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

Asymptotic approximations of transient behaviour for day-to-day traffic models

We consider a wide class of stochastic process traffic assignment models that capture the day-to-day evolving interaction between traffic congestion and drivers’ information acquisition and choice processes. Such models provide a description of not only transient change and ‘steady’ behaviour, but also represent additional variability that occurs through probabilistic descriptions. They are therefore highly suited to modelling both the disturbance and subsequent ‘drift’ of networks that are subject to some systematic change, be that a road closure or capacity reduction, new policy measure or general change in demand patterns. In this paper we derive analytic results to probabilistically capture the nature of the transient effects following such a systematic change. This can be thought of as understanding what happens as a system moves from varying about one equilibrium state to varying about a new equilibrium state. The results capture analytically the changes over time in descriptors of the system, in terms of link flow means, variances and covariances. Formally, the analytic results hold asymptotically as approximations, as we imagine demand increasing in tandem with capacities; however, our interest is in general cases where such tandem increases do not occur, and so we provide conditions under which our approximations are likely to work well. Numerical results of applying the methods are reported on several examples. The quality of the approximations is assessed through comparisons with Monte Carlo simulations from the true underlying process

The Long Term Behaviour of Day-to-Day Traffic Assignment Models

The dynamical behaviour of deterministic process, day-to-day traffic assignment models is sometimes characterised by convergence to a variety of different fixed equilibrium points dependent upon the initial flow pattern, even though individual trajectories are unique for a given start point. This non-uniqueness is seemingly in sharp contrast to the evolution of stochastic process, day-to-day models; under certain assumptions these converge in law to a unique stationary distribution, irrespective of the start point. In this article, we show how models may be constructed which exhibit characteristics of both deterministic models and stochastic models, and illustrate the ideas by using a simple example network

An Evolutionary Algorithm to Generate Real Urban Traffic Flows

In this article we present a strategy based on an evolutionary algorithm to calculate the real vehicle ows in cities according to data from sensors placed in the streets. We have worked with a map imported from OpenStreetMap into the SUMO traffic simulator so that the resulting scenarios can be used to perform different optimizations with the confidence of being able to work with a traffic distribution close to reality. We have compared the results of our algorithm to other competitors and achieved results that replicate the real traffic distribution with a precision higher than 90%.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. This research has been partially funded by project number 8.06/5.47.4142 in collaboration with the VSB-Technical University of Ostrava and Universidad de Málaga UMA/FEDER FC14-TIC36, programa de fortalecimiento de las capacidades de I+D+i en las universidades 2014-2015, de la Consejería de Economía, Innovación, Ciencia y Empleo, cofinanciado por el fondo europeo de desarrollo regional (FEDER). Also, partially funded by the Spanish MINECO project TIN2014-57341-R (http://moveon.lcc.uma.es). The authors would like to thank the FEDER of European Union for financial support via project Movilidad Inteligente: Wi-Fi, Rutas y Contaminación (maxCT) of the "Programa Operativo FEDER de Andalucía 2014-2020. We also thank all Agency of Public Works of Andalusia Regional Government staff and researchers for their dedication and professionalism. Daniel H. Stolfi is supported by a FPU grant (FPU13/00954) from the Spanish Ministry of Education, Culture and Sports

Estimation of annual average daily traffic with optimal adjustment factors

This study aimed to estimate the annual average daily traffic in inter-urban networks determining the best correlation (affinity) between the short period traffic counts and permanent traffic counters. A bi-level optimisation problem is proposed in which an agent in an upper level prefixes the affinities between short period traffic counts and permanent traffic counters stations and looks to minimise the annual average daily traffic calculation error while, in a lower level, an origin–destination (O–D) trip matrix estimation problem from traffic counts is solved. The proposed model is tested over the well-known Sioux-Falls network and applied to a real case of Cantabria (Spain) regional road network. The importance of determining appropriate affinity and the effect of localisation of permanent traffic counters stations are discussed

