parking management systems, and the d evelopment of parking simulation Based on a stylized setting, Chapter 3 establishes analytical models to compare the impacts of parking information and reservation services on the spatial distributi on of parking activities. Smart phone based parking reserv ation and navigation systems are proposed to manage a finite number of parking spaces in a downtown area in Chapter 4 and 5, respectively. A microscopic parking simulation is developed in Chapter 6. Chapter 7 concludes the dissertation and provides recomme ndations for follow up studies.
19 CHAPTER 2 LITERATURE REVIEW In this chapter, we first present the recent literature on the analysis and design of parking reservation and navigation systems which are still in their infancy We then have an overview of th e existing parking simulation models which aim at serving as tool s to analyze the impact of different parking policies. 2.1 Analysis and Design of Advanced Parking Management Systems 2.1. 1 Parking Reservation System Previous analytical studies of parki ng reservation service are limited. Among a few exceptions, Yang et al. (2013) pointed out that an appropriate provision of both reserved and unreserved parking spaces can spread the departure of those morning commuters and hence reduce their total travel cost. Assum ing that a residential area and a city center are connected by one highway containing a single bottleneck and one parallel transit line Yang et al. (2013) first proposed the morning bi modal commuting equilibrium with parking spaces constraint s at the city center. Three different scenarios are considered: (1) all parking spaces are reservable; (2) all parking spaces are non reservable; and (3) the mix of the above two. The system performance s of the three scenarios are then measured and compare d. It is found that the maximum percentage of total cost reduction is always not less than 50% when the system optimum is achieved by setting all parking spaces to be reservable; while it is always less than 50% when the system optimum occurs in the other scenarios. Liu et al. (201 4 a) extended the model of Yang et al. (2013) by considering expirable parking reservation s C ommuters with a parking reservation need to arrive at the parking spaces before the expiration time ; o therwise the parking reservati on will expire. Liu et al. (2014a) first explored the auto commuting equilibrium under the parking reservation scheme with identical
20 expiration times and then turned to the scheme with differentiated expiration times The design of the latter scheme inclu d es how to determine the number of reserv able parking spaces, how many groups these spaces should be classified and how to identify the expiration time for each group. The reservation scheme with multiple differentiated expiration times is found to be mor e effective with respect to reduce the total travel cost, compared with the non expirable reservation scheme proposed by Yang et al. (2013) as it can further smooth out s to the bottleneck Liu et al. (2014b) proposed a novel permit sche me t o implement parking reservation for mitigating parking competition and bottleneck congestion. Specifically, a certain number of tradable parking permits are distributed to commuters every day. The commuters without parking permits have to compete for t he rest parking spaces in which permits are not required on the FCFS basis, while those with parking permits can reserve the associated parking spaces but have to arrive the re before the expiration time ( if the permits are expirable ) Both the commuting eq uilibriums with homogeneo us and heterogeneous commuters regarding the value of time are considered. It is pointed out that, if all the parking spaces are requiring for permits, and the permits can be divided into an infinite number of classes, each of whic h has a certain expiration time, then the proposed permit scheme can eliminate the queuing delay at the bottleneck as well as the competition for parking spaces. Teodorovic and Lucic (2006) proposed a parking reservation system for revenue management, w for parking, considering uncertain future parking demand and supply An i nteger programming problem is first develop ed to explore the best parking strategies for various patt erns of vehicle arrivals :
21 (2 1) (2 2) where is the set of parking tariff classes; is the set of requests for park ing in the th class; is the tariff for parking in the th class; and denote the arrival and departure time of the th car belonging to the th parking tariff class respectively ; is a binary decision variable, equ al to 1 if the th request belonging to the th parking tariff class is accepted, and 0 otherwise; is the garage capacity; is the set of time intervals when the garage is operating; is a binary parameter, indicating whether the th car belonging to the th parking tariff class will be in the garage during the th time interval. Specifically, it is determined by : where is the garage opening time and is the length of one time interval. In the above, the objective is to maximize the revenue of the garage; Equations (2 1) are the garage capacity constraints, gu aranteeing the number of assigned spaces not to exceed the garage capacity; Equations (2 2) specify to be binary variables. Learning from the best strategies emerging from the above integer programming specific fuzzy logic rules are derived for the dec ision making. Numerical examples show that the proposed reservation system can generate more revenue than the one based on FCFS principle. Kokolaki et al. (201 4 ) proposed an auction based reservation system to allocate public parking spaces. In order to p ark at public parking spaces, drivers are required to submit bids to a central authority Three well known auction mechanism s including uniform price, discriminatory price and Vickrey auctions are implemented to award parking spaces to those with the highe st bids Numerical results demonstrate that the proposed reservation system can
22 increas e the revenue raised from the public parking spaces, and does not necessarily yield higher cost for drivers due to the e limination of cruising cost Suppose there ex ist s a platform in which the owners can lease their parking spaces and the drivers can reserve these shared parking spaces Shao et al. (2016) proposed a simple integer linear programming model to allocate the shared parking spaces in a way that maximize s the profit of the platform. It is assumed that the daily operation time of the platform is divided into intervals Let and be the total number of requests, i.e., parking demand, and parking spaces, respectively. Let if parking space is available in time interval and otherwise Let and be the start and end time interval of request where A binary indicator is introduced to represent whether parking req uest includes time interval That is , if ; otherwise. Furthermore, let represent that parking space is assigned to request and otherwise. Consequently, indicates whether parking space is occupied in time interval Given the above setting, the allocation model can be formulated as follows: (2 3 ) (2 4 ) (2 5) where and define the leasing and buying price of one parking space per time interval; is a predetermined positive parameter, representing the penalty of rejecting one request In the objective function, the first term rep resents the total revenue emerging from leasing parking spaces to drivers; the second term indicates the total cost for renting parking spaces from owners; and the third term is the negative effect due to request rejection. Constraint (2 3) ensure
23 that one request can be assigned to at mos t one parking space. Constraint (2 4) imply t hat each parking space can be assigned to at most one driver in each time interval. Constraint (2 5) ensure to be binary. Numerical results are provided to highlight that the profit under the proposed allocation model is not less than the one under the FCFS scheme. Furthermore, the former one reach its maximum value much earlier than the latter one imp lying the higher efficiency of the proposed model on raising revenue. Geng and Cassandras (2011 2012 ) designed a smart parking reservation system which can dynamically allocate parking spaces to drivers. It is worth highlighting that under the reservati on system, even if a driver has reserved a p arking space, s he still has chanc e to obtain a better one. In the system, drivers are classified into two groups. One is the waiting group, in which drivers are waiting for space assignment; while the other one i s the reserve group inclusive of drivers with assigned spaces. As it is a dynamic system, a set of decision points are considered. Let and define the drivers in the waiting and reserve groups a t the th decision point respectively Let d enote the total number of parking spaces, and describe the state of the th parking space at the th decision point, which is defined as below: Let define the cost for driver to reserve parking space at the th decision point defin e the walking distance from space to the destination of driver and represent the reservation status of driver at the th decision point which is given by :
24 Further, define by the set of free and reserved parking spaces at the th decision point. Then, the set of feasible parking spaces for driver at the th decision point can be specified as : where and are upper bounds of the cost for reserving a space, and the walking distance for driver respectively. The allocation of parking spaces is then formulated as the following mixed integer linear problem : (2 6 ) (2 7 ) (2 8) (2 9) (2 1 0 ) where is a decision variable. If parking space is assigned to driver then ; otherwise, represents the weighted cost for driver to be assigned to space which is defined as follows: where is a factor balancing the importance of the cost for reservation and the walking distance.
25 The first term of the objective function represents the total weighted cost of drivers and the second term is the penalty due to unsuccessful reservations. Constraint (2 6) delineate that drivers in the waiting group can be assigned to at most one parking space. Constraint (2 7) ensure each driver in the reserve group to be assigned to one space. Constraint (2 8) guarantee each parking space to be assigned to no more than one driver. Constraint (2 9) imply that drivers in the reserve group must be assigned to parking spaces that are not worse than their previous assigned spaces. Constraint (2 10) ensure to be a binary integer. A simple simulation is proposed to compare the performance of the developed system and the traditional navigation system, where vehicles are guided to their most favorable open parking spaces. Results demonstrate that the proposed system outperform the simple navigation system with respect to increasing the utilization o f parking spaces and reducing the parking cost. Boehle et al. (2008) conceptually described a city based parking r eservation and routing system. The reservation service allows participating drivers to reserve a parking space according to the FCFS basis Arnott and Rowse (1999) discussed the value of a particular parking reservation system where each driver is informed of the available parking space closest to her destination and if she decides to drive, the space will be reserved to her. They pointed out that the system is welfare improving when the parking occupancy is high without the system. 2.1. 2 Parking Navigation System Shin and Jun (2014) developed a smart parking navigation system in which drivers will be guided to the ir most favorable parking faci lity To use the system, drivers are required to provide their personal information, including their destination and current location T he appropriateness of a parking facility to vehicle is measured by a predefined parking utility function consideri ng driving distance (i.e., ) walking distance (i.e., ) parking price (i.e.,
26 ) traffic congestion level (i.e., ) and the degree of availability (i.e., ), which is shown as follows: where and are weight ed factors. In particular is equivalent to the number of cars heading to the parking facility under the navigation system, an d is given by : where is the driving duration for vehicle to arrive parking lot ; represents the number of free parking lots of parking facility at a certain time interval; an d delineates the average time headway of vehicles arriving parking facility at a certain time interval. A simulation conducted based on a city of Luxemburg points out that the proposed system is able to help increase the utilization of par king facilities and reduce the energy consumption. Delot et al. (2009) designed a cooperative parking protocol, in which a coordinator vehicle is designated for an available parking space and is responsible for broadcasting the availability information to a particular vehicle that is selected by the coordinator to occupy the space. First of all, the vehicle that departs a parking space is taken as the coordinator vehicle of the space, which is responsible to disseminate the availability information of the space. It sends a message describing the available parking space to the other vehicles in its vicinity within its communication range. However, this message does not specify the exact location of the parking space. If vehicles receiving the information are interested in the parking space, they have to provide their identifier as well as their personal information, such as their current location. Based on the provided information, the coordinator vehicle selects one of the interested vehicles,
27 according to p redefined rules, as the allocated vehicle, and sends it a nother message including detailed information about the parking space (e.g., exact location). Doing so, the competition of the parking space is expected to be mitigated. Numerical examples con ducted in the paper demonstrate that such protocol can reduce the average search time while increasing the percentage of useful provided parking information. Ayala et al. (2012a ,c ) presented a gravitational approach to guide drivers to parking spaces. Let define the function to measure the parking cost for vehicle parking at space then the gravitational force generated by parking space on vehicle is given by the following formula: whose directio n is from vehicle to space Define by as the composition of the computed force vectors generated by all available parking spaces on vehicle The proposed gravitational approach will guide vehicle to drive along the direction of Particularly, once vehicle is close enough to one specific available parking space e.g., less than a predefined distance it will be guided straightforward to that space. Simulation results imply that the gravitational approach can significantly red uce the parking search time compared against the traditional parking navigation algorithm, where each vehicle is guided to its most favorable available parking space As guiding more than one vehicle to one unoccupied parking space will inevitably aggrava te the parking competition Ayala et al. (2012c) considered the parking competition as a static game, and pointed out that the equilibrium parking assignment generated by the well known two sided matching algorithm (see, Gale and Shapley, 1962) can be used to allocate the parking resource to drivers such that each parking space will be assigned to no more than one vehicle, and each vehicle will have incentive to comply with the guidance ; Du and Gong (2016)
28 formulated the parking competition as a Poisson ga me, and further developed a decentralized and coordinated online parking mechanism to guide drivers to appropriate parking facility, such that the parking congestion can be reduced. Instead of simply assigning particular parking spaces to drivers, an algor ithm is proposed by Djuric et al. (2016) to design routing plans for each driver in order to maximize the expected utility along the routes. Suppose a rout ing plan consists of consecutive road segments, which are labeled as and Particularly, is the road segment where the driver is currently on. Let denote the probability of finding an available parking space on road segment define the driving time from segment to segment and define the walking time from segment Furthermore, define by as the utility of finding an available parking space on segment In this study, drive rs are assumed to park at the first available space they meet on their routing plan and then walk to their destination. Accordingly t he expected utility along the route is formulated as the following recursive formula: Given the parking probability of all road segments in th e network, a recursive routing algorithm is developed t o figure out the route plan with the maximum expected utility The basic idea is to extend the route plan segment by segment Specifically, if a neighbor segment can improve the expected utility and th e number of segments on the current route plan is less than then the segment will be added to the current route. Repeat this process until the number of segments on the route plan reaches Experiments based on the data obtained from 247 blocks
29 in San Francisco downtown area are provided. Results suggest that the proposed algorithm can reduce the parking search time considerably compared with the scenario with out using the system In addition to the above efforts on the parking resource assignment and routing plan of navigation system s several studies are proposed to explore the architecture of navigation system s the real time shortest path finding for navigation systems, the deployment and display configuration of parking variable message signs and the simulation of navigation systems For example, Idri s et al. (2009) explored a navigation architecture where drivers can be guided to the nearest empty parking space utilizing wireless sensor network and ultrasonic sensor Giuffre et al. (2012) presented an intelligent parking assistant system to manage off street parking lots. Boehle et al. (2008) designed a City Based Parking Routing System (CBPRS) where drivers can make parking reservation and further be guided to the reserved spaces. Particularly, an ant based distributed hierarchical routing algorithm i s adopted to find the shortest path for drivers considering the real time traffic condition Thompson et al. (2001) and Ni et al. (2015) developed mathematical programs to optimize the location and display configuration of parking variable message signs, s o as to reduce the parking cost, such as the queuing delay in parking lots, and travel times on the road Levy et al. (2015) applied an agent based simulation model, PARKAGENT (Benenson et al., 2008) to assess the benefit of using an intelligent parking n avigation system in a Diamond Exchange area in the Tel Aviv metropolitan area. Specifically, under the navigation system, drivers are assumed to always drive towards the non full parking lot that is closest to their destinations. If the parking lot turns o ut to be full when they arrive, they will drive to the second best non full parking lot in their list.
