Abstract
Taxi sharing is a promising method to save resource consumption and alleviate traffic congestion while satisfying people’s commuting needs. Existing research methods include taxi dispatching methods based on intelligent algorithms, single vehicle route recommendation algorithms, and route recommendation algorithms based on vehicle traffic history. However, these studies either focus on how to efficiently dispatch satisfactory vehicles for passengers, ignoring the effect of efficient routes on vehicle travel efficiency, or let vehicles follow the shortest detour distance recommended by the system, ignoring the traffic congestion caused by the influx of vehicles into the same road. To address the abovementioned problems, a noncooperative game for a taxi sharing model (NCG-TSM) in urban road networks is proposed in this paper combined with the traffic conditions of the optional routes, and a distribution estimation algorithm for the shared taxi game is designed to make multivehicle route selections reach Nash equilibrium. The effectiveness of NCG-TSM is verified through simulation experiments. When the number of vehicles reaches the congestion capacity of the road segment, compared to the three common frameworks, the travel time cost and fuel consumption cost can be reduced by 5.8% to 9.1% and 3.5% to 8.9%, respectively. Besides, the occupancy rate has been improved, especially compared to the BMP framework, by 5.5% to 40%.
1. Introduction
With the acceleration of urbanization, people’s travel needs are also increasing, and the increasing number of vehicles on the urban road network has aggravated the problem of road congestion. How to make the best use of resources, reduce energy consumption and ease traffic congestion has become an urgent issue [1–3]. Taxi sharing has become a better solution to travel difficulties and traffic congestion, meeting the individual needs of passengers and making full use of vehicle resources.
At present, the main solutions to travel difficulties and transport problems are as follows: frameworks for vehicle sharing, such as CARE-share [4] (a cooperative and adaptive distributed taxi sharing strategy) and coride [5] (collaborative preference- based taxi sharing and taxi dispatch) systems.
Optimal route recommendation algorithms, in the existing research on route problems, there are artificial immune system algorithms [6], ant colony algorithms [7], quantum genetic algorithms [8], reinforcement learning algorithms [9], Dijkstra’s algorithm [10], genetic algorithms [11], etc. To find the most reliable route, there are also research studies based on the user’s preferences in terms of travel time and road conditions to select the optimal route [12].
The abovementioned research on taxi scheduling and driver routing has achieved certain results, but the existing research still has shortcomings. First, most of the taxi sharing models are only studies of the vehicle dispatching methods involved, focusing only on how to efficiently dispatch satisfactory vehicles for passengers, ignoring the impact of driving paths on travel efficiency. Second, most of the cab-sharing studies guide single vehicles to follow the optimal route recommended by the system, ignoring the influence between vehicles, which leads to a large amount of traffic flow into a route and causes congestion on that route. Finally, the existing vehicle scheduling algorithm research faces the challenge of large computational volume.
In order to overcome the shortcomings of previous research, considering the impact of decision-making and resource competition among vehicle drivers, a noncooperative game is introduced to establish a taxi sharing model. In the taxi sharing model, taxi drivers are participants in the game. And, a candidate vehicle scheduling algorithm is proposed to schedule suitable candidate vehicles for passengers. Due to the large amount of calculation in the vehicle scheduling algorithm, the urban road network is first gridded. For the driver’s path decision problem, this paper designs a distribution estimation algorithm for the shared taxi game to solve the driver’s Nash equilibrium strategy, matching the appropriate vehicle from the candidate vehicles, providing an optimized route for passengers, and improving the overall benefits of all taxi drivers and reducing costs.
The contributions of this paper are summarized as follows:(1)A noncooperative game for a taxi sharing model (NCG-TSM) in urban road networks is established, which takes into account the local congestion of traffic caused by vehicles flooding into the same route at the same time(2)A candidate vehicle scheduling algorithm is proposed, which considers the impact of multiple influencing factors on vehicle scheduling and therefore can improve the efficiency and accuracy of vehicle scheduling(3)A distribution estimation algorithm for the shared taxi game is proposed, where the mixed strategies of the participants in the game are treated as each individual in the algorithm, the average utility of the participants is treated as the fitness function in the algorithm, and the strategy of the participants is the Nash equilibrium strategy when the fitness function reaches its maximum value
The rest of the paper is organized as follows. Section 2 describes the related work. Section 3 introduces the NCG-TSM in urban road networks. Section 4 presents the candidate vehicle scheduling algorithm. Section 5 presents the distribution estimation algorithm for the shared taxi game. Section 6 provides an experimental validation of the noncooperative game taxi sharing model under a real road network. Finally, Section 7 concludes the paper and provides future perspectives.
