A maximum entropy-least squares estimator for elastic origin-destination trip matrix estimation

In transportation subnetwork-supernetwork analysis, it is well known that the origin-destination (O-D) flow table of a subnetwork is not only determined by trip generation and distribution, but also a result from traffic routing and diversion, due to the existence of internal-external, external-internal and external-external flows. This result indicates the variable nature of subnetwork O-D flows. This paper discusses an elastic O-D flow table estimation problem for subnetwork analysis. The underlying assumption is that each cell of the subnetwork O-D flow table contains an elastic demand function rather than a fixed demand rate and the demand function can capture all traffic diversion effect under various network changes. We propose a combined maximum entropy-least squares estimator, by which O-D flows are distributed over the subnetwork in terms of the maximum entropy principle, while demand function parameters are estimated for achieving the least sum of squared estimation errors. While the estimator is powered by the classic convex combination algorithm, computational difficulties emerge within the algorithm implementation until we incorporate partial optimality conditions and a column generation procedure into the algorithmic framework. Numerical results from applying the combined estimator to a couple of subnetwork examples show that an elastic O-D flow table, when used as input for subnetwork flow evaluations, reflects network flow changes significantly better than its fixed counterpart.     

Improved bush-based methods for network contraction

Calculating equilibrium sensitivity on a bush can be done very efficiently, and serve as the basis for a network contraction procedure. The contracted network (a simplified network with a few nodes and links) approximates the behavior of the full network but with less complexity. The network contraction method can be advantageous in network design applications where many equilibrium problems must be solved for different design scenarios. The network contraction procedure can also be used to increase the accuracy of subnetwork analysis. This method requires calculating travel time derivatives between two nodes, with respect to the demand between them, assuming that the flow distributes in a way that equilibrium is maintained. Previous research describes two methods for calculating these derivatives. This paper presents a third method, which is simpler, faster, and just as accurate. The method presented in this paper reformulates the linear system of equations defining these sensitivities as the solution to a convex programming problem, which can be solved by making minor modifications to static user equilibrium algorithms. In addition, the model is extended to capture the interactions between the path travel times and network flows, and a heuristic is proposed to compute these interactions. The accuracy and complexity of the proposed methodology are evaluated using the network of Barcelona, Spain. Further, numerical experiments on the Austin, Texas regional network validate its performance for subnetwork analysis applications.     

Robust transit network design with stochastic demand considering development density

This paper analyzes the influence of urban development density on transit network design with stochastic demand by considering two types of services, rapid transit services, such as rail, and flexible services, such as dial-a-ride shuttles. Rapid transit services operate on fixed routes and dedicated lanes, and with fixed schedules, whereas dial-a-ride services can make use of the existing road network, hence are much more economical to implement. It is obvious that the urban development densities to financially sustain these two service types are different. This study integrates these two service networks into one multi-modal network and then determines the optimal combination of these two service types under user equilibrium (UE) flows for a given urban density. Then we investigate the minimum or critical urban density required to financially sustain the rapid transit line(s). The approach of robust optimization is used to address the stochastic demands as captured in a polyhedral uncertainty set, which is then reformulated by its dual problem and incorporated accordingly. The UE principle is represented by a set of variational inequality (VI) constraints. Eventually, the whole problem is linearized and formulated as a mixed-integer linear program. A cutting constraint algorithm is adopted to address the computational difficulty arising from the VI constraints. The paper studies the implications of three different population distribution patterns, two CBD locations, and produces the resultant sequences of adding more rapid transit services as the population density increases.     

Fuel burn and environmental implications of airline hub networks

Hubs act as switching points for interactions and so are places through which flows are concentrated. This research uses the interactions between a system of cities as an experimental context for understanding selected environmental costs and benefits of concentrated flow. Whether hub based networks create additional environmental costs has been debated in the literature. In this paper, fuel burn is used as an indicator of environmental cost. The essential ideas are: (1) to examine fuel costs associated with larger aircraft; (2) to determine implications of higher loads on dense routes; and (3) to model the resulting implications for hub and gateway location. Variants of these questions apply to passenger and freight flows, and the paper will initially concentrate on passenger models.The paper shows that by modeling fuel burn and introducing a fixed charge (like a set up cost), a multiple allocation hub and spoke model can be adjusted to direct more or less flow onto the inter-facility connector. In other words, usage of multiple connections and direct links can be controlled and modeled as a function of the fixed charge. The resulting networks are characterized by quite different levels of passenger miles, aggregate fuel burn and fixed charges. The preferred network in terms of minimal fuel burn is found by subtracting the fixed set up charge, thereby focusing attention on the modeled fuel burn. The lowest cost set up is a network with a high degree of connectivity, and a pure single assignment hub network has the highest fuel cost (as a result of larger passenger miles needed by connecting paths). The data also allow a tabulation of total passenger miles, which, not surprisingly, track very closely with the fuel burn. In an interesting application of the ideas, it is shown that a fuel efficient network may require a large number of smaller regional jets, and in the interests of avoiding noise and congestion from so many extra airport operations, the carriers may choose to substitute a smaller number of larger planes, thereby slightly increasing fuel needs. This paper also provides a key ingredient for models of an international network where it is impossible to serve many long distance market pairs without consolidation.     

