Showing papers in "Transportation Research Part B-methodological in 1995"

The cell transmission model, part ii: network traffic

Abstract: This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions. The method does not use ad hoc procedures to treat special situations. After a brief review of the basic model for one link, the article describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination (O-D) table is given and that the proportion of turns at every junction is known. These assumptions are reasonable for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times. For technical reasons explained in the text, the procedure is more complicated in this case, requiring more computer memory and more time for execution. The effort is estimated to be about an order of magnitude greater than for the static traffic assignment problem on a network of the same size. The procedure is ideally suited for parallel computing. It is hoped that the results in the article will lead to more realistic models of freeway flow, disaster evacuations and dynamic traffic assignment for the evening commute.

Requiem for second-order fluid approximations of traffic flow

Abstract: Although the “first order” continuum theory of highway traffic proposed by Lighthill and Whitham (1955) and Richards (1956)—the LWR model—can predict some things rather well, it is also known to have some deficiencies. In an attempt to correct some of these, “higher order” theories have been proposed starting in the early 70s. Unfortunately, the usefulness of these improvements can be questioned. This note describes the logical flaws in the arguments that have been advanced to derive higher order continuum models, and shows that the proposed high order modifications lead to a fundamentally flawed model structure. The modifications can actually make things worse. As an illustration of this, it is shown that any continuum model of traffic flow that smooths out all discontinuities in density will predict negative flows and negative speeds (i.e., “wrong way travel”) under certain conditions. Such unreasonable predictions are made by all existing models formulated as a quasilinear system of partial differential equations in speed, density, and (sometimes) other variables but not by the LWR model. The note discusses the available empirical evidence and ends with a (hopefully positive) commentary on what can be accomplished with first-order models.

A heteroscedastic extreme value model of intercity travel mode choice

Abstract: Estimation of disaggregate mode choice models to estimate the ridership share on a proposed new (or improved) intercity travel service and to identify the modes from which existing intercity travelers will be diverted to the new or upgraded service constitutes a critical part of evaluating alternative travel service proposals to alleviate intercity travel congestion. This paper develops a new heteroscedastic extreme value model of intercity mode choice that overcomes the ‘independence of irrelevant alternatives’ (IIA) property of the commonly used multinomial logit model. The proposed model allows a more flexible cross-elasticity structure among alternatives than the nested logit model. It is also simple, intuitive and much less of a computational burden than the multinomial probit model. The paper discusses the non-IIA property of the heteroscedastic extreme value model and presents an efficient and accurate Gaussian quadrature technique to estimate the heteroscedastic model using the maximum likelihood method. The multinomial logit, alternative nested logit structures, and the heteroscedastic model are estimated to examine the impact of improved rail service on business travel in the Toronto-Montreal corridor. The nested logit structures are either inconsistent with utility maximization principles or are not significantly better than the multinomial logit model. The heteroscedastic extreme value model, however, is found to be superior to the multinomial logit model. The heteroscedastic model predicts smaller increases in rail shares and smaller decreases in non-rail shares than the multinomial logit in response to rail-service improvements. It also suggests a larger percentage decrease in air share and a smaller percentage decrease in auto share than the multinomial logit. Thus, the multinomial logit model is likely to provide overly optimistic projections of rail ridership and revenue, and of alleviation in inter-city travel congestion in general, and highway traffic congestion in particular. These findings point to the limitations of the multinomial logit and nested logit models in studying intercity mode choice behavior and to the usefulness of the heteroscedastic model proposed in this paper.

