Degradable Transport Network Research Articles

A Multiclass Cumulative Prospect Theory-Based Stochastic User Equilibrium Model with Path Constraints in Degradable Transport Networks

The limited driving range and the unavailability or insufficiency of battery charging/swapping stations cause the so-called range anxiety issue for traffic assignment involving battery electric vehicle (BEV) users. In addition, expected utility theory-based stochastic user equilibrium (EUT-SUE) model generates the perfectly rational issue when the travellers make route choice decisions. To tackle these two problems, this article improves the cumulative prospect theory-based stochastic user equilibrium (CPT-SUE) model in a degradable transport network through incorporating the constraints of multiple user classes and distance limit. In this degradable network, the travellers experience stochastic travel times due to network link capacity degradations. For this improved CPT-SUE model, the equivalent variational inequality (VI) model and associated method of successive averages (MSA) based solution are provided. The improved CPT-SUE model is tested and compared with the EUT-SUE model with distance limit, with results showing that the improved CPT-SUE model can handle jointly the range anxiety issue and the perfectly rational issue.

Day-to-Day Evolution of Traffic Flow with Dynamic Rerouting in Degradable Transport Network

Random events like accidents and vehicle breakdown, degrade link capacities and lead to uncertain travel environment. And whether travelers adjust route or not depends on the utility difference (dynamic rerouting behavior) rather than a constant. Considering travelers’ risk-taking behavior in uncertain environment and dynamic rerouting behavior, a new day-to-day traffic assignment model is established. In the proposed model, an exponential-smoothing filter is adopted to describe travelers’ learning for uncertain travel time. The cumulative prospect theory is used to reflect route utility and its reference point is adaptive and set to be the minimal travel time under a certain on-time arrival probability. Rerouting probability is determined by the difference between expected utility and perceived utility of previously chosen route. Rerouting travelers choose new routes in a logit model while travelers who do not choose to reroute travel on their previous routes again. The proposed model’s several mathematical properties, including fixed point existence, uniqueness, and stability condition, are investigated through theoretical analyses. Numerical experiments are also conducted to validate the proposed heuristic stability condition, show the effects of four main parameters on dynamic natures of the system, and investigate the differences of the system based on expected utility theory and cumulative prospect theory and with static rerouting behavior and dynamic rerouting behavior.

A Reliability-Based Network Equilibrium Model with Adaptive Risk-Averse Travelers

In this paper, route free-flow travel time is taken as the lower bound of route travel time to examine its impacts on budget time and reliability for degradable transportation networks. A truncated probability density distribution with respect to route travel time is proposed and the corresponding travel time budget (TTB) model is derived. The budget time and reliability are compared between TTB models with and without truncated travel time distribution. Under truncated travel time distribution, the risk-averse levels of travelers are adaptive, which are affected by the characteristics of the used routes besides the confidence level of travelers. Then, a TTB-based stochastic user equilibrium (SUE) is developed to model travelers’ route choice behavior. Moreover, its equivalent variational inequality (VI) problem is formulated and a route-based algorithm is used to solve the proposed model. Numerical results indicate that route travel time boundary produces a great influence on decision cost and route choice behavior of travelers.

A mixed stochastic user equilibrium model considering influence of advanced traveller information systems in degradable transport network

Advanced traveler information systems (ATIS) can not only improve drivers’ accessibility to the more accurate route travel time information, but also can improve drivers’ adaptability to the stochastic network capacity degradations. In this paper, a mixed stochastic user equilibrium model was proposed to describe the interactive route choice behaviors between ATIS equipped and unequipped drivers on a degradable transport network. In the proposed model, the information accessibility of equipped drivers was reflected by lower degree of uncertainty in their stochastic equilibrium flow distributions, and their behavioral adaptability was captured by multiple equilibrium behaviors over the stochastic network state set. The mixed equilibrium model was formulated as a fixed point problem defined in the mixed route flows, and its solution was achieved by executing an iterative algorithm. Numerical experiments were provided to verify the properties of the mixed network equilibrium model and the efficiency of the iterative algorithm.

