Modeling capacity flexibility of transportation networks

Flexibility of the transportation system is one of the important performance measures needed to deal with demand changes. In this paper, we provide a quantitative assessment of capacity flexibility for the passenger transportation network using bi-level network capacity models. Two approaches for assessing the value of capacity flexibility are proposed. One approach is based on the concept of reserve capacity, which reflects the flexibility with respect to changes in terms of demand volume only. The second approach allows for variations in the demand pattern in addition to changes in demand volume in order to more fully capture demand changes. Two models are developed in the second approach to consider two types of capacity flexibility. The total capacity flexibility allows all users to have both route choice and destination choice when estimating capacity flexibility. The limited capacity flexibility estimates how much more demand volume could be added to a fixed demand pattern by allowing the additional demand to deviate from the fixed demand pattern. Numerical examples are provided to demonstrate the different concepts of capacity flexibility for a passenger transportation system under demand changes.     

A traffic flow simulator for network reliability assessment

This paper investigates the transportation network reliability based on the information provided by detectors installed on some links. A traffic flow simulator (TFS) model is formulated for assessing the network reliability (in terms of travel time reliability), in which the variation of perceived travel time error and the fluctuations of origin-destination (OD) demand are explicitly considered. On the basis of prior OD demand and partial updated detector data, the TFS can estimate the link flows for the whole network together with link/path travel times, and their variance and covariance. The travel time reliability by OD pair can also be assessed and the OD matrix can be updated simultaneously. A Monte Carlo based algorithm is developed to solve the TFS model. The application of the proposed TFS model is illustrated by a numerical example.     

The role of travel demand and network centrality on the connectivity and resilience of an urban street system

In the transportation literature, two major and parallel approaches exist to identify the critical elements of a transportation system. On the one hand, conventional transportation engineering emphasizes travel demand, often in terms of traffic volume (i.e., demand side). On the other hand, newer techniques from Network Science emphasize network topology (i.e., supply side). To better understand the relationship between the two approaches, we first investigate whether they correlate by comparing traffic volume and node centrality. Second, we assess the impact of the two approaches on the connectivity and resilience of a transportation network; connectivity is measured by the relative size of the giant component, and resilience is measured by the network’s adaptive capacity (the amount of extra flow it can handle). The urban road system of Isfahan (Iran) is used as a practical case study. Overall, we find that traffic volume indeed correlates with node centrality. In addition, we find that the weighted degree of a node, i.e., the sum of the capacities of its incident links (for small disruptions) and node betweenness (for large disruptions), best captures node criticality. Nodes with high weighted degree and betweenness should therefore be given higher priority to enhance connectivity and resilience in urban street systems. Regarding link criticality, roads with higher capacities showed a more important role as opposed to betweenness, flow, and congestion.

     

Modeling Capacity Reliability of Minor Roads at At-Grade Un-Signalized Intersections for Potential Performance Evaluation

Abstract

Given stochastic features of the demands on both the major road and the minor road at an at-grade un-signalized intersection, the capacity of the minor road is viewed as the vulnerable and critical part impacting on the overall capacity of the intersection. To facilitate the analysis of intersection performance reliability, the capacity reliability of the minor road is defined as the probability that the capacity of the minor road can accommodate a certain traffic demand at a certain degree of saturation. The headway distribution of traffic stream on major road is reflected by three types of distributions, namely, exponential distribution, shifted exponential distribution, and Cowan's M3 distribution. Based on field observations, the volumes on both major roads and minor roads are treated as correlated normal random variables. This paper presents the methods for modeling capacity reliability of the minor road at an at-grade un-signalized priority intersection. A method based on first-order reliability method is used to model the capacity reliability index. As important associated factors of capacity reliability analysis, the methods for modeling and analyzing capacity sensitivity of the minor road and reserve capacity of the priority intersection are also presented. A procedure for evaluating the intersection potential performance using capacity reliability, sensitivity and reserve capacity is developed and demonstrated with a numerical example. Finally, some new findings from the case studies are summarized.     

