# Optimizing the Location of Park-and-Ride Facilities in Suburban and Urban Areas Considering the Characteristics of Coverage Requirements

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Formulation

## 3. Model Building

#### 3.1. Location Model of P&R Facilities in Outer Suburbs Based on Travel Choice Behavior

_{iz}, d

_{ij}, d

_{ik}, d

_{jz}respectively represent the distance from demand point i to the city center z, the distance from demand point i to P&R facility j, the distance from the demand point i to the rail transit station k, and the distance from the P&R facility j to the city center z. P&R facilities j

_{1}and j

_{2}are set up near rail transit stations k

_{n−1}and k

_{n}to facilitate transfer. Defining the acceptable walking distance radius for transfer to rail transit as D

_{w}, the demand point collection is ${I}_{k}=\left\{i|{d}_{ik}\le {D}_{w},\exists k\in K\right\}$, and travelers who gather at I

_{k}choose to walk to the rail transit station to complete their trip. ${I}_{w}=\left\{i|i\notin {I}_{k},i\in I\right\}$ is a demand point outside the coverage area of D

_{w}of the rail transit station, the acceptable driving distance radius for a private vehicle traveling to a rail transit station is D

_{c}, and the collection of demand points covered by P&R facilities is ${I}_{p}=\left\{i|{d}_{ij}\le {D}_{c},\exists j\in J,i\in {I}_{w}\right\}$. Travelers in the assembly can choose P&R travel or private vehicle travel. The remaining demand points are defined as ${I}_{n}=\left\{i|i\notin {I}_{j},i\in {I}_{w}\right\}$, and all travelers in the assembly choose private vehicles to travel to the destination (city center z).

_{p}and the set of P&R facilities that can be selected for i is ${J}_{i}=\left\{j|{d}_{ij}\le {D}_{c},\forall i\in {I}_{p}\right\}$. The travel time of travelers using the P&R method at demand point i is composed of the travel time of the private vehicle driving to the P&R facility, the travel time of walking to the rail transit station, the waiting time, and the time of taking the rail transit to the destination as defined in (Equation (1)):

_{c}is the average speed of the private vehicle; v

_{tr}is the average speed of rail transit; F

_{tr}is the average departure frequency of the rail transit lines; t

_{p}is the parking search time in the P&R facility; ${t}_{i}^{c}$ is the travel time for the demand point i to choose a private vehicle to travel to the city center z; p

_{ij}is the probability that demand point i chooses P&R facility j; and θ is the user’s sensitivity to travel time.

_{j}indicates whether to build P&R facilities in the 0–1 variable at candidate point j; q

_{i}is the travel demand of demand point i; C is the maximum number of P&R facilities to be constructed; d

_{ij}is the distance from demand point i to P&R facility j; d

_{ik}is the distance from demand point i to rail transit station k; and d

_{iz}is the distance from demand point i to destination z in the city center.

_{iz}-d

_{ij}represents closure mileage of a unit vehicle. Equation (5) is the quantity constraint for the construction of P&R facilities and can also be expressed in the form of constraints such as construction cost constraints or land use constraints. Equation (6) indicates whether the demand point i is covered by rail transit station k, that is, whether the potential P&R travel demand is for travel by rail transit. If there is a rail transit station k covering demand point i, it is 0; otherwise, it is 1. Equation (7) indicates whether demand point i is within the coverage of P&R facility j. When demand point i is within the coverage of P&R facility j, that is d

_{ij}≤ D

_{c}, β

_{ij}is 1; otherwise, β

_{ij}is 0. That is, when there are many P&R facilities built in the network, not every P&R facility will be considered by travelers. If the traveler is not covered by the P&R facility j at the demand point i, they will choose other optional P&R facilities to travel or choose a private vehicle to travel. Equation (8) is the probability that demand point i chooses P&R facility j to travel, which is an improvement in Equation (3) based on the decision variables x

_{j}and parameters α

_{i}, β

_{ij}. When P&R facilities are not set at candidate point j, x

_{j}= 0, the probability of demand point i selecting point j is also 0. When P&R facilities are set at the candidate point j, x

_{j}= 1, and the ratio of the demand point i to point j is allocated according to Equation (3). At the same time, the pumped P&R facility j for demand point i should be within the range of acceptable mileage D

_{w}to D

_{c}, that is, d

_{ij}≤ D

_{c}and d

_{ik}> D

_{w}. Equation (9) is the 0–1 constraint of decision variables.

