A dynamic stochastic assignment model for the analysis of general networks

The paper adopts the framework employed by the existing dynamic assignment models, which analyse specific network forms, and develops a methodology for analysing general networks. Traffic conditions within a link are assumed to be homogeneous, and the time varying O-D travel times and traffic flow patterns are calculated using elementary relationships from traffic flow theory and link volume conservation equations. Each individual is assumed to select a departure time and a route by trading off the travel time and schedule delay associated with each alternative. A route is considered as reasonable if it includes only links which do not take the traveller back to the origin. The set of reasonable routes is not consistant but depends on the time that an individual decides to depart from his origin. Equilibrium distributions are derived from a Markovian model which describes the evolution of travel patterns from day to day. Numerical simulation experiments are conducted to analyse the impact of different work start time flexibilities on the time dependent travel patterns. The similarity between link flows and travel times obtained from static and dynamic stochastic assignment is investigated. It is shown that in congested networks the application of static assignment results in travel times which are lower than the ones predicted by dynamic assignment.     

Comparison of results of two models of transportation demand in Hong Kong: CDAM and a version of microTRIPS

CDAM is a new computer program for solving the combined trip distribution and assignment model for multiple user classes, which enables transport planners to estimate consistent Origin-Destination (O-D) matrices and equilibrium traffic flows simultaneously if the trip production and attraction of each user class at zone centroids are available. This paper reports an application of CDAM to the central Kowloon study area in Hong Kong. The coefficients of the model related to the components of generalized costs are calibrated on 1986 travel data. A comparison of results of CDAM and a version of MicroTRIPS models of transportation demand in Hong Kong are presented. Finally, some conclusions are drawn and the advantage of the CDAM are discussed.     

Estimating origin-destination matrices from roadside survey data

The purpose of this study is to develop a valid and efficient method for estimating origin-destination tables from roadside survey data. Roadside surveys, whether conducted by interviews or postcard mailback methods, typically have in common the sampling of trip origin and destination information at survey stations. These survey stations are generally located where roads cross “screenlines,” which are imaginary barriers drawn to intercept the trip types of interest.Such surveys also include counts of traffic volumes, by which the partial origin-destination (O-D) tables obtained at the different stations can be expanded and combined to obtain the complete O-D table which represents travel throughout the entire study area. The procedure used to expand the sample O-D information from the survey stations must recognize and deal appropriately with a number of problems:

• 1.(i) The “double counting” problem: Long-distance trips may pass through more than one survey station location; thus certain trips have the possibility of being sampled and expanded more than once, leading to a potentially serious overrepresentation of long-distance trips in the complete expanded trip table.
• 2.(ii) The “leaky screenline” problem: Some route choices, particularly those using very lightly traveled roads, may miss the survey stations entirely, leading to an underestimation of certain O-D patterns, or to distorted estimates if such sites are arbitrarily coupled with actual nearby station locations.
• 3.(iii) The efficient use of the data: There is a need to adjust expansion factors to compensate for double counting and leaky screenlines. How can this be accomplished such that all of the data obtained at the stations are used without loss of information?
• 4.(iv) The consequences of uncertainty and unknown travel behavior: Since the O-D data and other sampled variables are subject to random error, and since in general the probability of encountering a long-distance trip at some survey stations is affected by traveler route-choice behavior, which is not understood, the sample expansion procedure must rely on the use of erroneous input data and questionable assumptions. The preferred procedure must minimize, rather than amplify, the effects of such input errors.

Here, five alternate methods for expanding roadside survey data in an unbiased manner are proposed and evaluated. In all cases, it is assumed that traveler route choice generally follows the pattern described by Dial's multipath assignment method. All methods are applied to a simple hypothetical network in order to examine their efficiency and error amplification properties. The evaluation of the five methods reveals that their performance properties vary considerably and that no single method is best in all circumstances. A microcomputer program has been provided as a tool to facilitate comparison among methods and to select the most appropriate expansion method for a particular application.     

Road pricing: The right solution for the right problem?

Road-pricing theory asserts that the optimal speed of a road network is that where vehicles pay the marginal social cost of their journey, rather than an average private cost if no price is imposed. This paper aims to show that this is misconceived. In big congested cities, the running speed of the road network is set by the direct journey speed achieved on the appropriate mass-transit network, both within and to the city centre. After dividing by the appropriate route factors to convert running speed to direct speed and allowing for access to convert kerb-to-kerb to door-to-door speed, the average direct journey speeds by car are identical to those on the mass-transit system for equivalent journeys when there is suppressed demand for car travel. Road pricing should thus be seen, not as a tool for increasing road speeds, which it cannot do whilst sufficient suppressed demand exists, but as a tool for estimating the socially desirable demand level on the roads as opposed to on the mass-transit systems. Road speeds in big, congested cities can only be increased by increasing the direct speeds of the mass-transit systems. Methods of achieving such increases are discussed.     