2. Related Work
In order to alleviate traffic congestion and solve the problems of difficult travel, shared travel has become a very popular way of travel, which means that multiple passengers take a vehicle to their respective destinations. To improve the singularity of the optimization objectives of centralized ride sharing systems, Bathla et al. developed a new distributed cab ride sharing algorithm to solve the dynamic scheduling problem of sharing requests [13], thus improving the efficiency of ride request processing. Cheikh–Graiet et al. proposed a dynamic carpool optimization system that reduces the high complexity of dynamic carpooling using a new taboo search-based metaheuristic algorithm for making decision [14] improving matching of passengers and drivers. Wang solved the problem of dynamic cab scheduling based on driver interest, modeled on the basis of Q-learn algorithm and Markov decision process [15]. The optimal scheduling scheme is provided by a machine learning framework by Agrawal [16].
With the development of technology, more mature vehicle research has emerged. Zafar et al. provides a comprehensive survey on carpooling in autonomous and connected vehicles and covers architecture, components, and solutions, including scheduling, matching, mobility, and pricing models of carpooling [17]. To address the severe challenges of user location or route privacy, Xu et al. propose an efficient and privacy protected route matching scheme for the carpooling services [18]. The modern intelligent transportation system opts for accident prediction modules as a critical aspect for road safety. Here, an accident is predicted before it actually happens and precautionary measures be taken for its avoidance. Halim et al. presents a deep learning and artificial intelligence-based system of identifying driving risks for the light transport vehicles (LTVs) that generate early warnings before an anticipated accident [19]. Halim and Rehan present a machine learning-based approach to identify driving-induced stress patterns [20].
Finding a suitable path for commuting in real‐life complex traffic networks is an important research problem with many applications. To improve travel efficiency, Qu et al. developed a probabilistic network model to predict the probability and capacity of ride sharing at each location using Kalman filtering [21]. Zeng et al. proposed a new multitask joint learning framework to optimize traffic prediction models [22]. Tu et al. proposed a new real-time route recommendation system using large-scale cab GPS trajectory data, which led to an increase in driver revenue [23]. Sankaranarayanan et al. used a new fusion algorithm to provide route suggestions using vehicle speed and density information collected from a central location and used as a decision factor, and the method provided the best-fit route [24]. Ge et al. recommend a series of locations to drivers by their current location to maximize the success of their business [25]. Zou et al. used a genetic algorithm modified by the A search algorithm to generate multimodal travel routes which can effectively reduce the time cost of commuting between congested areas by generating mixed traffic routes [26]. Zhou et al. proposed a Markov decision process based on spatial networks with rolling horizon configurations to recommend better driving directions [27]. The abovementioned studies about routes have a single evaluation objective, focusing only on the optimal route for a single vehicle, without considering the influence of multiple vehicles on each other during simultaneous path selection. Halim et al. presents a mobile crowdsourcing‐based model to find suitable commuting path(s) by considering the factors that directly or indirectly influence the overall travel time [28].
In summary, there are still shortcomings in existing studies, some of which ignored the effect of vehicle travel paths in shared travel and some just focused on problems such as optimizing the goals of a single vehicle, not multiple vehicles. In order to dispatch vehicles efficiently for passengers and to take into account the impact of route congestion on the efficiency of vehicle travel, this paper proposes a noncooperative game-based sharing model for the first time. In this model, a vehicle scheduling algorithm based on constraint conditions is proposed. The calculation of utility value based on vehicle selectable routes is proposed considering multiple objectives of vehicles. Besides, a distribution estimation algorithm is introduced into the process of solving the Nash equilibrium of the game that enables multiple vehicles to pick up and drop off passengers as many as possible. It reduces the consumption of travel costs and waste of urban road resources, and to a certain extent, alleviates the local congestion of urban traffic.