30 2. 2 Parking Simulation Benenson et al., ( 2008 ) proposed an agent based model named PARKAGENT on the ArcGIS framework to simulate the parking search behav ior in the city. The road network is generated automatically from GIS databases. Below are the rules to model the cruising behaviors: 1. Vehicles are generated at a predetermined distance 250 m from their destination, and then keep d riving ahead to the destin ation at a certain speed i.e., 25 km/h until the distance from the ir destination is equal to a predetermined distance i.e., 100 m Specifically, for the route choice, drivers are assumed to choose the connected road segment whose farther junction is clo ser to the destination than the one of any other connected road segment (see Figure 2 1 ). Such route choice behavior is applied for the whole model. Also, during this period the fraction of unoccupied parking spaces is estimated by : where and are the number of occupied and vacant spaces observed during this driving distance 2. Searching for parking spaces at a certain speed i.e., 12 km/h before reaching the destination. To facilitate such process, the expected number of vacant spaces is estimated as follows: If is very small, then the driver should park at the first vacant space she meets with Otherwise if is very large, the driver will keep driving towards the destination even if there are vacant spaces around. Figu re 2 2 delineates the probability for drivers keep ing on driving In particular, and will be re calculated according to the updated value of and when the driver is traveling
31 3. Searching for parking spaces after passing the destination. In this case the searching circle increase from 100 m to 400 m at a rate 30 m/min If the search time reaches 10 min then drivers are assumed to park at a private parking garage located at the destination. 4. Leave the system which is predetermined for each driver. Given the above rules, parking search behavior can be simulated in the PARKAGENT, and results including search time and walking time can be obtained The PARKAGENT has been adopted to analyze the impact of providing additional parking supply (Benenson et al., 2008), the benefit brought by providing navigation system (Levy et al., 2015), and the optimal parking occupancy rate (Martens et al., 2010). Dieussaer et al. ( 2009 ) developed a n agent based Cellular Automation, i.e., CA (Nagel and Schreckenberg, 1992) simulation model ( SUSTAPARK ) to mimic the parking search behavior of drivers. In SUSTAPARK, the road network and parking spaces are loaded from the ESRI shapefi le. In particular, the network is divided into cells, each of which is assumed to hold at most one vehicle at a time step. Furthermore the activity schedule instead of trip schedule is considered for each driver. Figure 2 3 depic ts the simulation process. First ly drivers are assumed to depart from their current parking spaces towards the destination of their next activity. They are then routed to the corresponding parking search area based on the defined routing strategy (not spe cified in the paper) and start searching for parking spaces. Within the search area, vacant parking spaces that can be reached within one time step are proposed to the driver, and she will select one of the spaces with utility higher than the predetermine d threshold and park there If none of these vacant parking spaces can satisfy the driver, then she will keep on driving. It is worthwhile to note that with the search time increasing, the utility function of the driver will
32 also change. The simulation e nds until all the activities of all drivers are taken into account Output includes the parking occupancy of each street, the parking search time of the whole system, and bottlenecks within the parking search area. Similar to Dieussaer et al. (2009), Horn i et al. (2013) proposed a n agent based CA parking simulation tool. To simulate the parking search behavior, several rules are defined as follows: 1. Before arriving the pre determined search starting point, which is specified by the Euclidian distance to the river simply drives along a pre specified route. 2. When reaching the search starting point, the driver starts parking search Once she approaches an intersection the next link is chosen from the connected links based on the follow ing three criteria: a) destination approaching efficiency: similar to Benenson et al. (2008), the connected link whose farther junction is closer to the destination possesses higher probability to be chosen; b) memorized free parking spaces: a connected l ink with direction pointing to the parking lot with the most vacant spaces will be credited additional probability ; c) the connected links that have been visited recently will not be considered as the chosen link with high prob ability. 3. If there is parking lot with vacant spaces around the driver, the probability for her to park there is determined by a given function, which is related to the elapsed search time and the distance to her destination. T he above behavior rules are implemented in Matlab and simulation based on small and large scale networks are provided to demonstrate the effectiveness and efficiency of the model.
33 Figure 2 1 Route choice for drivers ( Benenson et al., 20 08 ) Figu re 2 2 The probability to continue driving towards the destination (Benenson et al., 2008)
34 Figure 2 3 Simulation procedure in SUSTAPARK (Dieussaert et al., 2009)
35 CHAPTER 3 ANALYSIS OF ADVANCE D MANAGEMENT OF CURBSIDE PARKING This chapter an attraction (destination) is located on a long one way street and on street parking spaces are scattered around the destination ; drive rs are assumed to find a space to park to minimize their walking time to the destination. Analytical models are established to describe the search outcomes and compare the impacts of parking information and reservation services. An agent based simulation e xperiment is then conducted to verify the results drawn from the analytical models. In the remaining of the chapter, Section 3.1 curbside parking on a one way street and how parking information or reservation service affects their parking search and choice. Section 3 .2 applies NetLogo to construct an agent based simulation model to validate the results obtained from the analytical models, and Section 3.3 further compares the performances of these parking management ser vices. Lastly, Section 3.4 concludes the chapter 3.1 Analytical Models For analytical tractability, we consider a long one way street where an attraction (destination) is located and on street parking spaces are scattered around the destination. More spe cifically, the parking space on the destination is marked as 0, from which the indices are decreasing towards the street direction and increasing at the opposite direction (see Figure 3 1 ). Drivers who go to the destination need t o select one of the available spaces to park. They are assumed to make this selection in a way that minimizes their walking time to the destination. Because the street is one way and very long, once a driver has passed a parking space, she would not be abl e to come back for it.
36 We further assume that the arrival headways of drivers and their parking durations follow exponential distributions. Let denote the arrival rate of drivers heading for the attraction and the departure rate of an occupied parking space. If there are parked vehicles, the total departure rate of the stretch of street is It is further assumed that the arrival headw ay for each parking space also follows an exponential distribution, which is a strong assumption and will be discussed later. 3.1.1 Steady State of Status Quo In this section, it is assumed that drivers have no access to parking information or reservation services, and thus they observe whether a space is available only when they reach it. One of the search strategies they may adopt is to start cruising for parking from a particular location (space) and then take the first vacant space and walk to the final destination ( Arnott and Rowse, 1999 ) Note that the models developed in this chapter can be extended to consider a situation where drivers observe a few parking spaces ahead and choose to park at the vacant one closer to the destination. Figure 3 1 is a network representation of the setting where we number individual parking spaces in a decreasing order in the direction of the street and the space at the destination is indexed by 0. Specifically, is the first space where drivers may start cruising for parking and is the walking time from to the final destination. is a large number such that a driver will always be able to find a parking space between and Note that will b e endogenously determined. Given that drivers have different risk taking attitudes, some (risk averse drivers) will start cruising for parking at spaces far from their destination, while others (risk seeking drivers) may drive very close to the destination and start from there. Suppose there are types of drivers,
37 who start cruising for parking at since no rational driver would start after the destination. Let be the proportion for each type of drivers who start cruising at space where is give n exogenously with and For each parking space we now calculate its parking and departure rates, i.e., and A driver will park at if it is available and all the spaces between the space she start cruising at and are occupied. Let denote the probability of space being available, and define the following two variables: Then we calculate the parking rate for each space as follows: Specifically, represents the rate of type drivers that actually park at space
38 The departure rate of a space is equal to multiplying the probability of that space bein g occupied: At a steady state, the probabilities of spaces being available should remain constant and every space will have equal parking and departure rates. These conditions yield: Therefore, for we have: For we have:
39 Below is the summary of the results: ( 3 1) As a demonstration, let's assume and and consider three types of dr ivers, who start searching for parking at space 2, 1, and 0, and their proportions are the same, i.e., The probability of each space being available at the steady state is then calculated in Figure 3 2 In Figure 3 2 the last space, i.e., 13, is always available, because we assume that the number of parking spaces is sufficient along the street and thus drivers can always overshoot the final destination long enough to find a v acant parking. Further, if we define as the driving time for the th type of driver to park at space then we can calculate the expected cruising time for parking as follows: Further, the expected wal king time can be written as follows: In the above example, assuming that and the expected cruising time and walking time are calculated to be 0. 409 and 3.615. 3.1.2 Steady State with Parking Information We now consider in this section that drivers have access to an information service, which can provide drivers with the real time availability of parking spaces. Note that albeit being
40 informed, it may not be wise for drivers to simply drive to the best currently available space, because another driver before them may take the space and other occupied spaces may soon become vacant. Various strategies can be adopted to play such a parking competition game (e.g., He et al., 2015 ). To be comparable with the above status quo steady state, we assume that drivers adopt the same parking search strategy, i.e., they start cruising for parking at a particular location (space) and then take the first vacant spa ce and walk to the final destination. However, owing to the parking information service and their day to day learning, drivers are assumed to obtain the knowledge of the probability for each space being available at the steady state. Consequently, drivers are able to select an optimal location to start their parking search such that their walking time to the final destination can be minimized. Note that another objective can be considered, such as minimizing a general cost that includes driving time and par king price as well. To simplify the analysis, we assume that all drivers start cruising for parking at the same space, which is denoted as Further, is set to be a large number such that a driver will always be able to find a parking space between and Both and are endogenous in this case. Similarly, a driver will park at if it is available and all the spaces from to are occupied. Hence, we can calculate the parking rate for each space as: and the departure rate for each space as:
41 Similar to Section 3.1 .1, at the steady state, the probabilities of spaces being available should remain constant and every space will have equal parking and departure rates. These conditions yield: Define We have: Thus, For we have: As a demonstration, consider the same numerical example where and The probability of each space being available at the steady state is shown in Figure 3 3 where is to be determined.
42 In Figure 3 3 the first space, i.e., is where drivers start cruising for par king and thus the probability of being available is the smallest. If we define as the driving time from to space given the steady state availability probability, we can calculate the expected cruising time for parking as follows: We are now ready to determine where drivers should start cruising for parking, i.e., the optimal value of If a driver reaches space and decides to park there, she will have to walk to the destination. Alternatively, the driver can proceed to the next parking space and start searching for parking there. If she chooses to do so, her expected walking time is as follows: The optimal value of is determined to be the largest such that Otherwise, the driver would be better off with proceeding to the next one and start searching for parking there. The optimal value can be obtained using a numerical procedure such as the bisection method. Specifically, denote as a sufficient large number such that and as a sufficient small nonnegative number such that Note that we can always set Now consider the midpoint If set Otherwise, set Repeat this procedure until and the optimal value o f is equal to In the above example, assuming that Table 3 1 shows the comparisons of walking times and expected walking times. Since and the optimal value of is 3, implying that the best parking search
43 strategy for drivers is to proceed to space #3 and start cruising there. This way the expected walking time will be 3.075. Some may argue that the expected walking time is minimized when i.e., 2.832, and thus drivers should choose to start searching at space #5. However, if space #5 is available, a driver still prefers to proceed to the next parking space and start for searching, instead of parking there. The reason is that the expected walking time of starting searching at space #4 is only 2.859 much less than the walking time from space #5, i.e., 5. 3.1. 3 Steady State with Parking Reservation The parking reservation service considered in this section would provide real time parking information and allow drivers to reserve parking spaces. With such a service, a driver is assumed to reserve the vacant one closest to the destination when she enters the street. Mathematically, the only difference that the reservation service makes is to change the sequence of parking spaces drivers search for. In the scenario of parking information, drivers start at ; if it is not available, then proceed to and so on. With parking reservation, drivers first check whether is available; if not, then , and so on. Therefore, in this scenario, the probability for the th space closest to the destinatio n being vacant is the same as the th space in the search list in the scenario of information. Consider the same numerical example in Section 3.1 .2, with parking reservation, the probability of being available of space , and is equal to t he one of space , and in the scenario of parking information respectively (see Figure 3 4 ). Consequently, the probability of each space being available at the steady state is shown in Figure 3 5 It can be observed that these probabilities are relatively symmetric with respect to the destination, while the ones in Section 3.1 .2 are monotonically increasing.