Interactions between driver information,route choice,and optimal signal timing on a simple network

The interaction between driver information, route choice, and optimal traffic signal settings was investigated using a simple two-route system with a single “T” intersection and a fixed O-D demand. The logit model and the method of successive averages (MSA) were used to calculate the route choice probabilities and the stochastic equilibrium assignment. Given an assignment, signal settings which minimized average intersection delay were calculated; flow reassignment and new optimal signal settings were then obtained and this iterative process continued until convergence. The calculations were performed either directly in a combined assignment/signal optimization model or in stages using the output flows of an assignment model as inputs to TRANSYT-7F and iterating between the two models. Results show that a unique joint signal timing/assignment equilibrium is reached in all cases provided that a certain precision in drivers' perceptions is not reached. If driver information increases to this precision (bifurcation point) and beyond, results show clearly that the unique joint signal timing/assignment equilibrium no longer exists. In fact, three joint equilibria points exist after the bifurcation point. Two of these points are stable and one is not. It was found that the system yields the lowest total intersection delay when the joint equilibrium is such that all traffic and hence the major part of green time is assigned to only one of the two routes. Although this may not be feasible to implement in practice, the results indicate clearly for this simple example that there is a trade-off between a system with minimum total delay but no unique joint signal-settings/assignment equilibrium (achieved when drivers have nearly perfect information about the system) and a system with a unique joint equilibrium but with higher total delay (achieved when drivers have reasonably good but somewhat limited information). In most cases the second system seems appropriate for a number of practical reasons.     

Speed,travel time and delay for intersections and road segments in the Montreal network using cyclist Smartphone GPS data

Very little is known about cyclist speeds and delays at the disaggregate level of each road segment and intersection in an entire city network. Speeds and delays serve as vital information for planning, navigation and routing purposes including how they differ for different times of the day and across road and bicycle facility types, after controlling for other factors. In this work, we explore the use of recent GPS cyclist trip data, from the Mon RésoVélo Smartphone application, to identify different performance measures such as travel time, speed and delay at the level of the entire network of roads and intersections on the island of Montreal. Also, a linear regression model is formulated to identify the geometric design and built environment characteristics affecting cyclist speeds on road segments. Among other results, on average, segment speeds are greater along arterials than on local streets and greater along segments with bicycle infrastructure than those without. Incorporating different measures of cyclist personality in the models revealed that the following characteristics all affect cyclist speeds along segments, each cyclist’s average speed on uphill, downhill and level segments as well as geometric design and built environment characteristics. The model results also identify that the factors that increase cyclist speeds along segments include, segments which have cyclists biking for work or school related purposes, segments used during morning peak and segments which do not have signalized intersections at either end.     

A model for assessing the effects of dynamic travel time information via variable message signs

In view of the serious traffic congestion during peak hours in most metropolitan areas around the world and recent improvement of information technology, there is a growing aspiration to alleviate road congestion by applications of electronic information and communication technology. Providing drivers with dynamic travel time information such as estimated journey times on major routes should help drivers to select better routes and guide them to utilise existing expressway network. This can be regarded as one possible strategy for effective traffic management. This paper aims to investigate the effects and benefits of providing dynamic travel time information to drivers via variable message signs at the expressway network. In order to assess the effects of the dynamic driver information system with making use of the variable message signs, a time-dependent traffic assignment model is proposed. A numerical example is used to illustrate the effects of the dynamic travel time information via variable message signs. This revised version was published online in June 2006 with corrections to the Cover Date.     

A new algorithm for optimal signal control in congested networks

Optimization of traffic lights in a congested network is formulated as a linear programming problem. The formulation adapted here takes into account particular capacity constraints for road links and for intersections. A necessary prerequisite for the determination of optimal green times is that representative a-priori information about the origin-destination and route choice pattern inside the network is available. Because any particular control strategy temporarily alters the effective turning rates at intersections, an iterative procedure is proposed here which accomplishes convergence of optimal signal control and resulting O-D flows. The efficiency of this optimization procedure is demonstrated in a case study for a network with fifteen intersections.     

A new class of dynamic methods for the identification of origin-destination flows

A new systems dynamics approach for the identification of origin-destination (O-D) flows in a traffic system is presented. It is the basic idea of this approach that traffic flow through a facility is treated as a dynamic process in which the sequences of short-time exit flow counts depend by causal relationships upon the time-variable sequences of entrance flow volumes. In that way enough information can be obtained from the counts at the entrances and the exits to obtain unique and bias-free estimates for the unknown O-D flows without further a priori information. Four different methods were developed: an ordinary least squares estimator involving cross-correlation matrices, a constrained optimization method, a simple recursive estimation formula and estimation by Kalman filtering. The methods need only moderate computational effort and are particularly useful for tracking time-variable O-D patterns for on-line identification and control purposes. An analysis of the accuracy of the estimates and a discussion of the convergence properties of the methods are given. Finally, a comparison with some conventional static estimation procedures is carried out using synthetic as well as real data from several intersections. These tests demonstrated that the presented dynamic methods are highly superior to conventional techniques and produce more accurate results.     

