Showing papers in "Transportation Research Part B-methodological in 1994"

The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory

Abstract: This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues. The easy-to-solve difference equations used to predict traffic's evolution are shown to be the discrete analog of the differential equations arising from a special case of the hydrodynamic model of traffic flow. The proposed method automatically generates appropriate changes in density at locations where the hydrodynamic theory would call for a shockwave; i.e., a jump in density such as those typically seen at the end of every queue. The complex side calculations required by classical methods to keep track of shockwaves are thus eliminated. The paper also shows how the equations can mimic the real-life development of stop-and-go traffic within moving queues.

Modeling and simulation of pedestrian traffic flow

Abstract: Questions about the efficiency and safety of pedestrian traffic systems are of major importance in the planning and design of such systems. As the use of functional—or performance-based—requirements becomes more popular, there is also an increasing need for methods and tools which can be used to evaluate if these functional requirements are met. This article presents a stochastic model based on the following assumptions: Any pedestrian facility can be modeled as a network of walkway sections. Pedestrian flow in this network can be modeled as a queueing network process, where each pedestrian is treated as a separate flow object, interacting with the other objects. Such a microscopic model is useful because it makes detailed modeling of human behavior possible. This article also presents a simulation tool, of which the main objective is to estimate the relevant performance measures of the pedestrian traffic system. The article includes two examples.

Computational-process modelling of household activity scheduling

Abstract: Models of households' travel choices are an important focus of research. For some time, it has been known that such models need to incorporate how travel depends on activity choices. It is argued that production system models constitute an alternative or necessary complementary approach if the goal is to develop models of interdependent activity and travel choices, or activity scheduling, which are based on behavioral science theories of higher cognitive processes. Several computational-process models (CPMs) which implement production systems as computer programs are reviewed. Currently, no encompassing CPM exists but some may be possible to integrate in a descriptive model of activity scheduling.

Traffic Assignment and Traffic Control in General Freeway-arterial Corridor Systems

Abstract: We consider a general traffic corridor consisting of two subsystems of a freeway network and a surface street network. The two systems are coupled by access ramps to provide multiple alternative routes for drivers from their origins to destinations. Each ramp can be metered to influence flow distributions in such a way that some system performance index (e.g. total travel time) is optimized, provided that each driver chooses an individual minimum cost route in response to any given ramp control. In this article we first present a bilevel programming formulation of the traffic assignment and traffic control problem in the traffic corridor system. The lower-level problem represents a traffic equilibrium model involving explicitly ramp queuing, which predicts how drivers will react to any given on-ramp control pattern. The upper-level problem is to determine ramp metering rates that optimize a system performance criterion, taking into account drivers' route choice behavior. We also present a sensitivity analysis for the queuing network equilibrium problem. Explicit expression of the derivatives of equilibrium link flows and equilibrium ramp queuing times with respect to ramp metering rates is derived. A heuristic algorithm, using the derivative information from the sensitivity analysis, is developed to solve the proposed bilevel on-ramp traffic control problem. A numerical example is provided to illustrate the bilevel control model and the solution algorithm.

A model and strategy for train pathing with choice of lines, platforms, and routes