Development of a transit network from a street map database with spatial analysis and dynamic segmentation

This paper presents an integrated transit-oriented travel demand modeling procedure within the framework of geographic information systems (GIS). Focusing on transit network development, this paper presents both the procedure and algorithm for automatically generating both link and line data for transit demand modeling from the conventional street network data using spatial analysis and dynamic segmentation. For this purpose, transit stop digitizing, topology and route system building, and the conversion of route and stop data into link and line data sets are performed. Using spatial analysis, such as the functionality to search arcs nearest from a given node, the nearest stops are identified along the associated links of the transit line, while the topological relation between links and line data sets can also be computed using dynamic segmentation. The advantage of this approach is that street map databases represented by a centerline can be directly used along with the existing legacy urban transportation planning systems (UTPS) type travel modeling packages and existing GIS without incurring the additional cost of purchasing a full-blown transportation GIS package. A small test network is adopted to demonstrate the process and the results. The authors anticipate that the procedure set forth in this paper will be useful to many cities and regional transit agencies in their transit demand modeling process within the integrated GIS-based computing environment.     

The treatment of uncertainty in the dynamic origin–destination estimation problem using a fuzzy approach

Regardless of existing types of transportation and traffic model and their applications, the essential input to these models is travel demand, which is usually described using origin–destination (OD) matrices. Due to the high cost and time required for the direct development of such matrices, they are sometimes estimated indirectly from traffic measurements recorded from the transportation network. Based on an assumed demand profile, OD estimation problems can be categorized into static or dynamic groups. Dynamic OD demand provides valuable information on the within-day fluctuation of traffic, which can be employed to analyse congestion dissipation. In addition, OD estimates are essential inputs to dynamic traffic assignment (DTA) models. This study presents a fuzzy approach to dynamic OD estimation problems. The problems are approached using a two-level model in which demand is estimated in the upper level and the lower level performs DTA via traffic simulation. Using fuzzy rules and the fuzzy C-Mean clustering approach, the proposed method treats uncertainty in historical OD demand and observed link counts. The approach employs expert knowledge to model fitted link counts and to set boundaries for the optimization problem by defining functions in the fuzzification process. The same operation is performed on the simulation outputs, and the entire process enables different types of optimization algorithm to be employed. The Box-complex method is utilized as an optimization algorithm in the implementation of the approach. Empirical case studies are performed on two networks to evaluate the validity and accuracy of the approach. The study results for a synthetic network and a real network demonstrate the robust performance of the proposed method even when using low-quality historical demand data.     

Consistent formulation of network equilibrium with stochastic flows

Traffic flows in real-life transportation systems vary on a daily basis. According to traffic flow theory, such variability should induce a similar variability in travel times, but this “internal consistency” is generally not captured by existing network equilibrium models. We present an internally-consistent network equilibrium approach, which considers two potential sources of flow variability: (i) daily variation in route choice and (ii) daily variation in origin–destination demand. We particularly aspire to a flexible formulation that permits alternative statistical assumptions, which allows the best fit to be made to observed variability data in particular applications. Joint probability distributions of route—and therefore link—flows are derived under several assumptions concerning stochastic driver behavior. A stochastic network equilibrium model with stochastic demands and route choices is formulated as a fixed point problem. We explore limiting cases which allow an equivalent convex optimization problem to be defined, and finally apply this method to a real-life network of Kanazawa City, Japan.     

Maintenance optimization for transportation systems with demand responsiveness

We present a quadratic programming framework to address the problem of finding optimal maintenance policies for multifacility transportation systems. The proposed model provides a computationally-appealing framework to support decision making, while accounting for functional interdependencies that link the facilities that comprise these systems. In particular, the formulation explicitly captures the bidirectional relationship between demand and deterioration. That is, the state of a facility, i.e., its condition or capacity, impacts the demand/traffic; while simultaneously, demand determines a facility’s deterioration rate. The elements that comprise transportation systems are linked because the state of a facility can impact demand at other facilities. We provide a series of numerical examples to illustrate the advantages of the proposed framework. Specifically, we analyze simple network topologies and traffic patterns where it is optimal to coordinate (synchronize or alternate) interventions for clusters of facilities in transportation systems.     