On the functional form of the speed-density relationship—I: General theory

Abstract: In this work a functional form for the speed-density relationship is presented This functional form is made up of a nondimensional spacing, the equivalent spacing and of a function, the generating function, whose argument is the equivalent spacing This functional form is derived by means of two different arguments The first argument is based on the set of properties that the volume-speed-density relationships should satisfy The second one arises when applying a dimensional analysis to a generic car-following model Finally, several examples of generating functions are shown

Heuristic algorithms for the bilevel origin-destination matrix estimation problem

Abstract: Recently, a bilevel programming approach has been used for estimation of origin-destination (O-D) matrix in congested networks This approach integrates the conventional generalized least squares estimation model and the standard network equilibrium model into one process We extend this approach and develop a more general model and efficient heuristic algorithms to handle more realistic situation where link flow interaction cannot be ignored The extended model is formulated in the form of a bilevel programming problem with variational inequality constraints The upper-level problem seeks to minimize the sum of error measurements in traffic counts and O-D matrices, while the lower-level problem represents a network equilibrium problem formulated as variational inequalities, which guarantees that the estimated O-D matrix and corresponding link flows satisfy the network equilibrium conditions Two computational techniques are presented for solving the bilevel O-D matrix estimation model One is a heuristic iterative algorithm between traffic assignment and O-D matrix estimation and the other one is a sensitivity analysis based heuristic algorithm Properties of the two algorithms are analyzed theoretically and compared numerically with small network examples It is concluded that both algorithms can be used as efficient approaches for the bilevel O-D matrix estimation problems

A finite difference approximation of the kinematic wave model of traffic flow

Abstract: This article shows that if the kinematic wave model of freeway traffic flow in its general form is approximated by a particular type of finite difference equation, the finite difference results converge to the kinematic wave solution despite the existence of shocks in the latter. This result, which applies to initial and boundary condition problems with and without discontinuous data, is shown not to hold for other commonly used finite difference schemes. In the proposed approximation, the flow between two neighboring lattice points is the minimum of the two values returned by: 1. (a) a “sending” function evaluated at the density prevailing at the upstream lattice point and 2. (b) a “receiving” function evaluated at the downstream lattice point. The sending and receiving functions correspond to the increasing and decreasing branches of the freeway's flow-density curve. The article presents an asymptotic formula for the errors introduced by the proposed finite difference approximation and describes quantitatively the finite difference's shock-capturing behavior. Errors are shown to be approximately proportional to the mesh spacing with a coefficient of proportionality that depends on the wave speed, on its rate of change with density, and on the slope and curvature of the initial density profile. The asymptotic errors are smaller than those of Lax's first-order, centered difference method which is also convergent. More importantly though, the proposed procedure never yields negative flows, and this makes it attractive in practical engineering applications when the mesh cannot be made arbitrarily small.

An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems

Abstract: As a means to obtain a more accurate description of traffic flows than that provided by the basic model of traffic assignment, there have been suggestions to impose upper bounds on the link flows. This can be done either by introducing explicit link capacities or by employing travel time functions with asymptotes at the upper bounds. Although the latter alternative has the disadvantage of inherent numerical ill-conditioning, the capacitated assignment model has been studied and applied to a limited extent, the main reason being that the solutions can not be characterized by the classical Wardrop equilibrium conditions; they may, however, be characterized as Wardrop equilibria in terms of a well-defined, natural generalized travel cost. The introduction of link capacity side constraints makes the problem computationally more demanding. The availability of efficient algorithms for the basic model of traffic assignment motivates the use of dualization approaches for handling the capacity constraints. We propose and evaluate an augmented Lagrangean dual method in which the uncapacitated traffic assignment subproblems are solved with the disaggregate simplicial decomposition algorithm. This algorithm fully exploits the subproblem's structure and has very favourable reoptimization capabilities; both these properties are necessary for achieving computational efficiency in iterative dualization schemes. The dual method exhibits a linear rate of convergence under a standard nondegeneracy assumption. The efficiency of the overall algorithm is demonstrated through experiments with capacitated versions of well-known test problems, with the conclusion that the introduction of link capacities increases the computing times with no more than a factor of four. The introduction of capacities and the algorithm suggested can be used to derive tolls for the reduction of flows on overloaded links. The solution strategy can be applied also to other types of traffic assignment models where side constraints have been added in order to refine a descriptive or prescriptive assignment model.