3. NCG-TSM Model
The impact of road congestion on vehicle travel time and fuel consumption when multiple vehicles choose the same route has not been considered in previous studies. Compared to other vehicle sharing models, this paper proposes NCG-TSM model which is designed to dispatch vehicles with a better match for passengers and reduce vehicle path costs when there are a large number of carpool requests. Section 3.1 describes the system overview. Section 3.2 introduces the problem description of the NCG-TSM model based on Section 3.1.
3.1. System Framework
The NCG-TSM proposed in this paper can be formulated as follows: the vehicle dispatch area consists of multiple vehicles and passengers that are used to pick up and drop off passengers. The vehicles may not be empty, may already have one or more passengers, and the number of passengers cannot be more than four. After receiving a passenger request, the dispatch center can send a dispatch request to the vehicle to dispatch an available vehicle to pick up the passenger. The vehicles in these dispatch areas can be recorded as , where is the number of vehicles in the dispatch area. These vehicles need to pick up passengers based on their ride requests, which can be recorded as , where is the number of passengers sending ride requests. Passengers send ride requests through their mobile devices, and when the dispatch center receives a ride request from a passenger, it screens the appropriate vehicles for the passenger and determines the sharing arrangement, taking into account the constraints, and each vehicle selects the best path to pick up the passenger through a noncooperative game. The taxi sharing framework is shown in Figure 1.
As shown in Figure 1, NCG-TSM model has the following steps:(1)When the dispatch center receives a request from a passenger and the status of the vehicle, it will process passenger’s carpool request using first-request-first-service(2)Dispatch of suitable vehicles for passengers by the vehicle scheduling algorithm(3)Insertion of passenger requests for each candidate vehicle’s status schedule and determination of passenger sharing scheduling(4)Generate a sequence of candidate vehicles that meet the requirements(5)The vehicles game based on the road network information to obtain the optimal strategy and return the route information to the passengers
3.2. Problem Description
The dispatch center uses passenger request information and vehicle status to dispatch vehicles for passengers and determines the final shared travel by gaming between vehicles.
3.2.1. Symbol Definition
In order to clearly describe the NCG-TSM model, some important symbols and terms are defined in the following:(1)Sharing requests , where is the passenger request time, is the departure point of the passenger, is the passenger’s destination, is the latest time a passenger can request the vehicle to arrive at the passenger’s point of departure, is the latest time a passenger can request the vehicle to arrive at the passenger’s destination, and is the maximum acceptable detour rate for shared passenger travel.(2)Vehicle status , where is the vehicle identifier, is the time for different states of the vehicle, is the number of passengers in the vehicle, is the position of the vehicle, and is a schedule of trips for the vehicle, which contains shared passenger routes, pick-up, and drop-off locations.
According to the passenger’s request, the vehicle status, and the route information, the vehicle drivers make autonomous decisions. Therefore, this paper uses a noncooperative game to model the driver’s route selection. The drivers of the vehicles are participants in the noncooperative game, denoted as . Each optional path recommended by the scheduling center is a strategy for the participants of the game. The set of policies is denoted as , and denotes all the optional policies of the vehicle. denotes the utility value of the vehicle. The utility value of each participant is not only related to the strategy chosen by itself but also related to the strategies chosen by other participants, so the utility value of vehicle can be expressed as , and denotes the strategy chosen by the vehicle.
3.2.2. Model Definition
When choosing a route, the vehicle considers both the time cost of travel, fuel consumption cost, distance cost, and occupancy rate based on the constraints which are vehicle dispatch constraints and how the utility value of a route is calculated.
