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

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

Pathways to achieving radically different urban walking and cycling futures in the UK by 2030

This paper builds upon earlier work which was presented at Walk21 in 2009 and 2010 which outlined the development of a number of radically different visions for the role of walking and cycling in urban areas in the year 2030. These visions, which were developed through consultation with a wide range of stakeholders, present a 2030 where walking and cycling play a significantly greater role in urban transportation than is currently the case, accounting for as much as 80% of urban trips in the most extreme vision. Previous reported work had focussed on the kinds of measures, contextual background and lifestyle changes which would be required to support such visions, how urban areas may appear and the practicalities of daily life. Subsequent research (not yet reported in the public domain) has developed methods for constructing pathways to show how these visions might be reached. A pathway (in a specific city) to the successful occurrence of a vision is defined as being made up of a combination of developments on two separate levels: a Macro level , involving both developments external to the transport system and developments within the transport system but “out of control” of the local authority of the city concerned ; and a Micro level, involving developments within the control of the city’s local authority. The trajectory of developments on a particular level is referred to as a ‘storyline’, so that a distinction is made between Macro - storylines and Micro- storylines. Whilst generic macro - storylines have been developed which are relevant to all UK cities, micro - storylines can only be constructed ‘locally’ by those with sufficient knowledge of a particular city. The focus of the current paper is upon two workshops carried out in the summer of 2011 in the UK cities of Leeds and Norwich. The main purpose of these workshops was to explore how one of the visions could be mapped/adapted to their specific local circumstances and to develop pathways for achieving this vision, taking into account three alternative macro - storylines. The workshops aimed to attract relatively senior people from the local authorities in each area and representatives of stakeholder groups . The workshop size was between 10 - 15 people. The underlying aim of such exercises is to encourage city authorities and stakeholders to think in a more structured, systematic way about how the various potentially -conflicting issues concerning walking and cycling would play out in a long - term future, taking into account that the ‘external environment’ (e.g. the national economy) is highly unpredictable. The paper presents the results from the Leeds and Norwich workshops in terms of the local visions and pathways that they produced. Special attention is paid to results concerned with policies that directly facilitate walking, whilst recognising that a large number of factors (all urban transport modes, land use patterns, ‘society’) have impacts (direct or indirect) on walking. Various conclusions are presented, both with regard to transport policy and the methodology for constructing the visions/pathways and running the workshops

Bryophytes of Uganda : 6., new and additional records, 3.

12 hepatics and 32 mosses are reported new to Uganda, 1 moss being also new to Africa, and 1 liverwort new to mainland Africa. Ectropothecium plumigerum (Broth.) Hedenäs is a new combination (basionym: Isopterygium plumigerum Broth.) with a new synonym Taxicaulis plumirameus Müll.Hal. nom. nud., and Taxiphyllum maniae (Renauld & Paris) M. Fleisch. is a new synonym of Taxiphyllum taxirameum (Mitt.) M.Fleisch. Three mosses are removed from the Uganda list

Brownian bridges to submanifolds

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold

Sensitivity analysis of the variable demand probit stochastic user equilibrium with multiple user classes

This paper presents a formulation of the multiple user class, variable demand, probit stochastic user equilibrium model. Sufficient conditions are stated for differentiability of the equilibrium flows of this model. This justifies the derivation of sensitivity expressions for the equilibrium flows, which are presented in a format that can be implemented in commercially available software. A numerical example verifies the sensitivity expressions, and that this formulation is applicable to large networks

Applications of sensitivity analysis for probit stochastic network equilibrium

Network equilibrium models are widely used by traffic practitioners to aid them in making decisions concerning the operation and management of traffic networks. The common practice is to test a prescribed range of hypothetical changes or policy measures through adjustments to the input data, namely the trip demands, the arc performance (travel time) functions, and policy variables such as tolls or signal timings. Relatively little use is, however, made of the full implicit relationship between model inputs and outputs inherent in these models. By exploiting the representation of such models as an equivalent optimisation problem, classical results on the sensitivity analysis of non-linear programs may be applied, to produce linear relationships between input data perturbations and model outputs. We specifically focus on recent results relating to the probit Stochastic User Equilibrium (PSUE) model, which has the advantage of greater behavioural realism and flexibility relative to the conventional Wardrop user equilibrium and logit SUE models. The paper goes on to explore four applications of these sensitivity expressions in gaining insight into the operation of road traffic networks. These applications are namely: identification of sensitive, ‘critical’ parameters; computation of approximate, re-equilibrated solutions following a change (post-optimisation); robustness analysis of model forecasts to input data errors, in the form of confidence interval estimation; and the solution of problems of the bi-level, optimal network design variety. Finally, numerical experiments applying these methods are reported