Flow Assignment Model Research Articles

Capacity-constrained mean-excess equilibrium assignment method for railway networks

The reliability and unreliability of travel time variability caused by stochastic train delays considerably influence passengers’ travel path choices. This paper proposes an equilibrium assignment method that can capture the passengers’ path choice behaviors considering both the reliability and unreliability of travel time variability in the railway network. The passengers’ travel path choices are modeled using the mean-excess travel cost (METC), which is the combination of the conditional expectation of travel cost exceeding the effective travel cost, and the endogenous advanced ticket booking cost associated with the rigid train capacity. In general, heterogeneous passengers with different risk-aversion attitudes toward stochastic train delays evaluate their travel options differently and have different requirements for successful transfer. Therefore, first, the passengers’ transfer options are modeled with the concept of METC based on the delay distribution of the two connecting trains. Subsequently, the METC of the passenger trips is calculated. A mean-excess passenger flow assignment model is formulated based on the user equilibrium condition. A path-based capacity-constrained passenger assignment algorithm is designed to solve the model. Moreover, three illustrative examples are presented to demonstrate the effectiveness of the model and solution algorithm.

Day-to-Day Dynamic Traffic Flow Assignment Model under Mixed Travel Modes Considering Customized Buses

In recent years, customized buses (CBs), a new form of public travel mode between bus and car, has sprung up in China. Its characteristics include flexible routes, each person having a seat and point-to-point travel have attracted travelers who seek high-quality travel, especially car travelers, alleviating traffic congestion at peak periods and leading to a change in urban travel modes. In addition to providing new travel modes, an exclusive bus lane (EBL) is also an effective means to alleviate traffic congestion. Therefore, this paper establishes link impedance functions under mixed travel modes considering the EBL, including customized buses on different kinds of links, and then presents a day-to-day dynamic traffic flow assignment model based on stochastic user equilibrium (SUE). Some conclusions were summarized by numerical case studies. First, the parameter of travelers’ sensitivity to route travel time affects the speed of traffic flow evolution. When it increases to positive infinity, the final state of the traffic network moves from SUE to deterministic user equilibrium (DUE). Second, the parameter on the degree of dependence of travelers on previous experience can not only influence the value size of actual travel time, but also influence the direction of actual travel time evolution. Third, conventional buses and customized buses have higher transportation efficiency than cars, but if the proportion of conventional bus travelers is too large, the total travel time of all travelers in the traffic network may increase. Fourth, when travel demands increase, the proportion of travelers who choose public transit is required to increase to achieve minimum total travel time. Lastly, from the perspective of the whole traffic network in any case, the EBL is not always beneficial. It is recommended to set EBLs when conventional buses and customized bus flows are heavy, which can be judged based on the model established in this paper.

Research on Passenger Flow Assignment of Integrated Cross-Line and Skip-Stop Operation between State Railway and Suburban Railway

The passenger flow assignment in the rail transit network is the basis for determining the passenger spatiotemporal distribution and train operation organization plan. In previous studies, the passenger flow assignment problem mainly focused on lines within the same rail system. Few studies focus on lines with the integrated mode of cross-line and skip-stop operation between state and suburban railway due to fewer cases in practice. In this study, passenger congestion and fare policy are taken into account in the generalized travel cost function, and a passenger flow assignment model based on the path-sized logit (PSL) model considering train capacity is proposed. Meanwhile, a schedule-based spatiotemporal digraph is established to search for the shortest spatiotemporal travel path. Furthermore, an improved method of successive averages (MSA) algorithm is designed to solve the proposed model. The proposed model is verified by a numerical example. The sensitivities of three main parameters which influence the results are also analyzed. The results show that the assignment model based on PSL is practicable in integrated operation mode. The higher the passenger’s familiarity with network information, the more accurate the assignment results. State trains are more attractive when the fare is lower than 0.5 CNY/km or the hourly wage is higher than 50 CNY/h.

Dynamic Traffic Assignment Model Based on GPS Data and Point of Interest (POI) in Shanghai.

