Method Of Successive Averages Research Articles

CHIDYN: a clustering-based hierarchical approach for dynamic traffic assignment

Dynamic Traffic Assignment (DTA) plays a crucial role in the efficient management of traffic, as it is adaptable to changing conditions, such as weather, accidents, and variations in demand. However, conventional DTA algorithms tend to be sluggish, which hinders their real-time effectiveness. Therefore, the development of faster algorithms is imperative to enable timely and precise adjustments in traffic assignment. This study outlines the initial phases of creating a distributed multi-agent system designed to handle dynamic scenarios. In this research, we utilized the Sioux Falls network and its two different scales as representative networks for conducting User Equilibrium (UE) computations. Specifically, we applied the Method of Successive Averages (MSA) algorithm in two distinct configurations: one without clustering and the other with clustering. In the case without clustering, we computed the average travel time (ATT) and total traffic flow, whereas with clustering, we further analyzed these values within each cluster. Additionally, we measured the total computation time for both MSA with clustering and MSA without clustering. The results revealed substantial improvements in overall runtime when employing clustering, with a remarkable 14-fold enhancement for the Sioux Falls network and a 35% improvement for the mixed network. However, it's important to note that the clustering process led to some loss of information. To quantify this lost information, we employed the KL-divergence metric, which characterizes the information loss from the perspective of the distribution of vehicle flows per link. According to the KL-divergence analysis, the lost information amounted to 31% for a sub-network of Sioux Falls, 28% for the Sioux Falls network as a whole, and merely 1% for the mixed network. These findings underscore the effectiveness of our approach, as it allows for UE values to be computed an order of magnitude faster while preserving a relatively minimal amount of information loss during the clustering process.

Cyclists' exposure to traffic-generated air pollution in multi-modal transportation network design problem.

Moving toward sustainable transportation is one of the essential issues in cities. Bicycles, as active transportation, are considered an important part of sustainable transportation. However, cyclists engage in more physical activity and air intake, making the quality of air that they inhale important in the programs that aim to improve the share of this mode. This paper develops a multi-modal transportation network design problem (MMNDP) to select links and routes for cycling, cars, and buses to decrease the exposure of cyclists to traffic-generated air pollution. The objective functions of the model include demand coverage, travel time, and exposure. The study also examined the effect of having exclusive lanes for bicycles and buses on the network. In the present study, the non-dominated storing genetic algorithm (NSGA-II) solves the upper-level and a method of successive average (MSA) unravels the lower level of the model. A numerical example and four scenarios evaluate the trade-off between different objective functions of the proposed model. The results reveal that considering exposure to air pollution in our model results in a slight increase in travel time (4%) while the exposure to traffic-generated air pollution for cyclists was reduced significantly (47%). Exclusive lanes also result in exposure reduction in the network (60%). In addition, the demand coverage objective function performs well in increasing the total demand in the network by 47%. However, more demand coverage leads to a rise in travel time by 28% and exposure by 58%. The model also showed an acceptable result in terms of exposure to traffic-generated air pollution compared to the model in the literature.

EV Fast Charging Station Planning Considering Competition Based on Stochastic Dynamic Equilibrium

The rapid growth of electric vehicles (EVs) and the deployment of fast charging infrastructures bring considerable impacts on the planning and operation of power systems. Integrating photovoltaic (PV) and energy storage system (ESS) with fast charging station (FCS) can alleviate the negative impacts and bring benefits to both power system operation and charging service provider. In this paper, an integrated procedure is proposed for the charging service provider to optimally plan fast charging stations integrated with PV and ESS in urban area, while taking the influence of its competitors, EV users' decision-making psychology, the uncertainties of charging demand and PV power output into consideration. Firstly, a charging demand estimation method based on average travel speed is presented. Secondly, a stochastic dynamic user choice equilibrium (SDUCE) model and its solution algorithm based on method of successive averages (MSA) are proposed. The model considers the key factors influencing the charging decision of EV users as well as the uncertainty of their perceptions of utility values. In addition, the time-varying queuing time and the temporal coupling among EVs arriving at a charging station in different time periods are also considered. Thirdly, based on the equilibrium model, a multi-scenario benefit maximization model is built from the perspective of charging service provider, and solved by genetic algorithm. Finally, a distributionally robust optimization (DRO) planning model based on the Wasserstein-metric is formulated to determine the capacities of PV and ESS. The proposed planning method is tested using real traffic data of Shenzhen City. Simulation results verify the effectiveness of the proposed method.