#### 3.2. Location Model of Urban P&R Facilities Based on Progressive Cooperative Coverage

_{1}. The demand intensity of type A demand points is higher than that of type B demand points. One of the reasons is that the closer the demand point is to the P&R facility, the higher the possibility that travelers will choose the P&R method, such as demand point i

_{2}. In addition, when multiple P&R facilities cover a certain demand point at the same time, the possibility of choosing P&R travel for type A is greater than that for type B demand points, such as demand point i

_{3}.

_{i}is the travel demand of demand point i; β is the distance attenuation coefficient; and β is greater than 0. As the distance d

_{ij}decreases, the greater the distance attenuation coefficient β, the faster the coverage demand attenuates.

_{ij}), then the parking and transfer supply capacity of facility j to demand point i is ∑f(d

_{ij})x

_{j}α

_{i}q

_{i}. If it is greater than the q

_{i}of demand point, it is considered that demand point i is completely covered and the potential demand covered is q

_{i}. Otherwise, it is considered that the demand point i is partially covered; that is, part of the potential P&R travel demand is transformed into the actual P&R travel demand, and the potential demand covered is ∑f(d

_{ij})x

_{j}α

_{i}q

_{i}. Equation (11) is a constraint on the number of P&R facilities. Equation (12) is a function of the demand intensity of P&R facilities in the coverage area, and the attenuation function of the coverage level of P&R facilities with distance is expressed in exponential form. Equation (13) determines whether the demand point i is covered by rail transit station k, that is, whether the potential P&R travel demand will directly choose to travel by rail transit. If there is a rail transit station k covering demand point i, it is 0; otherwise, it is 1. Equation (14) is 0–1 constraints on decision variables.

## 4. Model Solving

- Parameter initialization. The number of iterations, crossover probability, mutation probability, and population size are determined.
- The potential P&R travel demand distribution is entered, simplifying the transportation network structure and related parameters.
- An initial population is randomly generated. The chromosomes in the population contain the initial P&R facility location plan.
- According to the coverage of rail transit stations and the coverage of P&R facilities, the demand point set I
_{k}covered by the rail transit site, the P&R facility coverage demand set I_{p}, and the demand point i which can choose the P&R facility set J_{i}are determined. - In the P&R facility location model in the outer suburbs, the ratio of demand points to the selection of P&R facilities is calculated. In the urban P&R facility location model, the demand for incremental cooperation coverage is calculated where demand points are covered by P&R facilities.
- The fitness of the chromosomes in the population is calculated. Since the models constructed in this study all aim at the maximum target value, the objective function value is set to 0 when the location plan does not meet the constraints, and the fitness of the chromosome is set to the objective function value.
- The chromosomes in the population are selected, crossed, and mutated to generate a new population.
- The elite retention strategy is adopted to replace a chromosome in the new population with the chromosome with the highest fitness in Step 7, thereby improving the search speed and accuracy of the algorithm.
- The number of iterations is verified. If the maximum number of iterations is not reached, the process returns to Step 4; if the number of iterations is reached, the algorithm is terminated and the P&R facility location plan is output.

