Showing papers in "Transportation Research Part B-methodological in 1986"

A model for the structure of lane-changing decisions

Abstract: A structure is proposed to connect the decisions which a driver has to make before changing lanes. The model is intended to cover the urban driving situation, where traffic signals, obstructions and heavy vehicles all exert an influence. The structure is designed to ensure that the vehicles in traffic simulations behave logically when confronted with situations commonly encountered in real traffic. The specific mathematical expression of the questions embedded in the decision process and employed in the present implementation of the model are not critical and can be replaced by alternatives, but the heirarchy of the decisions is crucial. On the basis of experience to date, the lane changing model produces a realistic simulation of driver behaviour and has proved very robust under a wide range of conditions.

Bus network design

Abstract: This paper describes the bus network design problem, summarizes the different approaches that have been proposed for its solution and proposes a new approach incorporating some of the positive aspects of prior work. The proposed approach is intended to be easier to implement and less demanding in terms of both data requirements and analytical sophistication than previous methods. An algorithm is presented that can be used to design new bus routes taking account of both passenger and operator interests; however, this algorithm focuses on only a single component of the overall bus operations planning process described in this paper.

A heuristic algorithm for the multi-vehicle advance request dial-a-ride problem with time windows

Abstract: In this paper we describe a heuristic algorithm, Advanced Dial-A-Ride with Time Windows (ADARTW), for the advance-request version of the multi-vehicle, many-to-many Dial-A-Ride Problem (DARP) with service quality constraints. DARP is concerned with developing a set of routes for a fleet of vehicles carrying customers between specified origins and destinations. “Many-to-many” means that each customer can have a distinct origin and destination, while “advance-request” means that all the requests are received well before the time of vehicle dispatching. Finally, “service quality constraints” guarantee that (1) customers’ ride times will not exceed a prespecified maximum and (2) the time of pick-up or delivery of customers will not deviate from the most-desired pick-up or delivery time of these customers by more than pre-specified amounts (“the time windows”). The algorithmic approach to be described is interesting for two reasons. First, it addresses what is probably the most applicable and realistic version of the real-world problem in a way that avoids excessive abstraction and simplification and emphasizes flexibility and convenience to the algorithm’s user. Second, it can generate at low computation cost what are apparently high-quality solutions to much larger problems (e.g. 2500 customers and 30 simultaneously active vehicles) than have hitherto been attempted. Many North American systems serving elderly and handicapped passengers require reservations a day in advance, while in other cases return trips may be scheduled as immediate requests. This second scenario can also be handled with an extension of the algorithm presented in this paper. The DARP was first examined by Wilson et al. (1971, 1976, 1977) in connection with the development of real-time algorithms for the Dial-A-Ride systems of Haddonfield, NJ, and Rochester, NY. ADARTW derives some of its fundamental concepts (building tours through sequential insertion of customers, general form of the objective function) from that work. A paper by Roy et al. (1983) which appeared as this paper was being completed also uses similar concepts and solves essentially the same version of DARP. Hung et al. (1982) have been tackling the same problem but have adopted an entirely different approach involving processing (scheduling and routing) one vehicle at a time rather than all vehicles simultaneously, as is done by ADARTW. Psaraftis (1983a) has developed a dynamic programming algorithm for solving the single-vehicle DARP optimally for a small number of customers in the presence of time windows, and Solomon (1983) has recently published an excellent review of the vehicle routing problem (not DARP) with time-window constraints. Descriptions of several versions of DARP without time-window constraints can be found

Multicommodity, multimode freight transportation: A general modeling and algorithmic framework for the service network design problem

Abstract: We examine the freight transportation problem which occurs when the same authority controls and plans both the supply of transportation services (modes, routes, frequencies for the services and classification, consolidation, transfer policies for terminals) and the routing of freight. We present a general modeling framework, based on a network optimization model, which may be used to assist and enhance the tactical and strategic planning process for such a system. The problem is solved by means of an algorithm, described in some detail, based on decomposition and column generation principles. We also present detailed results on the behaviour and performance of the algorithm, as observed during experimentation with a specific rail application.

Experiments with departure time choice dynamics of urban commuters

Abstract: A modeling framework is presented for investigating the dynamic properties of a system of commuters located along a highway facility. The day-to-day evolution of the time-dependent user departure patterns and associated system performance are investigated in a series of simulation experiments. User departure time decisions are modeled through the use of simple heuristics, including mechanisms to incorporate the experience accumulated through repeated use of the facility. The performance of the facility given the users' decisions is obtained from a special-purpose macroscopic traffic simulation model. Alternative user choice rules and learning models are explored as to their effect on system performance and its dynamic properties.