Prediction of Traffic Flow considering Electric Vehicle Market Share and Random Charging

This paper mainly studies the multiclass stochastic user equilibrium problem considering the market share of battery electric vehicles (BEVs) and random charging behavior (RCB) in a mixed transport network containing electric vehicles and gasoline vehicles (GVs). In order to analyze the random charging and path choice behaviors of BEV users and extract the differences in travel behaviors between BEV and GV users, an improved logit-based model, multilabel algorithm, and queuing theory are applied. The influencing factors of charging possibility mainly include the initial state of charge (SOC), the SOC at the beginning of charging, and the psychologically acceptable safe SOC threshold arriving at the destination. Diversity choices of user paths and charging locations will result in changes in queuing traffic and differences in queuing time. Conversely, different stations have different queuing dwell times, which will also affect the routing and charging locations for BEVs with RCB. The path-based method of successive averages (MSA) is adopted to solve the model. Through the simulation of the test network Sioux Falls, the equilibrium traffic flow and possible charging flow under different market shares and initial SOC are predicted, and the properties of the model and the feasibility of the algorithm are verified.

Capacitated Preventive Health Infrastructure Planning with Accessibility-Based Service Equity

Hard-to-access health infrastructure is likely to lead to increased morbidity and mortality. The optimal layout of health facilities is significant for disease control and prevention. This study aims to propose a method to provide equitable access to capacitated preventive health facilities, which captures the key features of the effect of congestion in a competitive choice environment. The problem is formulated as a bilevel nonlinear integer programming model. The upper level is a biobjective programming model subject to investment budget (B) constraint, and the lower level is a user equilibrium analogous model resulting from the users’ choice of facility location. An efficient and operable heuristic algorithm was designed according to the bilevel decision structure where a genetic algorithm (GA) with elite strategy is developed to solve the upper-level problem and the method of successive averages (MSA) is adopted to solve the lower-level problem. A case study is employed to validate the performance of the proposed method. The results show that the method is robust and could reach an equal service quality in a reasonable computation time. However, the sensitivity analysis indicated that the marginal benefit of the investment decreased. There is an optimal B beyond which further increments in investment would not offset the benefits. In addition, the proposed method could be beneficial for other congested public service facilities that users are free to choose from.

Market competition oriented air-rail ticket fare optimization

In the business of intermodal passenger transport, fare optimization of intermodal products has significant effects on corporate revenue and passenger travel convenience. This study takes the competitive relationship between high-speed rail (HSR) and airlines as well as carrier connectivity as the starting point, analyzes the advantages and disadvantages of different carriers in the different markets, and researches the optimization of fares. The stochastic user equilibrium model based on elastic demand is used to establish a bi-level programming model for the optimization of fares; the upper and lower models are solved using the particle swarm algorithm and method of successive averages, respectively. The results suggest that airlines are willing to cooperate with the HSR sector and improve the connectivity between aviation and HSR, and a reasonable pricing strategy is more likely to motivate cooperation between aviation and HSR.

Modeling and Analysis of Driving Behaviour for Heterogeneous Traffic Flow Considering Market Penetration under Capacity Constraints

Based on analytical and simulation methods, this paper discusses the path choice behavior of mixed traffic flow with autonomous vehicles, advanced traveler information systems (ATIS) vehicles and ordinary vehicles, aiming to promote the development of autonomous vehicles. Firstly, a bi-level programming model of mixed traffic flow assignments constrained by link capacity is established to minimize travel time. Subsequently, the algorithm based on the incremental allocation method and method of successive averages is proposed to solve the model. Through a numerical example, the road network capacity under different modes is obtained, the impact of market penetration on travel time is analyzed, and the state and characteristics of single equilibrium flow and mixed equilibrium flow are explored. Analysis results show that the road network can be maximized based on saving travel time when all vehicles are autonomous, especially when the autonomous lane is adopted. The travel time can be shortened by increasing the market penetration of autonomous vehicles and ATIS vehicles, while the former is more effective. However, the popularization of autonomous vehicles cannot be realized in the short term; the market penetration of autonomous vehicles and ATIS vehicles can be set to 0.2 and 0.6, respectively, during the introduction period.