## 5. Model Verification

#### 5.1. Location of P&R Facilities in Outer Suburbs

_{1}to i

_{8}) and five P&R facility alternative points (j

_{1}to j

_{5}) distributed in the outer suburbs. The travel destination of the demand points is the initial city center. P&R facility options, potential P&R travel demand distribution, and demand are shown in Table 1. The Euclidean distance between the P&R facility alternative point and the demand point is taken as the travel distance by rail transit in the P&R travel mode. The rail transit frequency is set to five vehicles per hour; the average speed of rail transit trains and private vehicles are 150 and 60 km/h, respectively; the parking search time in P&R facilities is 3 min; and the travel choice behavior model parameter θ is 0.05. Taking into account the characteristics of outskirts travel, the acceptable distance D

_{w}from walking to the rail transit station is 0.5 km, the acceptable distance radius for driving to P&R facilities is 5 km, and the upper limit of the number of P&R facilities in the outer suburbs is 2.

_{i}and β

_{ij}in Equation (8) took constant 1, other formulas remained unchanged, and a location model 3 was established without considering the coverage characteristics. Model 1 was compared with model 3. The optimization results of P&R facility location scheme and the results of conventional location scheme are shown in Table 2.

_{2}, the location scheme of model 1 does not take j

_{4}as the location scheme, the demand points i

_{1}and i

_{7}are not included in the coverage, and the driving mileage of the closure private vehicle is less than that of model 3. The main reason for this result is that model 3 regards the demand point within the 500 meter coverage radius of the rail transit station as the P&R facility coverage demand, while model 1 does not count it as the actual demand point, so this part of the demand is not included in the closure mileage. Although the domestic demand points i

_{1}and i

_{7}of the 500 m coverage radius of the rail transit station are the source demand points for private vehicles, it is more reasonable to walk to the rail transit station than to travel. At the same time, if the coverage characteristics are not taken into account, assuming that all the demand is covered, it will lead to an increase in the size of the planned parking lot (the number of private vehicles truncated by model 3 is 1420 more than that of model 2). Part of the demand (d

_{ik}≤ D

_{w}or d

_{ij}> D

_{c}) will not use private vehicles to travel to rail transit transfer points but rather walking or shared bicycles. Therefore, although the driving mileage of the closure private car of model 1 is less than that of model 3, it seems that the result of model 3 is better, but it may lead to excessive waste of space resources. Therefore, the P&R facility location scheme obtained by model 1 is more in line with the actual situation and more reasonable.

_{2}and j

_{3}, as the demand points i

_{5}, i

_{6}, and i

_{8}are closer to the urban center and farther from P&R facilities, the proportion of private vehicles chosen by i

_{5}, i

_{6}, and i

_{8}is higher than that of i

_{2}, i

_{3}, and i

_{4}. In line with the conclusion of the literature [29], a survey was conducted on the users of P&R facilities in the metropolis of Seattle, WA, USA. According to Figure 7, the probability of selecting j

_{3}for demand points i

_{5}, i

_{6}, and i

_{8}is greater than that of j

_{2}, mainly because the demand point near the urban center is closer to j

_{3}. Similarly, the probability of choosing j

_{2}at demand points i

_{2}, i

_{3}, and i

_{4}is greater than that of j

_{3}. In addition, there is no significant difference in the selection probability of the demand point for different P&R facilities. The main reason is that there are overlapping road sections in the process of long-distance intercity travel, which accounts for a large proportion of the total travel distance; that is, the radius of the area formed by the demand point is much smaller than that of the urban area, resulting in a small difference in travel time between the demand point i and the P&R facility j to the urban center z. As a result, the difference of selection probability is not statistically significant. In addition, the logit model assumes that the selection behaviors are independent and uncorrelated (independence of irrelevant alternatives, IIA), which leads to no significant difference in facility selection. The P&R behavior is analyzed in the literature [30,31,32,33]. The results show that although the logit is independent from irrelevant alternatives, it still has a certain applicability. When there are multiple rail transit lines leading to the urban center, the overlap of paths can be avoided, which is reflected in the layout of P&R facilities in Shanghai [34].