Abstract: Train pathing is concerned with assigning trains and train times for a set of rail links, stations stops, etc., so as to meet a system of constraints on headways, trip times, dwell times, etc. while minimizing delays or costs and meeting travel demands. In a previous paper we presented a model, algorithms, and strategy for pathing trains of different speeds and stopping patterns for a double track rail line dedicated to trains in one direction. Here we extend this to more general more complex rail networks, with choice of lines, station platforms, etc, as is more typical of the high density scheduled passenger railways in Britain and Europe. We apply the model to a small network and find acceptable solution times. Applying addition search strategies from the previous paper should reduce solution times by further orders of magnitude. A previous paper (Carey & Lockwood, 1994) set out a model and algorithms for train pathing and planning. The basic model considered a line with multiple stations and multiple trains of different speeds, and with all trains on the line travelling in the same direction, as is usual on say British and European railways. Here, we extend the model to a more general network, introducing explicit choices among multiple lines in each direc- tion between stations (or other points), choice of platforms to use at stations, shared platforms, various types of intersections, trains in one or both directions, etc. We find that the model and algorithms from the previous paper extend very naturally to the present more complex rail context. Mathematical programming models and methods for train pathing have been devel- oped by Szpigel (1972), Sauder and Westerman (1983), Petersen, Taylor, and Martland (1986), Jovanovic and Harker (1991), Jovanovic (1989) and Kraay, Harker, and Chen (1988), and others. The last three papers appear to present the most general and most powerful models for train pathing to date. The approach in Kraay, Harker, and Chen is similar to that in Jovanovic and Harker, except that the former also considers the train acceleration/deceleration patterns and the effects these have on fuel consumption and hence on costs. We do not consider this here, partly because in Britain acceleration patterns are already largely determined by other considerations. The train pathing models just described focus on single track rail lines, with trains in both directions and meets and passes taking place at sidings located at intervals along the single line. We are concerned with more complex rail contexts, including general rail networks. The focus of the above research on single track corridors is appropriate for rail networks such as those in North America, which are mainly single track, long distance, low density freight railways. In Britain and Europe rail systems are mainly multi-track, shorter distance, higher density intercity passenger, or commuter networks. Headways are often tight, with a train every few minutes, and there is usually a choice of two or more unidrectional lines in each direction between stations. At stations there is often a choice of two or more "platforms" at which a train can stop for passengers to board or alight. Though such choices give managers some flexibility, they also introduce additional types of potential conflicts between trains. The conflicts are widespread and interdepen- dent, due to congestion, restrictions on line speeds and on dwell times, intersections, desired departure or arrival times, etc. However, some of the restrictions that make it

Exact local solution of the continuous network design problem via stochastic user equilibrium assignment

Abstract: The continuous Network Design Problem (NDP) deals with determining optimal expansions for the capacities of a street network, subject to the constraint that the street traffic volumes must be the outcome of a user-optimal equilibrium assignment. Although the use of deterministic equilibrium methods tends to produce computationally intractable problems, in this paper it is shown that a stochastic user equilibrium based on the logit model leads to a differentiable and large-scale, but tractable, version of the NDP. A procedure for computing the derivatives of the stochastic user equilibrium (SUE) assignment without having to first compute the route choice probabilities is given, and this procedure is coupled with two standard algorithms for solving nonlinear programs, the generalized reduced gradient method and sequential quadratic programming. These algorithms are tested on several example networks, and the results of these tests suggest that the SUE-constrained version of the NDP offers both a promising heuristic for solving DUE-constrained problems as well as a viable procedure in its own right.

Queue length and delay distributions at traffic signals

Abstract: Some new analytical results on statistical distributions of queue lenghts and delays at traffic signals are derived. For this purpose, the probability generating function of the queue length distribution is developed, from which the Laplace-transform of the delay distribution is obtained. A Poisson arrival process and fixed-time control are assumed. Similar techniques have successfully been employed to obtain the queue-length and delay distributions at priority intersections. Thus, a unified theory for both signalized and unsignalized intersections results.

Recursive estimation of time-varying origin-destination flows from traffic counts in freeway corridors

Abstract: This research presents a dynamic system model and its on-line estimation algorithm for time-varying freeway origin-destination (O-D) matrices. The proposed model employs information formation form mainline traffic counts, ramp flow measurements, and macroscopic traffic characteristics to construct a set of dynamic equations, which realistically consider the interrelations between O-D distributions and observed flows under congested conditions. To improve the operational efficiency necessary for real-time applications, a revised model with some approximation have also been developed. Due to the difficulty in acquiring the real-world data, the proposed model was evaluated with simulation experiments. The results of laboratory evaluation indicate that the proposed methods offers a promising direction for tackling this complex issue.