(1) Vehicle Dispatch Constraints. In order to efficiently dispatch vehicles to pick up passengers, this paper proposes three constraints, time constraint, detour rate constraint, and number of passenger constraints. Vehicles are dispatched for passengers when the constraints are satisfied. Time constraints: Suppose we receive a request for a ride , the ride request time is , the time taken to travel from the vehicle’s location to the passenger’s departure point is , the current time when the passenger was picked up was , the time taken by the vehicle to travel from the passenger’s point of departure to the destination is , and the vehicle arrives at the passenger’s departure and destination earlier than the latest time requested by the passenger, as shown in the following equation: Detour ratio constraint: When the vehicle has multiple passengers, the detour rate for each passenger in the shared vehicle is less than the maximum detour rate requested by the passenger. Assuming that there is and in the vehicle, the order in which the vehicles will pick up and drop off passengers is where the detour rate for passenger is , the detour rate for passenger is , indicates the distance between two points, and the detour ratio for and is calculated as follows: The detour rate constraint for passengers satisfies the following equation: Number of passenger constraints: The number of seats in the vehicle is denoted as , and the number of passengers in the vehicle must not exceed the number of seats in the vehicle, as shown in the following equation:
(2) Utility Value. Reasonable and effective use of dispatch center resources to meet the constraints of users and vehicles and reduce the waste of resources. The utility value of the driver’s route selection game can be expressed by the following equation:where denotes the optional path strategy chosen for the vehicle, denotes the utility value of the vehicle from the first passenger’s pick-up point , through m sections, via the path, to the last passenger’s destination location at moment , , , and denote the time cost, fuel cost, and distance cost of the corresponding route of the vehicle, respectively, denotes the occupancy rate in time period , and , , , and denote the weighting values for , , , and , respectively.
The occupancy rate is the ratio of the number of passengers to the number of seats in the vehicle, the distance cost is the ratio of the actual length of the path to the desired length of the path, the time cost of a route is the ratio of the product of the congestion factor and the average travel time to the travel time under free flow, and the fuel cost is the ratio of the product of the average fuel consumption of the route and the congestion factor to the desired fuel consumption; the congestion factor is calculated as follows:where is the actual number of vehicles on the section, is the threshold capacity of the section, and is the blockage capacity of the section.
According to the above description, our goal is to maximize the occupancy of the vehicle under constraints and reduce the time cost, distance cost, and fuel consumption. Mathematically, the NCG-TSM model is expressed as follows:
4. Candidate Vehicle Scheduling Algorithm
The whole process of vehicle sharing is depicted in Figure 1, and this section focuses on how to match up candidate vehicles for passengers. To solve the problem of large number of calculations, Section 4.1 describes the process of gridding the urban road network. The detailed procedure of the algorithm is given in Section 4.2. Section 4.3 presents the pseudocode of the algorithm.
4.1. Grid of the Road Network
To solve the problem of time consumption for a large number of calculations, the scheduling area is gridded and divided into m × m square areas. As shown in Figure 2(a), the road intersection closest to the geographic center of the cell is used as the anchor node, which is indicated by the blue dot. The distance between two anchor points indicates the distance between two grids. For example, to calculate the distance between the vehicle and the passenger in the diagram, we can calculate the distance between the grid and grid , denoted by . The distances between the grids are stored in a matrix as shown in Figure 2(b), which is called the grid distance matrix.
(a)
(b)
4.2. Vehicle Scheduling Algorithm
When a request is received from a passenger, we dispatch the vehicle for the passenger on a first-requested, first-served basis.
4.2.1. Time Constrained Filter
In the process of dispatching a suitable vehicle for the passenger, the vehicle is first checked for time constraints after receiving the passenger’s request, so that the vehicle arrives at the passenger’s departure point before the latest arrival time requested by the passenger, outputting a set of vehicles that satisfy equation (1) described in vehicle dispatch constraints.
4.2.2. Grid Distance Filter
After filtering by time constraints, a collection of vehicles is output, and then, the vehicles in the set are filtered by the grid distance. This means that the distance between the grid where the vehicle is located and the grid where the passenger is picked up does not exceed a search radius . In this paper, only vehicles that fall under this range are searched for, and the set of vehicles that satisfy is output, which is shown in Figure 3.
4.2.3. Road Network Distance Filter
The actual road network distance is calculated from the vehicle in the set to the location of the passenger pick-up point, which should not exceed the maximum distance of the network set by the dispatch system. Then, a new set of candidate vehicles is output that satisfies .