#### 5.2. Location of Urban P&R Facilities

_{1}to j

_{12}). The number of P&R facilities is restricted to 4, and 15 demand points (i

_{1}to i

_{15}) are distributed in the area. P&R facility options, potential P&R travel demand distribution, and demand are shown in Table 3. Euclidean distance is used as the travel distance between two points. Due to the short travel distance in the urban area, the acceptable distance to walk to the rail transit station is set to 0.5 km, and the acceptable distance radius D

_{c}for driving to the P&R facility is 3 km. The parameter β of the asymptotic cover function model is 0.2. MATLAB R2016a was used to solve the P&R facility location plan under the urban scenario. The maximum number of iterations in the genetic algorithm is 500, the crossover probability is 0.5, the mutation probability is 0.05, and the population size is 500.

_{i}= 1, respectively, and a progressive coverage location model 5 was established without considering the coverage characteristics. Model 2 was compared with model 4 and model 5. The optimization results of the P&R facility location scheme and the results of the conventional location scheme are shown in Table 4.

_{c}is 3 km, because the progressive coverage principle is not taken into account, different P&R facility location schemes can cover all the demand of the urban area. Because the coverage characteristics are taken into account, model 2 is the same as the uncovered demand points and potential requirements of model 4 and are much smaller than model 5. Compared with the three models, the actual coverage requirement of model 2 is the smallest. The main reason is that the domestic demand point in the 500 m coverage radius of the rail transit station is regarded as the coverage demand of P&R facilities. Although the domestic demand points i

_{1}, i

_{2}, i

_{3}, i

_{7}, and i

_{14}are the source demand points of private vehicles in the 500 m coverage radius of rail transit stations, it is more reasonable to choose to walk to rail transit stations to transfer to rail transit. In addition, with the increase in the distance between the demand point and P&R facilities, the demand for the conversion of potential P&R travel demand into actual P&R travel demand will gradually decrease. If model 4 and model 5 are adopted, the calculated demand will be 804 and 2825 more than that of model 2 because the principle of gradual progress and the principle of demand range characteristics are not taken into account. These requirements may involve travel to the rail transit station by walking or bicycle. Using these requirements for the construction of P&R facilities will greatly improve the construction scale and capital investment, which may lead to waste. Therefore, the P&R facility location scheme of model 2 is more in line with the actual situation.

## 6. Empirical Analysis

_{1}to i

_{9}) and five alternative points of P&R facilities (j

_{1}to j

_{5}). The travel destination of the demand point is the initial destination of the urban center. In the location of P&R facilities in the urban area, there are 11 alternative points (j

_{6}to j

_{16}), and 18 demand points (i

_{10}to i

_{27}) are distributed in the region. The optional locations of P&R facilities, the distribution of potential P&R travel demand, and the demand are shown in Table 5 and Table 6.

_{c}is 3 km, and the parameter β of progressive coverage function model is set to 0.2 km. The genetic algorithm was used to solve the problem. The maximum number of iterations is 500, the crossover probability is 0.5, the mutation probability is 0.05, and the population size is 500. The final location results are shown in Table 7.

_{2}, while the P&R facility in the urban area is located at j

_{7}, j

_{8}, j

_{11}, and j

_{16}. As a result, most of the demand points can be covered, and i

_{7}, i

_{8}, i

_{9}, i

_{11}, i

_{17}i

_{18}, i

_{21}, i

_{22}, and i

_{27}, which are not covered by P&R facilities, have walking access to the rail transit station, which is more in line with the actual situation.