44 As no driver needs to cruise for parking with the reservation service the expected cruising time in this case will always be zero. For each parking space similar to we define as follows: The expected walking time can thus be written as follows: For the above numerical example, the reservation service reduces the expected walking time to 2.679. Compared with the information service, the value of reservation is worth 0.396 (in the unit of walking time) for each driver. Detailed comparison of these services will be provided in Section 3.3 3.2 Verification We apply NetLogo ( http://ccl.northwestern.edu/netlogo/ ) to construct an agent based simulation model to verify the predictions drawn from the aforementioned analytical study. Specifically, for the status quo, three types of drivers who start cruising for parking from spaces #7, #6, and #5 are considered, and their proportions are assumed to be the same; while in the scenario of information, all drivers start cursing for parking at the optimal value of In the verification, we focus on the expected walking time as it is assumed to be the measure that drivers essentially care about.
45 The simulation and analytical results are shown in Figure 3 6 While the two results appear largely consistent, it can be observed that the walking times in the simulation are higher than the analytical results in most cases. The disc repancy varies from 0.6% to 11.2%, 2.6% to 15.4%, and 3.1% to 10.7% respectively for the status quo, with information and with reservation service scenarios. We believe that such discrepancy is largely caused by the assumption that the arrival headway for each parking space follows exponential distribution. This assumption behaves as an acceptable approximation for our serving system and has greatly simplified the formulation. However, strictly speaking, it omits the relationships between the states of adja cent parking spaces. As an example, a direct statistical test is implemented on the scenario of exponential distribution, when parking spaces are farther away from For each parking space, we fit the arrival headways with an exponential distribution, to obtain the exponential index as well as its 95% confidence intervals. The fitting degrees are compared using the following positive index, de fined as Fitting Index: The smaller this index is, the better fitted the samples are. We select seven sample groups of arrival headways, corresponding to ratios of arrival and departure rate, ranging from 0.9 to 36. Figure 3 7 depicts the relationships between the fitting index and the parking space under different ratios. In Figure 3 7 although the spans in x axis (i.e. the number of parking spaces being utilized) are different, the pattern of the fitness is consistent that parking spaces closer to the ly growing fitting indexes. This
46 headways. As the dependence betwee n adjacent parking spaces gradually accumulates, the relatively small. So the influences from the exponential arrival assumption, which may result in the discrepancies between the analytical models and real situations, are also limited. To relax this assumption, an approximate renewal model for the queueing system with gener al inter arrival times and service times may be considered. We leave this to our future investigation. On the other hand, we conclude that the analytical models are acceptable since they produce largely consistent results in the numerical experiments we co nducted. 3.3 Comparison To compare the expected walking times in three different scenarios, we combine the results obtained from the analytical models in the numerical setting described in Section 3 .1 (see Figure 3 8 ). For curbsid e parking on a one way street, we have three observations: 1) compared with the status quo, the reservation service reduces the expected walking time; 2) providing information does not necessarily improve the performance of the parking system, as it may in tensify the parking competition ; and 3) the expected walking time with reservation is always less than the one with real time information. Because the expected walking time at the status quo steady state largely depends on the proportion distribution of t he drivers specified exogenously for the analysis (recall that is assumed for the status quo curve in Figure 3 8 ). To further validate the impacts of information and reservation services, we are interested in finding the best case status quo, i.e.,
47 the status quo wit distributions. It can be obtained by solving the following mathematical program: s.t. ( 3 1) where and are both given and are sufficiently large. We solve the above program for our numerical examples with The curve of the best case status quo in Figure 3 8 depicts the obtained optimal objective value. It is straightforward that the best case expected walking time is always no t greater than the one with real time information, because the latter can be regarded as a special case of the former. It is interesting to observe that the best case walkin g times are still greater than those with reservation, suggesting that reservation is indeed a good policy for managing parking in our setting. Below we provide a proof to confirm our observation that reservation can always yield an expected walking time l ower than the best case status quo, and subsequently the one with real time information. For the proof, we definite the type of a driver as per the space at which he starts cruising under the status quo. More specifically, drivers of type are those who start cruising for parking at space where The arrival rate of type drivers is equal to If the demand for type drivers equals 0. Then, define as a series of sub scenarios. Under scenario dri vers from type 0 to type take the reservation strategy (R) on section ; and drivers of type or above take the original cruising strategy (O) before space and
48 switch to reservation (R) on section For each transition from t o the reservation section range expands from to If we only consider section the scenarios and respectively capture the situations under the status quo and reservation service. Then, we introduce an intermediate scenario (denote as ) between and under which drivers of type or below take the same strategy as drivers of type i n That is to let drivers of type or below start at space first and then take the reservation strategy on section .The flow charts of and are shown in Figure 3 9 for compariso n. The range of represents the set of driver types that the corresponding flow belongs to. Further, we denote and respectively. And denote as the rate of vehicles who start searching at space either by cruising or reservation. Lemma 3. 1 below concerns the relationship between these rates of consequent spaces. Denote as a set of spaces that drivers subsequently visit in a searching process. For any pair of sp aces along the searching chain, if space is visited before space under a certain strategy, then we have Lemma 3 1. Suppose there exists a space such that increases and remains the same for Then, both flow rates and also increase, ; vice versa. Proof. For any adjacent pair of parking spaces we have ( 3 2) and
49 (3 3 ) Taking the derivative of on both sides of ( 3 2) and ( 3 3), we obtain and As the coefficients and are positive, both and have the same sign as Since using the mathematical induction method, we have both and be positive for Then back to the transition from to and Lemma 3 2 and 3 3 below always hold in pace with the transition. Lemma 3 2. When switching from to does not increase for Proof. In scenarios and we have the following flow rate r elations: ( 3 4) ( 3 5) ( 3 6) B ehind each flow rate, the index within the parentheses labels the scenario where the rate belongs to. Then, by substituting ( 3 6) into ( 3 5) and then subtracting ( 3 4), we obtain
50 Since according to ( 3 6), we have As is the only inflow for section using Lemma 3. 1, is no greater than for And the equality holds if and only if Lemma 3 3. When switching from to does not decrease for and not increase for Besides, c annot stay invariable on both and simultaneously. Proof. We first prove the first half of the lemma: I. The flow rate in and has the relation that Since there are no additional inflows except for space section in both and we have does not decrease for according to Lemma 3. 1. The equality holds if and only if which also means for II. Comparing scenarios and the only difference is the searching order between space and section Thus, we have Since is the only inflow for section we have for As is no greater than for proven in Lemma 3. 2, should also be no larger than Similar to Lemma 3. 2, the equality holds if and only if The proof for the second half is straightforward. When transfers to if stays invariable on both and then for Therefore, the total demand should equal zero, which makes a contradiction to our assumption that the demand is nonzero.
51 Using L emma 3 3, we now present the proof for our observation. Theorem 3 1. The reservation service yields an expected walking time lower than the best case status quo. Proof. Define as the systematic expected walking time under scenario Then, w e know that and represent the expected walking time under status quo and reservation service respectively. The following proves for : Denote as Then, we set up the following relationship between and : The inequality results from the fact that and Further, based on Lemma 3. 3, we have on and on The two inequalities could not be bounded simultaneously. So we have for Therefore, That is, the rese rvation can always yield an expected walking time lower than the best case status quo. 3.4 Summary We have developed the analytical models for curbside parking on a one way street considering three different scenarios: status quo, providing real time pa rking availability information, and allowing reservations. To verify the performance of these analytical models, NetLogo has been applied to develop an agent based parking simulation. The results show that the analytical models can produce results largely consistent with the simulation. The discrepancy
52 can be attributed to the assumption that the arrival headway of each parking space follows an exponential distribution. We have concluded that in the particular setting considered in this chapter parking res providing parking information may worsen the performance of the parking system. Our future study will investigate how advanced parking management will affect parking competition and its outcome on a more general network with multiple destinations.
53 Table 3 1 Walking times and expected walking times at various starting spaces 11 5.257 10 4.469 9 3.817 8 3.319 7 2.988 6 2.832 5 2.859 4 3.075 3 3.482 2 4.084 1 4.884
54 Figure 3 1 An abstract setting of curbside parking at a one way street Figure 3 2 Probabilit y of being available in the status quo scenario Figure 3 3 Probability of being available with information Figure 3 4 The relation betwe en parking with real time information and reservation service Figure 3 5 Probability of being available
55 (a) Status quo (b) With real time information (c) With reservation Figure 3 6 Expected walking times from analytical model and simulation 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 16.00 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Expected Walking Time Ratio between Arrival and Departure Rates Analytical Simulation 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Expected Walking Time Ratio between Arrival and Departure Rates Analytical Simulation 0.00 2.00 4.00 6.00 8.00 10.00 12.00 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Expected Walking Time Ratio between Arrival and Departure Rates Analytical Simulation
56 Figure 3 7 Results of fitting index vs. parking spaces in different scenarios Figure 3 8 Results from analytical model in different scenarios 0 0.5 1 1.5 2 2.5 3 40 30 20 10 0 10 20 30 40 Fitting Index Parking Space Label Ratios of Arrival Rate and Departure Rate: 36 18 9 4.5 2.25 1.8 0.9 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 Expected Walking Time Ratio between Arrival and Departure Rate Status quo Information Reservation Best-case status quo
57 Figure 3 9 Flow charts of and
58 CHAPTER 4 PARKING RESERVATION FOR MANAGING DOWNTOWN CURBSIDE PARKING This chapter discusses a smartphone based parking reservation syste m that manages a finite number of curbside parking spaces located at different places in a downtown area. Parking reservation schemes are designed to minimize the total social cost of parking, which is assumed to be a weighted sum of the cruising times for drivers to travel from their current locations to allocated parking spaces, and the walking times from parking to their final destinations. Assuming a perfect information of cruising and walking times, we present a simple reservation scheme to achieve an optimum allocation of parking spaces. However, although the locations of drivers can be retrieved from their smartphones, we illustrate that drivers have incentive to misreport their final destinations for their own benefit, which compromises the system be nefit. We thus apply the Vickrey Clark Groves (VCG) mechanism to determine the allocation of parking spaces and parking fees to minimize the total social cost while ensuring all drivers to report truthfully their final destinations. Lastly, we discuss a re venue redistribution scheme to further reduce the financial burden of drivers and increase the public acceptance of the reservation system. For the remainder, Section 4.1 illustrates the necessity for a n optimal parking reservation scheme and further outl ines the scheme with perfect information of cruising and walking times. Section 4.2 illustrates the incentive for drivers to misreport their final destinations and appl ies the VCG mechanism on both static and dynamic parking reservation problem s with priv ate information Section 4.3 provides a numerical example to demonstrate the performance of our proposed schemes, followed by the introduction of revenue redistribution to reduce the financial burden of drivers in Section 4.4 Lastly, Section 4.5 concludes the chapter
59 4.1 Parking Reservation with Perfect Information 4.1.1 Static Scheme Design Parking reservation can be simply FCFS which allows a driver to select and reserve the best parking space among currently available ones. Without considering the imp act of each reservation on the social cost of the system, such a scheme may not be sensible. To illustrate this, we use a small example where three drivers (V 1 V 2 and V 3 ) make their parking reservations sequentially, and their parking costs (weighted sum s of cruising and walking times) to each space are shown in Table 4 1 where S 1 S 2 and S 3 represent three parking spaces. Based on the FCFS principle, the parking assignment will be (V 1 S 1 ), (V 2 S 2 ) and (V 3 S 3 ) and thus the t otal social cost is 17. However, another assignment of (V 1 S 3 ), (V 2 S 2 ) and (V 3 S 1 ) yields a social cost of 12, a nearly 30% saving. In fact, such an assignment is optimal, minimizing the social cost. The question of interest is how to design a reservat ion scheme to achieve the system optimum. For simplicity, we first consider a static parking reservation problem in which drivers at different locations reserve parking spaces at the same time, or drivers are patient enough to wait until the system receiv es all the requests and makes a final assignment decision. The reservation system can only take reservation requests up to the number of available parking spaces, and then decides the space allocation plan. Once a driver is assigned to a particular space, he or she will accept it and cannot make another reservation. Additionally, it is assumed that drivers will occupy the spaces for the whole planning horizon, i.e., an occupied parking space will not become available again. This assumption can only be justi fied for situations where drivers come to the downtown area to work or participate in a full day event. Our future study will relax this assumption to consider different parking durations.