4.2.4. Passenger Request Insert Check
When passengers share a vehicle, a feasibility insertion check is made to check whether the passenger’s carpool request can be added to the sharing schedule of the vehicles in the set , and the process of inserting a passenger carpool request into the trip schedule is shown in Figure 4.
Before we insert a new passenger request into the trip schedule, we check whether the number of passengers in the vehicle exceeds the number of seats, and if equation (8) is satisfied, then we perform an insertion check. Assuming that there are already two sharing requests and in the vehicle’s sharing schedule as shown in Figure 3 when inserting the departure and destination positions of a new request into the sharing schedule, the dispatch centre will choose a location with the shortest diversions to insert; supposing that is inserted between and and that is inserted between and , the order in which the vehicles will pick up and drop off passengers is , , and . We check whether the arrival times of the vehicles at and satisfy equation (1) and check whether the arrival times of the vehicles at and satisfy equation (2). If the time constraint is satisfied, we use equations (4) or (5) to calculate the detour ratio of the trip, and if the detour ratio satisfies equations (6) or (7), the request is inserted into the trip schedule.
4.3. Algorithm Flow
The candidate vehicle scheduling algorithm describes how to search for candidate vehicles and determine sharing schedule for passengers. Algorithm 1 is shown below. Given a set of sharing requests and a vehicle set , a new vehicle set is filtered by the time constraint, grid distance, and road network distance (Lines 3 to 10), and then, an insertion feasibility check is performed for each sharing request. The checked items include whether the vehicle still has empty seats, whether the passenger’s origin and destination points are inserted, and whether the time constraint and detour rate constraint are still satisfied. When the constraints are satisfied, the new sharing schedule for the vehicle is output (Lines 15 to 20).
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5. Distribution Estimation Algorithm for a Shared Taxi Game
Through the constraint-based vehicle scheduling algorithm in Section 4, multiple candidate vehicles are scheduled for each passenger. In this section, the distribution estimation algorithm for a shared taxi game is used to make all vehicles choose appropriate paths to obtain the Nash equilibrium strategy. All candidate vehicles can pick up more passengers at the lowest cost.
When the vehicles in the candidate set perform route selection, the drivers of the vehicles are rational persons who will choose the route that maximizes utility based on the distribution estimation algorithm to achieve the mixed Nash equilibrium. In this paper, the average utility in the game based on the mixed strategy space is used as the fitness function to solve the Nash equilibrium of the shared taxi game. Section 5.1 describes the distribution estimation algorithm based on the Gaussian model. Section 5.2 describes the vehicle sharing-based distribution estimation algorithm to solve the optimal vehicle decision.
5.1. Distribution Estimation Algorithm Based on the Gaussian Model
Each individual represents a mixture of the strategies of the players in the game. According to the concept of the Nash equilibrium of a game, the strategies of the players in the game are the optimal response to each other’s strategies, so the individual representing the Nash equilibrium has the optimal degree of adaptation.
Each vehicle selects its path independently of each other with a fixed probability based on past historical experience, let the mixed strategy of the taxi game be , denotes the probability that the driver chooses the path at time , and the mixed strategy space in a multiple driver game; then, the adaptation function based on the mixed strategy space is defined as follows:When the game has reached the mixed Nash equilibrium, then each driver’s strategy is the optimal strategy relative to the other drivers’ strategies, and the fitness takes its maximum value, where is the mixed Nash equilibrium strategy space, i.e., satisfying the following expression:
5.2. Algorithm Process
In order to solve the mixed Nash equilibrium of shared vehicles, this paper uses a distribution estimation algorithm based on the Gaussian model to enable the vehicles to choose the optimal path to pick up more passengers, reduce the empty seat rate of the vehicles, and alleviate the traffic situation:(1)Initializing the population: The initial population is randomly generated, and the fitness values of all individuals in the population are calculated, while the mean and variance of the Gaussian model are initialized according to the following equations: where is the value of the variable corresponding to the individual and is the size of the population.(2)Update the mean value : The mean value is updated using a linear approach, and let the mean value corresponding to the variable at generation be , i.e., where , , and denote the values corresponding to the best individual, the second best individual, and the worst individual, respectively.(3)Update variance : The variance is updated using a linear approach, and let the variance corresponding to the variable be at generation ; then, we have the following equation: where is the value of for the individual ranked in population fitness from largest to smallest and is the mean value of for the better populations selected, i.e.,(4)Update populations: the population is updated based on the updated Gaussian model to produce a new sample.(5)Output optimal strategy: When the algorithm reaches the maximum number of iterations, the individual with the best fitness is obtained, the optimal policy is output, and the optimal path for the driver is obtained; otherwise, steps (2) and (3) are repeated, and the population is updated.