Dynamic traffic flow, which can facilitate the efficient operation of traffic road networks, is an important prerequisite for the application of reasonable assignment of traffic demands in an urban road network. In order to improve the accuracy of dynamic traffic flow assignment, this paper proposes a dynamic traffic flow assignment model based on GPS trajectory data and the influence of POI. First, this paper explores the impact patterns of POI on regional road network congestion during peak hours through qualitative and quantitative analysis. Then, based on the user equilibrium theory, a dynamic traffic flow assignment model, in which the effect of POI on links is reflected using the link-node impedance function, is proposed. Finally, the accuracy of the model is validated by the GPS trajectory data and origin–destination (OD) traffic data of motor vehicles in Xuhui District, Shanghai, China. The results show that the model can be used to coordinate and optimize the traffic assignment of the regional road network under the influence of POI during peak hours and alleviate the congestion of the road network. The findings can provide a powerful reference for developing scientific and rational traffic assignment decisions and management strategies for urban road network traffic.

Evaluation of Operating Schemes on Municipal Rail Transit with Express/Local Mode

The express/local train mode has made municipal rail more competitive in connecting the city center with its suburbs. Therefore, how to design operating schemes is of concern to decision makers. Unlike earlier line planning optimization, this paper aims to provide a quick and comprehensive evaluation of operating performance in all feasible options through reasonable reduction of the scope of the operating schemes, rather than optimization for a single objective. To achieve this, the paper constructs a travel topology network structure based on the separation of trains, which regards express and local trains running on the common line as independent competitors. Focusing on the problems of uneven departure intervals and inconsistent dwell times caused by overtaking, a generalized cost model suitable for the express/local train mode is established. To solve the express/local line problems of multi-routes and high-overlapping, the improved Multinominal Logit (MNL) Model is used to construct a passenger flow assignment model, with the solution achieved by the Method of Successive Averages algorithm. Taking a municipal rail line in Guangzhou as a case study, this paper analyzes the advantages and disadvantages of feasible operation schemes with different characteristics in the express/local train ratio, the location and number of overtaking stations based on passenger flow assignment results and also the impacts of crowdedness on passenger flow dynamics. The results verified the effectiveness of our approach in the comprehensive evaluation of the express/local train mode and shed light on potential practical applications in determining a reasonable operating scheme.

Analyzing Influencing Factors of Transfer Passenger Flow of Urban Rail Transit: A New Approach Based on Nested Logit Model Considering Transfer Choices.

With the continuous improvement of the operation line network of urban rail transit, analyzing influencing factors of transfer passenger flow of urban rail transit is critical to improve the transfer demand analysis of urban rail transit. Using data collected from questionnaires, transfer passenger flow surveys and smart cards, this study proposes an approach base on nested logit passenger flow assignment model considering transfer choice behaviours of passengers. The transfer passenger flow at seven transfer stations in Nanjing is obtained. Subsequently, this study investigates the potential influencing factors of transfer passenger flow, including the node degree, geographic location (located in the city center, urban fringe, suburbs or suburban fringe), economic location (distance from the city center) and transportation locations (if it is close to a transportation hub or in combination with the hub) of rail transit transfer stations. The results indicate that a positive correlation between the transfer passenger flow and the node degrees of transfer stations. However, the relationship between transfer passenger flow and the economic, geographic, and transportation locations of transfer stations is not clear. The finding have reference value for the network design of rail transit transfer stations and transfer facilities, and provide reference for the analysis of passenger flow under network operation.

Resilience-Oriented Performance Assessment Method for Road-Traffic System: A Case Study in Beijing, China

The performance of an urban road-traffic system is affected by many factors, such as the average traffic demand, and the network structure, etc. At the same time, natural disasters, abnormal traffic volume and man-made accidents can result in disturbances which also influence the performance of the system. Resilience of an urban road-traffic system has been an emerging research field. This paper proposes a resilience-oriented performance assessment method based on a traffic flow assignment model to precisely capture the performance of an urban road-traffic system. System functionality is chosen as the key proxy for resilience, which can be calculated based on some index parameters including allocation rate of traffic flow, commuting efficiency on road sections, etc. A case study is implemented in a downtown area in Beijing, China. As to the resilience of the system when faced with huge traffic volume, the results show that the road-traffic system itself has a certain degree of absorption capacity for traffic pressure induced by huge volume. As to the resilience of the system when faced with local network failure, the results show that information dissemination of the network condition and the traffic volume are the key impact factors on system’s resilience curves.