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Li, M.; Guo, R.; Li, Y.; He, B.; Chen, Y.; Fan, Y. Distribution Characteristics of the Transportation Network in China at the County Level. IEEE Access
**2019**, 7, 49251–49261. [Google Scholar] [CrossRef] - Li, T.; Chen, Y.; Wang, Z.; Liu, Z.; Ding, R.; Xue, S. Analysis of Jobs–Housing Relationship and Commuting Characteristics around Urban Rail Transit Stations. IEEE Access
**2019**, 7, 175083–175092. [Google Scholar] [CrossRef] - Hamer, P. Analysing the effectiveness of park and ride as a generator of public transport mode shift. In Proceedings of the Australasian Transport Research Forum, Auckland, New Zealand, 29 September–1 October 2009. [Google Scholar]
- Rosli, N.S.; Adnan, S.S.; Ismail, F.D.; Hamsa, A.K. A Theoretical Review on Sustainable Transportation Strategies: The Role of Park and Ride Facility as a Generator of Public Transport Mode Shift. 2012. Available online: https://www.semanticscholar.org/paper/A-theoretical-review-on-sustainable-transportation-Rosli-Adnan/3d3d8b36a1183f8c6b8924750f346d4610e09a72#references (accessed on 8 November 2021).
- Chen, X.; Liu, Z.; Currie, G. Optimizing location and capacity of rail-based Park-and-Ride sites to increase public transport usage. Transp. Plan. Technol.
**2016**, 39, 507–526. [Google Scholar] [CrossRef] - Meek, S.; Ison, S.; Enoch, M. Role of Bus—Based Park and Ride in the UK: A Temporal and Evaluative Review. Transp. Rev.
**2008**, 28, 781–803. [Google Scholar] [CrossRef][Green Version] - Wang, J.; Wang, H.; Zhang, X. A hybrid management scheme with parking pricing and parking permit for a many–to–one park and ride network. Transp. Res. Part C Emerg. Technol.
**2020**, 112, 153–179. [Google Scholar] [CrossRef] - Kepaptsoglou, K.; Karlaftis, M.G.; Li, Z. Optimizing Pricing Policies in Park-and-Ride Facilities: A Model and Decision Support System with Application. J. Transp. Syst. Eng. Inf. Technol.
**2010**, 10, 53–65. [Google Scholar] [CrossRef] - Zhang, R.; Wang, L.; Yan, Z. Park-and-Ride Demand Analysis and Parking Pricing: A case study of Shanghai in rail transit park–and–ride operation. Urban Transp. China
**2009**, 7, 13–18. [Google Scholar] - Margail, F.; Auzannet, P. Evaluation of the Economic and Social Effectiveness of Park-and-Ride Facilities. In Proceedings of the Seminar F Held at the Ptrc European Transport Forum, London, UK, 2–6 September 1996. [Google Scholar]
- Wiseman, N.; Bonham, J.; Mackintosh, M.; Straschko, O.; Xu, H. Park and Ride: An Adelaide case study. Road Transp. Res. A J. Aust. N. Z. Res. Pract.
**2012**, 21, 39–52. [Google Scholar] - Duncan, M.; Christensen, R.K. An analysis of park–and–ride provision at light rail stations across the US. Transp. Policy
**2013**, 25, 148–157. [Google Scholar] [CrossRef] - Aros–Vera, F.; Marianov, V.; Mitchell, J.E. P–Hub approach for the optimal park-and-ride facility location problem. Eur. J. Oper. Res.
**2013**, 226, 277–285. [Google Scholar] [CrossRef] - Cavadas, J.; Antunes, A.P. Optimization-based study of the location of park–and–ride facilities. Transp. Plan. Technol.
**2019**, 42, 201–226. [Google Scholar] [CrossRef] - He, B. Study on Planning Methods of Park–and–Ride Facility. Ph.D. Thesis, Southeast University, Nanjing, China, 2006. [Google Scholar]
- Fang, D.; He, D.; Chen, X.; Yu, H.; Chen, K. Optimal Location of a Park-and-Ride System under Capture Rate and Capacity Constraints. J. Harbin Eng. Univ.