Estimation of origin-destination matrices from link traffic counts on congested networks

Conventional methods for estimating origin-destination (O-D) trip matrices from link traffic counts assume that route choice proportions are given constants. In a network with realistic congestion levels, this assumption does not hold. This paper shows how existing methods such as the generalized least squares technique can be integrated with an equilibrium traffic assignment in the form of a convex bilevel optimization problem. The presence of measurement errors and time variations in the observed link flows are explicitly considered. The feasibility of the model is always guaranteed without a requirement for estimating consistent link flows from counts. A solution algorithm is provided and numerical simulation experiments are implemented in investigating the model's properties. Some related problems concerning O-D matrix estimation are also discussed.     

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.     

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.     

Should I stay or should I go? Investigating route switching behavior from revealed preferences data

A large variety of factors influence the route choice decisions of road users, and modelers consider these factors within the perceived utility that road users are assumed to maximize. However, this perceived utility may be different even for the same origin–destination pair and this leads road users to choose different routes for different trips. In this study, we focus on this particular phenomenon of route switching behavior by estimating discrete choice models with the aim of understanding the key factors at its foundation. The estimated route choice models account for route characteristics, socio-economic information, activity based data, inertial mechanism and learning effects, and they are applied to revealed preference data consisting of 677 actual day by day route choices (referred to 77 road users) collected by GPS in Cagliari (Italy). Route switching models were estimated with both fixed and random coefficient models. The model estimation results show that the variables referred to habit and learning have an important relevance on explaining the route switching phenomenon. Specifically, the higher is the travel habit, the less is the propensity of the road users to switch their route. Moreover, the learning effect shows that the accumulation of past experiences has more influence on the choice than the most recent ones.

     

Evaluating the benefits of a combined route guidance and road pricing system in a traffic network with recurrent congestion

When drivers do not have complete information on road travel time and thus choose their routes in a stochastic manner or based on their previous experience, separate implementations of either route guidance or road pricing cannot drive a stochastic network flow pattern towards a system optimum in a Wardropian sense. It is thus of interest to consider a combined route guidance and road pricing system. A road guidance system could reduce drivers' uncertainty of travel time through provision of traffic information. A driver who is equipped with a guidance system could be assumed to receive complete information, and hence be able to find the minimum travel time routes in a user-optimal manner, while marginal-cost road pricing could drive a user-optimal flow pattern toward a system optimum. Therefore, a joint implementation of route guidance and road pricing in a network with recurrent congestion could drive a stochastic network flow pattern towards a system optimum, and thus achieve a higher reduction in system travel time. In this paper the interaction between route guidance and road pricing is modeled and the potential benefit of their joint implementation is evaluated based on a mixed equilibrium traffic assignment model. The private and system benefits under marginal-cost pricing and varied levels of market penetration of the information systems are investigated with a small and a large example. It is concluded that the two technologies complement each other and that their joint implementation can reduce travel time more efficiently in a network with recurrent congestion.     

Quantifying the Difference Between Self-Reported and Global Positioning Systems-Measured Journey Durations: A Systematic Review

Accurate measurement of travel behaviour is vital for transport planning, modelling, public health epidemiology, and assessing the impact of travel interventions. Self-reported diaries and questionnaires are traditionally used as measurement tools; advances in Global Positioning Systems (GPS) technology allow for comparison. This review aimed to identify and report about studies comparing self-reported and GPS-measured journey durations. We systematically searched, appraised, and analysed published and unpublished articles from electronic databases, reference lists, bibliographies, and websites up to December 2012. Included studies used GPS and self-report to investigate trip duration. The average trip duration from each measure was compared and an aggregated, pooled estimate of the difference, weighted by number of trips, was calculated. We found 12 results from eight eligible studies. All studies showed self-reported journey times were greater than GPS-measured times. The difference between self-report and GPS times ranged from over-reporting of +2.2 to +13.5 minutes per journey. The aggregated, pooled estimate of the difference, weighted by number of trips, was over-report of +4.4 minutes (+28.6%). Studies comparing self-reported and GPS-measured journey duration have shown self-reported to be consistently over-reported across the study sample. Our findings suggest that when using self-reported journey behaviour, the journey durations should be treated as an over-estimation.     