Dynamic traffic assignment in degradable networks: paradoxes and formulations with stochastic link transmission model

ABSTRACTThis paper proposes a simultaneous route and departure time choice (SRDTC) problem with fixed demand in a degradable transport network. In this network, travelers face with stochastic travel times. Their selection of routes and departure times follows the UE principle in terms of the mean generalized route cost, which is defined as the probabilistic dynamic user optimal (PDUO) principle. The proposed PDUO-SRDTC problem is formulated as a variational inequality (VI) problem. As a special case of PDUO-SRDTC problem, the PDUO route choice (PDUO-RC) problem is also proposed and formulated as a VI problem. Network degradation is defined on the degradation of the outflow capacity of each link. A Monte Carlo-based stochastic link transmission model (MC-SLTM) is developed to capture the effect of physical queues and the random evolution of traffic states during flow propagation to estimate mean generalized route costs. Both the extragradient algorithm and the route-swapping method with a variable sample size scheme are developed to solve the proposed VI problems. Numerical examples are developed to illustrate the paradoxical phenomena of the problems and the effectiveness of the solution methods. Numerical results show that constructing a new road, enhancing link outflow capacity, or reducing outflow capacity degradation can lead to poor network performance and it is important to consider both network degradation and queue spillback when making transportation policies aimed at improving network performance. The results also demonstrate that the variable sample size scheme can give a quicker and better solution than the traditional fixed sample size scheme.

Modeling Day-to-day Flow Dynamics on Degradable Transport Network.

Stochastic link capacity degradations are common phenomena in transport network which can cause travel time variations and further can affect travelers’ daily route choice behaviors. This paper formulates a deterministic dynamic model, to capture the day-to-day (DTD) flow evolution process in the presence of degraded link capacity degradations. The aggregated network flow dynamics are driven by travelers’ study of uncertain travel time and their choice of risky routes. This paper applies the exponential-smoothing filter to describe travelers’ study of travel time variations, and meanwhile formulates risk attitude parameter updating equation to reflect travelers’ endogenous risk attitude evolution schema. In addition, this paper conducts theoretical analyses to investigate several significant mathematical characteristics implied in the proposed DTD model, including fixed point existence, uniqueness, stability and irreversibility. Numerical experiments are used to demonstrate the effectiveness of the DTD model and verify some important dynamic system properties.

Cumulative prospect theory-based user equilibrium model with stochastic perception errors

The cumulative prospect theory (CPT) is applied to study travelers’ route choice behavior in a degradable transport network. A cumulative prospect theory-based user equilibrium (CPT-UE) model considering stochastic perception error (SPE) within travelers’ route choice decision process is developed. The SPE is conditionally dependent on the actual travel time distribution, which is different from the deterministic perception error used in the traditional logit-based stochastic user equilibrium. The CPT-UE model is formulated as a variational inequality problem and solved by a heuristic solution algorithm. Numerical examples are provided to illustrate the application of the proposed model and efficiency of the solution algorithm. The effects of SPE on the reference point determination, cumulative prospect value estimation, route choice decision and network performance evaluation are investigated.

Considering perception errors in network efficiency measure: an application to bridge importance ranking in degradable transportation networks