A computational model for the probit‐based dynamic stochastic user optimal traffic assignment problem

This paper focuses on computational model development for the probit‐based dynamic stochastic user optimal (P‐DSUO) traffic assignment problem. We first examine a general fixed‐point formulation for the P‐DSUO traffic assignment problem, and subsequently propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model‐based traffic performance model to calculate the actual route travel time used by the probit‐based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed‐point model. The Ishikawa algorithm is proposed to solve the computational model. A comparison study is carried out to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are used to assess the computational model and the algorithm proposed. Results show that Ishikawa algorithm has better accuracy for smaller network despite requiring longer computational time. Nevertheless, it could not converge for larger network. Copyright © 2010 John Wiley & Sons, Ltd.     

Design of public transit network in urban area with elastic demand

This research focuses on an efficient design of transit network in urban areas. The system developed is used to create, analyze and optimize routes and frequencies of transit system in the network level. The analysis is based on elastic demand, so the shift of demand between modes in network due to different service level is of prime consideration. The developed system creates all feasible routes connecting all pairs of terminals in the network. Out of this vast pool of routes, a set of optimal routes is generated for a certain predetermined number that maintains connectivity of significant demand. Based on these generated routes, the system fulfils transportation demand by assigning demand that considers path and route choices for non-transit users and transit users. Together with the assignment of demand, transit frequencies are optimized and the related fleet-size is calculated. Having an optimal setting of solution, the system is continued by reconnecting the routes to find some other better solutions in the periphery of the optimal setting. A set of mathematical programming modules is developed. Real data from Sioux Falls city network is used to evaluate the performance of the model and compare with other heuristic methods.     

A stochastic multimodal reliable network design problem under adverse weather conditions

This paper formulates a network design problem (NDP) for finding the optimal public transport service frequencies and link capacity expansions in a multimodal network with consideration of impacts from adverse weather conditions. The proposed NDP aims to minimize the sum of expected total travel time, operational cost of transit services, and construction cost of link capacity expansions under an acceptable level of variance of total travel time. Auto, transit, bus, and walking modes are considered in the multimodal network model for finding the equilibrium flows and travel times. In the proposed network model, demands are assumed to follow Poisson distribution, and weather‐dependent link travel time functions are adopted. A probit‐based stochastic user equilibrium, which is based on the perceived expected travel disutility, is used to determine the multimodal route of the travelers. This model also considers the strategic behavior of the public transport travelers in choosing their routes, that is, common‐line network. Based on the stochastic multimodal model, the mean and variance of total travel time are analytical estimated for setting up the NDP. A sensitivity‐based solution algorithm is proposed for solving the NDP, and two numerical examples are adopted to demonstrate the characteristics of the proposed model. Copyright © 2014 John Wiley & Sons, Ltd.     

Evaluating the assumption of independent turning probabilities

Several urban traffic models make the convenient assumption that turning probabilities are independent, meaning that the probability of turning right (or left or going straight through) at the downstream intersection is the same for all travelers on that roadway, regardless of their origin or destination. In reality most travelers make turns according to planned routes from origins to destinations. The research reported here identifies and quantifies the deviations that result from this assumption of independent turning probabilities.An analysis of this type requires a set of reasonably realistic “original” route flows, which were obtained by a static user-equilibrium traffic assignment and an entropy maximization condition for most likely route flows. These flows are compared with those route flows resulting from the Assumption of Independent Turning Probabilities (ITP). A small subnetwork of 3 km by 5 km in Tucson, Arizona, was chosen as a case study. An overall “typical ratio” of 2.2 between original route flows and ITP route flows was obtained. Aggregating route flows to origin–destination flows led to an overall “typical ratio” of 1.7. Such deviations are particularly high for routes that go back-and-forth, reaching a ratio of more than 3 in certain time periods. Substantial deviations for origins and destinations that are on the same border of the subnetwork are also observed in the analyses. In addition, under the ITP assumption, morning rush hour traffic peaking is the same in all directions, while in the original flows some directions do not exhibit a peak in the morning rush hour period. Overall, the conclusion of the paper is that the assumption of independent turning probabilities leads to substantial deviations both at the route level and at the origin–destination level, even for such a small network of the case study. These deviations are particularly detrimental when a network is being modeled and studied for route-based measures of effectiveness such as the number and types of routes passing a point – for monitoring specified vehicles and/or managing detouring strategies.     