Through Algorithm 2, the vehicle selects the corresponding strategy, making the path selection to maximize the fitness value and obtain the Nash equilibrium strategy. The pseudocode of the distribution estimation algorithm for the shared taxi game is shown in Algorithm 2.
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6. Evaluation
In order to verify the effectiveness of the cab sharing model based on a noncooperative game, this paper uses the experimental platform TaxiQueryGenerator [29] to simulate passenger ride requests and cab states, uses Sumo as a simulation experimental platform and Python for experimental analysis, and uses the traffic road network data of Eastern Massachusetts in the United States. Section 6.1 describes the experimental data and the setting up of the experimental environment. Section 6.2 focuses on validating the optimization of the model in this paper through three more classical carpooling frameworks.
6.1. Experiment Setup
In this paper, an area of Eastern Massachusetts in the USA is selected as an experimental scenario as shown in Figure 5. The roads in the area consist of 13 intersections; each road in the road network is a two-way section. Each segment has a different length and a different vehicle capacity. When the traffic flow on the road exceeds the capacity of the path, it will affect the travel time of the vehicle. The experimental platform TaxiQueryGenerator simulates passenger ride requests and taxi status as experimental data to verify the validity of our mode.(1)Dataset In order to validate the NCG-TSM model proposed in this paper in a real environment, the ride requests and vehicle status are generated by the TaxiQueryGenerator platform, which contains 5000 requests and 5000 vehicle statuses. The map matching method is used to map the taxi status and the passenger’s journey to the road section composed of 13 intersections in Figure 5.(2)Parameter setting In the NCG-TSM model, the utility value of a vehicle is related to a set of weight values for the attribute, including , , , and . Occupancy rates are a major consideration in the travel of a vehicle picking up or dropping off passengers, where fuel costs, time costs, and distance costs also play a part. Therefore, the corresponding weight values for the attributes in the experiments are shown in Table 1.
6.2. Algorithm Performance
In order to evaluate the performance and convergence of Algorithms 1 and 2, the performance of the algorithm is shown as follows:(1)Algorithm 1 analysis From Table 2, it can be seen that as the number of passenger sharing requests increases, the running time of Algorithm 1 gradually increases. The running time of Algorithm 1 is between the best-case and the worst-case average time.(2)Algorithm 2 analysis
According to Figure 6, the fitness function tends to be stable after about 200 iterations, and the optimal fitness function value is obtained. When the number of iterations is from 20 to 50, the fitness value increases rapidly, which shows that the convergence speed of Algorithm 2 designed in this paper shows an upward trend and gradually converges to the optimal fitness function value in the later stage. This also reflects the effectiveness and convergence of Algorithm 2 in this paper.
