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Sharing economy is seen as an essential building block for sustainability. Yet, inefficient utilizing of parking spaces needs more attention, by which both direct and indirect traffic congestions may be caused, jeopardizing the economic potential of sustainable development. Conventional parking service may gradually lose favour in analogy to its counterpart, of which a novel approach solving shortage of urban parking resources is offered by shared parking. Hence, in this paper, problems of how to redistribute the available private-owned parking slots that be shared are focused due to the parking slot location properties that can be labelled as random, disordered, unstable, widely distributed, etc. Specifically, shared parking greatly enhances reasonability by considering satisfaction. Based on the mechanism of time matching between supply and demand, this paper thoroughly takes the bilateral preference of both parking demanders and parking space suppliers into account in terms of maximization of the utilization rate of shared parking spaces as well as the satisfaction of parking demanders, in which a multiobjective optimization model is established and the weighted sum method combined with the Hungarian method is adopted. Compared with the first-come-first-served (FCFS) strategy, the performance of the proposed method enjoys more advantages in utilizing shared parking spaces and in satisfying parking demanders. The model established and algorithm conducted in this paper meet the requirements induced by parking space redistribution in which inequalities exist between supply and demand, facilitating automobile parking and realizing higher efficiencies in using public resources regarding shortage of parking spaces in urban areas.

Transportation is a representative of energy-dependent industry which results in excessive energy consumption and environmental pollution. Under energy and environment pressures, how to alleviate shortage of parking resources without occupying too much space poses a serious challenge for transportation [

Owing to the severe imbalance between supply and demand of parking spaces, to which the major component is composed of private-owned ones, urban residents have to face great inconveniences and even difficulties when parking cars. For many cities, contradiction between creating more parking spaces and finite resources has become the inescapable problem, to which enormous increase in financial expenditure may not help within a short period of time. Under such circumstances, improving the utilization rate of public- and private-owned parking spaces seems a better alternative regarding the scarcity of parking resources [

Therefore, the scheme of shared parking is rendered as acceptable to alleviate inconveniences and difficulties of parking [

The rest of the paper is organized as follows. An overview of the related issues is performed in Section

Some scholars, foreign and domestic, have verified the feasibility and effectiveness of shared parking from multiple perspectives [

In researching shared parking matching strategy, Shao et al. [

Most of the existing researches concerning shared parking focused on the following three factors, namely, the analysis of the feasibility of shared parking, the construction of shared parking allocation model, the design of third-party shared parking platform [

The research objects are therefore sketched as residential area-located parking demanders who are featured with multiple parking demands and sharable parking spaces in multiple sharable periods. This paper considers shared parking space preference (parking space utilization) and parking demanders preferences (such as walking distance after parking, parking fees, and safety) in terms of redistributing and matching time of both shared private parking space and parking demanders. Accordingly, the preference is divided into three terms by the shared parking platform with regard to the different expressions of the parking preference, including clear numbers, interval numbers, and language term preference, which maximizes the utilization of shared parking spaces and the satisfaction degree of parking demanders. The key contributions of this paper can be recapitulated as constructing a multiobjective optimization model for shared parking in terms of bilateral preference, to which a relevant algorithm is designed. Shared parking is formulating its tendency throughout the developing process of the sharing economy. Our work will be reasonable for policymakers and business supervisors who wish to satisfy users’ experience of parking.

In this section, the shared parking scene for matching parking demanders with parking suppliers is sketched. Related notations are therefore defined to denote the sets and variables included.

In specific cases with finite parking spaces in public parking areas, there is a partial overflow parking seeker. Parking spaces located in residential areas within a certain distance around the public parking area can provide shared parking spaces due to the tidal effect. Such parking spaces are identified as shareable parking spaces. According to the different use of the land properties, the shared parking with maximum satisfaction refers to the parking space allocation that maximizes the preference of the supply and demand by implementing the different time sharing [

In the study of the simulated shared parking scenario, we set the following definitions with explanations: an owner of the shared parking space is identified as a “supplier,” whilst a parking demander is regarded as a “demander” and two types of participants are connected through a “shared parking platform.” Therefore, the shared parking scenario can be identified as follows (as shown in Figure

The shared parking scenario.