A linear programming approach for synthesizing origin-destination trip tables from link traffic volumes

Abstract: We present a nonproportional-assignment, user-equilibrium motivated, linear programming model for estimating origin-destination (O-D) trip tables from available data on link traffic volumes. The model is designed to determine a traffic equilibrium network flow solution that reproduces the link volume data, if such a solution exists. However, it recognizes that due to incomplete information, the traffic may not conform to an equilibrium flow pattern, and moreover, there might be inconsistencies in the observed link flow data. Accordingly, the model permits violations in the equilibrium conditions as well as deviations from the observed link flows but at suitable incurred penalties in the objective function. A column generation solution technique is presented to optimally solve the problem. This methodology is extended to the situation in which a specified prior target trip table is available and one is required to find a solution that also has a tendency to match this table as closely as possible. Implementation strategies are discussed and the proposed method is illustrated using some sample test networks from the literature.

Stochastic approximation to the effects of headways on knock-on delays of trains

Abstract: In train planning and timetabling, the trip time on each link is assumed to depend on the type of train and characteristics of the link, but is usually treated as independent of the time interval (headway) between trains. However, in practice trains are subject to delays from a variety of causes, and since normally they are not allowed to pass each other on a link, any delay to one train may cause “knock-on” delays to following trains. This is especially true of the high density double and multiple track railways in Britain and Europe. The shorter the scheduled headway between trains, the greater is the expected knock-on delay and hence the greater the expected trip times of following trains. We develop simple stochastic approximations to these knock-on train delays. To test and calibrate the approximations, we conduct detailed stochastic simulation of the interaction between trains as they traverse sections of the link. The approximate relationships that we derive between scheduled headways and knock-on delays can be used, for example, (a) to provide correction factors for other stochastic or deterministic models of train planning, dispatching, or control; (b) to adjust train timetables, which are currently produced without explicitly considering the expected knock-on effects, and (c) to make it feasible to conduct larger scale simulations of train networks, by reducing or removing the need to simulate behaviour within each link.

Extending a train pathing model from one-way to two-way track

Abstract: A train pathing model and algorithms for a rail network was presented and tested in a previous paper. There, it was assumed that each rail line has two or more tracks and each was dedicated to traffic in one direction as is usual in Europe. Here, we show how to adapt and extend that model and algorithms so as to handle trains on single line two-way track, as is usual in North America. Though introducing two-way track makes the formulation appear more complex, I show that somewhat surprisingly, (a) it does not increase the number of constraints or variables, including 0–1 variables, and (b) the model with two-way track should generally be easier to solve.

The equilibrium-based origin-destination matrix estimation problem

Abstract: This paper examines a model due to Nguyen for estimating origin-destination (O-D) matrices from observed traffic flows on each network link. It is shown that the previous bilevel optimization models for choosing an O-D matrix can be transformed into single convex programs. Under the condition that the observed link flow pattern is an equilibrium, Nguyen's model is demonstrated to be equivalent to an underspecified system of linear equations with non-negative variables. By exploiting the properties of the system's feasible region, simpler methods, such as a least squares technique, can be used to obtain an O-D matrix that, when user-optimally assigned to the network, reproduces the observed link flows.

The reaction time of drivers and the stability of traffic flow

Abstract: In this work, a condition for any traffic flow model is proposed: the consistency condition. An expression for the reaction time of drivers as a function of traffic density is derived from this condition. The changes introduced in the Payne model by the adoption of this expression for the reaction time are investigated. A comparison analysis of the resulting Payne model with others proposed by several authors and with the Simple Continuum Model is carried out. This analysis leads to the conclusion that the results of the Payne model are almost identical to those given by the Simple Continuum Model. Finally, the stability of traffic flow is studied by linearizing the Payne model and the car-following models modified by the adoption of the new formulation for the reaction time. The analysis shows that the inclusion of stochastic terms in the models would be necessary to explain instability phenomena in traffic flow.