Network design: selection and design of links and facility location

In this paper we introduce new network design problems. A network of potential links is given. Each link can be either constructed or not at a given cost. Also, each constructed link can be constructed either as a one-way or two-way link. The objective is to minimize the total construction and transportation costs. Two different transportation costs are considered: (i) traffic is generated between any pair of nodes and the transportation cost is the total cost for the users and (ii) demand for service is generated at each node and a facility is to be located on a node to satisfy the demand. The transportation cost in this case is the total cost for a round trip from the facility to each node and back. We will consider two options in regard to the links between nodes. They can either be two-way only, or mixed, with both two-way and one-way (in either direction) allowed. When these options are combined with the two objective functions, four basic problems are created. These problems are solved by a descent algorithm, simulated annealing, tabu search, and a genetic algorithm. Extensive computational results are presented.     

Basic concepts and future directions of road network reliability analysis

The stability of road networks has become an increasingly important issue in recent times, since the value of time has increased considerably and unexpected delay can results in substantial loss to road users. Road network reliability has now become an important performance measure for evaluating road networks, especially when considering changes in OD traffic demand and link flow capacity over time. This paper outlines the basic concepts, remaining problems and future directions of road network reliability analysis. There are two common definitions of road network reliability, namely, connectivity reliability and travel time reliability. As well, reliability analysis is generally undertaken in both normal and abnormal situations. In order to analyse the reliability of a road network, the reliability of the links within the network must be first determined. A method for estimating the reliability of links within road networks is also suggested in this paper.     

Multicriteria evaluation on accessibility‐based transportation equity in road network design problem

This paper investigates the performance of accessibility‐based equity measurements in transportation and proposes a multiobjective optimization model to simulate the trade‐offs between equity maximization and cost minimization of network construction. The equity is defined as the spatial distribution of accessibilities across zone areas. Six representative indicators were formulated, including GINI coefficient, Theil index, mean log deviation, relative mean deviation, coefficient of variation, and Atkinson index, and incorporated into an equity maximization model to evaluate the performance sensitivity. A bilevel multiobjective optimization model was proposed to obtain the Pareto‐optimal solutions for link capacity enhancement in a stochastic road network design problem. A numerical analysis using the Sioux Falls data was implemented. Results verified that the equity indicators are quite sensitive to the pattern of network scenarios in the sense that the level of equity varies according to the amount of overall capacity enhancement as well as the assignment of improved link segments. The suggested multiobjective model that enables representing the Pareto‐optimal solutions can provide multiple options in the decision making of road network design. Copyright © 2012 John Wiley & Sons, Ltd.     

Traffic signal timing problems with environmental and equity considerations

Traffic signal timings in a road network can not only affect total user travel time and total amount of traffic emissions in the network but also create an inequity problem in terms of the change in travel costs of users traveling between different locations. This paper proposes a multi‐objective bi‐level programming model for design of sustainable and equitable traffic signal timings for a congested signal‐controlled road network. The upper level of the proposed model is a multi‐objective programming problem with an equity constraint that maximizes the reserve capacity of the network and minimizes the total amount of traffic emissions. The lower level is a deterministic network user equilibrium problem that considers the vehicle delays at signalized intersections of the network. To solve the proposed model, an approach for normalizing incommensurable objective functions is presented, and a heuristic solution algorithm that combines a penalty function approach and a simulated annealing method is developed. Two numerical examples are presented to show the effects of reserve capacity improvement and green time proportion on network flow distribution and transportation system performance and the importance of incorporating environmental and equity objectives in the traffic signal timing problems. Copyright © 2013 John Wiley & Sons, Ltd.     

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.     

