A General Stochastic Process for Day-to-Day Dynamic Traffic Assignment: Formulation, Asymptotic Behaviour, and Stability Analysis

This paper presents a general modelling approach to day-to-day dynamic assignment to a congested network through discrete-time stochastic and deterministic process models including an explicit modelling of users’ habit as a part of route choice behaviour, through an exponential smoothing filter, and of their memory of network conditions on past days, through a moving average or an exponentially smoothing filter. An asymptotic analysis of the mean process is carried out to provide a better insight. Results of such analyses are also used for deriving conditions, about values of the system parameters, assuring that the mean process is dissipative and/or converges to some kind of attractor. Numerical small examples are also provided in order to illustrate the theoretical results obtained

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

Dynamic Bayesian belief network to model the development of walking and cycling schemes

This paper aims to describe a model which represents the formulation of decision-making processes (over a number of years) affecting the step-changes of walking and cycling (WaC) schemes. These processes can be seen as being driven by a number of causal factors, many of which are associated with the attitudes of a variety of factors, in terms of both determining whether any scheme will be implemented and, if it is implemented, the extent to which it is used. The outputs of the model are pathways as to how the future might unfold (in terms of a number of future time steps) with respect to specific pedestrian and cyclist schemes. The transitions of the decision making processes are formulated using a qualitative simulation method, which describes the step-changes of the WaC scheme development. In this article a Bayesian belief network (BBN) theory is extended to model the influence between and within factors in the dynamic decision making process

Computation of Equilibrium Distributions of Markov Traffic-Assignment Models

Markov traffic-assignment models explicitly represent the day-to-day evolving interaction between traffic congestion and drivers' information acquisition and choice processes. Such models can, in principle, be used to investigate traffic flows in stochastic equilibrium, yielding estimates of the equilibrium mean and covariance matrix of link or route traffic flows. However, in general these equilibrium moments cannot be written down in closed form. While Monte Carlo simulations of the assignment process may be used to produce “empirical” estimates, this approach can be extremely computationally expensive if reliable results (relatively free of Monte Carlo error) are to be obtained. In this paper an alternative method of computing the equilibrium distribution is proposed, applicable to the class of Markov models with linear exponential learning filters. Based on asymptotic results, this equilibrium distribution may be approximated by a Gaussian process, meaning that the problem reduces to determining the first two multivariate moments in equilibrium. The first of these moments, the mean flow vector, may be estimated by a conventional traffic-assignment model. The second, the flow covariance matrix, is estimated through various linear approximations, yielding an explicit expression. The proposed approximations are seen to operate well in a number of illustrative examples. The robustness of the approximations (in terms of network input data) is discussed, and shown to be connected with the “volatility” of the traffic assignment process

Mechanisms that Govern how the Price of Anarchy varies with Travel Demand

Selfish routing, represented by the User-Equilibrium (UE) model, is known to be inefficient when compared to the System Optimum (SO) model. However, there is currently little understanding of how the magnitude of this inefficiency, which can be measured by the Price of Anarchy (PoA), varies across different structures of demand and supply. Such understanding would be useful for both transport policy and network design, as it could help to identify circumstances in which policy interventions that are designed to induce more efficient use of a traffic network, are worth their costs of implementation. This paper identifies four mechanisms that govern how the PoA varies with travel demand in traffic networks with separable and strictly increasing cost functions. For each OD movement, these are expansions and contractions in the sets of routes that are of minimum cost under UE and minimum marginal total cost under SO. The effects of these mechanisms on the PoA are established via a combination of theoretical proofs and conjectures supported by numerical evidence. In addition, for the special case of traffic networks with BPR-like cost functions having common power, it is proven that there is a systematic relationship between link flows under UE and SO, and hence between the levels of demand at which expansions and contractions occur. For this case, numerical evidence also suggests that the PoA has power law decay for large demand

Forest Plant and Bird Communities in the Lau Group, Fiji

We examined species composition of forest and bird communities in relation to environmental and human disturbance gradients on Lakeba (55.9 km²), Nayau (18.4 km²), and Aiwa Levu (1.2 km²), islands in the Lau Group of Fiji, West Polynesia. The unique avifauna of West Polynesia (Fiji, Tonga, Samoa) has been subjected to prehistoric human-caused extinctions but little was previously known about this topic in the Lau Group. We expected that the degree of human disturbance would be a strong determinant of tree species composition and habitat quality for surviving landbirds, while island area would be unrelated to bird diversity.All trees > 5 cm diameter were measured and identified in 23 forest plots of 500 m² each. We recognized four forest species assemblages differentiated by composition and structure: coastal forest, dominated by widely distributed species, and three forest types with differences related more to disturbance history (stages of secondary succession following clearing or selective logging) than to environmental gradients (elevation, slope, rockiness). Our point counts (73 locations in 1 or 2 seasons) recorded 18 of the 24 species of landbirds that exist on the three islands. The relative abundance and species richness of birds were greatest in the forested habitats least disturbed by people. These differences were due mostly to increased numbers of columbid frugivores and passerine insectivores in forests on Lakeba and Aiwa Levu. Considering only forested habitats, the relative abundance and species richness of birds were greater on the small but completely forested (and uninhabited) island of Aiwa Levu than on the much larger island of Lakeba.Forest disturbance history is more important than island area in structuring both tree and landbird communities on remote Pacific islands. Even very small islands may be suitable for conservation reserves if they are protected from human disturbance