In this paper, a new network efficiency measure that takes into account of traveller's perception errors as well as flows, behaviours, and costs is developed for assessing link importance in congested transportation networks. The core component of the network efficiency measure is a probabilistic route choice model embedded in a network equilibrium framework, which explicitly captures the interactions between travellers’ perception errors and link cost functions to produce a stochastic user equilibrium (SUE) flow pattern. The importance measure defined as the relative network efficiency drop is developed to rank the links in the network. The network efficiency and importance measures can work for both uncongested and congested transportation networks. To show proof of concept, we use two networks to demonstrate the features and applicability of the proposed measures. In the Braess network, we examine the value of link efficiency, link importance, and link ranking in comparison with the topological measure and the user equilibrium (UE) measure. In addition, we investigate the effects capacity degradation level, demand level, and degree of perception error. In the Winnipeg network, we apply the network efficiency and importance measures to assess the bridges in the city of Winnipeg, Manitoba, Canada. We compare the SUE importance with the localised volume to capacity (V/C) ratio method, and investigate the bridge importance measures in the context of a flooding scenario to examine the effect of providing information to drivers. The results demonstrate that the SUE network efficiency and importance measures are useful in both theory and applications.

Effect of speed limits in degradable transport networks

This paper studies how link-specific speed limits influence the performance of degradable transport networks, in which the capacity of each link is a degradable random variable. The distribution and cumulative distribution of link travel time have been presented with the effect of speed limits taken into account. The mean and variance of link and route travel time are formulated. Three link states have been classified, and their physical meanings have been discussed. The relationship between critical capacity, travel time and speed limit has been elaborated. We have proposed a Speed Limit- and Reliability-based User Equilibrium (SLRUE), adopting travel time budget as the principle of travelers’ route choice. A heuristic method employing the method of successive averages is developed to solve the SLRUE in degradable networks. Through numerical studies, we find that for some networks both the mean and standard deviation of the total travel time could be reduced simultaneously by imposing some speed limits. The speed limit design problem has been studied, and it is found that imposing speed limits cannot always reduce the total travel time budget of a network.

Depot location in degradable transport networks

Areas subject to natural or man-made disasters, such as earthquakes, fires, floods or attacks, are reliant on the residual transport network for the rescue of survivors and subsequent recovery. Pre-disaster planning requires assumptions about how the transport network may degrade. This paper presents a game theoretic approach modelling network degradation and applies this to depot location, with a case study based on Sichuan province in China, which is prone to earthquakes. To facilitate a cautious approach to depot location, the method assumes that the transport network is subject to attack by node-specific demons with the power to degrade links. The mixed strategy Nash equilibrium for the non-cooperative zero sum game between dispatchers and demons is used to define rescue hyperpaths. These in turn define the best depot locations. Two forms of the drop heuristic are used to find good depot locations.

Access for Performance of Transportation Planning and Operations: Case Study in Beijing Metropolitan Region

Considering the importance of maintaining effective performance at desired levels, the Transportation Adaptability Performance Index, as a weighted multi-criteria combination approach, is proposed to continuously identifying the performance of degradable transportation networks and making effective supplement, contrapuntal revision and intime adjustment of the program implementation process, in response to new requirements of the urban system. For the design of strategic and quantitative methodology, 50 variables belonging to 8 domains in 2 components are chosen as the original input inherently reflecting the various interests of involved stakeholders. Specifically, the paired comparison matrix of the domain is constructed by the analytic hierarchy process to weight the importance of each single variable. If the consistency of the matrix is acceptable, the domain weight in two components is determined directly through the singular value decomposition approach and while the consistency level is unacceptable, the significant element in the matrix is identified and revised until the consistency satisfies the constraint. The methodology is then applied to evaluate the performance of transportation networks in Beijing metropolitan region using the derived 2000~2010 data and the findings indicate that the hidden and potential problems could be quantitatively identified by this approach that can be used as a user-friendly tool for metropolitan planning organizations in assessing the effectiveness and efficiency of in-service infrastructures, updating plans, setting priorities and optimizing resource allocation for next step.