60 With the above consideration, let and represent the sets of drivers requesting parking reservations and the available parking spaces respectively. Let denote the parking cost for driver to park at space Again, the cost is a weighted sum of his cruising and walking times. Then the system optimum ass ignment (SO) can be obtained by solving the following linear program (He et al., 2015) SO: s.t. ( 4 1) ( 4 2) ( 4 3) where is the varia ble representing whether space is assigned to vehicle The first constraint suggests that every driver whose reservation request is accepted by the system should be assigned with one and only one parking space, while the second constrain ensures that every parking space can be assigned to at most one driver. Since the matrix associated with the first two constraints is totally unimodular, the optimum solutions are integer. 4.1.2 Dynamic Scheme Design Nevertheless, in practice, it is unrealistic to req uire drivers to wait patiently until all the reservation requests are in before receiving a reservation decision. Realistically, drivers will send their reservation requests to the system over time and expect a decision with in a short period of time To ad dress this issue, we divide the whole planning horizon into a finite number of short
61 time intervals. At the end of each interval, the reservation system will make decisions on the requests received within the interval. For a reservation decision, drivers c an take it or leave it. A dynamic programming approach may be adopted to design a reservation scheme to achieve some form of global optimality, considering uncertain reservation requests and parking supply at future intervals. We leave this to our future i nvestigation. In this chapter we propose to solve the above SO at each interval to achieve a myopic system optimum This approach is simple to implement and computationally efficient. 4.2 Parking Reservation with Private Information 4.2.1 Incentive to Lie As aforementioned, the parking cost is a combination of cruising and walking times. Figure 4 1 shows a scenario where two vehicles (V 1 and V 2 ) reserve for two spaces (S 1 and S 2 ), and D 1 and D 2 are their actual final destinations. In the figure, the number beside each link represents the cruising or walking time. To be simple, suppose the weights of cruising time and walking time are both 1, i.e., As a result, the parking costs of vehicles to spaces a re shown in Table 4 2 Obviously, according to the definition of system optimum, the best assignment is (V 1 S 2 ) and (V 2 S 1 ), and the total cost is 57. However, V 1 may misreport his or her destination to get assigned with S 1 wh ich leads to a lower parking cost for him or her. Figure 4 2 shows such a situation. Consequently, the parking costs change to those in Table 4 3 Thus, the system optimum assignment becomes (V 1 S 1 ) and (V 2 S 2 ) with a social cost of 74. However, in such a situation, the real social cost is 77, much larger than the one when both drivers report their destinations truthfully, i.e., 57. Unfortunately, V 1 does have incentive not to do so. Since the truthful parking costs are unknown to the parking reservation system, the system optimum reservation can only be defined as the one that minimizes the total reported
62 parking social cost. Define as the parking cost calculated based on the reported destination from the driver. Similar to SO, the system optimum based on the reported parking costs (SO R) can be formulated as follows. SO R: s.t. (4 1) (4 3) 4.2.2 Static Scheme Design To address potentially harmful misreporting, we apply mechanism design techniques to design a parking reservation scheme. Mechanism design is a subfield of economics that considers the problem of providing incentives to self interested agents to provide the truthful information and further achieve desired system wide outcomes in the system (Parkes et al., 2004) A mechanism design should be efficient, i.e., the output can always ensure the desired system outcome; strateg y post individual rationality (IR), i.e., participating in the mechanism is always not worse than not participating. Further, agents are supposed to have private information, and assumed to be ra tional to maximize their utility. The parking reservation problem of interest in this chapter does satisfy these assumptions: all drivers have their private information of their final destinations and they attempt to minimize their individual parking cost. Classical mechanism design is concerned with static, one shot problems, in which all agents are assumed to make a one time decision and be patient enough to wait for the decision (Parkes and Singh, 2003) such as the first price sealed auction, second pri ce sealed auction, VCG mechanism. Among them, the VCG mechanism ( Vickrey 1961; Clarke 1971; Groves 1973) is the most well known mechanism for allocating multiple items, and has been widely applied to areas such as network rate allocation (Yang and Hajek 2006) base station resource
63 allocation (Hong and Garcia, 2012) and Internet advertising (Varian, 2009) In this chapter we apply the VCG mechanism to design a static parking reservation system where all drivers make reservations at the same time or th ey are patient enough to wait for the final decision. As per the VCG mechanism, each driver will be allocated a parking space and charged a parking fee. The fee is equal to the harm they cause to the other drivers. Such a reservation scheme is supposed to provide incentive for drivers to report truthfully and eventually achieve the desired outcome, i.e., the minimal social cost. Let represent the actual or real parking cost for driver when acceptin g the parking space assignment from the reservation system, where denotes the solution to SO R; is a vector describing the real parking costs to all parking spaces for driver i.e., ; and representing all reported parking costs. The parking fee for driver denoted as is calculated below: ( 4 4) where denotes the solution to SO R when driver is excluded. Define as the individual total cost, i.e., the sum of the cruising time, walking time and parking fee of driver Mathematically, we have: ( 4 5) Due to the fact that the real social cost obtained when all drivers report their destination truthfully is less than the one when driver reports untruthfully, we have: ( 4 6) Further, considering another situation where the real parking costs are and all the drivers except driver report their truthful destinations, ( 4 6) yields the following:
64 ( 4 7) Propositio n 4. 1. Suppose that under the VCG reservation scheme, driver misreports his or her destination, i.e., Consequently, his or her individual total cost will be more than the one when he or she reports the destination truthfully, regardle ss of whatever the other drivers report. Proof. where the first equality fo llows from ( 4 4) and ( 4 5); the first inequality comes from ( 4 7); and the second equality is from ( 4 4). Figure 4 1 where the system optim um assignment is (V 1 S 2 ) and (V 2 S 1 ). Take V 1 as an example. When V 1 is present, the total parking cost of the other driver, V 2 is 27; when V 1 drops out, the total parking cost is still 27, because the new system optimum assignment is (V 2 S 1 ). Accordin g to the VCG mechanism, the parking fee charged on V 1 is Thus, the individual total cost of V 1 is On the other hand, if V 1 misreports his or her destination like in Figure 4 2 then the system opt imum assignment becomes (V 1 S 1 ) and (V 2 S 2 ). Similarly, the parking fee charged on V 1 can be calculated as and thus his or her individual total cost becomes much larger than before, i.e., 30. Therefore, by charging a p arking fee on V 1 according to the VCG mechanism, there is no
65 incentive for the driver to misreport his or her destination. This is true for V 2 as well. Thus the reservation scheme yields the system optimum prescribed by SO. 4.2.3 Dynamic Scheme Design Sim ilar to the dynamic scheme with perfect information, we now design a dynamic reservation scheme with private information, which can be described as an online mechanism design problem. Online mechanism design is to provide a sequence of decisions over time rather than a decision at the end (Parkes et al., 2004) For example, Friedman and Parkes (2003) considered the online VCG mechanism to design a pricing scheme of WiFi at Starbucks to maximize the total profit. In their study, the agents have various valua tions for the WiFi service, and they arrive over time and can only announce their arrivals only after they arrived, i.e., reservations are not allowed. Gershkov and Moldovanu (2010) discussed the allocation of a set of distinct durable goods to a set of bu yers by applying the online mechanism design to maximize the welfare. Specifically, the buyers are assumed to be impatient and arrive sequentially based on a Poisson or renewal process, and further, they share the same ranking of the goods. Gerding et al. (2011) proposed a model free (no assumption of future demand and supply of electricity) online mechanism design based on the greedy allocation algorithm for electric vehicle charging, in order to achieve a higher electricity allocation efficiency. Unfortun ately, none of these online mechanism designs is applicable to our parking reservation problem because of the characteristics of parking spaces. First of all, all parking spaces must be reserved before drivers arrive. Secondly, there is no generic ranking of parking spaces, as destinations. Thirdly, unlike electricity, once a parking space is assigned to one driver, it cannot be assigned to another driver before the dri ver leaves the space.
66 To design a dynamic reservation scheme with private information, we similarly divide the whole planning horizon into a finite number of short time intervals. At the end of each interval the reservation system will a llocate spaces to the requests received within the interval and determine the corresponding parking fees. Similar to the perfect information case, we propose to apply the above VCG mechanism at each interval to achieve a myopic system optimum. Such a schem e is called as an iterative mechanism in this study. Obviously, by using the iterative mechanism, no drivers have incentive to misreport their parking costs at each interval. Further, as assumed before, no new spaces will become available during the planni ng horizon. We have thus the following proposition. Proposition 4. 2. For any driver, the earlier the reservation is made, the less individual total cost he or she will experience. Proof. Suppose makes a reservation at interval and receives an allocated space As a result, its individual total cost will be more than or equal to (it will be equal to if the parking fee charged on is 0) On the other hand, if makes a reservation at an earlier interval i.e., and space is assigned to If since remains at interval such allocation will not affect the parking space assignment of the other drivers, thus Consequently, his or her individual total cost If to be assigned with could misreport his or her destination and consequently However, because of the strategy proof property of the VCG mechanism, there is no incentive for to do so, i.e., Therefore, the individual total cost of when making reservation at interval will be no larger than the one when his or her reservation is made at interval ( ).