A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows☆

Abstract: In transportation planning, a large class of problems is characterized by multiple levels of decision making. Examples include selection of links for capacity improvements (network design), pricing of freight transportation services and traffic signal setting. In each of these problems, government or industry officials make one set of decisions, which seek to improve the network’s performance. At another level, users make choices with regard to route, mode, origin-destination, etc. Although the responses of users to a given improvement can be predicted, their decisions cannot be dictated. For example, officials choose locations for network improvements, and drivers then choose whatever routes they perceive to be best. Likewise, freight carriers determine shipment rates and transit times, and shippers choose the best mode of shipment. In this paper, we show how to formulate such problems as bilevel programming models, and propose solution algorithms for evaluation. For the transportation network design problem, we show that this model can be solved exactly for networks with a few hundred nodes. The general form of a bilevel program is

Prediction of intercity freight flows i. theory

Abstract: This paper presents the conceptual framework for a predictive network equilibrium model of a freight transportation system in which the generation, distribution, modal split and assignment of freight movements are performed simultaneously. A neoclassical profit maximization model is stated for the supply-side of the transportation market, the demand-side is represented by a spatial price equilibrium model, and the economic mechanism which integrates the supply and demand submodels is described. The theoretical limitations imposed on the model by the requirement that it be capable of solving large-scale problems are also addressed.

Prediction of intercity freight flows, II: Mathematical formulations

Abstract: This paper presents alternative mathematical representations of the predictive intercity freight model developed by Harker and Friesz (1986). A nonlinear complementary formulation is developed and is then used to develop criteria for the existence and uniqueness of a solution to this model. A variational inequality formulation of the model is also developed, and its relationship to an equivalent optimization problem is demonstrated.

Design of multiple-vehicle delivery tours i. a ring-radial network

Abstract: Certain aspects of what is commonly described as the “Vehicle Routing Problem” are discussed. We wish to deliver items to a large number of points randomly distributed over some region by means of vehicles, each of which can deliver to only C points. The key to any detailed routing to minimize the cost of delivery (by hand or computer) is first to partition the region into zones in which individual vehicles make deliveries. We assume here that there are many such zones, an average density of points δ, that the “unit of length” δ -1/2 is large compared with the spacing between roads, and C ⪢ 1. To minimize the delivery cost, zones should be approximately rectangular in shape with a width comparable with δ -1/2 and length comparable with C δ -1/2 . In order to illustrate some numerical methods of approximation, we will first analyze, in considerable detail, the routing of vehicles on an idealized ring-radial network including how one would distort the shape of the zones near the origin and at boundaries. In Part II we will generalize this to other network geometries, and in Part III consider modifications in strategy if the items (people, for example) are valuable. In contrast with presently available computer programs for which the accuracy may decrease with increasing number of points in the region, the methods described here are essentially asymptotic approximations; the more points there are in the region, the more accurate are the results.

Design of multiple-vehicle delivery tours ii. other metrics

Abstract: The methods described in Part I for a ring-radial metric are generalized to a network having a fine nearly rectangular grid of local roads, but possibly with a few fast roads superimposed. To select delivery zones, one should first draw the equi-travel-time contours from the source and then choose nearly rectangular zones with suitable width and orientation relative to the network grid and the local contour lines. Some illustrations are given for an idealized square grid of roads. In this case the rectangular delivery zones should be oriented at 45° to the grid, perpendicular to the contour lines.

A flexible gravity-opportunities model for trip distribution

Abstract: This paper develops a flexible gravity-opportunities model for trip distribution in which standard forms of the gravity and opportunities models are obtained as special cases of a general opportunities (GO) model. Hence the question of choice between gravity or opportunities approaches is decided empirically and statistically by restrictions on parameters which control the global functional form of the trip distribution mechanism. The test for the gravity model is shown to be equivalent to a test of the IIA axiom where alternatives are destinations. The notational dichotomy between the two approaches is resolved by employing ordered trip matrices and transformations to permit row and column sum constraints to be applied. These constraints, often interpreted in various ways, are treated as normalisation terms and are therefore not strictly part of the form of the model. Doubly constrained, singly constrained and unconstrained versions of both models are developed throughout. A key step in the integration is the specification of an opportunity function which has as arguments destination-attribute variables such population, income or some other measure of opportunities and generalized cost/impedance-type variables relating origin and destination. This device obviates the mutual exclusiveness ordinarily required of these two sets of variables. The opportunity function is incorporated into a general proportionality factor which is defined by the difference in functions of cumulative opportunities; the latter are subjected to a convex combination of direct and inverse Box-Cox transformations. Different values of the parameters controlling these transformations generate contrasting families of models, notably the exponential and logarithmic intervening opportunities models and the gravity model. All models are shown to be embedded in a transformed triangular region over which likelihood function, response surface or simultaneous confidence interval contours may be plotted. These generalised gravity-opportunity concepts are applied to two well-known models: direct demand multimodal travel demand models, and the estimation of the OD matrix from link volumes. The second case is estimated empirically and here it is shown that a significant improvement is obtained over the gravity model, which is rejected, along with the logarithmic intervening opportunity model, in favour of a more general direct opportunities version.