A double time-scale passenger assignment model for high-speed railway networks with continuum capacity approximation

This study models spatiotemporal passenger flow distribution for high-speed railway (HSR) networks with capacity constraints. The HSR travel demand involves two time-dimensions, i.e., the ticket booking time and the desired departure time. Under the principle of first-booked-first-served, a passenger flow assignment model is formulated, where a later ticket booking time may result in less available travel options. A solution algorithm is then designed for solving the ticket-booking-time-dependent assignment model. The model is tested and illustrated with two numerical examples: a toy network example and a large-scale Chinese HSR network example.

Extracting the Relationship and Evolutionary Rule Connecting Residents' Travel Demand and Traffic Supply Using Multisource Data.

Urban rail transit (URT) systems are often regarded as the backbone of their respective city. The evolutionary features of URT systems have attracted much attention in recent years, but their evolution and their distinct function in contrast to other transit modes have seldom been investigated, especially quantitatively from the perspective of work–residence separation. Accordingly, we propose a framework for exploring the evolution of URT topological networks and demand-weighted networks, comparing the different impacts of all transit modes on work–residence separation. In this study, a URT passenger flow assignment model was formulated on the basis of travel cost function and an improved logit model was proposed that takes into account the heterogeneity of passengers. This model was used to generate a section load, which is regarded as a weight and able to reflect the residents’ demand for travel by URT. Then, the fractal dimensions for a non-weighted network and demand-weighted network are proposed and their indications for transportation explained. Finally, the Beijing Subway System (BSS) is used as a case study by employing fifty years of network data and ten years of smart card data. Using fractal approaches, the different characteristics illustrated by the two networks were investigated and the reasons behind the observed patterns explained. In addition, the spatial features of the rail network, in terms of fractal indictors, were compared with population distribution and urban mobility for all modes, extracted from phone data as a proxy. Thus, the relationship between the residents’ travel demand and traffic supply can be revealed to some extent. The main finding of this work is that demand must be taken into account when analyzing the fractal features of a transport network, lest the demand side be separated from the supply and important issues missed such as inconsistencies between demand and supply. Additionally, the role of rail transit in work–home imbalance can be investigated in the context of urban mobility for an entire city.

An extended dynamic model for pedestrian traffic considering individual preference

Complexity, dynamics and mutability are basic characteristics of pedestrian evacuation. However, most models for pedestrian traffic still lack an explanatory mechanism of the individual choice process. This study concerns a cell transmission model (CTM) for pedestrian traffic. But we focus on a new issue, namely, how to illustrate the decision-making process of each individual pedestrian. The decision field theory (DFT), a cognitive model to capture the deliberation process in decision making, is introduced to the cell transmission model and an extended dynamic pedestrian flow assignment model based on DFT and CTM is proposed. Pedestrian attitudes towards distance and crowdedness are considered and the individual preferences of pedestrians in the dynamic decision-making for the evacuation process are explored. Numerical studies show that the initial pedestrian distributions can have an effect on the evacuation process and different individual preferences of pedestrians will lead to different pedestrian choices. Even in the same cell, pedestrians’ route and exit choices may be different. Furthermore, some interesting phenomena can be observed, which illustrate that the preference reversals can be depicted in our model.

Research on Passenger Flow Assignment of High-Speed Trains Based on Personalized Itinerary Choice

Under the condition that ticket fare for high-speed train could fluctuate around a benchmark price in China, aimed at predicting how the passengers will distribute among different trains given a ticket fare, the passenger flow assignment method for high-speed trains is studied. Different from the classical researches on the passenger flow assignment, by introducing a variable that represents the value of time, this research allows passengers to make their personalized choice between the principles of time minimization and expense minimization, so as to demonstrate how the passengers holding different time values respond to each ticket fare scheme. An equilibrium passenger flow assignment model based on personalized choice is built and an improved Monte-Carlo random simulation algorithm is designed for solving the model. The actual ticket sale data for Beijing-Shanghai high-speed railway are used to verify the feasibility of the proposed model and algorithm. The passenger flow assignment results under various fare schemes show how the distribution of passenger flow changes with the adjustment of ticket fare.

