Sensitivity analysis on stochastic equilibrium transportation networks using genetic algorithm

This study deals with the sensitivity analysis of an equilibrium transportation networks using genetic algorithm approach and uses the bi‐level iterative sensitivity algorithm. Therefore, integrated Genetic Algorithm‐TRANSYT and Path Flow Estimator (GATPFE) is developed for signalized road networks for various level of perceived travel time in order to test the sensitivity of perceived travel time error in an urban stochastic road networks. Level of information provided to drivers correspondingly affects the signal timing parameters and hence the Stochastic User Equilibrium (SUE) link flows. When the information on road system is increased, the road users try to avoid conflicting links. Therefore, the stochastic equilibrium assignment concept tends to be user equilibrium. The GATPFE is used to solve the bi‐level problem, where the Area Traffic Control (ATC) is the upper‐level and the SUE assignment is the lower‐level. The GATPFE is tested for six‐junction network taken from literature. The results show that the integrated GATPFE can be applied to carry out sensitivity analysis at the equilibrium network design problems for various level of information and it simultaneously optimize the signal timings (i.e. network common cycle time, signal stage and offsets between junctions).     

Evaluation of network reliability using stochastic user equilibrium

When we evaluate the performance reliability of a network, it is necessary to describe user's behaviour in a partially degraded network. This paper shows that the Stochastic User Equilibrium (SUE) model assuming user's route choice behaviour under uncertain network conditions can be incorporated in the performance reliability model. The effects of providing information are analyzed using the SUE model with two different groups of route choice; informed drivers and non informed drivers. It is found that providing information generally increases network performance reliability. This depends, however, on the probability distribution of the network states.     

The marginal cost taxation of a transportation network

The paper shows that if the cost and demand functions satisfy certain weak smoothness conditions then the marginal cost taxation of a transportation network is optimal in the usual local sense. Interactions between the cost of travel along a link and flow along other links and between the demand for travel along a route and flow along other routes are permitted.     

A continuous network design model in stochastic user equilibrium based on sensitivity analysis

The continuous network design problem (CNDP) is known to be difficult to solve due to the intrinsic properties of non‐convexity and nonlinearity. Such kinds of CNDP can be formulated as a bi‐level programme, in which the upper level represents the designer's decisions and the lower level the travellers' responses. Formulations of this kind can be classified as either Stackelberg approaches or Nash ones according to the relationship between the upper level and the lower level parts. This paper formulates the CNDP for road expansion based on Stackelberg game where leader and follower exist, and allows for variety of travellers' behaviour in choosing their routes. In order to solve the problem by the Stackelberg approach, we need a relation between link flows and design parameters. For this purpose, we use a logit route choice model, which provides this in an explicit closed‐form function. This model is applied to two example road networks to test and briefly compare the results between the Stackelberg and Nash approaches to explore the differences between them.     

Three-player game-theoretic model over a freight transportation network

With recent development in freight transportation industry, its network structure has become more complicated, as many decision-makers competing for profits with each other are involved. While most recent research in this area is focused on the perfectly competitive market and the prices are given as a constant tariff rate, little attention has been paid to the system optimization problem in the absence of regulatory authority. In this paper, we investigate the competitive equilibrium in an oligopolistic market on a freight network. A partially non-cooperative game among shippers, carriers and infrastructure companies (IC) is examined. All three kinds of players act as profit maximizing agents, except that the carriers and ICs are assumed to behave cooperatively in their own coalitions. We consider the vertically efficient nonlinear tariff schedules which are commonly used in the transportation industry. By introducing a three-stage game-theoretic model, we show that the equilibrium flows can also maximize total system profits if the IC and the carrier both use vertically efficient nonlinear pricing schedules. The division of the surplus associated with each shipment is obtained by solving a linear programming problem. We provide a few examples under different situations to show the existence of the resulting equilibrium.     

Solving a discrete multimodal transportation network design problem

This paper investigates the multimodal network design problem (MMNDP) that optimizes the auto network expansion scheme and bus network design scheme in an integrated manner. The problem is formulated as a single-level mathematical program with complementarity constraints (MPCC). The decision variables, including the expanded capacity of auto links, the layout of bus routes, the fare levels and the route frequencies, are transformed into multiple sets of binary variables. The layout of transit routes is explicitly modeled using an alternative approach by introducing a set of complementarity constraints. The congestion interaction among different travel modes is captured by an asymmetric multimodal user equilibrium problem (MUE). An active-set algorithm is employed to deal with the MPCC, by sequentially solving a relaxed MMNDP and a scheme updating problem. Numerical tests on nine-node and Sioux Falls networks are performed to demonstrate the proposed model and algorithm.     