67 The above proposition suggests that drivers will make their reservations as early as possible under the proposed iterative mechanism. For the proposed dynamic reservation scheme, if the interval is sufficiently long to be the planning horizon, it reduces to a static VCG mechanism; if the interval is short enough, it is essentially a FCFS scheme, because at each interval there is at most one driver. 4. 3 Numerical Example To demonstrate the performance of our proposed reservation schemes, we conside r that 100 drivers travel to a downtown area and reserve parking via a reservation system, which manages 100 parking spaces in the area. That is, We randomly create 100 different scenarios by generating parking costs (sum of cruising and walking times) from and determining the request sequences of all drivers from both in a uniform manner. For each scenario, diffe rent durations of time interval are considered, including 1, 2, 5, 10, 20, 25, 50, and 100. Correspondingly, the number of intervals is 100, 50, 20, 10, 5, 4, 2, and 1 respectively. The optimum assignment of each situation is obtained by solving SO, and pa rking fees are calculated according to Equation ( 4 4). Table 4 4 presents the average social cost, revenue and individual total cost for the problem with private information. The results are the same for the problem with the perfe ct information except that the parking fees will be 0. As expected, when the number of time intervals increases, the social cost increases while the revenue decrease s Specifically, when the number of intervals is one, i.e., static parking reservation, the scheme can achieve the system optimum, and the social cost is only 38% of that under the FCFS principle. However, in this situation, the revenue is also largest, i.e., 308.56, increasing the individual total cost of drivers to 4.70, as compared to 4.24 un der the FCFS principle. In fact, the FCFS principle leads to the smallest individual cost because all the parking
68 fees are 0. Our reservation scheme manages to achieve system optimum, but has to charge quite significant amount of parking fee to ensure all drivers to report truthfully. The scheme performs well from a societal perspective, but individual drivers may have a different opinion. 4.4 Revenue Redistribution It has been recognized in the literature that the VCG mechanism is not budget balanced (Bai ley et al., 1997) Myerson and Satterthwaite (1983) pro ved that it is impossible for a mechanism to be efficient, strategy proof, ex post IR, and exactly budget balanced simultaneously. In recent years, some attempted to achieve the budget balance by scari fying either the strategy proofness or efficiency (Faltings, 2005; Parkes et al., 2001) Others proposed to redistribute the surplus to agents without affecting the properties of the VCG mechanism but achieve approximately the budget balance (Bailey et al. 1997; Cavallo, 2006; Gujar and Narahari, 2008; Guo and Conitzer, 2009) In this chapter we consider redistributing the parking revenue to reduce individual travel costs of drivers. The rebate to each driver can be computed as the revenue collected by th e reservation system without the driver divided by the total number of drivers (Bailey et al., 1997) More specifically, the rebate to driver is: Since depends only on the information provided by the other drivers regardless of driver Therefore, the efficiency, strategy proofness, and ex post IR will not be affected. Howeve r, such a rebate scheme may run a deficit (Guo et al., 2011) Further, Proposition 4. 2 may not hold due to the effect of rebates. To demonstrate the revenue redistribution scheme, consider the example in the above section with a single time interval, i.e. static reservation. Figure 4 3 shows the percentage of revenue redistributed to drivers. It can be observed that at least 43% of the revenue will be
69 redistributed, and the rebate percentage can reach to more than 90% in some scena rios. On average, 76% of the revenue is redistributed. As a result, the average individual total cost of parking reduces to 2.34, which is much smaller than the one under the FCFS principle, i.e., 4.24. Moreover, in all 100 random scenarios, there is no de ficit for the reservation system. To analyze the relationship between individual parking fees and rebates, we plot them for one selected scenario in Figure 4 4 It is easy to observe that individual rebates are relatively uniform while individual parking fees vary drastically. This demonstrates that the amount of charged with a higher parking fee may receive a less amount of rebate or vice versa. 4.5 Summary We have discussed a smartphone based parking reservation system to manage downtown curbside parking and designed reservation schemes to allocate parking spaces. We first illustrated the need for designing a reservation scheme to mi nimize the total parking cost. Given that the parking cost is closely related to a private information of drivers, their final destinations, we showed that drivers have incentive to misreport the information. Consequently, we applied the VCG mechanism to d etermine parking fees to ensure all drivers to provide truthful information and allocate parking spaces optimally. We also verified that the iterative VCG mechanism can be used for dynamic parking reservation, and achieve a myopic system optimum. In this r eservation scheme, all the drivers have incentive to make their reservations as early as possible. A numerical example was conducted to demonstrate the performance of the proposed schemes. As compared to the FCFS principle, the schemes can reduce the parki ng social cost up to 38%. To deal with the large amount of parking revenue, which increases individual costs of drivers, we examined a revenue redistribution mechanism. While achieving efficiency and strategy proofness, the mechanism rebates, on average, 7 6% of the revenue in the same
70 numerical example, demonstrating its potential of making the proposed reservation system appealing to both society and individual drivers. Our future research will relax the assumption of homogenous parking duration and allow new parking spaces to become available in the planning horizon. Moreover, the revenue redistribution mechanism may be viewed by some as inequitable because drivers charged more may receive less rebate, and vice versa. More sophisticated forms of rebates c an be investigated to address such an equity concern.
71 Table 4 1 Parking costs and request sequences S1 S2 S3 Request Sequence V1 2 4 3 1 V2 3 5 8 2 V3 4 6 10 3 Table 4 2 Parking costs at syst em optimum S1 S2 V1 15 30 V2 27 62 Table 4 3 Untruthful parking costs S1 S2 V1 12 55 V2 27 62 Table 4 4 Experimental results Number of Periods Average Social Cost Average Revenue Individua l Total Cost 1 161.17 308.56 4.70 2 214.34 267.33 4.82 4 266.47 211.42 4.79 5 283.03 194.77 4.78 10 329.20 119.20 4.48 20 371.84 70.54 4.42 50 395.11 32.77 4.28 100 (FCFS) 424.47 0.00 4.24
72 Figure 4 1 Parking reservation scenario Figure 4 2 Parking reservation scenario with misreported destination
73 Figure 4 3 Percentage of revenue redistributed to drivers Figure 4 4 Individual parking fee and rebate of every driver in a selected scenario 0 10 20 30 40 50 60 70 80 90 100 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 Rebate Percentage (%) Scenario ID 0.00 1.00 2.00 3.00 4.00 5.00 6.00 1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94 97 100 Parking fee/Rebate Driver ID Individual Parking Fee Individual Rebate
74 CHAPTER 5 AN ADVANCED PARKING NAVIGATION SYSTEM FOR DOWNTOWN PARKING This chapter propose s to develop an advanced parking naviga tion system for downtown parking The system manages a finite number of parking spaces located in a downtown area. It is envisioned that the system can access the availability of parking facilities via sensing and wireless communication technologies, and d rivers can access the system via their smartphones. Assigning drivers to open spaces is essentially a two sided matching problem: drivers are on one time locations and their parking spac e preferences, a two sided matching algorithm will first be developed to achieve a stable driver optimal matching. Under such a stable matching, drivers will be assigned to their most appropriate spaces (if any) at all times, and thus no driver can benefit from disobeying the navigation system. Moreover, the proposed matching algorithm will be strategy proof, implying that drivers will have no incentive to misreport their private information (e.g., real time parking vate information is required for applying the proposed matching algorithm, an efficient decentralized solution procedure will be applied to achieve the space assignment without disclosing such information. To demonstrate the performance of the proposed nav based simulation experiment will be conducted to show how the matching system improves the management of curbside parking compared with other navigation systems. For the remainder, S ection 5.1 describes the architecture and the procedure of the parking navigation system. Section 5.2 introduces the two sided matching model and the relevant results rooted in the stable driver optimal matching strategy, and a decentralized solution proce dure is proposed in Section 5.3. An agent based simulation experiment is conducted in Section 5.4. Section 5.5 concludes the paper.
75 5.1 Parking Navigation System Figure 5 1 delineates the architecture of the parking navigation sys tem. Specifically, on the provider side, the status information of parking spaces can be reported to the management center via sensing and wireless communication technologies. On the client side, drivers can communicate with the management center via their smart phones. On one hand, drivers can access the parking information and then report their parking preferences to the management center. Specifically, the preference list over parking spaces can be generated according to could be composed of walking distance (time), driving distance (time), parking pricing, safety factors and so on. On the other hand, based on the collected information of both parking spaces and drivers, and their locations, the management center can prov ide parking navigation to each driver. Figure 5 2 shows the procedure of the parking navigation system. Particularly, the parking navigation system can be designed as an app installed in any smart phone, and the procedure will be executed at each time step. Assigning drivers to spaces is a two sided matching problem: cruising drivers are on one side and open spaces are on the other side, a two sided matching mechanism is therefore adopted to design the parking navigation strategy. The introduction and properties of this matching mechanism will be described in the following section. 5. 2 Matching Mechanism Design 5 2 .1 Two Sided Match The two sided matching problem is also referred to as the stable marriage problem, which is first int roduced by Gale and Shapley (1962). In their setting, a set of applicants apply to a set of colleges. Each applicant has an ordered preference for the colleges, and each college has an ordered preference for the applicants as well. A deferred acceptance pr ocedure was proposed to yield a stable assignment of applicants, in which there is no applicant preferring to be assigned to
76 a college that is not assigned to him or her while the college preferring the applicant over a currently accepted applicant. Follow ing their study, a substantial number of applications in various areas (e.g., labor market, networking, and parking) have been explored using this model. For example, the stable matching framework has been adopted by more than three dozen labor market clea ringhouses, e.g., the medical residencies in the U.S. and Canada (Roth, 2008). Xu and Li (2011) applied it to solve networking problems, where various types of limited resource (e.g., channels and video segments) need to be distributed. Ayala et al. (2012b ) established the equivalency between the Nash equilibrium of the parking slot assignment game and the stable assignment. Different from Ayala et al. (2012b), this study has the following contributions: (1) among all the stable assignments, only the stable driver optimal assignment is found to be strategy proof, which is critically important to a parking navigation system; (2) a decentralized solution procedure is adopted to achieve the stable driver optimal assignment without disclosing formation; (3) the performance of the two sided matching mechanism on the parking system is demonstrated by simulation experiments. Next, we proceed to formulate the parking assignment problem in the two sided matching framework. We consider a downtown are a where there are a finite number of parking spaces. Let and denote the set of drivers cruising for parking spaces and the set of open spaces at time Note that can be any time. Based on the current location, final destination and other personal favors (e.g., parking price, safety, etc.), open spaces are ranked for each driver. It is worthwhile to highlight that a driver may not prefer to be assigned to certain open spaces all the time, as those which are too expensive or too far from his or her final destination. On the other hand, each open space has a preference ranking for cruising drivers, which is measured by the travel time for drivers to arrive at the space. That is, a space would
77 (drivers) exist for any driver (space). Otherwise, some of the results presented in this chapter may not hold. To concisely describe the preference ordering, a preference list is defined, say, for driver as on the set of For example, It implies that the most preferred space of driver is space and then ; further, any other spaces are unacceptable for the driver. Definition 5. 1 A matching is an assignment of drivers to spaces such that each driver is assigned to at most one space and vice versa, and if and only if and , Definition 5.2. A matching is individually rational if no a gent prefers to be unmatched rather than matched to It implies that under any individually rational matching, no agent is matched with an unacceptable partner. Definition 5.3. An unmatched pair of a driver and a space is said to be blocked if th ey prefer to be matched with each other rather than with their current matched partner. Definition 5.4. A match is unblocked if no blocked pair exists. Definition 5.5. A match is stable if it is individually rational and unblocked. Below is a simple examp le to illustrate the above definitions. Suppose there are three vehicles, i.e., and competing for three open spaces and Their preference lists are shown in Table 5 1 It is easy to verify that matches and are stable, as they are individually rational and unblocked.
78 However, we can find that match is unstable, as and are bloc ked. More specifically, they can both benefit by being matched to each other. Proposition 5.1 (Gale and Shapley, 1962) There always exist s at least one stable match for every two sided matching problem. The basic idea is that a stable match can alway s be constructed by the deferred acceptance algorithm (see Algorithm 5. 1). Algorithm 5. 1 The driver oriented deferred acceptance algorithm Step 1: Each driver requests her most preferred space. Repeat Step 2: Each space keeps its most prefer red application (if any) and rejects the rest (if any). Step 3: E ach driver who was rejected at the previous step requests her next acceptable space (if any). until no driver requests in the last step. Definition 5.6 (Gale and Shapley, 1962) A stable match is driver optimal if every driver is at least as well off under it as under any other stable match. In Table 5 1 we can see that match is a driver optimal match, as all drivers are assigned to their most preferred spaces. The following proposition demonstrates the existence and uniqueness of the driver optimal stable match. Propo sition 5.2 (Gale and Shapley, 1962) The match given by the driver oriented deferred acceptance algorithm (see Algorithm 5. 1) is a driver optimal stable match. Proposition 5. 3 (Roth, 1989) When all drivers and spaces have strict preferences, there always exists a unique driver optimal stable match. preferences can be thought of as consisting of two parts: a mechanism for eliciting the preferences of the agents, and a mechanism fo r aggregating these elicited preferences to
79 the question must be asked: is there any stable matching mechanism that can guarantee that revealing the true pref erence for each agent is a dominant strategy? In other words, is it possible to design a stable matching mechanism that is strategy proof for all agents? Otherwise, the mechanism may not achieve the desired outcome. Proposition 5. 4 (Roth, 1982) There is no stable matching mechanism that is strategy proof for all agents. The above proposition implies that being strategy proof cannot be guaranteed for every agent (driver and space). Nevertheless, in the parking navigation system, the preferences of spaces cannot be manipulated, because they are measured by the travel time necessary for drivers s and the location of the spaces, nt location can always be detected via their smart phones Accordingly, the problem turns out to be: is there any stable matching mechanism that is a dominant strategy for each driver to state his or her true preferences? The following proposition provides an answer. Proposition 5.5 (Dubins and Freedman, 1981) The driver optimal stable matching mechanism makes it a dominant strategy for each driver to state his or her true preferences. The proof can be found in Theorem 5 in Roth (1982) or Theorem 9 in Dubi ns and Freedman (1981). The following proposition further highlights that coalition among some drivers is also not a good option. Proposition 5 .6 (Dubins and Freedman, 1981) Suppose several drivers collude in a driver optimal stable matching mechanism, ea ch using a false rank ordering. They cannot all get better spaces.