A review of models for the temporal distribution of peak traffic demand

Abstract: The existing models for predicting the temporal distribution of peak traffic demand are reviewed in this paper. Based on their assumptions and concepts, the models are classified into three groups as follows: deterministic user equilibrium (DUE), stochastic user equilibrium (SUE) and system optimum (SO). The merits and weaknesses of each group are discussed with regards to the validity of their assumptions and computational problems associated with them. Most of the models were developed for the single origin-destination pair with simple network system which is an oversimplification of a practical problem involving multiple origin-destination pairs with complex network systems. This is a major limitation when considering the application of the existing models to real life problems. Directions for future research are then proposed.

Optimum polar networks for an urban bus system with a many-to-many travel demand

Abstract: The spacing and headway configuration of a bus system comprising a series of ring and radial routes which minimizes travel time is found by the use of the calculus of variations. A many-to-many travel demand is described by a continuous function of the positions of a commuter's home and workplace. It is assumed that buses travel at a constant speed and are subject to a fleet size constraint. Under optimal conditions it is found that both spacing between routes and headway between buses should be inversely proportional to the cube root of the proportion of commuters joining and leaving the route. A simple numerical example is worked in which homes and workplaces are independently and uniformly distributed.

Time-dependent queueing at road junctions: Observation and prediction

Abstract: Measurements of queue lengths and vehicle delays have been used to test the predictions of time-dependent queueing models. Observations were made at eight public road sites for a number of peak periods at each site. In all, sixty-eight peaks were studied. The model predictions of the time-dependent trials-average queues and delays agreed with the observations within the limits set by day-to-day variability for seven of the sites, but for the eighth there was consistent overprediction.

A mathematical model for headway variance of fixed-route buses

Abstract: A mathematical model for computing and analysing headway variance of fixed-route buses offering scheduled service is developed. The model assumes a situation where both the passengers' OD pattern and the bus-route structure do not have any particular form but the number of passengers served at any bus station is a stationary Poisson process. Basic probability concepts are mostly used in deriving the model. Innovations in the model are the inclusion of a skip probability at a stop and the correlation factors between successive bus loads at a loading point and between the travel times of successive buses on a link. The model is, therefore, applicable to a wider range of situations than was possible with the earlier models. Results indicate that bus loading conditions and traffic conditions along the route are the major factors responsible for headway variability. The developed model can be used to determine the relative importance of these factors on headway variance at individual stopping station and thereby simplify the task of evolving effective countermeasures in any given situation. A numerical example that illustrates the application of the model is also given.

The capacity of a priority intersection

Abstract: We present simple formulae for the maximum capacity of an intersection of a single stream of minor traffic with a single stream of major (priority) traffic. The method allows for both mixed (nonhomogeneous) vehicle types and for inconsistent driver behaviour in the minor traffic stream. For a realistic class of major headway distributions the capacity is the harmonic mean of the capacities for each individual vehicle type. The formulae include generalisations of Tanner's formula for the cases of inconsistent and/or nonhomogeneous minor vehicles.

Optimum zone structure during peak periods for existing urban rail lines

Abstract: The problem of optimizing the service along an existing two-track rail line by adopting a zone-stop schedule during the peak periods is investigated. A dynamic programming technique is employed to determine the number of zones, the stations that belong to each zone, the headway between trains to the same zone and the fleet size. The general objective of the analysis is to minimize the total transportation cost, defined as the sum of the costs of time to the passengers and the relevant rail capital and operating costs. The optimization problem is subject to several constraints including avoidance of train conflicts, limitations on the value of the headway and an available fleet size. The applicability of the model is demonstrated through a numerical example using field data.

A note on endogenous variables in household vehicle utilization equations

Abstract: This paper presents an empirical analysis of the statistical bias resulting from the endogeniety of vehicle specific attributes in econometric models of household vehicle utilization. Using data from a recent U.S. household survey, both corrected and uncorrected vehicle utilization models are estimated. A comparison of these estimation results reflects the substantial bias in model coefficients, price elasticities and income elasticities that can result if the endogeneity of vehicle specific attributes is not considered.