A procedure for real-time signal control that considers transit interference and priority

Abstract: A rule-based procedure for determining real-time signals timings at a signalized intersection is described. It incorporates the effects of the traffic interference caused by on-line loading/ unloading of transit vehicles at the intersection. This procedure generates a number of short-term alternative real-time phase sequences for various levels of transit priority, based on a number of decision rules. It then evaluates these signal sequences and selects the one with the least overall cost to all traffic. The procedure is illustrated in terms of a simulated application to a critical intersection in Toronto's Queen Street corridor using real data. The preliminary simulation tests indicate the potential reduction in total compared to fixed-time operation, which results largely from selectively ushering transit vehicles to their loading positions at strategic times and serving cross-street traffic while the transit vehicles are loading.

An algorithm for the inflow control problem on urban freeway networks with user-optimal flows

Abstract: A successive linear optimization method is proposed to efficiently solve the on-ramp traffic control problem on urban freeway networks with user-optimal flows. A linear approximation of the implicit, nonlinear capacity constraint is formulated using the first-order derivatives of the link flows with respect to input on-ramp flows. The derivative information required for the algorithm is based on the theory of sensitivity analysis for network equilibrium problems. The performance of the algorithm is illustrated and compared with the previous iterative linear programming and assignment algorithm using numerical examples.

The demand for transport and communication in the United Kingdom and Australia

Abstract: This paper investigates the substitution/complementarity relationship among the demands for private transport, public transport and communication in the United Kingdom and Australia for the period 1960–1986. We use the Rotterdam Demand System for the analysis. The results identify major similarities and some important differences in consumption of these goods in the two countries. Further, they show that in both countries (a) private transport is a luxury and public transport is a necessity; (b) the demand for all three goods are price inelastic and (c) public transport, private transport and communications are pair-wise substitutes.

Pricing of track time in railroad operations: An internal market approach

Abstract: This paper presents a computable equilibrium model of an internal market for track resources in a railroad. The problem of estimating the value to each train of track capacity, which in turn is used to create the actual train schedules, is formulated as an N-player, noncooperative game with nondisjoint strategy sets. In this model, the effects of other traffic on a given train schedule (the mean and variance of total travel time) are represented by a line delay model for a scheduled railroad on a partially double track rail line. The generalized Nash equilibrium for the resulting game-theoretic model is found as a solution to a quasi-variational inequality problem. The goal of this model is to ascertain how close the prices from the internal market system (the game-theoretic model) comes to globally optimal prices. Data from a major Class I railroad are used to explore this issue in detail.

Maximum likelihood estimation of an origin-destination matrix from a partial registration plate survey

Abstract: Previous techniques for analysing partial registration plate data are firstly reviewed. These generally fall into one of two broad categories: statistically based methods for single origin, single destination problems; and simple-minded, deterministic approaches using vehicle passage time data ( i.e. , the times at which vehicles pass the observation points), for surveys with multiple origins and destinations. The present paper addresses the problem of finding a maximum likelihood estimator (MLE) of an origin-destination matrix and of journey time statistics—when passage time data are available, in the multiple origin/destination case. These estimators possess the well-known large sample properties of asymptotic unbiasedness, normality, and efficiency. The proposed approach also has the advantage over the deterministic methods (used in most existing registration plate matching packages) of simultaneously analysing all possible matches between all origins and destinations, rather than considering them in some arbitrary, priority order. Since the MLEs cannot be obtained analytically, alternative numerical techniques for determining them are evaluated, with respect to their convergence properties and computational efficiency. The most appropriate of these (based on a general-purpose statistical algorithm for “missing data” problems) is described in greater detail, including issues relevant to its computer implementation. Selected results from a more comprehensive simulation study are used to illustrate the performance of the maximum likelihood approach. In the (limited) results reported, the MLEs are seen to have considerably smaller mean square errors than the deterministic methods mentioned above, but are only marginally superior to the estimators produced by an efficient heuristic technique proposed previously by the author. Further empirical work would, however, be required to establish that the patterns observed in these simulations are examples of more general phenomena. Finally, possible extensions to the method and future research directions are discussed.