Scientific planning of urban cordon sanitaire for desired queuing time

The outbreak of the COVID-19 pandemic disrupted ofur normal life. Many cities enforced a cordon sanitaire as a countermeasure to protect densely inhabited areas. Travelers can only cross the cordon after being checked. To minimize the waiting time in the queue, this paper proposes a method to determine the scientific planning of urban cordon sanitaire for desired queuing time, which is a significant problem that has not been explored. A novel two-stage optimization model is proposed where the first stage is the transportation system equilibrium problem to predict traffic inflow, and the second stage is the queuing network design problem to determine the allocation of test stations. This method aims to minimize the total health infrastructure investment for the desired maximum queuing time. Note that queuing theory is used to represent the queuing phenomenon at each urban entrance. A heuristic algorithm is designed to solve the proposed model where the Method of Successive Averages (MSA) is adopted for the first stage, and the Genetic Algorithm (GA) with elite strategy is adopted for the second stage. An experimental study with sensitivity analysis is conducted to demonstrate the effectiveness of the proposed methods. The results show that the methods can find a good heuristic optimal solution. This research is helpful for policymakers to determine the optimal investment and planning of cordon sanitaire for disease prevention and control, as well as other criminal activities such as drunk driving, terrorists, and smuggling.

Rice supply chain network equilibrium optimization using the successive average method

Maximizing the surplus received by each actor is an ongoing issue in the current rice supply chain model. This study assesses a supply chain network that involves five business actors, namely collectors, wholesalers, retailers, demand markets and freight carriers. The interconnectedness of the actors results in a dynamic supply chain problem and free competition. The Supply Chain Network Equilibrium (SCNE) method is commonly used to solve this problem but poses the important issue of the ease of computation. Another method to achieve network equilibrium is the method of successive average (MSA). The MSA is more capable of optimization to generate accurate results with fewer iterations than the SCNE method. The simple case and real case results demonstrate that the MSA method can be used as an alternative for optimizing rice supply chains.

Health resource allocation method at cordon sanitaire for pandemic control and prevention

<p style='text-indent:20px;'>The outbreak of COVID-19 and its variants has profoundly disrupted our normal life. Many local authorities enforced cordon sanitaires for the protection of sensitive areas. Travelers can only cross the cordon after being tested. This paper aims to propose a method to determine the optimal deployment of cordon sanitaires in terms of minimum queueing delay time with available health testing resources. A sequential two-stage model is formulated where the first-stage model describes transportation system equilibrium to predict traffic flows. The second-stage model, a nonlinear integer programming, optimizes health resource allocation along the cordon sanitaire. This optimization aims to minimize the system's total delay time among all entry gates. Note that a stochastic queueing model is used to represent the queueing phenomenon at each entry link. A heuristic algorithm is designed to solve the proposed two-stage model where the Method of Successive Averages (MSA) is adopted for the first-stage model, and a genetic algorithm (GA) with elite strategy is adopted for the second-stage model. An experimental study is conducted to demonstrate the effectiveness of the proposed method and algorithm. The results show that these methods can find a good heuristic solution, and it is not cost-effective for authorities to keep adding health resources after reaching a certain limit. These methods are useful for policymakers to determine the optimal deployment of health resources at cordon sanitaires for pandemic control and prevention.</p>

Location and capacity planning for preventive healthcare facilities with congestion effects

<p style="text-indent:20px;">A painful lesson got from pandemic COVID-19 is that preventive healthcare service is of utmost importance to governments since it can make massive savings on healthcare expenditure and promote the welfare of the society. Recognizing the importance of preventive healthcare, this research aims to present a methodology for designing a network of preventive healthcare facilities in order to prevent diseases early. The problem is formulated as a bilevel non-linear integer programming model. The upper level is a facility location and capacity planning problem under a limited budget, while the lower level is a user choice problem that determines the allocation of clients to facilities. A genetic algorithm (GA) is developed to solve the upper level problem and a method of successive averages (MSA) is adopted to solve the lower level problem. The model and algorithm is applied to analyze an illustrative case in the Sioux Falls transport network and a number of interesting results and managerial insights are provided. It shows that solutions to medium-scale instances can be obtained in a reasonable time and the marginal benefit of investment is decreasing.</p>

Multi-objective optimization of cordon sanitaire considering operation cost and queueing equity

ABSTRACT This paper aims topropose a method to determine the optimal deployment of cordon sanitaire for epidemic control. A bi-level multi-objective programming model is proposed where the lower level is transportation system equilibrium with queueing time to predict link traffic flow, and the upper level is queueing network design, which is a multi-objective integer nonlinear programming model. The primary objective is to minimize the total operation cost of servers with a predetermined waiting time constraint, and the secondary objective is to reach queueing equity. A heuristic algorithm is designed where the method of successive averages is adopted for the lower-level model, and a genetic algorithm is designed for the upper-level model. The computational results show that the methods can find a good heuristic optimal solution. These methods are useful for planners to determine the optimal deployment of cordon sanitaire for disease control and prevention purposes.