Computational comparisons of algorithms for general asymmetric traffic equilibrium problems with fixed and elastic demands

Abstract: In this note we compare the computational efficiency of projection and relaxation methods for the solution of the asymmetric traffic equilibrium problem with elastic demands with their computational efficiency for the fixed demand problem. In particular, we tested networks with three different classes of travel cost and travel disutility functions. Our experiments suggest that the form of the travel cost and disutility functions affects not only the relative efficiencies of these two methods but also their overall efficiencies.

Delay processes at unsignalised junctions : the interrelation between geometric and queueing delay

Abstract: The interrelation between geometric delay—the delay caused by the need for isolated vehicles to slow down to negotiate a junction—and the queueing delay due to vehicle-vehicle interactions is considered. The delay elements present in measurements of geometric delay are identified, and some overlap is seen with those normally included in the service mechanisms in queueing models. The total delay per vehicle is not, therefore, the sum of the measured geometric delay and the queueing delay. Although the geometric delay can be redefined so as to eliminate the overlap, it is not then measurable. A framework is developed in which the relationships between the “pure” and measured geometric delay and the queueing delay are expressed for the population mean values. Approximate expressions are developed for the elements of delay. The framework is extended to allow queueing delays to be represented by time-dependent functions allowing approximately for non-randomness in arrival and departure patterns and service time differences between queueing and non-queueing vehicles. Numerically, geometric delay elements constitute a significant proportion of total delay except at traffic intensities approaching unity. In this region time-dependent effects dominate the queueing process.

Gravity models with multiple objectives— Theory and applications

Abstract: The gravity model has been widely used to predict trip matrices in transportation planning both as a descriptive and an optimizing model In this paper we present multiobjective programming formulations of the gravity model The models use the concept of entropy, both as a measure of interactivity in the system, and as a distance measure, for measuring the distance from a reference or target point suggested by the planner We also present gravity model formulations which do not require consistent estimates for the demand and supply in the different sites These relaxed multiobjective gravity models include objectives for the demands and supplies, where the distance from some a priori given values is measured in entropy terms The use of the models is illustrated on 1975 census data from the county of Oestergoetland, Sweden (Author/TRRL)

Extreme value methods for estimating road traffic capacity

Abstract: Common sense suggests that, at any point on a road network, there is an absolute limit to the volume of traffic which can be carried. But previous attempts to measure this “limiting capacity” have met with difficulties. First, there may not be enough vehicles to saturate the section of road under observation. Second, the flow may be constrained by a bottleneck upstream or downstream. Third, even under favourable conditions, the flows actually observed at saturation point tend to vary over a wide range, giving little clear indication as to what the value of the limiting capacity might be. In this paper, consideration is given to the variations in flow which occur over a time during normal traffic conditions, and to the characteristics of the extreme values which occur from time to time under these conditions. Two distinct types of statistical theory can be applied to extreme values. First, one can apply straight- forward probability theory, to predict the largest flows likely to be observed during a given period, assuming an idealised traffic stream with a known flow counting distribution. Second, one can attempt to deduce an upper limit from observed flow data using asymptotic methods of the kind which are frequently used in connection with meteorological and flood defense problems. Both methods are applied to a sample of 9000 flow values recorded at a site in London. Both methods are shown to fit the data reasonably well, but only the asymptotic method reveals a clear upper limit. Possible applications of the method are briefly discussed.

Design of multiple-vehicle delivery tours—III valuable goods

Abstract: For the delivery of valuable goods (such as people in a van pool), we assume that it costs cv per unit time during a round trip time of a vehicle and it costs cu/C per unit time for each of C items being delivered only during the travel time from the source to the point of delivery. The objective is to design delivery routes so as to minimize the (expected) total cost of delivery in some region containing N ⪢ C delivery points. With nearly rectangular shaped delivery zones for each vehicle route it is shown that if cu/2 cv, however, one should deliver only on the outbound leg and deadhead back from the far end of the zone. In each case there is an optimal width and orientation of the rectangular zone relative to the local grid of roads and the travel-time contours from the source.