Traffic assignment in a congested discrete/ continuous transportation system

Abstract: Consider a city where all workplaces are concentrated in a highly compact central business district (CBD) and the commuters' homes are continuously dispersed over the residential area surrounding the CBD. The transportation facilities in the city comprise a discrete freeway network and a two-dimensional continuum of dense surface streets. The freeway network is assumed to be superimposed on the continuum and connected with it at a limited number of points (freeway ramps). During the morning peak-hours, the commuters traveling to work have a choice between two routes to the CBD: traveling along the minor access roads to enter the freeways and then proceeding along the freeway to the CBD, or using only minor street roads straight to the CBD. Given this transportation system, it is important to estimate the total trips using each freeway ramp and their spatial distribution. In this paper, an optimization model is developed to deal with this traffic assignment problem, provided that each commuter seeks to minimize his individual congested travel time. The model is formulated by intergrating the conventional network and continuum equilibrium models and its dual formation is derived. A dual-based solution method is developed using the finite element technique, and illustrated with a numerical example for a hypothetical city.

The potential for using fuzzy set theory in airline network design

Abstract: This paper develops a model to design an airline network and determine flight frequencies. The basic input data are the estimated numbers of passengers between pairs of cities. It is often impossible to estimate these numbers with enough precision (i.e. there is a degree of uncertainty surrounding the numbers of passengers between pairs of cities). Uncertainty is also frequent in the estimation of future airline carrier costs. The fuzzy set theory is an extremely convenient mathematical device with which to solve problems containing uncertainty, sujectivity, ambiguity and indetermination. Without aspiring to revolutionize airline netqork design, the basic goal of this paper is to present the fuzzy set tools and their potential application to a generic airline network design problem. The model developed is based on the fuzzy set theory. The first part of the model uses fuzzy logic to determine the route candidates to make the flights, and the second part of the model is based on fuzzy linear programming to determine flight frequencies on the route candidates. The model is supported by numerical examples.

Traffic jams and the congestion toll

Abstract: The theory of congestion tolls, in particular, the traffic jam, is developed. A dynamic model of traffic flow is presented that describes the formation and development of the traffic jam based on the theory of kinematic waves. I demonstrate the dynamic externality present when traffic is jammed. Furthermore, I obtained some results that differ from those based on the conventional approach: (a) the cost curve for travel on a long road does not include the backward-bending section that appears in the conventional approach; (b) I allow for traffic jams during optimal use of road.

Linear or nonlinear utility functions in logit models? The impact on German high-speed rail demand forecasts

Abstract: We have shown that nonlinearity of the representative utility functions of the Logit model applied to an intercity mode choice model implied the presence of asymmetry and of thresholds in the response curve, as well as results that had more reasonable properties (diminishing marginal values of time savings, elasticities and values of time that differed among the modes), and yielded very different high-speed rail market shares for Germany than results obtained with the usual linear utility functions.

An alternative formulation of d'este's trip assignment model

Abstract: An alternative formulation of D'Este's trip assignment model is given as a minimization problem of an objective functional. The equivalence to the origin formulation and uniqueness of the solution are proved. The minimization problem is first discretized by means of power series expansion, and then the Newtonian algorithm is employed to solve for the unknown coefficients of the series. An example is given to illustrate the effectiveness of the proposed method.

The instability of motorway traffic

Abstract: This paper presents an analysis of the dynamic behaviour of the motorway traffic system, in order to single out its characteristics that are responsible for instability. It is shown that, besides the parameters considered in the traditional car-following theory, a great importance in determining instability of a vehicle platoon is the amplitude spectrum of the speed function of the leader vehicle. The results obtained provide a theoretical validation of the reliability theory of motorway traffic, which was founded on experimental basis, and by which the probability of instability of a traffic stream can be experimentally measured.