Analysis of passenger traffic in Bohai Strait Tunnel

China envisages building a new undersea tunnel called Bohai Strait Tunnel to connect Dalian to Yantai, for the purpose of solving the detour problem in transportation. This paper analyses the passenger traffic in Bohai Strait Tunnel. A modified negative exponent network flow assignment model and an increasing rate method are used to predict the network flow assignment and passenger traffic volume after the completion of Bohai Strait Tunnel in 2050. Two formulas of economic benefits are employed to evaluate the effect of undersea tunnel on passenger traffic. The result indicates that the new undersea tunnel can shorten the distance, reduce the transport cost, save travel time, and produce good economic benefits. Tunnel transportation will attract a large number of passengers and become main transportation way. The analysis result can provide technical storage and references for the future undersea tunnel construction.

A Day-to-Day Stochastic Traffic Flow Assignment Model Based on Mixed Regulation

In many cases, the final path selection of travellers’ is not the shortest path, due to the limited computing power and high cost of path search. To solve the problem, this paper proposes a day-to-day (DTD) stochastic traffic flow assignment model that regulates the traffic flow based on the travel time (travel cost) and residual congestion of optional paths. The regulation mechanism is called the mixed regulation. Then, the authored proved the existence, uniqueness and stability of the model solution. The proposed model was verified through simulation on a Nguyen-Dupuis road network. The results show that traffic flows and travel times of all paths reached the equilibrium state, thanks to the DTD mixed regulation for 20~30 days. From the traffic flows and congestion degrees of different sections, it can be seen that our model with mixed regulation diverts the traffic flow to the sections with a low congestion degree, and encourages travellers to drive through the sections with a low traffic flow. In addition, the congestion degrees of the four most congested sections decreased by 5.8%, 4%, 7% and 1.2%, respectively, and the entire road network exhibited a slight downward trend in mean congestion degree. These results prove that our model can uniformize the traffic flow, improve the operation efficiency and alleviate the congestion of the road network. These findings shed new light on the control, guidance and planning of traffic flow in road networks.

Yen’s Algorithm-Based Charging Facility Planning Considering Congestion in Coupled Transportation and Power Systems

To promote the penetration of electric vehicles (EVs), a charging facility (CF) planning model based on Yen’s algorithm is proposed for coupled transportation and distribution systems (DSs) considering traffic congestion. This model not only takes into account the influence of new CFs on the power system but also considers the impact of CF locations on traffic flow distribution and congestion level in the transportation system (TS). Yen’s algorithm is innovatively employed to offer multiple possible choices for EV drivers’ route selection considering CF locations determined in the traffic flow assignment model. Overall, the total cost of both distribution and TSs is minimized to obtain the optimal CF planning results. For the DS, generation cost, energy loss, and penalty cost for voltage deviation are included. For the TS, the main objective is to ensure EVs can reach their destinations at the lowest cost, while the travel time due to different path selections and the delay time caused by congestion can be minimized. Finally, a comprehensive case study on the integrated IEEE 30-bus and a 25-node TS is conducted to validate our approach.

Passenger Flow Pushing Assignment Method for an Urban Rail Network Based on Hierarchical Path and Line Decomposition

: For urban rail transit, an environmentally-friendly transportation mode, reasonable passenger flow assignment is the basis of train planning and passenger control, which is conducive to the sustainability of finance, operation and production. With the continuous expansion of the scale of urban rail networks, passenger travel path decision-making tends to be complex, which puts forward higher requirements of networked transportation organization. Based on undirected graphs and the idea of the recursive divide-and-conquer algorithm, this paper proposes a hierarchical effective path search method made up of a three-layer path generation strategy, which consists of deep search line paths, key station paths composed of origin–destination (O-D) nodes and transfer stations, and the station sequence path between the key stations. It can effectively simplify the path search and eliminate obvious unreasonable paths. Comparing the existing research results based on the classical polynomial Logit model, a practical Improved C-Logit multi-path passenger flow assignment model is proposed to calculate the selection ratio of each path in the set of effective paths. Combining the hierarchical path search strategy, the O-D pairs of passenger flow are divided into local-line and cross-line situations. The time-varying cross-line passenger flow is decomposed into a series of passenger sections along the key station paths. A passenger flow pushing assignment algorithm based on line decomposition is designed, which satisfies the dynamic, time-varying and continuous characteristics. The validation of Guangzhou Metro’s actual line network and time-varying O-D passenger demand in 2019 shows that the spatio-temporal distribution results of the passenger pushing assignment have a high degree of coincidence with the actual statistical data.

Integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network: A space-time-state hyper network-based assignment approach

In this study, we focus on one of practically important research problems of integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network. The task is accomplished by using a triple of flow, density, and speed to construct a discretized passenger flow state, further constructing a space-time-state (STS) hyper network so that we can utilize a better defined three-dimensional solution space to integrate structurally heterogeneous data sources. The monitoring data include passenger transaction records and identification space-time samples observed over a possible range of a few hours from origins to destinations (Lagrangian observations), and time-dependent passenger counts collected at some key bottleneck locations (Eulerian observations). To describe the complex urban-rail passenger flow evolution, passenger traveling and fixed sensor state transition processes can be unified within a STS path representation. To estimate the consistent system internal states between two different types of observations, we formulate a hyper network-based flow assignment model in a generalized least squares estimation framework. For applications in large-scale transportation networks, we decompose the proposed model into three easy-to-solve sub-problems. The proposed model is applied to a real-world case based on the Beijing subway network with complete smart card data for each passenger at his/her origin and destination and time-dependent passenger counts in several key transfer corridors, while the specific space-time trajectories of all passengers and high-resolution time-dependent congestion levels at platforms, in trains, and in transfer corridors are estimated. This proposed passenger flow state inference method can provide a rich set of state inferences for advanced transit planning and management applications, for instance, passenger flow control, adaptive travel demand management, and real-time train scheduling.

Optimal Adjustment Schemes on the Long Through-Type Bus Lines considering the Urban Rail Transit Network

It is of great importance to optimize the schemes of long through-type bus lines to adapt to the urban rail transit network. Focusing on the long through-type bus lines close to metro stations, a bilevel programming model on the adjustment schemes of bus lines is proposed, taking the impacts of urban rail transit network into account. The upper level model aims at adjusting the setting decisions of stop stations and vehicle headways of bus lines to minimize the passenger travel cost and maximize the benefits of bus operators. The lower level model is a passenger flow assignment model based on Logit-SUE considering the crowding perception of passengers in bus vehicles. Moreover, the constraint of average load factor of the bus line sections is considered. Then the genetic algorithm is applied to solve the proposed model, and a numerical example is conducted to verify the effectiveness. Results show that the value of the objective function of the model is improved by 27.2%, in comparison with the original scheme. Even though the average travel cost of passengers increases slightly, the bus line operation cost and the imbalance degree of load factors are reduced by 46.1% and 18.6%, respectively. The sensitivity analyses show that it is better to divide the long through-type bus line into several separate bus lines with independent operation, respectively, under the condition of unbalanced passenger flow distribution. Meanwhile, the multiple bus lines are more adapted to the unbalanced passenger flow distribution when the weight of the benefits of the bus operators in the total objective function is bigger. Besides, the lower time value that the passengers perceive, the more passengers willing to take bus than metro trains. As the increment of the passenger time value, the combination of feeder bus lines and a longer bus line is better for passengers’ trip demand than the long through-type bus line.

Traffic Flow Assignment Model with Modified Impedance Function

In this paper, we study a mixed-mode traffic network, in which Battery Electric Vehicles (BEVs) and Gasoline Vehicles (GVs) can be driven freely. We propose a new piecewise impedance function and, based on this new impedance function, we present a convex but nonsmooth optimization model for the traffic network. In order to deal with the nonsmoothness, we introduce a binary variable. Furthermore, we report some numerical examples to show the efficiency of the model. %is effective and robust. In particular, our numerical results illustrate that, if the distance limit of BEVs is long enough and the unit operating cost of BEVs is lower than GVs, more travelers prefer to choosing BEVs.

Potential-based dynamic pedestrian flow assignment

This study proposes a potential-based dynamic pedestrian flow assignment model to optimize the evacuation time needed for all pedestrians to leave an indoor or outdoor area with internal obstacles and multiple exits, e.g., railway station, air terminal, plaza, and park. In the model, the dynamic loading of pedestrian flows on a two-dimensional space is formulated by a cell transmission model, the movement of crowds is driven by space potential, and the optimization of evacuation time is solved by a proportional swapping process. In this way, the proposed model can be applied to not only efficiently optimize the evacuation process of a crowd with large scale but also recognize local congestion dynamics during crowd evacuation. Finally, a set of numerical examples are presented to show the proposed model’s effectiveness for optimizing crowd evacuation process and its application to design a class of variable guide sign systems.

Passenger flow analysis of Beijing urban rail transit network using fractal approach

To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.