A Reliability-Based Stochastic Traffic Assignment Model for Signalized Traffic Network with Consideration of Link Travel Time Correlations

Traffic assignment model (TAM) is an important research issue of urban traffic design and planning. Most of the existing studies are conducted under deterministic conditions. In reality, the link travel time and waiting time at signalized intersections are stochastic due to many uncertain factors in transportation networks. Under this circumstance, this paper proposes a new travel time reliability-based user equilibrium (TRUE) traffic assignment model with consideration of link travel time correlations and waiting time at signalized intersections in stochastic traffic networks. Under the assumption that link travel times and waiting times at signalized intersections follow normal distributions, the proposed model is transformed into a variational inequality (VI) model. It is rigorously proven that there is at least one solution for the VI problem, and the method of successive average (MSA) is employed to solve the proposed model. The numerical experiments are used to illustrate the applications and effectiveness of the proposed model.

Proposing a Simulation-Based Dynamic System Optimal Traffic Assignment Algorithm for SUMO: An Approximation of Marginal Travel Time

User equilibrium (UE) and system optimal (SO) are among the essential principles for solving the traffic assignment problem. Many studies have been performed on solving the UE and SO traffic assignment problem; however, the majority of them are either static (which can lead to inaccurate predictions due to long aggregation intervals) or analytical (which is computationally expensive for large-scale networks). Besides, most of the well-known micro/meso traffic simulators, do not provide a SO solution of the traffic assignment problem. To this end, this study proposes a new simulation-based dynamic system optimal (SB-DSO) traffic assignment algorithm for the SUMO simulator, which can be applied on large-scale networks. A new swapping/convergence algorithm, which is based on the logit route choice model, is presented in this study. This swapping algorithm is compared with the Method of Successive Average (MSA) which is very common in the literature.  Also, a surrogate model of marginal travel time was implemented in the proposed algorithm, which was tested on real and abstract road networks (both on micro and meso scales). The results indicate that the proposed swapping algorithm has better performance than the classical swapping algorithms (e.g. MSA). Furthermore, a comparison was made between the proposed SB-DSO and the current simulation-based dynamic user equilibrium (SB-DUE) traffic assignment algorithm in SUMO. This proposed algorithm helps researchers to better understand the impacts of vehicles that may follow SO routines in future (e.g., Connected and Autonomous Vehicles (CAVs)).

Characteristics Analysis and Equilibrium Optimization of Mixed Traffic Flow considering Connected Automated and Human-Driven Vehicles

Considering the impact of informatization condition, vehicles on the road network are divided into connected automated vehicles (CAVs) and human-driven vehicles (HDVs), which follow the principle of system optimization and stochastic user equilibrium, respectively. Taking the road network reserve capacity maximization model under the condition of road capacity constraint as the upper-level programming and the traffic assignment model under heterogeneous flow environment as the lower level programming, then a bilevel programming model is constructed. Among them, the nonuniform demand growth multiplier is adopted for each OD pair to reflect the inconsistency of traffic demand structure growth, and the calculation of link capacity is related to the market penetration of CAVs. The incremental method, method of successive averages, and simulated annealing algorithm are used to solve the model, and the effects of different market penetration on road network capacity, travel time, and saturation are analyzed through a numerical example. The relevant data under different weights are normalized and the optimal deployment scheme of CAVs and HDVs in different periods is obtained by comprehensive evaluation. Meanwhile, the mixed equilibrium flow state is explored under the premise of given market penetration to verify the feasibility of the model and algorithm.