Alternatives to Dial's logit assignment algorithm

Abstract: Two logit assignment methods for transportation networks are proposed as alternatives to Dial's algorithm. While retaining the absence of a need for the enumeration of paths, they dispense with both forward and backward passes. They, therefore, do not require minimum node-to-node cost information beforehand. Both methods admit loops and paths that are otherwise inefficient in the Dial sense, which can arise in practice as a result of driver searching behaviour. The first method considers a finite number of paths and the second method an infinite number of paths in the presence of loops. The absence of any efficiency constraint on the set of feasible paths makes the algorithms attractive for use in stochastic user equilibrium methods or in the approximation of a user equilibrium assignment through stochastic user equilibrium methods. The similarity of the structure of one of the proposed algorithms with that of the Floyd-Warshall shortest path algorithm would allow the two to be combined.

On the functional form of the speed-density relationship--ii: empirical investigation

Abstract: In this part we applied the theory developed in Part I. Some speed-density curves having the functional form proposed in Part I are fitted to traffic data. The goodness of fit is excellent, except in the case of the left lane detectors. A procedure for isolating stationary traffic periods is also explained. This procedure satisfactorily eliminates the dispersion of the individual measurements.

The household activity pattern problem: general formulation and solution

Abstract: The household activity pattern problem of analyzing/predicting the optimal path of household members through time and space as they complete a prescribed agenda of out-of-home activities is posed as a variant of the pickup and delivery problem with time windows. The most general case of the model includes provision for vehicle transfer, selective activity participation, and ridesharing options. A series of examples are solved using generic algorithms. The model is purported to remove existing barriers to the operationalization of activity-based approaches in travel behavior analysis.

Stochastic user equilibrium assignment in networks with queues

Abstract: A stochastic user equilibrium assignment algorithm is presented for steady state store-and-forward networks. The links of the network have constant travel times and the links or nodes have finite capacities. When capacity is reached, delay sufficient to match demand to the available capacity is generated. It has been shown by others that the equilibrium assignment in networks of this kind is the solution to a particular linear programming problem. By adding an entropy term to the objective function, a convex nonlinear programming problem is formed which yields a stochastic user equilibrium assignment. For the case of link constraints, it is proven that the Lagrange multipliers of both the linear and the non-linear programming problems give the equilibrium delays in the network. The requirements for uniqueness are investigated. Iterative algorithms are formulated for solving the nonlinear programming problem with either link or node constraints and convergence is proven. For networks where path enumeration is likely to be a problem, a column generation technique is proposed. An illustrative example is presented.

Properties of link travel time functions under dynamic loads

Abstract: This article examines a general form of link travel time functions considered in the dynamic traffic assignment literature and shows that it only makes some physical sense in the special case where each function denotes either a link with no spatial dimension containing a point queue or a link with constant travel time and no queueing. Roadway segments exhibiting both phenomena must be represented by two links in series.

A pareto optimum congestion reduction scheme

Abstract: This article shows that certain congestion reduction schemes have the potential for not penalizing anyone. The traditional social welfare approach is modified to address the distribution of gains and losses across the population. As a first step in this line of research, we consider a transportation system where congestion delay is simply given by a function of its user flow. We show that a particular pricing scheme with variable tolls, that can be viewed as hybrid between rationing and pricing, can benefit everyone (unlike pure pricing alone) even if the collected revenues are not returned to the population. The simple conditions under which this is possible are identified. Few data are needed to choose a beneficial policy. Examples are given.

Real-time scheduling of freight railroads

Abstract: This article presents a model for the optimization of freight trains schedules that is intended to be used as part of a real-time control system. The goal of this model is to provide a link between strategic schedules, which might be decided every month, and line dispatching or CAD models which need to know the scheduled arrival and departure times for each train at the ends of each lane at very frequent intervals. An algorithm for the problem along with an efficient heuristic are described and then tested on a portion of a major North American railroad to ascertain their efficiency and efficacy.