6.3. Comparison Experiments
In order to verify the optimization of the NCG-TSM proposed in this paper on the efficiency of vehicle travel, the model is experimentally analyzed in comparison with three commonly used carpooling frameworks: the T-share framework [30], the Flexi-Sharing framework [31]; and the BMP framework [32]. The T-share framework proposes a taxi search algorithm that uses a spatio-temporal index to quickly retrieve candidate taxis that are likely to satisfy the user’s query. The Flexi-Sharing framework considers alternative pick-up and drop-off locations nearby to arrange flexible routes that reduce the distance cost of travel by allowing some passengers to travel a short and acceptable distance. The BMP framework considers passengers meeting at a pick-up point, sharing a ride, and separating at a drop-off point. The three classic carpooling frameworks above only focus on single vehicle routes. To observe the performance of the NCG-TSM, three carpooling framework algorithms were selected and compared with NCG-TSM in terms of time cost, fuel consumption, and occupancy rate in simulation experiments, the results of which are shown as follows:(1)Time cost(i)From the results of Figure 7, it can be seen that when the number of travelling vehicles does not exceed the threshold capacity of the road, the travel time of the route chosen by the vehicles in NCG-TSM is not the lowest. The travel time of the vehicles in the BMP model, which considers having all passengers concentrate on one point for boarding and also concentrate on one point for disembarking, is therefore the lowest. The flexi-sharing model considers nearby pick-up and drop-off points, and the travel time is also relatively low. When the number of travelling vehicles exceeds the threshold capacity of the road, all vehicles in the T-sharing model, the BMP model, and the flexi-sharing model flock to one path, causing premature saturation of the path, resulting in congestion on the road, and increasing the vehicle travel time.(ii)In NCG-TSM, path selection through the game between vehicles can make vehicles better dispersed in the road network, so that the road will not be prematurely congested, which has a significant effect in solving the local congestion of the road network. However, when the number of vehicles exceeds the congestion capacity of the road, the effect on the dispersal of traffic is not very obvious.(2)Fuel consumption(i)As can be seen from Figure 8, the BMP and flexi-sharing frameworks have lower fuel consumption when the road is smooth as the distance travelled is reduced by not picking up or dropping off passengers at their exact location. But when the number of vehicles increases, the influx of vehicles causes congestion on the road and the vehicles keep accelerating and decelerating due to the congestion, resulting in an increase in fuel consumption.(ii)When the number of vehicles exceeds the jammed capacity of the road, the speed of the vehicles is kept very low, and therefore, the fuel consumption does not change much as the number of vehicles increases. However, NCG-TSM has a significant effect on the reduction of fuel consumption due to the dispersal of vehicles and the localized congestion on the road, thus reducing the consumption of resources.(3)Occupancy rate(i)The occupancy rate of taxis reflects the seat utilization rate between the time passengers submit their requests and the time the driver responds. From the Figure 9, we can see that as the number of passenger requests increases, the occupancy rate in the four carpooling models also increases and the chance of successful carpooling increases, but because the number of seats in taxis is limited, the occupancy rate increases more slowly as the number of ride requests increases.(ii)The occupancy rate of the NCG-TSM is relatively high compared to the other three models, as the impact of the driver’s efficient path on the efficiency of vehicle travel is taken into account in this paper, reducing the cost of the driver and making the cost of carpooling lower for the passenger, with a higher occupancy rate.
7. Conclusion and Future Work
In order to solve the problems of difficult travel and waste of resources, as well as to alleviate traffic road congestion, we propose a noncooperative game for a taxi sharing model (NCG-TSM) in urban road networks. Candidate vehicles are dispatched for passengers through requests submitted by passengers and taxi status. Combining the traffic conditions of the available routes, drivers make their route choices through the noncooperative game. The distribution estimation algorithm is introduced to solve the Nash equilibrium strategy of the vehicles so that the vehicles can pick up more passengers while reducing the driving cost of the vehicles and maximizing the utilization of resources. To verify the performance of NCG-TSM, experiments were conducted based on real traffic road networks. The effectiveness of NCG-TSM is verified through simulation experiments, which reduces time cost and fuel consumption cost and improves the occupancy rate of vehicles compared with three carpooling framework algorithms.
In future work, there are some research studies to be further studied. For example, the impact of road integrity and the frequency of traffic accidents on vehicle movements will be studied, and consideration will be given to balance the interests of taxi drivers with the cost of carpooling for passengers.
Data Availability
The data used in this study are the experimental platform TaxiQueryGenerator to simulate passenger ride requests and cab states, using the traffic road network data of Eastern Massachusetts in the United States.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This work was partially supported by the National Natural Science Foundation of China (Grant nos. 62002117 and 61862023) and the project of Jiangxi Natural Science Foundation (Grant no. 20224BAB202021).