Locating new passenger facilities on a transportation network

This paper examines the problem of locating additional passenger facilities on a transportation network to supplement ones that already exist. A distinction is made between “supporting” facilities which operate only in concert with already existing ones and “new” facilities which are self-sufficient and operate independently. It is shown that, when the objective is to maximize the utility of travel times to all users, at least one set of optimal locations for the new facilities exist on the nodes of the network if the utility function for travel times is convex. This result is proven under very general conditions including the assumption of a probabilistic transportation network, i.e. a network where travel times on network branches are random variables. A straightforward algorithm for solving a specific simple case is also provided and the results are illustrated by examples.     

Economic resilience to transportation failure: a computable general equilibrium analysis

This study develops and applies a multimodal computable general equilibrium (CGE) framework to investigate the role of resilience in the economic consequences of transportation system failures. Vulnerability and economic resilience of different modes of transportation infrastructure, including air, road, rail, water and local transit, are assessed using a CGE model that incorporates various resilience tactics including modal substitution, trip conservation, excess capacity, relocation/rerouting, and service recapture. The linkages between accessibility, vulnerability, and resilience are analyzed. The model is applied to the transportation system failures in the aftermath of Hurricane Katrina to illustrate its capabilities. The analytical framework, however, has broader applications and can provide insights for resource allocations to enhance emergent responses to unexpected events and to improve resilient design of transportation infrastructure systems.     

Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city

This paper investigates the intermodal equilibrium, road toll pricing, and bus system design issues in a congested highway corridor with two alternative modes - auto and bus - which share the same roadway along this corridor. On the basis of an in-depth analysis of the demand and supply sides of the bimodal transportation system, the mode choice equilibrium of travelers along the continuum corridor is first presented and formulated as an equivalent variational inequality problem. The solution properties of the bimodal continuum equilibrium formulation are analytically explored. Two models, which account for different infrastructure/system regulatory regimes (public and private), are then proposed. In the public regulatory model, the road toll location and charge level are simultaneously optimized together with the bus service fare and frequency. In the private regulatory model, the fare and frequency of bus services, which are operated by a profit-driven private operator, are optimized for exogenously given toll pricing schemes. Finally, an illustrative example is given to demonstrate the application of the proposed models. Sensitivity analysis of residential/household distribution along the corridor is carried out together with a comparison of four different toll pricing schemes (no toll, first best, distance based, and location based). Insightful findings are reported on the interrelationships among modal competition, market regulatory regimes, toll pricing schemes, and urban configurations as well as their implications in practice.     

The convergence of diagonalization algorithms for asymmetric network equilibrium problems

We provide a sufficient condition for the convergence of diagonalization algorithms for equilibrium traffic assignment problems with asymmetric Jacobian matrix B(v) of the link user cost mapping s(v) of the flow v. When

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, where D(v^*) > 0 is the diagonal of B(v^*) and v^* is the equilibrium flow, we demonstrate a local convergence theorem for nonlinear cost functions. The implication of this result for practical applications of the model are outlined.     

Transportation policy analysis with a geographic information system: The virtual network of freight transportation in Europe

This paper presents a multi-modal freight transportation model based on a digitized geographic network. A systematic analysis and decomposition of all the transport operations i.e. moving, loading and unloading, transshipping and transiting, leads to the development of a virtual network where each virtual link corresponds to a specific operation, and all transportation modes and means are inter-linked. Software, called NODUS, automatically generates the virtual network so that the model can be conveniently applied to large networks. The analytical structure of the links notation makes it easy to attach specific cost functions to each virtual link. The model is applied to the trans-European freight network of roads, railways and inland waterways for the transportation of wood. Cost functions are built up for each operation by each mode/means combination. A detailed point-to-point origin-destination matrix, calibrated on Eurostat statistics, is generated by a Monte-Carlo technique. Then, the total transportation cost is minimized with respect to the choices of routes, modes and means. This provides estimations of transportation services demands as well as modal splits, to the extent that the two hypotheses of demand based on generalized cost minimization and market contestability are accepted. A sensitivity analysis on the relative road cost is made, which provides measures of arc-elasticities.     