80 The proof can be found in Theorem 17 in Dubins and Freedman (1981). We already know that under the driver optimal stable matching mechanism, each driver is at least as well off as under an y other mechanisms. Also, such a matching mechanism is strategy proof. In light of these properties, it seems a good option to adopt the driver optimal matching mechanism as the assignment method for a parking navigation system. However, we need to further ensure that drivers will have incentives to obey such a navigation system instead of cruising for parking spaces by themselves. Proposition 5.7. Obeying the navigation system is a dominant strategy. Proof : Suppose it is not true, and one driver, say, can find a better space without following the navigation system. From the definition of stable matching, we can see that such a space must prefer its current matched driver to driver Otherwise, such a matching is blocked, as this pair of unmatched driver and space can both benefit by acting together. Therefore, a better space has been assigned to another driver, who is closer than driver That is, driver cannot win this space even if it is a better option than the current matched one. 5. 2 .2 Distributed Stable Match Although the classic driver optimal deferred acceptance procedure in Algorithm 5. 1 can information (i.e., preferences regarding spaces and final matched spaces). Accordingly, in this section, we present a distributed stable matching procedure (Brito and Meseguer, 2005) to minimize the centralized coordination. Specifically, it consists of two procedures, including driver and space procedures (see Algorithm 5. 2 and Algorithm 5. 3), and they are executed iteratively and asynchronously. To facilitate the procedures, four types of messages exchanged within the procedures are defined, including a parking request message from drivers to spaces,
81 accep t and reject messages from spaces to drivers, and a terminal message sent by a server which can detect quiescence. Algorithm 5. 2 shows the driver procedure executed for every driver. First of all, each unmatched driver sends a request to her most favorabl e open space with respect to the current preference list. If a reject message is received, she deletes the space from her preference list and keeps on sending her request; otherwise, she does nothing. The matched space is the one obtained at the end of the procedure. Apparently, not every driver can be assigned to a space when the number of vacant spaces is less than the number of drivers. Algorithm 5. 3 shows the space procedure executed for every open space, where is a sufficiently large number. When an open space receives a request message, if it is not matched to any driver yet, an accept message will be sent to the sender; if it is already matched, but the message sender is preferred (i.e., closer) to its curr ent matched driver, then it will send an accept message to the sender and a reject message to the current matched driver; otherwise, it will reject the request. Algorithm 5. 2 Driver procedure of the distributed stable matching (Brito and Meseguer, 2005) ; ; while do if and then ; ; sendMsg(request, ); ; getMsg(); switch accept: do nothing; reject : ; ; stop : ;
82 Algorithm 5. 3 Space procedure of the distributed stable matching algorithm (Brito and Meseguer, 2005) ; ; while do getMsg(); switch req uest: ; if then sendMsg(reject, ); else if then se ndMsg(reject, ); sendMsg(accept, ); ; ; stop : ; 5. 3 Simulation Experiment In thi s section, the matching system will be simulated on NetLogo and further compared guides drivers to their most preferred open spaces, and a status quo scenario wit h neither navigation nor information provision. More specifically, in the latter, each driver will cruise for parking from the closest space to their final destination, then the next closest one, and so on, until an open space is found or her maximum searc h time is reached. As the focus of the simulation experiment is on the influence of different navigation systems on parking competition, considering the network topology will not have a great impact on the result, but will complicate the experiment. Theref ore, no network topology is considered in the simulation, and vehicles can thus go in any direction. Figure 5 3 shows a screenshot of the parking simulation in NetLogo. 20 destinations (the green buildings) and 400 parking spaces (the gray rectangles) are randomly generated within a downtown area (the blue rectangle), and
83 vehicles (the yellow cars) come from outside of the downtown area, which is consistent with reality. Table 5 2 presents the simulation s etting for the basic scenario. The arrival rate of vehicles for each destination is set to be the same, i.e., 20 veh/h for each destination in the basic scenario. Furthermore, we assume that each driver has her own maximum search time following a uniform d istribution [10, 15] min, and a parking duration following an exponential distribution with a mean value of 1 hour. To simplify, if a driver cannot park successfully within the maximum search time, we assume that she will park at a parking garage far away from the downtown area, and be subjected to a give up driving time and a give up walking time of 10 min each. In addition, we set the maximum unmatched time at 4 min. If the navigation system cannot assign any parking space to a driver within the maximum u nmatched time, it is assumed the driver will park at a parking garage. The total simulation time is set to be 200,000 seconds, and the warm up time is 50,000 seconds. Table 5 3 shows the simulation result for the basic scenario. As we can observe, all three systems can substantially increase the parking space utilization and the percentage of successful trips, while reducing the average driving time. Particularly, the matching system reduces the average driving time by 59%, much m ore than the other two systems, which are 27% and 25%, respectively. However, the matching system may bring a negative impact on the average walking time, while the other two systems may not. This is because the matching system attempts to achieve a stable the assignment rule of t he other two systems as well as the status quo. Nevertheless, compared with the decreased driving time, i.e., 6 minutes, the increased walking time is very small, about 30 seconds. In view of this, we believe that most of the drivers are willing to adopt t he matching
84 system to make such a tradeoff, although they may value walking time much more than driving time. Using the matching and the greedy navigation systems, the guided parking space for a driver may change during her trip. For example, a driver m ay be guided to space #1 when she starts her trip, and then be guided to space #2 when she is on the way. If such a situation happens frequently, i.e., the assigned parking space changes frequently, the driving comfort will be negatively affected, and the level of parking competition is implied to be high. To capture such an effect, we define the times of changed assignment for each driver. More precisely, if a driver is assigned to two different parking spaces during her trip, then the times of changed ass ignment is equal to 2. For convenience, we also use such a measure to identify the number of spaces that a driver has searched for in the status quo scenario. Note that it seems impossible to calculate the times of changed assignment for the gravitational system, as it only provides drivers with search directions, instead of guiding them to specific parking spaces. From Table 5 3 it is observed that, the average times of changed assignment of the greedy system is higher than that in the status quo; while the average times of changed assignment of the matching system is only 0.92, much less than the former two. This finding reveals the substantial advantage of our proposed navigation system on alleviating the level of parking compet ition and improving the driving comfort. Figure 5 4 delineates the effects of varied arrival rates on different performance measures. In Figure 5 4 (a) and (b), the parking space utilization and the perce ntage of successful trips of the three navigation systems are all higher than that in the status quo scenario. The improvement do not vary much among different navigation systems, which implies their similar capability on increasing parking space utilizati on rate as well as the percentage of successful
85 trips. Figure 5 4 (c) indicates that the matching system may result in higher average walking time, especially when the parking demand is close to the supply; while the other two syst ems may not, as they always guide drivers to their most preferred open spaces, which are closest to their destinations. Figure 5 4 (d) points out that the matching system can lead to a larger amount of average driving time saving t han the other two navigation systems, and such superiority can become more remarkable when the parking demand increases. In Figure 5 4 (e), with the increasing parking demand, the average times of changed assignment under the statu s quo and the greedy system increases significantly. This result makes sense, since under the se two scenarios, higher parking demand will lead to more severe parking competition, and drivers have to frequently drive toward distinguishing parking spaces in order to find an open one. In contrast, the average times of changed assignment associated with the matching system is relatively stable, and even decreases as the parking demand increases from 300 veh/h. The reason is straightforward. According to the mat ching system, one open parking space can be assigned to no more than one vehicle at any time, and thus some drivers may not be guided to any open parking space. Consequently, the total times of changed assignment may not vary much as the demand increases, which results in a decrease in the average times of changed assignment. Figure 5 5 illustrates how the market penetration will affect the performance of the matching system. To simplify, we assume that drivers will adopt either t he matching system or the status quo search approach for their parking search. For example, if the market penetration of the matching system is 60%, then the remaining 40% of drivers will adopt the status quo search approach. From a social standpoint, we c an find that as the adoption rate of the matching system increases, both the parking utilization and the percentage of successful trips will increase to a stable level, i.e., 100% and 70%, respectively (see, Figure 5 5 (a) and (b)) while the average
86 driving time and the times of changed assignment will keep on decreasing (see, Figure 5 5 (d) and (e)). Particularly, the average walking time is relatively stable over the changing market penetration (see, Figure 5 5 (c)). On the other hand, comparing drivers using the matching system and adopting the status quo search approach, the former is found to outperform the latter with respect to all performance measures, no matter under what le vel of market penetration (see, Figure 5 5 (b) (e) ) The above findings further demonstrate the substantial benefit brought by the matching system and its potential to be ready for practical implementation. 5. 4 Summary This cha pter has proposed a novel parking navigation system for guiding drivers to their most appropriate parking spaces without disclosing their private information. First, given time locations and their preferences regarding parking spaces, a two s ided matching algorithm is adopted to achieve a stable driver optimal matching, under which drivers can always be guided to their most appropriate spaces, and thus have no incentive to misreport their private information. A distributed stable matching algo rithm is then applied to achieve the space assignment without disclosing their private information. Simulation experiments based on NetLogo are conducted to demonstrate the performance of the matching system. As compared with the status quo, greedy and gra vitational systems, the matching system is found to be able to reduce the average driving time and the average times of changed assignment substantially, but may increase the average walking time slightly. In particular, as the parking demand increases, th e average times of changed assignment under the matching system becomes rather stable, while the ones under the status quo scenario and the greedy system increase significantly. In addition, considering the impact of varied market penetrations of the match ing system on the parking system, we have found that a higher adoption rate of the matching system can lead to a higher space utilization rate, a higher percentage of successful trips, lower average driving time
87 and less times of changed assignment, but wi ll not result in higher average walking time. More importantly drivers using the matching system always are shown to have better performance than those adopting the status quo search approach. Our plan for a future study is to develop a mobile app to inte grate with the matching system, which is ready for practical implementation. To this end, we need to explore how to considering the impact due to traffic conge stion and signal control, in order to match the preferences of drivers and spaces.
88 Table 5 1 Preference list of three drivers and three spaces Table 5 2 Simulation setting for the basic scenario Parameters Value Description Number of destinations 20 Constant Number of parking spaces 300 Constant Arrival rate of vehicles 400 veh/h Exponential distribution Average parking duration 1 h Exponential distribution Driving sp eed 25 mi/h Constant Walking speed 3.4 mi/h Constant Maximum search time [10,15] min Uniform distribution Maximum unmatched time 4 min Constant Give up driving time 10 min Constant Give up w alking time 10 min Constant Simulation time 200,000 sec Cons tant Warm up time 50,000 sec Constant Table 5 3 Simulation result Performance Measures Status Quo Matching System Greedy System Gravitational System Parking space utilization (%) 79.30 99.40 99.35 99.32 Percentage of succ essful trips (%) 55.39 70.55 69.49 69.10 Average walking time (sec) 327.82 357.17 330.55 335.10 Average driving time (sec) 788.20 322.73 578.74 587.34 Average times of changed assignment 25.92 0.92 30.53
89 Figure 5 1 Architecture of parking navigation system Figure 5 2 Procedure of parking navigation system
90 Figure 5 3 Screenshot of the p arking simulation
91 Figure 5 4 Effects of arrival rate on different system performance measures: (a) parking space utilization, (b) percentage of successful trips, (c) average walking time, (d) average driving time, and (e) average times of ch anged assignment
92 Figure 5 5 Effects of market penetration on different system performance measures: (a) parking space utilization, (b) percentage of successful trips, (c) average walking time, (d) average driving time, and ( e) average times of changed assignment
93 CHAPTER 6 MICROSCOPIC PARKING SIMULATION It is rather difficult, if not impossible, to develop analytic al model s to explore the impacts of different parking policies on a general network. Therefore, it is of critic al importance to develop a parking simulation which is capable to mimic parking search behavior subtly under complicated road conditions and serve as a tool for decision makers to analyze different parking policies. To this end, this chapter propose s to ad opt AnyLogic to construct an agent based microscopic parking simulation model. Based on a real network in San Francisco, d ifferent scenarios, including status quo, with information provision, and with reservation service, will be conducted to illustrate th e proposed simulation In the remaining of the chapter, Section 6.1 describes the parking simulation model, and corresponding applications are proposed in Section 6.2 Lastly, Section 6.3 concludes the chapter 6.1 Parking Simulation Model AnyLogic ( http://www.anylogic.com/ ) is a dynamic simulation tool developed by the AnyLogic Company in 2000. It is an agent based simulator, and facilitate capture the complexity and heterogeneity of various systems, such as business, economy, and social systems. Up to now, its application areas have covered supply chains and logistics, healthcare and pharma, marketing and competition, manufacturing and production, pedestrian flows, business processes and serv ice systems, railroads, strategic planning and management, and so on. Particularly, at the end of 2015 it has released the Road Traffic Library, which enables the modeling of road traffic in a microscopic level. More specifically, unlike the other traffic simulation tools, such as VISSIM ( http://vision traffic.ptvgroup.com/en us/products/ptv vissim/ ) Paramics ( http://www.paramics on line.com/ ) and CORSIM
94 ( http://mctrans.ce.ufl.edu/featured/TSIS/ ) it facilitates the modeling of the dynamic change of to model the parking s earch behavior. 6.1.1 Transportation Network In the AnyLogic the Road Traffic Library consists of six components i.e., Road, Intersection, Stop Line, Bus Stop, Parking Lot, and Traffic Light (see Figure 6 1 ). To create a genera l network, we just need to drag these components to appropriate spaces, and they will connect each other automatically. Fi gure 6 2 presents a small road network and we can revise their properties by click ing them Figure 6 3 shows the properties of the Parking Lot component, in which we can design the type (parallel or perpendicular), the number the length, and the position of corresponding parking spaces Besides manually creating a transportation netwo rk the GIS function in the AnyLogic can be applied to convert GIS shapefile data to road network shapes automatically However, as each generated road defaults to two way two lane corresponding modification is still needed Furthermore the other compone nts, such as bus stop, parking lot, as well as traffic signal also need supplied. 6.1.2 Parking Behavior of Drivers Given the road network, parking behaviors corresponding to different scenarios are delineated in Figure 6 4 Spec ifically, in the status quo scenario, following the shortest path, each driver will first drive to a particular road, in which they will start cruising from (hereinafter, we refer to it as cruising road ), If there are vacant parking space s on the cruisin g road, she will directly part at the first one and then walk to her destination ( Arnott and Rowse, 1999 ) Otherwise the driver needs to select one of the connected roads to keep on cruising In this study, a logit model is applied to determine the proba bility of a connected road being selected Suppose there are connected roads denoted by T hen the probability of road being selected is given by
95 where is the disutility of choosing to cruise To simplify, we assume that drivers only consider about the walking distance from their parking spaces to their destinations. Accordingly is defined as below: where is the walking dis tance from to th e destination, and represents the availability of parking spaces on Specifically, if there is at least one vacant parking space on ; otherwise. is a positive l arge number, which is used to ensure that a connected road with vacant parking spaces will have a much higher probability of being selected than those without any vacant parking space Once a driver find s a vacant space she will park there for a predeterm ined time period, and then disappear from the network For the scenario with parking reservation, each driver will make a reservation to the best vacant parking space at the beginning of her trip, and then drives there Specifically the best parking spac e can be the closest parking space to her final destination if a driver is assumed to minimize her walking time If there is no vacant parking space on the network, a driver will choose to cancel her trip. With parking information, each driver is assumed to drive toward the best current ly vacant parking space (Levy et al., 2015) If it turns out to be occupied by other drivers when she arrives there, she will figure out the updated best current ly vacant parking space, and drive s there. Similarly, if there is no parking space available on the network, a driver will choose to cancel her trip.