Road pricing and network equilibrium

Abstract: The paper presents a deterministic static equilibrium model for urban transport networks with elastic demand and capacity constraints. It is shown that this model may have no solution which satisfies the capacity constraints, but additional costs can be imposed on some network links so that an equilibrium solution that satisfies the capacity constraints always exists. These additional costs could be used as road pricing, in order to prevent traffic flow becoming unstable and/or producing unacceptable environmental damage. A method to calculate the additional costs is proposed and is used in a simple numerical example. The results so obtained are compared with the congestion tolls derived from the traditional economic theory.

Access: The transport-land use economic link

Abstract: The notion of access has evolved from a physical measure of trip interaction to a more economic concept associated with transport benefits. This paper follows the economic interpretation forward in order to understand the potentiality of access as a consistent economic link between the land use system and the transport system. Consistency is achieved in an economic approach based upon the argument that trips are made only if the benefit derived from making contact with other activities exceeds the transport generalized cost. This framework provides economic measures of access, as evidence of impact on origin and destination of trips, which can be calculated from the analysis of the transport system in some relevant cases. This paper analyses how to calculate measures of access from transport demand models and how to allocate transport benefits to the origin and destination activities. Finally, it describes the use of herein proposed access measures in land use-transport interaction modelling.

A model for the dynamic system optimum traffic assignment problem

Abstract: We describe a deterministic queueing assignment model which seeks to reduce total travel delays in a road traffic network by routeing drivers according to the total delay caused on each link (the local marginal delay). The model is approximate and is applicable to networks with many origin-destination pairs and many bottlenecks. Optimality of the solution determined by the model is discussed. It is particularly shown that, unlike in the steady state (Dafermos and Sparrow, 1969), reducing total travel times by using the local marginal delay will not generally result in an optimal solution. Results are provided for two networks.

A phenomenological model for dynamic traffic flow in networks

Abstract: A macroscopic model for dynamic traffic flow is presented. The main goal of the model is the real time simulation of large freeway networks with multiple sources and sinks. First, we introduce the model in its discrete formulation and consider some of its properties. It turns out, that our non-hydrodynamical ansatz for the flows results in a very advantageous behavior of the model. Next the fitting conditions at junctions of a traffic network are discussed. In the following sections we carry out a continuous approximation of our discrete model in order to derive stationary solutions and to consider the stability of the homogeneous one. It turns out, that for certain conditions unstable traffic flow occurs. In a subsequent section, we compare the stability of the discrete model and the corresponding continuous approximation. This confirms in retrospection the close similarities of both model versions. Finally we compare the results of our model with the results of another macroscopic model, that was recently suggested by Kerner and Konhauser [Phys. Rev. E 48, 2335–2338 (1993)].

Dynamic user optimal traffic assignment model for many to one travel demand

Abstract: A freeway or expressway corridor where all vehicles travel to the same destination such as the city centre is considered in this article, similar to the morning commute problem. A continuous time optimal control model that deals with the dynamic user optimal assignment for multiple origins and single destination is proposed. The splitting rates of traffic flows at each network node are defined as the control variables in this model. The optimality conditions are proved to be equivalent to the dynamic user optimal principle or user equilibrium of instantaneous travel cost. In order not to solve the complicated two-point boundary-value problem with substantial computational times for obtaining the optimal control solution, a steady state-costate solution algorithm is developed that generates an approximate solution to the network optimal control problem. This algorithm exploits advantage of the embedded network structure of the problem and would be computationally efficient. A numerical example with two peak period traffic demands which was drawn from the road network problem between Hong Kong and several adjacent cities of inland China is used to demonstrate the performance of the proposed algorithm.

Derivatives of the performance index for the traffic model from transyt

Abstract: This paper forms a starting point for the investigation of phase-based optimisation of signal timings for area traffic control. A conventional performance index, which is a weighted combination of delays of stops, is evaluated by the traffic model from the well-known stage-based procedure TRANSYT, but is considered here as a function of phase-based control variables, start and duration of green phases. In the paper, approximate expressions for the derivatives of performance index with respect to phase-based control variables are derived. The contribution from upstream, downstream and further downstream links and platoon dispersion are taken into account. The derivatives calculated from the expressions are compared with those from numerical differentiation using a trial network from Leicestershire as an example to illustrate the effectiveness of the formulae.