Effects of queue spillover in networks considering simultaneous departure time and route choices

This paper explores the effects of queue spillover in transportation networks, in the context of dynamic traffic assignment. A model of spatial queue is defined to characterize dynamic traffic flow and queuing formation in network links. Network users simultaneously choose departure time and travel route to minimize the travel cost including journey time and unpunctuality penalty. Using some necessary conditions of the dynamic user equilibrium, dynamic network flows are obtained exactly on some networks with typical structure. Various effects of queue spillover are discussed based on the results of these networks, and some new paradoxes of link capacity expansion have been found as a result of such effects. Analytical and exact results in these typical networks show that ignoring queuing length may generate biased solutions, and the link storage capacity is a very important factor concerning the performance of networks.     

Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts to constrain link flows to capacity. Capacity constrained models with residual queues are often referred to as quasi-dynamic traffic assignment models. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a first order node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in general transportation networks. This model includes a first order (steady-state) node model that yields more realistic turn capacities, which are then used to determine consistent capacity constrained traffic flows, residual point (vertical) queues (upstream bottleneck links), and path travel times consistent with queuing theory. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques to find a solution. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks.     

Transport Network Design Problem under Uncertainty: A Review and New Developments

This paper aims to provide a state-of-the-art review of the transport network design problem (NDP) under uncertainty and to present some new developments on a bi-objective-reliable NDP (BORNDP) model that explicitly optimizes the capacity reliability and travel time reliability under demand uncertainty. Both are useful performance measures that can describe the supply-side reliability and demand-side reliability of a road network. A simulation-based multi-objective genetic algorithm solution procedure, which consists of a traffic assignment algorithm, a genetic algorithm, a Pareto filter, and a Monte-Carlo simulation, is developed to solve the proposed BORNDP model. A numerical example based on the capacity enhancement problem is presented to demonstrate the tradeoff between capacity reliability and travel time reliability in the NDP.     

Adaptive traffic signal control with equilibrium constraints under stochastic demand

This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters’ route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.     

A reliability‐based network design problem

This paper presents a reliability‐based network design problem. A network reliability concept is embedded into the continuous network design problem in which travelers' route choice behavior follows the stochastic user equilibrium assumption. A new capacity‐reliability index is introduced to measure the probability that all of the network links are operated below their capacities when serving different traffic patterns deviating from the average condition. The reliability‐based network design problem is formulated as a bi‐level program in which the lower level sub‐program is the probit‐based stochastic user equilibrium problem and the upper level sub‐program is the maximization of the new capacity reliability index. The lower level sub‐program is solved by a variant of the method of successive averages using the exponential average to represent the learning process of network users on a daily basis that results in the daily variation of traffic‐flow pattern, and Monte Carlo stochastic loading. The upper level sub‐program is tackled by means of genetic algorithms. A numerical example is used to demonstrate the concept of the proposed framework.     

Planning for the unexpected: The value of reserve capacity for public transport network robustness

Public transport networks (PTN) are subject to recurring service disruptions. Most studies of the robustness of PTN have focused on network topology and considered vulnerability in terms of connectivity reliability. While these studies provide insights on general design principles, there is lack of knowledge concerning the effectiveness of different strategies to reduce the impacts of disruptions. This paper proposes and demonstrates a methodology for evaluating the effectiveness of a strategic increase in capacity on alternative PTN links to mitigate the impact of unexpected network disruptions. The evaluation approach consists of two stages: identifying a set of important links and then for each identified important link, a set of capacity enhancement schemes is evaluated. The proposed method integrates stochastic supply and demand models, dynamic route choice and limited operational capacity. This dynamic agent-based modelling of network performance enables to capture cascading network effects as well as the adaptive redistribution of passenger flows. An application for the rapid PTN of Stockholm, Sweden, demonstrates how the proposed method could be applied to sequentially designed scenarios based on their performance indicators. The method presented in this paper could support policy makers and operators in prioritizing measures to increase network robustness by improving system capacity to absorb unexpected disruptions.