**2017**, 38, 207–214. [Google Scholar] - Farhana, B.; Murray, A.T. Siting park-and-ride facilities using a multi–objective spatial optimization model. Comput. Oper. Res.
**2008**, 35, 445–456. [Google Scholar] [CrossRef] - Lu, X.; Guo, R. A Bi–Objective Model for Siting Park-and-Ride Facilities with Spatial Equity Constraints. Promet–Traffic Transp.
**2015**, 27, 301–308. [Google Scholar] [CrossRef] - Chen, J. The Research of Park and Ride Planning. Master’s Thesis, Chang’an University, Xi’an, China, 2011. [Google Scholar]
- Zhang, Q. Study on Park and Ride Facilities Location Method of Mountain—Group Cities. Master’s Thesis, Chongqing Jiaotong University, Chongqing, China, 2015. [Google Scholar]
- Lu, X.; Huang, H. Bi–Objective Programming Model for P&R Facility Location with Spatial Equity Constraints. Syst. Eng. Theory Pract.
**2014**, 34, 2379–2385. [Google Scholar] - Horner, M.W.; Groves, S. Network flow–based strategies for identifying rail park–and–ride facility locations. Socio Econ. Plan. Sci.
**2007**, 41, 255–268. [Google Scholar] [CrossRef] - Wang, X. The Research of Park and Ride Facilities in Urban Planning—A Case Study in Xi’an. Master’s Thesis, Chang’an University, Xi’an, China, 2009. [Google Scholar]
- Cheng, H. Method and Model of P&R Location Based on Urban Rail Transit Network. Master’s Thesis, Beijing Jiaotong University, Beijing, China, 2018. [Google Scholar]
- Gong, Y. Research on Site Selection of Park and Ride Facilities along with Subway—Based on the Case Study in Suzhou. Master’s Thesis, Southeast University, Nanjing, China, 2015. [Google Scholar]
- Yang, M.; Yang, Z.; Liu, Z. Urban Park-and-Ride Facility Location Model. J. Chang. Univ. Sci. Technol.
**2015**, 12, 11–16. [Google Scholar] - Yang, Z. The Research on Urban Park-and-Ride Facility Location. Master’s Thesis, Changsha University of Science and Technology, Changsha, China, 2016. [Google Scholar]
- Yu, J. P&R Behavior Analysis and Modeling of Commuting Travel on Beijing Suburb. Master’s Thesis, Beijing Jiaotong University, Beijing, China, 2020. [Google Scholar]
- Spillar, R.J. Park-and-Ride Planning and Design Guidelines. Fringe Parking
**1997**, 26, 299–300. [Google Scholar] - Yuan, Z. Analysis of Influencing Factors and Study of Charging Scheme of Park and Ride Based on cross Nested Logit Model. Master’s Thesis, Southeast University, Nanjing, China, 2020. [Google Scholar]
- Shi, F.; Zhu, Z.; Chen, J.; Qiu, S. Analysis on the Research Progress of Park and Ride in Urban Rail Transit Stations. Logist. Eng. Manag.
**2021**, 43, 88–92. [Google Scholar] - Qian, Q.; Gan, H. Investigation of Park-and-Ride Choice Behavior under the Influence of Multi–model Traveler Information. Logist. Eng. Manag.
**2021**, 43, 108–111. [Google Scholar] - Zhao, F.; Si, B.; Wang, Q.; Wen, X. A Model and Algorithm for Park–and–Ride Location in Urban Considering Multiple Objectives. China J. Highw. Transp.
**2021**. Available online: https://kns.cnki.net/kcms/detail/61.1313.U.20211103.1820.004.html (accessed on 15 November 2021). - Liu, T.; Pan, H. Park and Ride Practice in Shanghai. Urban Transp. China
**2020**, 18, 45–49, 74. [Google Scholar]