An equilibrium route choice model with explicit treatment of the effect of intersections

Abstract: This paper describes the implementation of a framework for incorporating detailed models of intersection operation into a user-optimal route choice model. It is assumed that signal settings are flow-responsive; this yields a combined route choice-intersection control problem, which is formulated as a non-separable network equilibrium problem with asymmetric cost functions. Such cost functions represent delays incurred by vehicles at intersections under various types of control (signalized, major/minor priority and all-way stop), and are based on an approach to capacity analysis widely used in traffic engineering practice, namely the methodologies of the 1985 Highway Capacity Manual and related amendments. The combined route choice-control problem is solved using a diagonalization algorithm; computational tests carried out on a real network indicate that the algorithm converges to a user equilibrium consistent with the control policy, despite violation of the sufficient conditions for convergence. The application also provides empirical evidence that the values of signal timing parameters, which are usually chosen solely on the basis of traffic engineering considerations, may have a substantial impact on the equilibration pattern. Finally, numerical experiments carried out to test the model for solution uniqueness suggest that ‘reasonably’ close equilibrium flow patterns arise starting from greatly different initial solutions. The modelling framework described in this paper could be typically applied in urban road networks for the assessment of alternative intersection control strategies, or, more generally, to carry out detailed traffic analyses and forecasts for the evaluation of TSM options.

Meuse: an origin-destination matrix estimator that exploits structure

Abstract: This article proposes an improvement of existing methods of origin-destination matrix estimation by an explicit use of data describing the structure of the matrix. These data can be obtained from parking surveys. The new model is applied on both illustrative and real examples, and the results are discussed. Comparisons with the results obtained with SATURN/ME2 and the generalized least-squares method are also presented.

Intermodal pricing using network flow techniques

Abstract: Traditional cost calculations do not accurately estimate the opportunity costs of using conveyances in intermodal operations, thus, results in many short-term pricing problems. The objective of this research is to develop a framework for estimating the opportunity costs of using conveyances in trailer-on-flatcar (TOFC) operations to assist carriers in improving their pricing strategies under highly competitive market conditions. The framework is based on a network model that simulates current operations in order to find the reduced costs and the opportunity costs of serving the loads. The network model is formulated as a linear network flow problem with side constraints. To find the reduced costs, a technique using Lagrangian Relaxation, a minimum cost algorithm, and a shortest path algorithm were developed in the research. We illustrate this model with a case study of a major north American railroad. The results show that opportunity costs do affect the accuracy of calculated system contributions for services. Moreover, the opportunity costs and system incremental costs (SICs) are unstable over time. To handle the instability we make use of a new risk-pricing approach.

On the functional form of the speed density relationship (ii)..

Abstract: In this part we applied the theory developed in Part I. Some speed-density curves having the functional form proposed in Part I are fitted to traffic data. The goodness of fit is excellent, except in the case of the left lane detectors. A procedure for isolating stationary traffic periods is also explained. This procedure satisfactorily eliminates the dispersion of the individual measurements.

A portfolio analysis of market investments in dry bulk shipping

Abstract: By considering a shipowner's financial commitments as investments, the development of a hedging strategy in shipping can be treated as a portfolio optimization problem. This is especially necessary now freight futures provide a comparatively novel medium for hedging risk in dry bulk shipping markets. Logical and useful results are produced by an empirical application of the Markowitz portfolio selection methodology to dry bulk shipping markets. The portfolios that the optimization process prescribes imply the potential power of freight futures as a tool for hedging risk in shipping. With greater acceptance of their role amongst decision makers in the industry, it is concluded that new patterns of chartering will emerge in the future and that traditional methods of appraising shipping investments, which take no account of portfolio risk, will become increasingly inadequate with greater interdependency between investment options.