Modeling stochastic perception error in the mean-excess traffic equilibrium model

In this paper, we extend the α-reliable mean-excess traffic equilibrium (METE) model of Chen and Zhou (Transportation Research Part B 44(4), 2010, 493-513) by explicitly modeling the stochastic perception errors within the travelers’ route choice decision processes. In the METE model, each traveler not only considers a travel time budget for ensuring on-time arrival at a confidence level α, but also accounts for the impact of encountering worse travel times in the (1 − α) quantile of the distribution tail. Furthermore, due to the imperfect knowledge of the travel time variability particularly in congested networks without advanced traveler information systems, the travelers’ route choice decisions are based on the perceived travel time distribution rather than the actual travel time distribution. In order to compute the perceived mean-excess travel time, an approximation method based on moment analysis is developed. It involves using the conditional moment generation function to derive the perceived link travel time, the Cornish-Fisher Asymptotic Expansion to estimate the perceived travel time budget, and the Acerbi and Tasche Approximation to estimate the perceived mean-excess travel time. The proposed stochastic mean-excess traffic equilibrium (SMETE) model is formulated as a variational inequality (VI) problem, and solved by a route-based solution algorithm with the use of the modified alternating direction method. Numerical examples are also provided to illustrate the application of the proposed SMETE model and solution method.     

Comparative analysis of three user equilibrium models under stochastic demand

Recent empirical studies on the value of time and reliability reveal that travel time variability plays an important role on travelers' route choice decision process. It can be considered as a risk to travelers making a trip. Therefore, travelers are not only interested in saving their travel time but also in reducing their risk. Typically, risk can be represented by two different aspects: acceptable risk and unacceptable risk. Acceptable risk refers to the reliability aspect of acceptable travel time, which is defined as the average travel time plus the acceptable additional time (or buffer time) needed to ensure more frequent on‐time arrivals, while unacceptable risk refers to the unreliability aspect of unacceptable late arrivals (though infrequent) that have a travel time excessively higher than the acceptable travel time. Most research in the network equilibrium based approach to modeling travel time variability ignores the unreliability aspect of unacceptable late arrivals. This paper examines the effects of both reliability and unreliability aspects in a network equilibrium framework. Specifically, the traditional user equilibrium model, the demand driven travel time reliability‐based user equilibrium model, and the α‐reliable mean‐excess travel time user equilibrium model are considered in the investigation under an uncertain environment due to stochastic travel demand. Numerical results are presented to examine how these models handle risk under travel time variability.     

Impact analysis of cordon-based congestion pricing on mode-split for a bimodal transportation network

This paper investigates the impact of cordon-based congestion pricing scheme on the mode-split of a bimodal transportation network with auto and rail travel modes. For any given toll-charge pattern, its impact on the mode-split can be estimated by solving a combined mode-split and traffic-assignment problem. Using a binary logit model for the mode-split, the combined problem is converted into a traffic-assignment problem with elastic demand. Probit-based stochastic user equilibrium (SUE) principle is adopted for this traffic-assignment problem, and a continuously distributed value of time (VOT) is assumed to convert the toll charges and transit fares into time-units. This combined mode-split and traffic-assignment problem is then formulated as a fixed-point model, which can be solved by a convergent Cost Averaging method. The combined mode-split and traffic-assignment problem is then used to analyze a multimodal toll design problem for cordon-based congestion pricing scheme, with the aim of increasing the mode-share of public transport system to a targeted level. Taking the fixed-point model as a constraint, the multimodal toll design problem is thus formulated as a mathematical programming with equilibrium constraints (MPEC) model. A genetic algorithm (GA) is employed to solve this MPEC model, which is then numerical validated by a network example.     

First-best marginal cost toll for a traffic network with stochastic demand

First-best marginal cost pricing (MCP) in traffic networks has been extensively studied with the assumption of deterministic travel demand. However, this assumption may not be realistic as a transportation network is exposed to various uncertainties. This paper investigates MCP in a traffic network under stochastic travel demand. Cases of both fixed and elastic demand are considered. In the fixed demand case, travel demand is represented as a random variable, whereas in the elastic demand case, a pre-specified random variable is introduced into the demand function. The paper also considers a set of assumptions of traveler behavior. In the first case, it is assumed that the traveler considers only the mean travel time in the route choice decision (risk-neutral behavior), and in the second, both the mean and the variance of travel time are introduced into the route choice model (risk-averse behavior). A closed-form formulation of the true marginal cost toll for the stochastic network (SN-MCP) is derived from the variational inequality conditions of the system optimum and user equilibrium assignments. The key finding is that the calculation of the SN-MCP model cannot be made by simply substituting related terms in the original MCP model by their expected values. The paper provides a general function of SN-MCP and derives the closed-form SN-MCP formulation for specific cases with lognormal and normal stochastic travel demand. Four numerical examples are explored to compare network performance under the SN-MCP and other toll regimes.     