Application of catastrophe theory to traffic flow variables

Abstract: This paper describes the results of the application of catastrophe theory to real traffic flow data. Using information from the Queen Elizabeth Way Freeway Traffic Management System (QEW FTMS), near Toronto, Ontario, Canada, it shows that catastrophe theory can be effectively applied to traffic flow. Following previous work done by Navin (1986) and Hall and others (1987; Dillon & Hall, 1988; Persaud & Hall, 1989; Forbes & Hall, 1990), this paper demonstrates how a transformation of variables and axes, including translation and rotation of the axes, is able to provide a good fit for a catastrophe theory model to traffic data. The paper also describes the criteria for the selection of the position of a new origin and the determination of the angle for rotating the axes.

Estimating an origin-destination table using a method based on shortest augmenting paths

Abstract: The most well-known origin-destination estimation methods involve entropy maximization or information minimization. However, these methods often require much more information than is available in reliable form, namely, target trip tables and the extent to which each origin-destination path uses each link. In this paper, a second version of the Shortest Augmenting Path Estimation method (SHAPE-2) is introduced, in which target trip tables and path use proportions are not required. In tests to date, SHAPE-2 has produced good results. It has demonstrated good sensitivity to changes in link loadings on small test networks and, on a real network of special interest to the authors, it performed better than any method previously applied.

An overlapping choice set model of automotive price elasticities

Abstract: This paper focusses on choice models in which individuals (a) determine which of the many available products are worthy of detailed consideration. We refer to the resulting smaller set of products as the individual's choice set; (b) choose among products in the choice set using a fairly simple logit model. The nested logit model (McFadden, 1978; 1983) is one common example of this model in which choice sets are mutually exclusive and collectively exhaustive. Unfortunately, there is strong empirical evidence suggesting that automobile buyers have overlapping choice sets. Thus, some buyers will consider both small and medium-sized cars whereas other buyers will consider both large and medium-sized cars. Hence, the nested logit model appears to unrealistically limit the allowable patterns of interproduct similarity. To avoid these problems, I allow choice sets to overlap but will restrict all choice sets to include the same number of products. As I describe, the resulting model is estimable with data on individual first and second choice preferences. We illustrate the model's utility by deducing demand-price elasticities for the automotive market.

Aggregation and heterogeneity of choice sets in discrete choice models

Abstract: Aggregation methods for making aggregate predictions from disaggregate discrete choice models have previously been developed and analyzed by several authors. The representative agent, classification, and statistical differentials methods are modified to account for heterogeneity of choice sets. An empirical analysis that makes comparisons between the adjusted and unadjusted methods is also provided. The results indicate that the adjusted methods produce much more accurate aggregate predictions than the unadjusted methods.

Swapping the order of scheduled services to minimize expected costs of delays

Abstract: In operating scheduled public transport services, by bus, train, or airline, any delay in the start time of one activity may cause “knock-on” delays to the next activity: for example, a train departure delay may delay the next train. In view of this, dispatchers and operators often have to decide whether delays and costs may be reduced by swapping the order of the delayed activities. We consider this decision problem here, with trains as an example. We analyse a minimal information model in which the only information about departure delays is the probability distribution of the “ready to depart” times. We show that in this case the optimal (cost minimizing) swapping policy usually reduces to one of two “bang-bang” policies: swap immediately or never swap. We develop simple heuristics for deciding which of these two policies is best. We also consider the effect of new or updated information about “ready to start” times becoming available as that time approaches, and extend this to a full information model in which the exact delays are known in advance. We discuss the application of these methods developed for pairs of trains to multiple trains and stations.

A note on “departure time and route choice for the morning commute”

Abstract: This note corrects a small but important error in the uniform portion of the socially optimal step toll derived by Arnott et al. (1990a). In particular, we show that this toll is actually a function of the values of travel time, early arrival time, and late arrival time (i.e., not just the value of travel time). In addition, we show that the toll needed to obtain the optimal route split in the presence of a time-varying step-toll is different from the one that is needed in the absence of any time-varying toll.