On the definition of traffic equilibrium

Abstract: Three alternative definitions of traffic equilibrium are compared in terms of the mechanisms of route-choice inherent in them These definitions are the usual Wardrop equilibrium and user-optimised ones and a new one Conditions on the cost function are established under which the Wardrop definition is equivalent to each of the other two Some circumstances are identified in which these conditions are satisfied A detailed discussion is given of an example in which these conditions are not satisfied and the three definitions are not equivalent

The effect of omission of variables on choice model transferability

Abstract: The transferability of disaggregate choice models has received considerable attention in recent years. Past studies observe varying levels of model transferability but do not characterize the conditions which lead to high or low levels of transferability. Differences in transferability appear to arise due to a variety of differences in the characteristics of the estimation and application contexts and the specification of the model used. This paper reports an investigation into the effect of omission of relevant explanatory variables on the level of transfer effectiveness. The relationship between variable omission and its impact on estimation and prediction is analytically formulated. An empirical analysis of transferability among three sectors within an urban area is undertaken to verify and clarify the analytical results. The analytic and empirical investigations indicate that inclusion of relevant variables leads to an absolute improvement in transfer effectiveness which is approximately proportional to the improvement in goodness of fit which is obtained by the corresponding specification improvement in the application environment.

Multidimensional choice model transferability

Abstract: Transferability studies have focused on the component models of the conventional four-step urban travel forecasting model system. This study extends previous analyses by examining the transferability of models describing multidimensional travel and related choices. In particular, we examine the hypothesis that joint and sequential choice models are equally transferable against the alternative hypotheses that either of the model types is more transferable. Measures of goodness of fit and transfer effectiveness are formulated for sequential choice models to provide a consistent comparison between the joint and sequential models. An empirical analysis is undertaken in the context of joint (multinomial logit) and sequential (nested logit) models of automobile ownership and mode choice to work. This study finds little difference between the transferability of these joint and sequential models. However, this conclusion appears to be dependent on the similarity of the estimation results for the joint and sequential models in this case. These results suggest a need for additional testing in other empirical contexts to identify the relative transferability of joint versus sequential models when the estimation results are distinct.

Dynamic forecasting of urban shopping travel demand

Abstract: A time-dependent model for commercial activity location and travel demand is developed based on the assumptions that instantaneous interzonal shopping travel demand can be described by a gravity formulation, whereas the incremental individual zonal retail space allocations are such that they maximize the aggregate, net resulting profit from retail sales. Over time, link travel costs are updated as a function of the current link volumes, whereas commercial space development costs are updated as a function of current zonal activity levels. Constraints on commercial space allocation are at the individual zonal level, as well as at the aggregate level of the overall area. The objective function for the corresponding mathematical program is then linearized, and the model programmed for implementation using a linear programming routine. The results of several simulations illustrate the dynamic impacts various urban development policies have on commercial activity location. In particular, periodic oscillations in zonal activity levels, as well as sudden changes in the spatial pattern of interzonal shopping travel, may appear for certain model parameter values. Several directions for future refinement of the model, including inclusion of economic variables and interaction with other urban activities, are discussed in conclusion.

A comparison of heuristics for a school bus scheduling problem

Abstract: The study was carried out in North carolina to identify which procedure gave good bus schedules for realistically sized problems using a reasonable amount of computer time, so that multiple runs with parameter changes were economically possible. The main objective is to combine trips to minimise the size of the required fleet and travel costs. The three heuristics used were 'assmt', 'orl', and 'ilp' and were used on a group of 30 sample problems from actual bus data gathered from 113 routes and 15 schools with 10 distinct opening times. Results suggested that each of the heuristics could provide good schedules. However, although significantly faster, assmt appeared to produce some combinations needing manual adjustment. Although icp provided consistently good solutions, it required a large linear programming package, and could give non integer solutions. Feasible combinations were generated by orl, but it required the largest amount of computer time and often gave inferior solutions. It is suggested that for trips of 200 or more the potential savings in capital costs could not justify the use of ilp and orl, at the same time, the manual adjustments required by assmt could be excessive. (TRRL)

An analytical method for aircraft collision risk estimation

Abstract: Transportation system safety is difficult to assess, particularly when examining future systems that are unlike existing systems. The absence of consensus concerning safety metrics and associated mathematical techniques inhibits implementation of improvements. One method for assessing safety was recently applied to assess new air traffic control procedures. The method contains several steps, including use of a collision risk model. The model uses probability theory to assess collision risk between aircraft due to random deviations from course. Techniques that recognize human monitoring and intervention to avoid collisions must be combined with the model to obtain absolute values of risk. Examples of model application are presented, together with a discussion of model limitations and use.

Numerical simulation of transient bulk queues with general vehicle dispatching strategies

Abstract: Relatively simple iterative procedures are developed for simulating the queue length distribution for transient bulk arrival, bulk service queues The method allows the study of holding strategies where the length of time a vehicle is held can depend on both the length ofthe queue and how long the vehicle has been held The system is modeled in discrete time, and a series of numerical experiments are presented that examine the errors introduced by this discretization