Network impacts of a road capacity reduction: Empirical analysis and model predictions

In spite of their widespread use in policy design and evaluation, relatively little evidence has been reported on how well traffic equilibrium models predict real network impacts. Here we present what we believe to be the first paper that together analyses the explicit impacts on observed route choice of an actual network intervention and compares this with the before-and-after predictions of a network equilibrium model. The analysis is based on the findings of an empirical study of the travel time and route choice impacts of a road capacity reduction. Time-stamped, partial licence plates were recorded across a series of locations, over a period of days both with and without the capacity reduction, and the data were ‘matched’ between locations using special-purpose statistical methods. Hypothesis tests were used to identify statistically significant changes in travel times and route choice, between the periods of days with and without the capacity reduction. A traffic network equilibrium model was then independently applied to the same scenarios, and its predictions compared with the empirical findings. From a comparison of route choice patterns, a particularly influential spatial effect was revealed of the parameter specifying the relative values of distance and travel time assumed in the generalised cost equations. When this parameter was ‘fitted’ to the data without the capacity reduction, the network model broadly predicted the route choice impacts of the capacity reduction, but with other values it was seen to perform poorly. The paper concludes by discussing the wider practical and research implications of the study’s findings.     

A discrete dynamical system of formulating traffic assignment: Revisiting Smith’s model

Through relaxing the behavior assumption adopted in Smith’s model (Smith, 1984), we propose a discrete dynamical system to formulate the day-to-day evolution process of traffic flows from a non-equilibrium state to an equilibrium state. Depending on certain preconditions, the equilibrium state can be equivalent to a Wardrop user equilibrium (UE), Logit-based stochastic user equilibrium (SUE), or boundedly rational user equilibrium (BRUE). These equivalence properties indicate that, to make day-to-day flows evolve to equilibrium flows, it is not necessary for travelers to choose their routes based on actual travel costs of the previous day. Day-to-day flows can still evolve to equilibrium flows provided that travelers choose their routes based on estimated travel costs which satisfy these preconditions. We also show that, under a more general assumption than the monotonicity of route cost function, the trajectory of the dynamical system converges to a set of equilibrium flows by reasonably setting these parameters in the dynamical system. Finally, numerical examples are presented to demonstrate the application and properties of the dynamical system. The study is helpful for understanding various processes of forming traffic jam and designing an algorithm for calculating equilibrium flows.     

Modelling route choice behaviour in a tolled road network with a time surplus maximisation bi-objective user equilibrium model

In this paper, we propose a novel approach to model route choice behaviour in a tolled road network with a bi-objective approach, assuming that all users have two objectives: (1) minimise travel time; and (2) minimise toll cost. We assume further that users have different preferences in the sense that for any given path with a specific toll, there is a limit on the time that an individual would be willing to spend. Different users can have different preferences represented by this indifference curve between toll and time. Time surplus is defined as the maximum time minus the actual time. Given a set of paths, the one with the highest (or least negative) time surplus will be the preferred path for the individual. This will result in a bi-objective equilibrium solution satisfying the time surplus maximisation bi-objective user equilibrium (TSmaxBUE) condition. That is, for each O–D pair, all individuals are travelling on the path with the highest time surplus value among all the efficient paths between this O–D pair.We show that the TSmaxBUE condition is a proper generalisation of user equilibrium with generalised cost function, and that it is equivalent to bi-objective user equilibrium. We also present a multi-user class version of the TSmaxBUE condition and demonstrate our concepts with illustrative examples.     

Development of a differential route share model for railroad freight traffic

This paper summarizes work undertaken towards development and calibration of a model to predict the distribution of rail freight traffic among competing routes. The model is designed for use in analyzing the traffic effects of changes in the level-of-service on selected rail lines. The model predicts route shares based on the overall network configuration of each railroad participating in a given market. The model selects feasible routes, discards those routes which appear to be too circuitous or costly, and then assigns traffic to the remaining routes in accordance with several network characteristics. It is designed to be sensitive to level-of-service changes, and to simulate the response of shippers and railroads to a competitive environment. A multiple route-finding algorithm was used to find possible routes based on the number of railroads operating at the originating and terminating end of a market. Multiple routes were determined and matched with observed traffic flows from the ICC One-Percent Waybill Sample. Physical network characteristics for each route, including distance, junction frequency, and “impedance,” were calculated from the network model and were correlated with the traffic share observed on each route in the market. A two-stage model was developed to find feasible routes from the set of possible routes and to allocate traffic to feasible routes based on levels-of-service. The model was calibrated on 9,793 routes from 1,199 markets with twenty or more carloads from the 1977 One-Percent Carload Waybill Sample. Model calibration supported the hypothesis that network route characteristics did indeed influence shipper choice of route, and that a normative model could be used to assess relative attractiveness of routes under various railroad corporate ownership restructuring scenarios.     