Evaluation of Link Criticality for Day-to-Day Degradable Transportation Networks

The evaluation of link criticality is an important step for public officials to apply when planning hazard mitigation. However, this type of analysis presents numerous challenges for capturing the impact of highly stochastic hazard events accurately. An analytical framework and an efficient solution procedure for the evaluation of link criticality are proposed: those tools consider the impact of day-to-day degradable conditions in transportation networks. Link capacity was examined as a multistatus variable, and a sampling technique was used to generate realizations of capacity value for transportation networks. With different capacity realizations, traffic demand was repeatedly assigned on the regional planning model network. The assignment results were measured with multiple criteria and analyzed with several statistical indices. A case study based on a section of the New Jersey roadway network verified the proposed approach.

AN APPROXIMATE RELIABILITY EVALUATION METHOD FOR IMPROVING TRANSPORTATION NETWORK PERFORMANCE

Considering the importance of maintaining network performance at desired levels under uncertainty, network reliability, as a new approach to assessing the performance of degradable urban transportation networks, has become increasingly developed in two recent decades. In this paper, a method for optimizing resource allocation to meet the required levels of transportation network reliability is proposed. The worked out method consists of two stages: at stage one, a method for computing the reliability of network connectivity based on the reliability of computing arc performance with an assumption that capacities are random variables for each arc is presented. These random variables are assumed to be conformed to especial probability density functions which can be modified through investing to improve the performance reliability of the arcs. At stage two, a mixed integer nonlinear programming model is developed to optimize resource allocation in the network. Numerical results are also provided in a simple network to demonstrate the capability of the employed method.

Critical Link Identification for Traffic Incident Management Programme under Degradable Stochastic Network

This paper proposed a new index called traffic incident management ratio (TIMR) for identifying appropriate roads to be installed with traffic incident management system. The TIMR is defined as the ratio between the expected total travel costs of the degradable transport network without and with traffic incident management programme (TIMP). The traffic flow pattern under the degradation network without TIMP is assumed to follow User Equilibrium (UE) condition, whereas the system optimum (SO) assignment is used to characterise the degradable network condition controlled by TIMP. The main function of TIMP considered in this paper is re-routing of traffic after the incident. An optimisation programme is then proposed for identifying critical roads in the network for an installation of TIMP. The critical roads for TIMP is identified by maximising the TIMR which implies that incidents on these critical roads can significantly increase the total network travel time without TIMP in which the installation of TIMP...

Network-based Accessibility Measures for Vulnerability Analysis of Degradable Transportation Networks

Accessibility is a fundamental concept in transportation analysis and urban planning. Typically, accessibility refers to the ‘ease’ of reaching opportunities for activities and services and can be used to assess the performance of a transportation and urban system. In this paper, we present network-based accessibility measures for assessing vulnerability of degradable transportation networks. The network-based accessibility measures consider the consequence of one or more link failures in terms of network travel time or generalized travel cost increase as well as the behavioral responses of users due to the failure in the network. To model different dimensions of travel behavioral responses, a combined travel demand model is adopted to estimate the long-term equilibrium network condition due to network disruptions. Numerical examples are conducted to demonstrate the feasibility of the proposed vulnerability measures for assessing degradable transportation networks. The results indicate that the accessibility measures derived from the combined travel demand model are capable of measuring the consequences of both demand and supply changes in the network and have the flexibility to reflect the effects of different travel choice dimensions on the network vulnerability.

Degradable transport network: Travel time budget of travelers with heterogeneous risk aversion

Empirical studies have suggested that travel time reliability plays an important role in travelers’ route choice behavior. This study develops an approach to relate the travel time variability due to stochastic network link capacity variations with travelers’ risk aversive route choice behaviors. We postulate that travelers acquire the variability of route travel times based on past experiences and factor such variability into their route choice consideration in the form of a travel time budget. This travel time budget varies with individuals and trip purposes and is related to the requirement on punctual arrivals. Moreover, all travelers want to minimize their travel time budgets. We formulate a multi-class mixed-equilibrium mathematical program to capture the route choice behaviors of travelers with heterogeneous risk aversions or requirements on punctual arrivals. Such an understanding has important implications on strengthening critical network links. This study then conducts numerical studies to illustrate its properties.