An empirical study of simulation-based dynamic traffic assignment procedures

Abstract

Under Intelligent Transportation Systems (ITS), real-time operations of traffic management measures depend on long-term planning results, such as the origin–destination (OD) trip distribution; however, results from current planning procedures are unable to provide fundamental data for dynamic analysis. In order to capture dynamic traffic characteristics, transportation planning models should play an important role to integrate basic data with real-time traffic management and control. In this paper, a heuristic algorithm is proposed to establish the linkage between daily OD trips and dynamic traffic assignment (DTA) procedures; thus results from transportation planning projects, in terms of daily OD trips, can be extended to estimate time-dependent OD trips. Field data from Taiwan are collected and applied in the calibration and validation processes. Dynamic Network Assignment-Simulation Model for Advanced Road Telematics (DYNASMART-P), a simulation-based DTA model, is applied to generate time-dependent flows. The results from the validation process show high agreement between actual flows from vehicle detectors (VDs) and simulated flows from DYNAMSART-P.     

An equilibrium algorithm for the spatial aggregation problem of traffic assignment

Present traffic assignment methods require that all possible origins and destinations of trips taking place within a study area be represented as if they were taking place to and from a small set of points or centroids. Each centroid is supposed to represent the location of all trip-ends within a given zone, and this necessarily misrepresents points located at the edges of the zone.In order to alleviate this problem (which we refer to as the spatial aggregation problem) one could use smaller zones and more centroids, but existing traffic assignment algorithms cannot efficiently handle many centroids.This paper introduces an algorithm procedure which is designed to handle a substantially larger number of centroids. In the paper that follows, the technique is further developed to take into account a continuous distribution of population.     

A congested and dwell time dependent transit corridor assignment model

This research proposes an equilibrium assignment model for congested public transport corridors in urban areas. In this model, journey times incorporate the effect of bus queuing on travel times and boarding and alighting passengers on dwell times at stops. The model also considers limited bus capacity leading to longer waiting times and more uncomfortable journeys. The proposed model is applied to an example network, and the results are compared with those obtained in a recent study. This is followed by the analysis and discussion of a real case application in Santiago de Chile. Finally, different boarding and alighting times and different vehicle types are evaluated. In all cases, demand on express services tends to be underestimated by using constant dwell time assignment models, leading to potential planning errors for these lines. The results demonstrate the importance of considering demand dependent dwell times in the assignment process, especially at high demand levels when the capacity constraint should also be considered. Copyright © 2017 John Wiley & Sons, Ltd.     

Estimating time dependent O‐D trip tables during peak periods

Intelligent transportation systems (ITS) have been used to alleviate congestion problems arising due to demand during peak periods. The success of ITS strategies relies heavily on two factors: 1) the ability to accurately estimate the temporal and spatial distribution of travel demand on the transportation network during peak periods, and, 2) providing real‐time route guidance to users. This paper addresses the first factor. A model to estimate time dependent origin‐destination (O‐D) trip tables in urban areas during peak periods is proposed. The daily peak travel period is divided into several time slices to facilitate simulation and modeling. In urban areas, a majority of the trips during peak periods are work trips. For illustration purposes, only peak period work trips are considered in this paper. The proposed methodology is based on the arrival pattern of trips at a traffic analysis zone (TAZ) and the distribution of their travel times. The travel time matrix for the peak period, the O‐D trip table for the peak period, and the number of trips expected to arrive at each TAZ at different work start times are inputs to the model. The model outputs are O‐D trip tables for each time slice in the peak period. 1995 data for the Las Vegas metropolitan area are considered for testing and validating the model, and its application. The model is reasonably robust, but some lack of precision was observed. This is due to two possible reasons: 1) rounding‐off, and, 2) low ratio of total number of trips to total number of O‐D pair combinations. Hence, an attempt is made to study the effect of increasing this ratio on error estimates. The ratio is increased by multiplying each O‐D pair trip element with a scaling factor. Better estimates were obtained. Computational issues involved with the simulation and modeling process are discussed.     

On the variance of recurrent traffic flow for statistical traffic assignment

This paper generalizes and extends classical traffic assignment models to characterize the statistical features of Origin-Destination (O-D) demands, link/path flow and link/path costs, all of which vary from day to day. The generalized statistical traffic assignment (GESTA) model has a clear multi-level variance structure. Flow variance is analytically decomposed into three sources, O-D demands, route choices and measurement errors. Consequently, optimal decisions on roadway design, maintenance, operations and planning can be made using estimated probability distributions of link/path flow and system performance. The statistical equilibrium in GESTA is mathematically defined. Its multi-level statistical structure well fits large-scale data mining techniques. The embedded route choice model is consistent with the settings of O-D demands considering link costs that vary from day to day. We propose a Method of Successive Averages (MSA) based solution algorithm to solve for GESTA. Its convergence and computational complexity are analyzed. Three example networks including a large-scale network are solved to provide insights for decision making and to demonstrate computational efficiency.