Bus arrival time prediction at bus stop with multiple routes

Provision of accurate bus arrival information is vital to passengers for reducing their anxieties and waiting times at bus stop. This paper proposes models to predict bus arrival times at the same bus stop but with different routes. In the proposed models, bus running times of multiple routes are used for predicting the bus arrival time of each of these bus routes. Several methods, which include support vector machine (SVM), artificial neural network (ANN), k nearest neighbours algorithm (k-NN) and linear regression (LR), are adopted for the bus arrival time prediction. Observation surveys are conducted to collect bus running and arrival time data for validation of the proposed models. The results show that the proposed models are more accurate than the models based on the bus running times of single route. Moreover, it is found that the SVM model performs the best among the four proposed models for predicting the bus arrival times at bus stop with multiple routes.     

A model‐based demand‐balancing control for dynamically divided multiple urban subnetworks

Traffic control is an effective and efficient method for the problem of traffic congestion. It is necessary to design a high‐level controller to regulate the network traffic demands, because traffic congestion is not only caused by the improper management of the traffic network but also to a great extent caused by excessive network traffic demands. Therefore, we design a demand‐balance model predictive controller based on the macroscopic fundamental diagram‐based multi‐subnetwork model, which can optimize the network traffic mobility and the network traffic throughput by regulating the input traffic flows of the subnetworks. Because the transferring traffic flows among subnetworks are indirectly controlled and coordinated by the demand‐balance model predictive controller, the subnetwork division can variate dynamically according to real traffic states, and a global optimality can be achieved for the entire traffic network. The simulation results show the effectiveness of the proposed controller in improving the network traffic throughput. Copyright © 2016 John Wiley & Sons, Ltd.     

Planning and Evaluation of Passenger Ferry Service in Hong Kong

A predominant observation in Hong Kong is the continuous loss in ferry patronage. There are two main reasons for this: poor level-of-service and better competitors. New roads, bridges, and tunnels are serving the buses, and to some extent the railways; whereas the investment in ferry terminals is relatively at a lower level. On the one hand, there is no need to promote the ferries in a free market environment; but on the other hand, the ferries have the best safety record, can only relieve some traffic congestion and need water access that is one of the characteristics of Hong Kong. The goal of this paper is to design a planning approach combined with an evaluation procedure on how to make the best use of the existing water and pier resources in Hong Kong through the provision of commercially viable ferry services. The approach used covers the impact of future developments planning up to 2006 comprising all public transport modes in Hong Kong (heavy rail, metro, bus, and ferry). The planning tool is based on a newly developed multi-objective evaluation method in order to assess the ferry routes with scientific, practical, and simplified analyses for future use. This assessment is applied to the existing ferry routes and candidate routes and can also be carried out on an individual route basis or on a given set of routes. The objective functions set forth analytically in the evaluation method take into account the interests of the three participants: the passengers, the operators and the government. The proposed ferry network design formulation and the suggested new ferry routes will have a positive impact on changing the ferry system’s image in Hong Kong.     

Routing aspects of electric vehicle drivers and their effects on network performance

This study investigates the routing aspects of battery electric vehicle (BEV) drivers and their effects on the overall traffic network performance. BEVs have unique characteristics such as range limitation, long battery recharging time, and recuperation of energy lost during the deceleration phase if equipped with regenerative braking system (RBS). In addition, the energy consumption rate per unit distance traveled is lower at moderate speed than at higher speed. This raises two interesting questions: (i) whether these characteristics of BEVs will lead to different route selection compared to conventional internal combustion engine vehicles (ICEVs), and (ii) whether such route selection implications of BEVs will affect the network performance. With the increasing market penetration of BEVs, these questions are becoming more important. This study formulates a multi-class dynamic user equilibrium (MCDUE) model to determine the equilibrium flows for mixed traffic consisting of BEVs and ICEVs. A simulation-based solution procedure is proposed for the MCDUE model. In the MCDUE model, BEVs select routes to minimize the generalized cost which includes route travel time, energy related costs and range anxiety cost, and ICEVs to minimize route travel time. Results from numerical experiments illustrate that BEV drivers select routes with lower speed to conserve and recuperate battery energy while ICEV drivers select shortest travel time routes. They also illustrate that the differences in route choice behavior of BEV and ICEV drivers can synergistically lead to reduction in total travel time and the network performance towards system optimum under certain conditions.     