In order to describe the matching problem between the shared parking space and the parking demanders, the following symbols are used in this paper:

In this section, a model-based method is proposed to solve the abovementioned problem regarding private parking slot sharing. An optimization model of parking time matching is established in terms of satisfaction, under which an algorithm is designed accordingly.

The parking time is discretized during the time period involved in the model. The time interval ranging from

Depending on the shareable parking period and the parking demanders period provided by the shared parking space,

By analyzing whether there is an intersection of the parking time windows for different vehicles, it can be judged whether different vehicles can be allocated to the same parking space within the available time provided by the shared spaces so that

By judging whether there is an intersection between the time of parking demanders and the time of the shared parking space, the demand column vector can be constructed as

For example,

The decision variable

The target model

In the scene of shared parking, the shared parking spaces prefer the allocation scheme with high utilization rate. Therefore, the objective function is to maximize the efficiency of the shared parking spaces during the time period involved in the model, where

The shared parking platform analyzes the previous parking data and counts the key factors affecting the parking space selection. The platform is divided into three forms, clear numbers, interval numbers, and language term preference, in terms of the different expression forms of the parking factors [

When the platform provides parking spaces to the parking demanders, whether the real evaluation level of each shared parking space reaches the aspiration level of parking demanders should be taken into serious consideration. Inasmuch as measuring the degree of the aspiration level, it is necessary to calculate the parking demanders satisfaction of each attribute, thereby obtaining the overall satisfaction degree regarding the weight of each attribute.

The following process of calculation describes the satisfaction degree with three formats of attribute values.

When

For benefit attribute,

When the attribute value type including the expectation level and the evaluation level attribute

If

for benefit attribute,

The overall satisfaction of the parking demanders to the shared parking space regarding satisfaction degree of each attribute

Based on the principle of time matching and the satisfaction degree

The abovementioned model consists of two objective functions. The objective function (

The model

Let

The parking demander can select a satisfactory parking space from the multiple matching results of the parking space-demander with regard to the difference of satisfaction between the two parties. Similarly, the shared parking space can also select a satisfactory demander from multiple matching demanders. The abovementioned analysis shows that the model

It is known that by the objective function of the model

The objective of the Hungarian algorithm is to minimize the objective function. In order to establish a standard allocation model, it is necessary to convert the maximization problem into a minimization problem. In specific cases, the parking demander has only one parking demander in the matching cycle involved in the model, the parking space can be shared only one shareable time period and the number of parking demanders equals to the number of shared parking spaces, and the adoption of the Hungarian algorithm maximizing the problem can be directly translated into an equivalent of minimization problem. However, in reality, a person who seeks for parking may have multiple parking demanders. A shareable parking space may have multiple different shareable time periods. The number of parking demanders and shareable parking spaces may not be equal, which in turn generates the following method conducted in this paper.

Inasmuch as the principle of the Hungarian method in specific cases, we know that if there is a person who seeks for parking with multiple parking demanders within the period involved in the model, the demander is transformed into multiple demanders with the same preference but different parking periods. By converting parking demanders who are featured with multiple parking needs into parking demanders with only one parking requirement,

Finding the maximum value of the initial comprehensive satisfaction

Judging whether there is only one parking demander for a parking seeker, whether one shared parking space has only one shareable time period, and whether the value of these two factors equals to each other. If so, proceed to the third step. If not, convert the parking demanders and the shareable parking space to only one parking requirement and only one shareable time period, respectively. Setting

The maximum value

In the model

In summary, the matching problem solver proposed in this paper has 6 steps (as shown in Figure

1^{st} step: matching supply and demand time. The shared parking platform receives demand information from the parking demander and the shared information from the shared parking space, respectively, thereby matching and building the model

2^{nd} step: satisfaction calculation is performed. The parking demanders will submit the expectation level of each attribute of the shareable parking space to the platform. The platform generates the evaluation level of the shareable parking space in terms of the parking space information submitted by the owner of the shared parking space whereby the satisfaction of the demander is calculated.

