A Comparison of System Optimal and User Optimal Route Guidance.

The work described in this paper (carried out under the EC `DRIVE' programme) extends the simulations described in Working Paper 315, with the aim of studying the likely benefits to and reactions of drivers to system optimal (SO) route guidance - in particular, these effects are compared with those obtained under user optimal (UE) guidance. The model used is again one of a multiple user class equilibrium assignment, so that equipped drivers may be directed to more than one route per origin-destination movement. UE and SO guidance are compared, at different levels of equipped vehicles and demand levels, on the basis of the number of routes they recommend and the similarity of the flows on these routes, as well as link-based properties such as actual flows and queues resulting. These serve to demonstrate the extent to which the routes recommended under UE guidance serve as proxies to those under SO guidance. Secondly, a comparison is made of average (dis)benefits to guided drivers as well as the excess travel time incurred by individual equipped drivers in following SO, as opposed to UE guidance, in order to determine the extent of user sub-optimality of SO routing. Thirdly, input from a parallel DRIVE project, investigating user reactions to guidance information, is used to infer the extent to which drivers are likely to accept the sub-optimality of SO guidance, and the factors which are likely to influence their acceptance. Finally, some preliminary analysis is performed on combined strategies, which aim to strike a balance between the system benefits of SO guidance and the user benefits of UE routing

A Comparison of System Optimal and User Optimal Route Guidance.

The work described in this paper (carried out under the EC `DRIVE' programme) extends the simulations described in Working Paper 315, with the aim of studying the likely benefits to and reactions of drivers to system optimal (SO) route guidance - in particular, these effects are compared with those obtained under user optimal (UE) guidance. The model used is again one of a multiple user class equilibrium assignment, so that equipped drivers may be directed to more than one route per origin-destination movement. UE and SO guidance are compared, at different levels of equipped vehicles and demand levels, on the basis of the number of routes they recommend and the similarity of the flows on these routes, as well as link-based properties such as actual flows and queues resulting. These serve to demonstrate the extent to which the routes recommended under UE guidance serve as proxies to those under SO guidance. Secondly, a comparison is made of average (dis)benefits to guided drivers as well as the excess travel time incurred by individual equipped drivers in following SO, as opposed to UE guidance, in order to determine the extent of user sub-optimality of SO routing. Thirdly, input from a parallel DRIVE project, investigating user reactions to guidance information, is used to infer the extent to which drivers are likely to accept the sub-optimality of SO guidance, and the factors which are likely to influence their acceptance. Finally, some preliminary analysis is performed on combined strategies, which aim to strike a balance between the system benefits of SO guidance and the user benefits of UE routing

Route Guidance Algorithms Effective for All Levels of Take-Up and Congestion.

This paper describes work carried out under the EC `DRIVE' programme, the aim being to develop route guidance strategies which direct users to multiple routes between each origin-destination pair, and thereby provide stable and effective guidance even when a large proportion of drivers are guided. A model is proposed in which guided and unguided drivers have different route choice assumptions, but are still able to interact with one another; the guidance may be based on either user or system objectives. Conditions are deduced under which the resulting route pattern is guaranteed to exist and be stable. To assess the performance of the strategies, simulations are carried out on two real-life networks, for a number of different demand levels, levels of equipped vehicles, levels of error in (or adherence to) the guidance recommendations, and different guidance criteria. The simulations are extended, in order to examine firstly the influence of behaviour of unguided drivers on the benefits obtained, and secondly the performance of the strategies in cases of unforeseen variations in network conditions. Finally, some comparisons are drawn with a route guidance strategy developed in a parallel `DRIVE' project, where only one route is recommended per origin-destination pair

A Review of Models of Urban Traffic Networks (With Particular reference to the Requirements for Modelling Dynamic Route Guidance Systems)

This paper reviews a number of existing models of urban traffic networks developed in Europe and North America. The primary intention is to evaluate the various models with regard to their suitability to simulate traffic conditions and driver behavior when a dynamic route guidance system is in operation

The Dynamics and equilibria of day-to-day traffic assignment models

Traffic network modelling is a field that has developed over a number of decades, largely from the economics of predicting equilibria across route travel choices, in consideration of the congestion levels on those routes. More recently, there has been a growing influence from the psychological and social science fields, leading to a greater interest in understanding behavioural mechanisms that underlie such travel choice decisions. The purpose of the present paper is to describe mathematical models which aim to reflect day-to-day dynamic adjustments in route choice behaviour in response to previous travel experiences. Particularly, the aim is to set these approaches in a common framework with the conventional economic equilibrium models. Starting from the analysis of economic equilibria under perturbations, the presentation moves onto deterministic dynamical system models and stochastic processes. Simple illustrative examples are used to introduce the modelling approaches. It is argued that while such dynamical approaches have appeal, in terms of the range of adaptive behavioural processes that can be incorporated, their estimation may not be trivial. In particular, the obvious solution technique (namely, explicit simulation of the dynamics) can lead to a rather complex problem of interpretation for the model-user, and that more “analytical” approximation techniques may be a better way forward