**Figure 8.**Analysis of location results under the constraints of the construction quantity of different P&R facilities.

**Figure 11.**Analysis of location results under the constraints of the construction quantity of different P&R facilities.

**Figure 12.**Schematic diagram of location of P&R facilities in the suburbs and urban area of Changchun.

Rail Station | x Axis (m) | y Axis (m) | Demand Points | x Axis (m) | y Axis (m) | Demand (veh) |
---|---|---|---|---|---|---|

j_{1} | 45,517 | 1654 | i_{1} | 45,147 | 1318 | 762 |

j_{2} | 44,449 | 3654 | i_{2} | 46,232 | 3308 | 581 |

j_{3} | 42,267 | 4755 | i_{3} | 44,588 | 4813 | 367 |

j_{4} | 41,182 | 2538 | i_{4} | 43,280 | 3058 | 287 |

j_{5} | 38,983 | 2972 | i_{5} | 42,780 | 1712 | 814 |

j_{k} | 2983 | 3221 | i_{6} | 40,531 | 1058 | 432 |

– | – | – | i_{7} | 40,934 | 2962 | 673 |

– | – | – | i_{8} | 40,408 | 4885 | 768 |

Index | Model 1 | Model 3 |
---|---|---|

P&R facility location plan | 2, 3 | 2, 4 |

Demand points within coverage | 2, 3, 4, 5, 6, 8 | 1–8 |

Closure number of private vehicles (veh) | 2339 | 3759 |

Closure private vehicle mileage (km) | 8.4 × 10^{3} | 12.3 × 10^{3} |

P&R Facility Alternatives | x Axis (m) | y Axis (m) | Demand Points | x Axis (m) | y Axis (m) | Demand (veh) |
---|---|---|---|---|---|---|

j_{1} | 5967 | 7398 | i_{1} | 6274 | 7777 | 942 |

j_{2} | 4165 | 6306 | i_{2} | 5049 | 8692 | 658 |

j_{3} | 4607 | 4384 | i_{3} | 5117 | 9409 | 741 |

j_{4} | 6160 | 2831 | i_{4} | 2704 | 4428 | 871 |

j_{5} | 7712 | 3828 | i_{5} | 4607 | 2402 | 278 |

j_{6} | 8098 | 5901 | i_{6} | 4980 | 1219 | 517 |

j_{7} | 5094 | 9030 | i_{7} | 6749 | 872 | 781 |

j_{8} | 2420 | 6560 | i_{8} | 8645 | 3376 | 347 |

j_{9} | 3224 | 2638 | i_{9} | 9602 | 1860 | 456 |

j_{10} | 6500 | 1108 | i_{10} | 9537 | 4410 | 343 |

j_{11} | 9752 | 3318 | i_{11} | 10,217 | 5907 | 182 |

j_{12} | 8653 | 8056 | i_{12} | 9367 | 7097 | 477 |

– | – | – | i_{13} | 10,184 | 7437 | 329 |

– | – | – | i_{14} | 8517 | 8457 | 687 |

– | – | – | i_{15} | 7417 | 9517 | 531 |

Index | |||
---|---|---|---|

Considering | |||

Coverage Characteristics1/2 pt Not Considering Coverage Characteristics | |||

Model 2 | Model 4 | Model 5 | |

P&R facility location plan | 3, 9, 11, 12 | 2, 5, 9, 12 (or other solutions) | 7, 10, 11, 12 |

Demand that is not covered by P&R facilities | 1, 2, 3, 7, 14 | 1, 2, 3, 7, 14 | 4 |

Potential coverage of P&R travel demand (veh) | 4331 | 4331 | 7269 |

Actual coverage of P&R demand (veh) | 3527 | 4331 | 6379 |

**Table 5.**Distribution of alternative points and demand points of P&R facilities in the suburbs of Changchun.

P&R Facility Alternative Points | Longitude | Latitude | Demand Points | Longitude | Latitude | Demand (veh) |
---|---|---|---|---|---|---|