3^{rd} step: construction of a dual-objective model. A dual-objective optimization model

4^{th} step: transforming into a single-objective model. By adopting the weighted sum method, the dual-objective model

5^{th} step: model standardization is done. Through conducting the specific cases of Hungarian algorithm, the transformation of the original model is therefore described as follows. A parking seeker has only one parking demand, a shareable parking slot has only one shareable time period, and the number of demanders and parking slots is the same.

6^{th} step: establishing a standard allocation model. Transforming the maximization problem into a minimization problem. Establishing the standard allocation model

Matching method framework.

In this section, an example for shared parking is presented to illustrate the implementation of the proposed method. Simulations are performed to test the effectiveness and fairness of the proposed model and of the optimization algorithm, which is conducted by comparing with the first come first serve (FCFS) allocation method.

In order to verify the validity of the proposed model and the optimization algorithm (OA), the simulation experiment is designed according to the idle time characteristics of the parking space in the residential area and compared with the first come first serve (FCFS) allocation method (the result is shown in Figure

FCFS method assignment result.

Parking seekers’ time information.

Parking seekers | Parking seekers period | Parking seekers | Parking seekers period |
---|---|---|---|

_{1} | [8:30, 14:00] | _{6} | [13:30, 18:00] |

_{2} | [15:30, 18:30] | _{7} | [7:00, 14:00] |

_{3} | [9:00, 13:00] | _{8} | [14:30, 18:00] |

_{4} | [14:30, 18:00] | _{9} | [8:00, 12:00] |

_{5} | [8:30, 11:00], [18:00, 20:00] | _{10} | [12:00, 15:00] |

Shared parking space sharing time information.

Shared parking space number | Parking space sharing time |
---|---|

_{1} | [7:00, 15:30] |

_{2} | [8:30, 20:00] |

_{3} | [8:00, 12:00], [13:30, 18:00] |

_{4} | [9:00, 18:00] |

_{5} | [8:30, 18:30] |

The shared parking platform provides a level of shared parking space with five attributes, including unit parking cost

Evaluation level of shared parking spaces.

Parking space/attribute | _{1} | _{2} | _{3} | _{4} | _{5} |
---|---|---|---|---|---|

_{1} | 8 | 8 | 150 | _{3} | _{4} |

_{2} | 9 | 8 | 220 | _{4} | _{5} |

_{3} | 10 | 9 | 180 | _{3} | _{3} |

_{4} | 8 | 10 | 290 | _{4} | _{3} |

_{5} | 8 | 9 | 270 | _{4} | _{2} |

In Table

The demand level of parking seekers for shared parking spaces.

_{1} | _{2} | _{3} | _{4} | _{5} | |
---|---|---|---|---|---|

_{1} | 7 | 8 | [280, 300] | _{3} | _{4} |

_{2} | 8 | 7 | [300, 350] | _{4} | _{3} |

_{3} | 9 | 8 | [250, 290] | _{5} | _{5} |

_{4} | 8 | 9 | [270, 330] | _{4} | _{5} |

_{5} | 8 | 9 | [230, 300] | _{3} | _{4} |

_{6} | 10 | 9 | [300, 340] | _{3} | _{3} |

_{7} | 8 | 8 | [260, 290] | _{5} | _{3} |

_{8} | 9 | 9 | [200, 350] | _{5} | _{5} |

_{9} | 5 | 8 | [230, 290] | _{4} | _{5} |

_{10} | 8 | 7 | [270, 300] | _{3} | _{3} |

We assume that the shared parking platform uses AHP to determine the weight vector, where

Satisfaction of parking seekers with shared parking spaces.