96 Figure 6 4 shows the parking simulation process of different scenarios in AnyLogic. Note that, the text in the figure is merely used to explain the process. It is worth to highlight that, in the AnyLogic, the impact of the sophisticated parking behavior will be considered inherently. For example, when a driver finds a vacant space and slows down its speed to park there, some of the following veh icles may slow down their speed and wait to go ahead, while some others may change their lane to overpass it 6.2 Simulation Experiment 6.2.1 Simulation Setting In the simulation, we buil d up the network topology based on a small area in San Francisco, whi ch contains a large number of on street parking spaces (see Figure 6 6 ). 10 origin destination pairs are considered in the simulation. Among them, two ori gin destination pairs only generate through vehicles, which do not need to s earch for park ing ; while the others only generate cruising vehicles that need to cruise for parking in the network and then walk to their final destinations. Specifically, b efore cruising, the speed of these vehicles is set as 30 mph; while it decreases t o 15 mph once they start cruising for parking. The walking speed is set as 3.4 mph. The total simulation time is set to be 2.5 hours, and the warm up time is 1 hour. For the status quo scenario, all cruising vehicles are set to cruise for parking from the second closest roads along the shortest path to their destinations. 6.2.2 Simulation Result Figure 6 7 shows a screenshot of the parking simulation and Table 6 1 calculates the average driving and walki ng time s for different scenarios As we can observe from Table 6 1 both cruising and through vehicles can benefit via parking reservation. More specifically, compared with the status quo scenario, in the reservation scenario, the average driving and walking times of cruising vehicles are reduced by 14.7% and 45.5%, respectively. For the
97 through vehicles, their driving time also decreases a little bit, from 133.09 to 129.89 sec. W ith parking information, the average walking time of cruising vehicles will decrease a lot, even lower than the one in the reservation scenario. That is because, with the information, drivers will always try to park at the closest parking spaces to the ir destination s which results in the higher occupancy r ate of those parking spaces and thus a lower average walking time However, a lthough goals on improv ing the parking system performance, providing information will substantially increase the average dri ving time of both cruising and through vehicles. More precisely, the driving time of cruising vehicles increases by about 2.5 times, and the one of through vehicles becomes triple. The reason is that providing information will intensify the parking competi tion, as a good vacant parking space can normally attract more than one drivers, among whom only one can win it. What is worse, providing information can aggregate the traffic congestion via increasing the traffic volume in the road network. Figure 6 8 plots the number of parked, cruising, and through vehicles every ten minutes from the end of warm up time. Based on Figure 6 8 (a) (b), i t is easy to find that compared with the other two scenarios, providin g information leads to less parked vehicles but more cruising vehicles. That is, it is much more difficult for cruising vehicles to park successfully, although more parking spaces remain vacant. Accordingly, as more vehicles are cruising on the road networ k, the through vehicles have to slow down their travel speed. As a result, more and more through vehicles remain on the road network ( Figure 6 8 (c)), which further intensifies the traffic congestion. As drivers may have different risk taking attitudes, some will start cruising for parking at spaces far from their destination, while others may drive very close to the destination and start from there. We further consider different cruising strategies for the status quo scenario by
98 ch anging their cruising roads. Table 6 2 illustrates the average driving and walking times for different cruising cruising until they reach the roads close st to their final destinations. We can observe that, the earlier the cruising vehicles start cruising, the less driving time they will suffer. However, in this case, they will often park at the spaces far from the final destinations, which results in highe r average walking time. 6.3 Summary In this chapter, we have successfully develop ed a microscopic parking simulation, which is capable to subtly mimic the parking search behavior considering car following and lane changing behaviors under different types of parking management services, including status quo, with information provision, and with reservation service. A simulation experiment is conducted based on a small area in San Francisco. Results show that allowing parking reservation can improve the sys tem performance by reducing the average driving and walking times of cruising vehicles, and speeding up through vehicles; while providing information may substantially increase the average driving times of cruising and through vehicles, and further make th e network more congested. L astly, we also consider the impact of different cruising strategies on the system performance.
99 Table 6 1 Average d riving time and walking time in different scenarios Status Quo Reservation Infor mation Average d riving time of cruising vehicles (sec) 217.57 185.65 748.25 Average w alking time of cruising vehicles (sec) 400.22 218.29 160.59 Average d riving time of through vehicles (sec) 133.09 129.89 406.88 Table 6 2 Average d riving time and walking time in status quo scenarios with different cruising roads The Closest Road The Second Closest Road The Third Closest Road Average d riving time of cruising vehicles (sec) 231.98 217.57 188.68 Average w alking time of cru ising vehicles (sec) 388.78 400.22 514.99 Average d riving time of through vehicles (sec) 122.54 133.09 135.28 Figure 6 1 Components in the Road Traffic Library
100 Fi gure 6 2 A s mall r oad n etwork r epresentation Figure 6 3 Properties of p arking l ot
1 01 Figure 6 4 Parking s imulat ion f lowchart of d ifferent s cenarios
102 Figure 6 5 Parking s imulation p rocess of d ifferent s cenarios in AnyLogic
103 Figure 6 6 Parking s imulation n etwork t opology
104 Figure 6 7 A s creenshot of the p arking s imulation
105 Figure 6 8 Number of different types of vehicles in the network at different simulation times: (a) parked vehicles; (b) cruising vehicles; (c) t hrough vehicles
106 CHAPTER 7 CONCLUSION Advanced parking management services, including parking information, reservation and navigation, are expected to help drivers find parking spaces quickly. This dissertation devotes to evaluating the impacts and implic ations of those emerging parking management services, and providing guidance on their development and deployment. We have developed analytical models for curbside parking on a one way street considering three different scenarios: status quo, providing rea l time parking availability information, and allowing reservations. To verify the performance of these analytical models, NetLogo has been applied to develop an agent based parking simulation. The results show ed that the analytical models can produce resul ts largely consistent with the simulation. The discrepancy can be attributed to the assumption that the arrival headway of each parking space follows an exponential distribution. We have concluded that in the particular setting considered in our study par providing parking information may worsen the performance of the parking system. In light of the above finding, w e then discussed a smartphone based parking reservation system to manage downtown curbside parking and designed reservation schemes to allocate parking spaces. We first illustrated the need for designing a reservation scheme to minimize the total parking cost. Given that the parking cost is closely related to a priva te information of drivers, their final destinations, we showed that drivers have incentive to misreport the information. Consequently, we applied the VCG mechanism to determine parking fees to ensure all drivers to provide truthful information and allocate parking spaces optimally. We also verified that the iterative VCG mechanism can be used for dynamic parking reservation, and achieve a myopic system optimum. In this reservation scheme, all the drivers have incentive to make their
107 reservations as early as possible. A numerical example was conducted to demonstrate the performance of the proposed schemes. As compared to the FCFS principle, the schemes can reduce the parking social cost up to 38%. To deal with the large amount of parking revenue, which increa ses individual costs of drivers, we examined a revenue redistribution mechanism. While achieving efficiency and strategy proofness, the mechanism rebates, on average, 76% of the revenue in the same numerical example, demonstrating its potential of making t he proposed reservation system appealing to both society and individual drivers. As the reservation service may result in the waste of public resource, we proceed to propose a novel parking navigation system for guiding drivers to the most appropriate park ing spaces without disclosing their private information. time locations and their preferences regarding parking spaces, a two sided matching algorithm was adopted to achieve a stable driver optimal matching, under which drivers c an always be guided to their most appropriate spaces, and thus have no incentive to misreport their private information. A distributed stable matching algorithm was then applied to achieve the space assignment without disclosing their private information. Simulation experiments based on NetLogo were conducted to demonstrate the performance of the matching system. As compared with the status quo, greedy and gravitational systems, the matching system was found to be able to reduce the average driving time and the average times of changed assignment substantially, but may increase the average walking time slightly. In particular, as the parking demand increases, the average times of changed assignment under the matching system becomes rather stable, while the o nes under the status quo scenario and the greedy system increase significantly. In addition, considering the impact of varied market penetrations of the matching system on the parking system, we found that a higher adoption rate of the matching system can lead to a higher space
108 utilization rate, a higher percentage of successful trips, lower average driving time and less times of changed assignment, but will not result in higher average walking time. Furthermore, simulation experiments demonstrated that dri vers using the matching system always have better performance than those adopting the status quo search approach. Lastly, as it is rather difficult to develop analytical models to explore the local impacts of different parking management services on a gen eral network, we have developed a microscopic parking simulation It is capable to subtly mimic the parking search behavior considering car following and lane changing behaviors under different types of parking management services, including status quo, wi th information provision, and with reservation service. A simulation experiment was conducted based on a small area in San Francisco. Results show ed that allowing parking reservation can improve the system performance by reducing the average driving and wa lking times of the cruising vehicles, and speeding up the through vehicles; while providing information may substantially increase the average driving times of cruising and through vehicles, and further make the network more congested. In addition we have consider ed the impact of different cruising strategies on the system performance.
109 LIST OF REFERENCES Arnott, R., Inci, E., 2006. An integrated model of downtown parking and traffic congestion. Journal of Urban Economics 60( 3), 418 442. Arnott, R., Inci, E., 2010. The stability of downtown parking and traffic congestion. Journal of Urban Economics 68( 3), 260 276. Arnott, R., Rowse, J., 1999. Modeling parking. Journal of Urban Economics 45(1), 97 124. Ayala, D., Wolfson, O., Xu, B., Dasgupta, B., Lin, J., 2 011. Parking slot assignment games. In Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems ACM, 299 308. Ayala, D., Wolfson, O., Xu, B., DasGupta, B., Lin, J. 2012a. Parking in competitive setting s: A gravitational approach. In Mobile Data Management (MDM), 2012 IEEE 13th International Conference on IEEE, 27 32 Ayala, D., Wolfson, O., Xu, B., DasGupta, B., Lin, J., 2012b. Pricing of parking for congestion reduction. In Proceedings of the 20th Int ernational Conference on Advances in Geographic Information Systems ACM, 43 51. Ayala, D., Wol fson, O., Xu, B., DasGupta, B., Lin, J., 2012c. Stability of marriage and vehicular parking. In MATCH UP 2012: the Second International Workshop on Matching Unde r Preferences 7 Bailey, M. J. 1997. The demand revealing process: to distribute the surplus. Public Choice 91 ( 2 ) 107 126. Benenson, I., Martens, K., Birfir, S., 2008 PARKAGENT: An agent based model of parking in the city. Computers, Environment and Urb an Systems 32(6), 431 439. Boehle, J. L Roth krantz, L.J. M. van Wezel, M., 2008. CBPRS: a City Based Parking and Routing System ERS 2008 029 LIS, Erasmus Research Institute of Management. Boyles, S. D., Tang, S., Unnikrishnan A., 2015 Parking search equ ilibrium on a network. Transportation Research Part B 81, 390 409 Brito, I. Meseguer, P., 2005. Distributed stable matching problems. In International Conference on Principles and Practice of Constraint Programming 152 166 Caicedo, F., 2009. The use o times in parking facilities. Transportation Research Part C: Emerging Technologies 17(1), 56 68. Caicedo, F., 2010. Real time parking information management to reduce search time, vehicle displacement and emissions. Transportation Research Part D: Transport and Environment 15(4), 228 234.