Sequential optimization approach for the multi‐class user equilibrium problem in a continuous transportation system

We consider a city region with several facilities that are competing for customers of different classes. Within the city region, the road network is dense, and can be represented as a continuum. Customers are continuously distributed over space, and they choose a facility by considering both the transportation cost and market externalities. More importantly, the model takes into account the different transportation cost functions and market externalities to which different customer classes are subjected. A logit‐type distribution of demand is specified to model the decision‐making process of users' facility choice. We develop a sequential optimization approach to decompose the complex multi‐class and multi‐facility problem into a series of smaller single‐class and single‐facility sub‐problems. An efficient solution algorithm is then proposed to solve the resultant problem. A numerical example is given to demonstrate the effectiveness and potential applicability of the proposed methodology.     

Integrated modeling of urban hierarchy and transportation network planning

A major problem addressed during the preparation of spatial development plans relates to the accessibility to facilities where services of general interest such as education, health care, public safety, and justice are offered to the population. In this context, planners typically aim at redefining the level of hierarchy to assign to the urban centers of the region under study (with a class of facilities associated with each level of hierarchy) and redesigning the region’s transportation network. Traditionally, these two subjects – urban hierarchy and transportation network planning – have been addressed separately in the scientific literature. This paper presents an optimization model that simultaneously determines which urban centers and which network links should be promoted to a new level of hierarchy so as to maximize accessibility to all classes of facilities. The possible usefulness of the model for solving real-world problems of integrated urban hierarchy and transportation network planning is illustrated through an application to the Centro Region of Portugal.     

Data attribution and network representation issues in GIS and transportation

Geographic Information System (GIS) is an “intelligent” technology which integrates attribute data and spatial features and manages the relationship between them. GIS is widely used in many activities, but its application in transportation is less common. The extension of GIS into transportation (GIS‐T) offers the potential to integrate transportation data into GIS. The integration of transportation data in GIS faces a number of barriers that are discussed in the paper. These barriers can be broadly categorized into data attribution and network representation issues. This paper analyzes these issues and reviews the potential for overcoming these constraints with current GIS technology. A fully developed GIS‐T has to meet many diverse needs including transportation inventory, modeling and operational problems. If GIS is to succeed as a transportation technology, it must be capable of integrating different levels of network representation and data attribution and have the ability to link with other transportation technologies.     

Development of an Eurasian transportation network: Potential and possibilities

Eurasia is the place in which the political and social situations are changing rapidly. In particular, the recent changes in the Soviet Union, China and North Korea will bring about big changes in transportation network in Eurasia. The difficulties of the existing transportation network in this area are examined. Directions for developing transportation networks between Korea, China, Mongolia and Russia are suggested with a focus to the unified Korea. Access to the Middle East, India and Southeast Asia by rail would be possible by connecting the missing links, and its competitiveness could be increased. The establishment of direct air routes can also reduce air passenger-km and fuel consumption quite a lot.     

A comparison of user-optimum versus system-optimum traffic assignment in transportation network design

In this report, we compare the computational efficiency and results of solving two alternative models for the problem of determining improvements to an urban road network. Using a 1462 link, 584 node test network of the north Dallas area, we compare a model which assumes user-optimum behavior of travelers with a model which assumes system-optimum flows. Both of these models allow improvements to the road network to take on any nonnegative value, rather than requiring discrete improvement values. Investment costs are modeled by functions with decreasing marginal costs. Unfortunately, the user-optimum model, which is much more realistic than the system-optimum one, normally cannot be solved optimally. However, the simpler system-optimum model can be optimally solved, provided that investment costs are approximated by linear functions. Thus, for this network design problem we compare an accurate representation which can be solved only approximately with an approximate representation which can be solved optimally. Our computational testing showed that the system-optimum model produces solutions as good as those from the user-optimum model, and thus seems justified when favored by other considerations, such as ease of coding, availability of “canned” programs, etc.