A conceptual approach for estimating resilience to fuel shocks

We examine a conceptual approach to the estimation of resilience of transport systems to fuel shocks, i.e. a severe and long lasting reduction in the availability of fuel for motorised transport. Adaptive capacity is an element of resilience and is defined in the paper. There is currently no indicator of adaptive capacity of individuals in small geographies sensitive to a variety of policy measures, such as those affecting fitness, obesity, bicycle availability and bicycle infrastructure, whose impacts (at least in the short term) are on a smaller scale than large-scale land use and urban morphology change. We propose a conceptual approach for designing a method to quantify this indicator. The indicator shows the proportion of the population of areas who would have the capacity to commute to work principally by bicycle or walking following the shock. It assesses capacity grounded in current data and avoids as far as possible the need for speculation about the future. We believe this makes progress towards producing a good indicator with relatively un-controversial, transparent simplifying assumptions. The indicator can compare the resilience of different areas and can be updated over time

Optimal queue placement in dynamic system optimum solutions for single origin-destination traffic networks

The Dynamic System Optimum (DSO) traffic assignment problem aims to determine a time-dependent routing pattern of travellers in a network such that the given time-dependent origin-destination demands are satisfied and the total travel time is at a minimum, assuming some model for dynamic network loading. The network kinematic wave model is now widely accepted as such a model, given its realism in reproducing phenomena such as transient queues and spillback to upstream links. An attractive solution strategy for DSO based on such a model is to reformulate as a set of side constraints apply a standard solver, and to this end two methods have been previously proposed, one based on the discretisation scheme known as the Cell Transmission Model (CTM), and the other based on the Link Transmission Model (LTM) derived from variational theory. In the present paper we aim to combine the advantages of CTM (in tracking time-dependent congestion formation within a link) with those of LTM (avoiding cell discretisation, providing a more computationally attractive with much fewer constraints). The motivation for our work is the previously-reported possibility for DSO to have multiple solutions, which differ in where queues are formed and dissipated in the network. Our aim is to find DSO solutions that optimally distribute the congestion over links inside the network which essentially eliminate avoidable queue spillbacks. In order to do so, we require more information than the LTM can offer, but wish to avoid the computational burden of CTM for DSO. We thus adopt an extension of the LTM called the Two-regime Transmission Model (TTM), which is consistent with LTM at link entries and exits but which is additionally able to accurately track the spatial and temporal formation of the congestion boundary within a link (which we later show to be a critical element, relative to LTM). We set out the theoretical background necessary for the formulation of the network-level TTM as a set of linear side constraints. Numerical experiments are used to illustrate the application of the method to determine DSO solutions avoiding spillbacks, reduce/eliminate the congestion and to show the distinctive elements of adopting TTM over LTM. Furthermore, in comparison to a fine-level CTM-based DSO method, our formulation is seen to significantly reduce the number of linear constraints while maintaining a reasonable accuracy

Sensitivity analysis of optimal routes, departure times and speeds for fuel-efficient truck journeys

Embedded within the vehicle "routing" problem of determining the order in which customers are served, is the route choice problem of which sequence of roads to use between a pair of pick-up/drop-off locations, and this latter is the focus of the paper. When the objective is something other than travel time, such as fuel consumption, an additional control dimension is that of speed, and in a time-varying context the question of optimal speed determination is no longer a local one, due to potential downstream interactions. This also brings in the possibility to adjust departure times. Recently this problem, of joint route, departure time and speed determination for fuel minimization in a time-varying network, was shown to be efficiently solvable using a Space-Time Extended Network (STEN). In the present paper, we explore the sensitivity of the optimal solutions produced to: i) the fidelity of the within-day traffic information; ii) the currency of between-day traffic information in comparison with historical mean conditions; iii) the availability of historical information on variability for risk-averse routing; and iv) competition from other equally-optimal or near equally-optimal solutions. We set out the methods by which each of these tests may be achieved by adaptation of the underlying STEN, taking care to ensure a consistent reference basis, and describe the potential real-life relevance of each test. The results of illustrative numerical experiments are reported from interfacing the methods with real-time data accessed through the Google Maps API

Stabilisation strategy for unstable transport systems under general evolutionary dynamics

Stability of equilibria in transport systems has been discussed for decades. Even in deterministic cases, where stochasticity is ignored, stability is not a general property; a counterexample has been found in (within-day) dynamic traffic assignment problems. Instability can be a source of uncertainty of travel time and although pricing may stabilise an unstable transport system, pricing is not always acceptable to the public. This study aims to develop a pricing strategy that stabilises a transport system with minimum tolls. We show that with our stabilising pricing system tolls are bounded above and converge to zero when the error in estimation of a no-toll equilibrium converges to zero. We then show that the proposed toll scheme stabilises a wide range of evolutionary dynamics. We also propose a heuristic procedure to minimise the toll level. The procedure can also be viewed as a method of finding a possibly unstable equilibrium solution of a transport system. This suggests that, while we have not provided a rigorous proof, we may be able to find an equilibrium solution of any transport problem including problems which arise in dynamic traffic assignment (DTA); in these DTA cases, how to construct a solution algorithm that always converges to an equilibrium solution is still an open question. The methods proposed here will be extended so that they apply in more realistic behavioural settings in future work

Optimization of route choice, speeds and stops in time-varying networks for fuel-efficient truck journeys

A method is presented for the real-time optimal control of the journey of a truck, travelling between a pair of pick-up/drop-off locations in a time-varying traffic network, in order to reduce fuel consumption. The method, when applied during the journey, encapsulates the choice of route, choice of speeds on the links, and choice of stop locations/durations; when applied pre-trip, it additionally incorporates choice of departure time. The problem is formulated by using a modified form of space-time extended network, in such a way that a shortest path in this network corresponds to an optimal choice of not only route, stops and (when relevant) departure time, but also of speeds. A series of simple illustrative examples are presented to illustrate the formulation. Finally, the method is applied to a realistic-size case study