j_{1} | 125.4478 | 43.9949 | i_{1} | 125.4190 | 43.9570 | 154 |

j_{2} | 125.4344 | 43.9813 | i_{2} | 125.4049 | 43.9992 | 67 |

j_{3} | 125.4178 | 43.9832 | i_{3} | 125.4281 | 44.0127 | 79 |

j_{4} | 125.4095 | 43.9733 | i_{4} | 125.4618 | 44.0143 | 55 |

j_{5} | 125.3880 | 43.9693 | i_{5} | 125.4789 | 43.9709 | 47 |

– | – | – | i_{6} | 125.4530 | 43.9619 | 177 |

– | – | – | i_{7} | 125.4216 | 43.9759 | 134 |

– | – | – | i_{8} | 125.4422 | 43.9984 | 88 |

– | – | – | i_{9} | 125.3994 | 43.9777 | 96 |

**Table 6.**Distribution of alternative points and demand points of P&R facilities in the urban area of Changchun.

P&R Facility Alternative Points | Longitude | Latitude | Demand Points | Longitude | Latitude | Demand (veh) |
---|---|---|---|---|---|---|

j_{6} | 125.3411 | 43.9291 | i_{10} | 125.3580 | 43.9283 | 287 |

j_{7} | 125.3378 | 43.9128 | i_{11} | 125.3511 | 43.9147 | 193 |

j_{8} | 125.3691 | 43.8783 | i_{12} | 125.3850 | 43.9100 | 511 |

j_{9} | 125.3300 | 43.8782 | i_{13} | 125.3855 | 43.8944 | 332 |

j_{10} | 125.2938 | 43.8828 | i_{14} | 125.3549 | 43.8896 | 307 |

j_{11} | 125.3263 | 43.8602 | i_{15} | 125.3464 | 43.8627 | 289 |

j_{12} | 125.3651 | 43.8601 | i_{16} | 125.3457 | 43.8495 | 143 |

j_{13} | 125.3895 | 43.8759 | i_{17} | 125.3768 | 43.8602 | 197 |

j_{14} | 125.3638 | 43.8982 | i_{18} | 125.3812 | 43.8797 | 226 |

j_{15} | 125.2710 | 43.8907 | i_{19} | 125.2897 | 43.8570 | 251 |

j_{16} | 125.3102 | 43.8982 | i_{20} | 125.3102 | 43.8731 | 334 |

– | – | – | i_{21} | 125.2747 | 43.8756 | 421 |

– | – | – | i_{22} | 125.2676 | 43.8973 | 262 |

– | – | – | i_{23} | 125.2829 | 43.9062 | 187 |

– | – | – | i_{24} | 125.2965 | 43.9205 | 179 |

– | – | – | i_{25} | 125.3134 | 43.9303 | 225 |

– | – | – | i_{26} | 125.3011 | 43.9023 | 358 |

– | – | – | i_{27} | 125.3107 | 43.8902 | 270 |

Index | Location of P&R Facilities in the Suburbs | Location of P&R Facilities in the Urban Area |
---|---|---|

P&R facility location scheme | 2 | 7, 8, 11, 16 |

Covered demand points | 1, 2, 3, 4, 5, 6 | 10, 12, 13, 14, 15, 16, 19, 20, 23, 24, 25 |

Uncovered demand points | 7, 8, 9 | 11, 17, 18, 21, 22, 26, 27 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Liu, H.; Li, Y.; Li, J.; Hou, B.; Zhao, S. Optimizing the Location of Park-and-Ride Facilities in Suburban and Urban Areas Considering the Characteristics of Coverage Requirements. *Sustainability* **2022**, *14*, 1502.
https://doi.org/10.3390/su14031502

**AMA Style**

Liu H, Li Y, Li J, Hou B, Zhao S. Optimizing the Location of Park-and-Ride Facilities in Suburban and Urban Areas Considering the Characteristics of Coverage Requirements. *Sustainability*. 2022; 14(3):1502.
https://doi.org/10.3390/su14031502

**Chicago/Turabian Style**

Liu, Huasheng, Yu Li, Jin Li, Bowen Hou, and Shuzhi Zhao. 2022. "Optimizing the Location of Park-and-Ride Facilities in Suburban and Urban Areas Considering the Characteristics of Coverage Requirements" *Sustainability* 14, no. 3: 1502.
https://doi.org/10.3390/su14031502