Routing through dynamic ocean currents: general heuristics and empirical results in the gulf stream region

Abstract: Anticipating the availability of good quality ocean current data in the near future, we formulate the problem of routing an ocean vessel through currents to minimize fuel consumption, propose methods to increase the efficiency of the solution techniques, and simulate voyages to investigate the performance of our approach. We formulate the problem as a dynamic program (DP) with two variables: Heading and Power (H&P). We then develop two heuristics, Headingthen-Power (H/P) and Heading-Alone (HA), that reduce the complexity of the formulation by decomposing the heading optimization from the power-setting optimization. To improve computational efficiency, we propose three approaches based on ship and ocean current dynamics to limit the spatial and temporal ranges that must be investigated to solve our DP formulations. In our simulation study, these approaches reduced the spatial ranges by over one third and the temporal ranges by over 70%. The study simulated minimum fuel current routing of 96 voyages in the Gulf Stream region, leading to average fuel savings of 7.4% and 4.5% for eastbound and westbound voyages, respectively. Moreover, the simplest HA heuristic, which emphasizes heading over power optimization, provided solutions as good as those provided by the most complete H&P formulation while reducing the computational time by a factor of 40. This indicates that the shipping industry's practice of emphasizing heading considerations seems appropriate in the current routing case and that current routing implementations and algorithmic developments might be able to reduce problem complexity by concentrating on spatial variables at the expense of temporal variables.

Discrete choice with an oddball alternative

Abstract: A discrete choice model is presented that explicitly recognizes differences in the error structure associated with a single “oddball” alternative within the choice set that has properties not common to the other alternatives. The model purportedly resolves questions related to the use of alternative-specific variables in transportation choice models to capture the effects of attributes unique to a single travel alternative, such as “schedule frequency” in the case of modal choice between personal auto and public transit. The model, which shares the general error structure of multinomial logit, is shown to be a modification of a multinomial logit subchoice by terms involving the exponential integral. The model is shown to yield different results from those produced by an equivalent multinomial logit specification. Comparisons to multinomial probit and nested logit formulations are also made.

On deterministic developments of traffic stream models

Abstract: Classical deterministic (or “mechanical”) developments of traffic stream models from car-following models are criticized on the following basis The evaluation of the constant of integration for initial conditions corresponding to speed zero and headway equal to the reciprocal of jam density ignores large numbers of possibly relevant solutions of the underlying car-following model Some undesirable consequences, particularly the restriction to temporally and spatially constant flow conditions, of viewing traffic stream models as being deterministic consequences of car-following models are also noted It is suggested that an approach to traffic stream models via kinetic models possibly would be more appropriate and useful

Spatial aspects of traffic circulation: I. A review of alternative systems

Abstract: One of the key aims of traffic management is to encourage drivers to follow an efficient routing pattern (ie a set of routes that collectively minimise the potential for delays and accidents and possibly also minimise travel distance) At present, little is known about the relative merits of different patterns or how they could be accommodated or encouraged within existing city centre networks A number of archetypes are compared using total vehicle conflicts and total travel distance as the main criteria They include several that have not previously appeared in the literature, and, the conflicts are weighted to reflect variations in the severity of the interactions between vehicles carrying out different turning movements at junctions The results indicate wide variations in the characteristics of different routing patterns and suggest new ways of organising the spatial pattern of traffic circulation as possible alternatives to the conventional gyratory system

Spatial aspects of traffic circulation: II. Routing patterns that exactly minimise path crossings

Abstract: The total number of path crossings between vehicles following different routes on a road network can be taken as a rough proxy for congestion and accident risk. It is therefore useful to identify ways of routing traffic in the plane such that the numbers of crossings are minimised; these can serve as models for the design of traffic management schemes in urban areas. The authors have previously investigated a number of routing patterns; the best ones generated path crossings whose number exceeded a conjectured minimum by 33%. In this article, two configurations are put forward that achieve the minimum value. The networks required to support such routing patterns are probably not realisable in practice, but the exercise provides a useful insight into the traffic circulation problem and suggests a yardstick against which other routing patterns can be evaluated.