110 Caliskan, M., Graupner, D., Mauve, M., 2006. Decentralized discovery of free parking places. In Proceedings of the 3rd International Workshop on Vehicular Ad Hoc Networks VANET '06, New York, NY, USA. ACM, 30 39. Cao, J., Menendez, M., 2015 System dynamics of urban traffic based on its parking related states. Transportation Research Part B: Methodological 81, 718 736. Cavallo, R. 2006. Optimal decision m aking with minimal waste: Strategyproof redistribution of VCG payments. In Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems ACM, 882 889. Clarke, E. H. 1971. Multipart pricing of public goods. Public Choi ce 11 ( 1 ) 17 33. Delot, T., Cenerario, N., Ilarri, S., Lecomte, S. 2009. A cooperative reservation protocol for parking spaces in vehicular ad hoc networks. In Proceedings of the 6th International Conference on Mobile Technology, Application & Systems AC M, 30. Dieussaert, K., Aerts, K., Steenberghen, T., Maerivoet, S., Spitaels, K., 2009. SUSTAPARK: A n agent based model for simulating parking search. In AGILE International Conference on Geographic Information Science, Hannover Djuric, N., Grbovic, M. Vu cetic, S., 2016. ParkAssistant: A n a lgorithm for g uiding a c ar to a p arking s pot. In Transportation Research Board 95th Annual Meeting 16 5433 Dubins, L. E., Freedman, D. A., 1981 Machiavelli and the Gale Shapley algorithm. The American Mathematical Month ly 88(7), 485 494. Du, L., Gong, S. 2016 Stochastic Poisson game for an online decentralized and coordinated parking mechanism. Transportation Research Part B: Methodological 87, 44 63. Faltings, B. 2005. A budget balanced, incentive compatible scheme f or social choice. In Agent Mediated Electronic Commerce VI Theories for and Engineering of Distributed Mechanisms and Systems, Springer, 30 43. Federal Highway Administration (FHWA), 2007. Advanced parking management systems: A cross cutting study: Taking the stress out of parking FHWA JPO 07 011. Fosgerau, M., de Palma, A., 2013. The dynamics of urban traffic congestion and the price of parking. Journal of Public Economics 105, 106 115. Friedman, E. J., Parkes D. C 2003. Pricing wifi at starbucks: issue s in online mechanism design. In Proceedings of the 4th ACM Conference on Electronic Commerce ACM, 240 241. Gale, D. Shapley, L.S., 1962. College admissions and the stability of marriage. The American Mathematical Monthly 69(1), 9 15. Glazer, A., Niskane n E 1992. Parking fees and congestion. Regional Science and Urban Economics 22 ( 1 ) 123 132.
111 Geng, Y. Cassandras, C.G., 2011 In 2011 IEEE International Symposium on Computer Aid ed Control System Design (CACSD) IEEE 1 6. Geng, Y. implementation. Procedia Social and Behavioral Sciences 54, 1278 1287. Gerding, E. H., Robu, V., Stein, S., Parkes, D.C., Rogers, A., Jennings N.R 2011. Online mechanism design for electric vehicle charging. In The 10th International Conference on Autonomous Agents and Multiagent Systems Volume 2, International Foundation for Autonomous Agents and Multiagent Systems, 811 818. Gers hkov, A., Moldovanu, B., 2010. Efficient sequential assignment with incomplete information. Games and Economic Behavior 68 ( 1 ) 144 154. Giuffr e T., Siniscalchi, S.M. Tesoriere, G., 2012. A novel architecture of parking management for smart cities. Proced ia Social and Behavioral Sciences 53, 16 28. Groves, T. Incentives in teams. Econometrica: Journal of the Econometric Society 617 631. Gujar, S., Narahari Y 2008. On optimal linear redistribution of VCG payments in assignment of heterogeneous objects. arXiv preprint arXiv:0812.4792. Guo, L., Huang, S., Zhuang, J. Sadek, A.W., 2013. Modeling parking behavior under uncertainty: a static game theoretic versus a sequential neo additive capacity modeling approach. Networks and Spatial Economics 13(3), 327 3 50. Guo, M., Conitzer V 2009. Worst case optimal redistribution of VCG payments in multi unit auctions. Games and Economic Behavior 67 ( 1 ) 69 98. Guo, M., Naroditskiy, V., Conitzer, V., Greenwald, A., Jennings N.R 2011. Budget balanced and nearly eff icient randomized mechanisms: Public goods and beyond. In Internet and Network Economics 158 169. He, F., Yin, Y., Chen, Z., Zhou J 2015. Pricing of parking games with atomic players. Transportation Research Part B : Methodological 73 1 12. Hong, M., G arcia A 2012. Mechanism design for base station association and resource allocation in downlink OFDMA network. Selected Areas in Communications, IEEE Journal on 30 ( 11 ) 2238 2250. Horni, A., Montini, L., Waraich, R.A., Axhausen, K.W., 2013. An agent bas ed cellular automaton cruising for parking simulation. Transportation Letters 5(4), 167 175. Idris, M.Y. I. Tamil, E.M., Noor, N. M., Razak, Z., Fong, K.W., 2009 Parking guidance system utilizing wireless sensor network and ultrasonic sensor. Information T echnology Journal 8(2), 138 146.
112 Inci, E. 2015 A review of the economics of parking. Economics of Transportation 4(1), 50 63. Kokolaki, E., Karaliopoulos, M., Stavrakakis, I. 2013 Leveraging information in parking assistance systems. Vehicular Technolo gy, IEEE Transactions on 62(9), 4309 4317. Kokolaki, E., Karaliopoulos, M. Stavrakakis, I., 2014. Trading public parking space. In World of Wireless, Mobile and Multimedia Networks (WoWMoM), 2014 IEEE 15th International Symposium IEEE, 1 6 Leurent, F., Boujnah, H., 2014 Traffic equilibrium in a network model of parking and route choice, with search circuits and cruising flows. Transportation Research Part C : Emergining Technology 47, 28 46 Levy, N., Render, M., Benenson, I. 2015 Spatially explicit m odeling of parking search as a tool for urban parking facilities and policy assessment. Transport Policy 39, 9 20. Liu, W., Yang, H., Yin, Y., 2014 a Expirable parking reservations for managing morning commute with parking space constraints. Transportation Research Part C: Emerging Technologies 44, 185 201. Liu, W., Yang, H., Yin, Y., Zhang, F., 2014b. A novel permit scheme for managing parking competition and bottleneck congestion. Transportation Research Part C : Emerging Technologies 44, 265 281. Liu, W., and Geroliminis, N., 2016. Modeling the morning commute for urban networks with cruising for parking: An MFD approach. Transportation Research Part B: Methodological 93, 470 494. Mackowski, D., Bai, Y., Ouyang, Y., 2015 Parking space management via dynam ic performance based pricing. Transportation Research Part C: Emerging Technologies 59, 66 91. Martens, K., Benenson, I., Levy, N., 2010 The dilemma of on street parking policy: exploring cruising for parking using an agent based model. In Geospatial Anal ysis and Modelling of Urban Structure and Dynamics 121 138 Myerson, R. B., Satterthwaite M.A 1983. Efficient mechanisms for bilateral trading. Journal of Economic Theory 29 ( 2 ) 265 281. Nagel, K. Schreckenberg, M. 1992. A cellular automaton for freew ay traffic, Journal de physique I 2 (12), 2221 2229 Ni, X.Y., Sun, D.J. Peng, Z.R., 2015. An improved incremental assignment model for parking variable message sign location problem. Journal of Advanced Transportation 49(7), 817 828. Parkes, D.C., Singh S.P., 2003 An MDP based approach to online mechanism design. In Advances in Neural Information Processing Systems
113 Parkes, D. C., Kalagnanam, J.R., Eso, M., 2001. Achieving budget balance with Vickrey based payment schemes in exchanges. In Proceedings of t he Seventeenth International Joint Conference on Artificial Intelligence 1161 1168. Parkes, D. C., Singh, S., Dimah Y 2004. Approximately efficient online mechanism design. In Advances in Neural Information Processing Systems Qian, Z., Rajagopal, R., 2 014. Optimal occupancy driven parking pricing under demand uncertainties and traveler heterogeneity: A stochastic control approach. Transportation Research Part B : Methodological 67 144 165. Qian, Z., Xiao, F., Zhang, H. M., 2012. Managing morning commute traffic with parking. Transportation Research Part B : Methodological 46, 894 916. Roth, A. E. 1982 The economics of matching: Stability and incentives. Mathematics of O perations R esearch 7(4), 617 628. Roth, A.E., 1989 Two sided matching with incomplete information about others' preferenc es. Games and Economic Behavior 1(2), 191 209. Roth, A. E. 2008 Deferred acceptance algorithms: History, theory, practice, and open questions. International Journal of G ame Theory 36(3 4), 537 569. Shao, C., Yang, H., Zh ang, Y. Ke, J., 2016. A simple reservation and allocation model of shared parking lots. Transportation Research Part C: Emerging Technologies 71, 303 312. Shin, J. H., Jun, H. B. 2014 A study on smart parking guidance algorithm. Transportation Research Pa rt C: Emerging Technologies 44, 299 317. Shoup, D. C., 2006. Cruising for parking. Transport Policy 13(6), 479 486. Statista, 2016 a http://www.statista.com/sta tistics/201182/forecast of smartphone users in the us/ Statista, 2016b. http://www.statista.com/statistics/330695/number of smartphone users worldwide/ Tang S., Rambha, T., Hatridge, R., Boyles, S., Unnikrishnan A., 2014 Modeling parking search on a network by using stochastic shortest paths with history dependence. Transportation Research Record : Journal of the Transportation Research Board 2467, 73 79. T eodorovi c D., Lu c i c P. 2 006 Intelligent parking systems. European Journal of Operational Research 175(3), 1666 1681. Thompson, R.G., Takada, K. Kobayakawa, S., 2001. Optimisation of parking guidance and information systems display configurations. Tran sportation Research Part C: Emerging Technologies 9(1), 69 85.
114 Varian, H. R. 2009. Online ad auctions. The American Economic Review 430 434. Vickrey, W. 1961. Counterspeculation, auctions, and competitive sealed tenders. The Journal of Finance 16 ( 1 ) 8 3 7. Xu, H. Li, B., 2011. Seen as stable marriages. In INFOCOM, 2011 Proceedings IEEE IEEE 586 590 Yang, H., Liu, W., Wang, X. Zhang, X., 2013. On the morning commute problem with bottleneck congestion and parking space constraints. Transportation Research Part B: Methodological 58, 106 118. Yang, S., Hajek B 2006. VCG Kelly mechanisms for allocation of divisible goods: Adapting VCG mechanisms to one dimensional signals. In Information Sciences and Systems, 2006 40th Annual Confere nce on IEEE, 1391 1396. Zakharenko, R., 2016. The time dimension of parking economics. Transportation Research Part B: Methodological 91, 211 228.
115 BIOGRAPHICAL SKETCH transportation engineering from Sun Yat sen University, China, in 2012. Since 2013, he has started his Ph.D. studies at the University of Florida under the supervision of Dr. Yafeng Yin. transportation network modeling and optimization and s o far he has c o authored nine papers and made ten presentations at various conferences. During his doctoral studies Zhibin has won the Graduate School Fellowship from the University of Florida, the Stella Dafermos Best Paper Award and the Ryuichi Kitamura Best Paper A ward at the 95th TRB Annual Meeting.