_{1} | _{2} | _{3} | _{4} | _{5} | |
---|---|---|---|---|---|

_{1} | 1 | 1 | 0.93 | 0.93 | 0.85 |

_{2} | 0.85 | 1 | 0.85 | 1 | 0.85 |

_{3} | 0.63 | 0.95 | 0.84 | 0.64 | 0.59 |

_{4} | 0.56 | 0.72 | 0.79 | 0.90 | 0.85 |

_{5} | 0.72 | 0.65 | 1 | 0.93 | 0.85 |

_{6} | 0.51 | 0.62 | 1 | 0.79 | 0.64 |

_{7} | 0.89 | 0.95 | 0.89 | 0.95 | 0.80 |

_{8} | 0.35 | 0.67 | 0.79 | 0.74 | 0.59 |

_{9} | 0.84 | 1 | 0.79 | 0.90 | 0.85 |

_{10} | 1 | 1 | 1 | 1 | 0.85 |

In line with the rule of equality, we settle

Optimizing the method assignment result.

Comparing the abovementioned two results, two parking demanders are not allocated to the shareable parking space. The resource utilization rate stays low and the shared parking space does not reach its expected value in the FCFS allocation scheme. Under the same supply and demand conditions, the shared parking space allocation scheme of the proposed paper can increase the parking space utilization time from 26 h to 42 h, and the parking space utilization rate is increased by 33.68%. The satisfaction level is increased from 55.64% to 79.73%, and the parking satisfaction is increased by 24.09%, which meet the requirements of the practical applications.

To further evaluate the feasibility and applicability of the optimization model, simulation experiments are performed between the proposed method and the FCFS allocation method. We suppose the modeling time interval is 0.5 h and the modeling period is 12 h starting from 8:00 AM and ending at 8:00 PM on a typical day. In the basic case, we suppose that a total number of shared parking lots is 100. Furthermore, we suppose that, in any minute during the whole modeling period, the arrival of the parking demander follows a Poisson distribution and parking duration follows a negative exponential distribution, as usually considered in the literature [

Comparison of parking utilization between FCFS and OA.

Comparison of parking satisfaction degree between FCFS and OA.

Simulation results showed that, under same conditions, the matching results of the shared parking space model and the algorithm adopted far outweighed the FCFS allocation method. These findings help the shared parking platform set better targeted policies to optimize indicators involving the parking utilization rate and total preference of the whole system, making breakthroughs in shared parking applications as well as in figuring out the satisfactory solution of parking allocations.

As a novel approach alleviating difficulties in car parking in terms of the scarcity of spaces amid urban environment, shared parking has proven an effective mechanism as one of the cornerstones in shared economy. To realize full use of the shared private-owned parking slots and to improve the satisfaction of both demander and supplier sides, this paper presents a novel method determining the satisfied matching between shared parking spaces and parking demanders. Firstly, a time matching model regarding supply and demand is built. Secondly, the preference is divided into three forms by the shared parking platform with regard to the different expressions of the parking preference, through which an optimization model considering the satisfaction degree is therefore constructed and an algorithm is accordingly designed. Thirdly, the superiority of the proposed model is verified and validated by comparing it with the first come first served (FCFS) strategy.

The model is ready to be applied to the shared parking system of Xi’an. The parking space allocation model of this paper is based on the known demand period of the parking demanders and the sharable time of the shared parking space. In reality, the demand of the parking demanders and the shareable time of the shared parking space are changing dynamically. The model can be further extended by considering the priority attributes of demanders and the dynamic matching between the supply and demanders considering bilateral preference, which will be the future interest of our research works.

The data used to support the findings of this study are available from the corresponding author upon request.

The authors declare no conflicts of interest.

This study was financially supported by the National Social Science Foundation of China (Grant number. 15BGL040).