Unequal regional impacts of high speed rail on the tourism industry: a simulation analysis of the effects of Kyushu <Emphasis Type="Italic">Shinkansen</Emphasis>

Many high speed rail (HSR) routes are under construction in various cities of the world. Although tourism is one of the industries affected by HSR, not much is known about its effects on the same. This paper studies the impact of Kyushu’s HSR (Shinkansen) on tourism using computable general equilibrium modeling in the context of regional economies and transportation. The results show that the HSR has unequal effects on tourism among prefectures. The presence of these inequalities depends on whether the prefecture is a served by HSR, whether it is a terminal or an intermediate HSR station, and its current popularity with the tourists. Despite these inequalities, the economies of all the prefectures are benefited by the HSR owing to general equilibrium effects.     

A traffic-condition-based route guidance strategy for a single destination road network

Most of existing route guidance strategies achieves user optimal equilibrium by comparing travel time. Measuring travel time, however, might be uneasy on an urban road network. To contend with the issue, the paper mainly considers easily obtained inflow and outflow of a link and road capacity as input, and proposes a route guidance strategy for a single destination road network based on the determination of free-flow or congested conditions on alternative routes. An extended strategy for a complex network and a feedback approximation for avoiding forecast are further explored. Weaknesses of the strategy are also explicitly analyzed. To test the strategy, simulation investigations are conducted on two networks with multiple parallel routes. The results indicate that the strategy is able to provide stable splitting rates and to approximate user optimal equilibrium in different conditions, in particular when traffic demand is high. This strategy has potential to be applied in an urban road network due to its simplicity and easily obtained input data. The strategy is also applicable for single destination if some alternatives and similar routes are available.     

Likelihood-based offline map matching of GPS recordings using global trace information

In batch map matching the objective is to derive from a time series of position data the sequence of road segments visited by the traveler for posterior analysis. Taking into account the limited accuracy of both the map and the measurement devices several different movements over network links may have generated the observed measurements. The set of candidate solutions can be reduced by adding assumptions about the traveller’s behavior (e.g. respecting speed limits, using shortest paths, etc.). The set of feasible assumptions however, is constrained by the intended posterior analysis of the link sequences produced by map matching. This paper proposes a method that only uses the spatio-temporal information contained in the input data (GPS recordings) not reduced by any additional assumption.The method partitions the trace of GPS recordings so that all recordings in a part are chronologically consecutive and match the same set of road segments. Each such trace part leads to a collection of partial routes that can be qualified by their likelihood to have generated the trace part. Since the trace parts are chronologically ordered, an acyclic directed graph can be used to find the best chain of partial routes. It is used to enumerate candidate solutions to the map matching problem.Qualification based on behavioral assumptions is added in a separate later stage. Separating the stages helps to make the underlying assumptions explicit and adaptable to the purpose of the map matched results. The proposed technique is a multi-hypothesis technique (MHT) that does not discard any hypothesized path until the second stage.A road network extracted from OpenStreetMap (OSM) is used. In order to validate the method, synthetic realistic GPS traces were generated from randomly generated routes for different combinations of device accuracy and recording period. Comparing the base truth to the map matched link sequences shows that the proposed technique achieves a state of the art accuracy level.     

Information provision strategies eliminating deluded equilibrium caused by travellers’ misperception

Providing travel time information may be effective at reducing travel costs. However, this information does not always match the actual travel time that travellers will experience. Furthermore, the information is often asymmetrically provided within the network, owing to the limitations of observation devices, prediction model calibration, and uncertainty about road conditions. The purpose of this study is to investigate the effects of predictive travel time information that is asymmetrically provided to travellers. This study formulated a dynamic traffic assignment model in origin–destination (OD) pair with two parallel routes, while considering travellers’ learning processes and within-day and day-to-day dynamics. In this study, it is assumed that different information will be provided to each traveller, according to within-day traffic dynamics. Furthermore, the information is provided for only one of two possible routes, because of observation limitations. The effects of information accuracy are also discussed in this study. The results of numerical analysis indicated that information provisions possibly reduced the negative effects of deluded equilibrium state, even when the information was only provided for one of the routes. Different effects of the travel time information and its variation were illustrated according to the allocation of the bottleneck capacities of two routes.