Exhaust Emission Assessment with Energy Structural Evolution in Transportation Network

Electric vehicles have become a ubiquitous form of transportation in the transition period from the petroleum era to the electricity era. The development of electric vehicles is of great interest to researchers, policy-makers, consumers, and industries. However, the dynamic environmental impact assessment along with energy structural evolution in transportation network is still wondering as the vehicular exhaust emissions are highly dependent on their market shares and working conditions. In this paper, a Markov chain model is formulated to represent the transition process between traditional internal combustion engine vehicles (ICEVs), plug-in electric vehicles (PEVs), and hybrid electric vehicles (HEVs), with which the dynamic market penetration level of three vehicle types can be predicted. Therefore, the amount of pollutants can be figured out based on their market penetration level and network traffic conditions. For a given transportation network, system equilibrium is proposed to calculate network traffic conditions. It is a four-step sequential model with feedback which can be solved by method of successive averages (MSA) with decreasing weights effectively. A simulation experiment using Nguyen–Dupuis network demonstrates the effect of the proposed method. It is found that the proposed method is effective to assess the dynamics of environmental impacts as the penetration of electric vehicles into transportation system. The method is particularly operable for policy designs stimulating the development of electric vehicles.

Deploying Public Charging Stations for Battery Electric Vehicles on the Expressway Network Based on Dynamic Charging Demand

There is an obvious gap between the rapid growth of battery electric vehicle (BEV) intercity travel demand and the worse deployment of charging facilities on the expressway network. With the consideration of dynamic charging demand, a bilevel model is proposed to deploy charging stations for the expressway network. The upper model aims at determining the location of charging stations and the number of chargers in each station to minimize the construction cost and total BEV travel cost. The dynamic charging demand is obtained by the lower model, which is constructed as a multiclass dynamic traffic assignment model, including charging, queuing, and flow transmission processes. A genetic algorithm incorporating the method of successive averages is adopted to solve the bilevel model. A real case in the Shandong province of China is employed to evaluate the effectiveness of the proposed model and algorithm. The sensitivity analyses show that a high level of charging service can encourage the usage of BEVs. In addition, when the BEV percentage is at a low level, planners should give priority to the quantity and location to expand charging service coverage and BEV’s travel range; then, with the increasing of BEV percentage, the construction emphasis should change to charging station’s capacity.

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.

Optimal On‑Ramp Metering of Urban Freeway Network for the Coronavirus Disease Control

The outbreak of COVID-19 disrupted our everyday life. Many local authorities enforced a cordon sanitaire for the protection of sensitive areas. Travellers can only pass the cordon after tested. This paper aims to propose a method to design an on-ramp control scheme to maximise urban freeway network throughput with a predetermined queuing delay constraint at all off-ramps around cordon sanitaire. A bi-level programming model is formulated where the lower-level is a transportation system equilibrium to predict traffic flow, and the upper-level is onramp metering optimisation that is nonlinear programming. A stochastic queuing model is used to represent the waiting phenomenon at each off-ramp where testing is conducted, and a heuristic algorithm is designed to solve the proposed bi-level model where a method of successive averages (MSA) is adopted for the lower-level model; A genetic algorithm (GA) with elite strategy is adopted for the upper-level model. An experimental study is conducted to demonstrate the effectiveness of the proposed method and algorithm. The results show that the methods can find a good heuristic optimal solution. These methods are useful for freeway operators to determine the optimal on-ramp control for disease control and prevention.

An electric vehicle charging station access equilibrium model with M/D/C queueing

Despite the dependency of electric vehicle (EV) fleets on charging station availability, charging infrastructure remains limited in many cities. Three contributions are made. First, we propose an EV-to-charging station user equilibrium (UE) assignment model with a M/D/C queue approximation as a nondifferentiable nonlinear program. Second, to address the non-differentiability of the queue delay function, we propose an original solution algorithm based on the derivative-free Method of Successive Averages. Computational tests with a toy network show that the model converges to a UE. A working code in Python is provided free on Github with detailed test cases. Third, the model is applied to the large-scale case study of New York City Department of Citywide Administrative Services (NYC DCAS) fleet and EV charging station configuration as of July 8, 2020, which includes unique, real data for 563 Level 2 chargers and 4 Direct Current Fast Chargers (DCFCs) and 1484 EVs distributed over 512 Traffic Analysis Zones. The arrival rates of the assignment model are calibrated in the base scenario to fit an observed average utilization ratio of 7.6% in NYC. The model is then applied to compare charging station investment policies of DCFCs to Level 2 charging stations based on two alternative criteria. Results suggest a policy based on selecting locations with high utilization ratio instead of with high queue delay.