Mannose Binding Lectin Is Required for Alphavirus-Induced Arthritis/Myositis

Mosquito-borne alphaviruses such as chikungunya virus and Ross River virus (RRV) are emerging pathogens capable of causing large-scale epidemics of virus-induced arthritis and myositis. The pathology of RRV-induced disease in both humans and mice is associated with induction of the host inflammatory response within the muscle and joints, and prior studies have demonstrated that the host complement system contributes to development of disease. In this study, we have used a mouse model of RRV-induced disease to identify and characterize which complement activation pathways mediate disease progression after infection, and we have identified the mannose binding lectin (MBL) pathway, but not the classical or alternative complement activation pathways, as essential for development of RRV-induced disease. MBL deposition was enhanced in RRV infected muscle tissue from wild type mice and RRV infected MBL deficient mice exhibited reduced disease, tissue damage, and complement deposition compared to wild-type mice. In contrast, mice deficient for key components of the classical or alternative complement activation pathways still developed severe RRV-induced disease. Further characterization of MBL deficient mice demonstrated that similar to C3−/− mice, viral replication and inflammatory cell recruitment were equivalent to wild type animals, suggesting that RRV-mediated induction of complement dependent immune pathology is largely MBL dependent. Consistent with these findings, human patients diagnosed with RRV disease had elevated serum MBL levels compared to healthy controls, and MBL levels in the serum and synovial fluid correlated with severity of disease. These findings demonstrate a role for MBL in promoting RRV-induced disease in both mice and humans and suggest that the MBL pathway of complement activation may be an effective target for therapeutic intervention for humans suffering from RRV-induced arthritis and myositis

Evaluating the Number of Stages in Development of Squamous Cell and Adenocarcinomas across Cancer Sites Using Human Population-Based Cancer Modeling

BACKGROUND: Adenocarcinomas (ACs) and squamous cell carcinomas (SCCs) differ by clinical and molecular characteristics. We evaluated the characteristics of carcinogenesis by modeling the age patterns of incidence rates of ACs and SCCs of various organs to test whether these characteristics differed between cancer subtypes. METHODOLOGY/PRINCIPAL FINDINGS: Histotype-specific incidence rates of 14 ACs and 12 SCCs from the SEER Registry (1973-2003) were analyzed by fitting several biologically motivated models to observed age patterns. A frailty model with the Weibull baseline was applied to each age pattern to provide the best fit for the majority of cancers. For each cancer, model parameters describing the underlying mechanisms of carcinogenesis including the number of stages occurring during an individual's life and leading to cancer (m-stages) were estimated. For sensitivity analysis, the age-period-cohort model was incorporated into the carcinogenesis model to test the stability of the estimates. For the majority of studied cancers, the numbers of m-stages were similar within each group (i.e., AC and SCC). When cancers of the same organs were compared (i.e., lung, esophagus, and cervix uteri), the number of m-stages were more strongly associated with the AC/SCC subtype than with the organ: 9.79±0.09, 9.93±0.19 and 8.80±0.10 for lung, esophagus, and cervical ACs, compared to 11.41±0.10, 12.86±0.34 and 12.01±0.51 for SCCs of the respective organs (p<0.05 between subtypes). Most SCCs had more than ten m-stages while ACs had fewer than ten m-stages. The sensitivity analyses of the model parameters demonstrated the stability of the obtained estimates. CONCLUSIONS/SIGNIFICANCE: A model containing parameters capable of representing the number of stages of cancer development occurring during individual's life was applied to the large population data on incidence of ACs and SCCs. The model revealed that the number of m-stages differed by cancer subtype being more strongly associated with ACs/SCCs histotype than with organ/site

Significance of vascular endothelial growth factor in growth and peritoneal dissemination of ovarian cancer

Vascular endothelial growth factor (VEGF) is a key regulator of angiogenesis which drives endothelial cell survival, proliferation, and migration while increasing vascular permeability. Playing an important role in the physiology of normal ovaries, VEGF has also been implicated in the pathogenesis of ovarian cancer. Essentially by promoting tumor angiogenesis and enhancing vascular permeability, VEGF contributes to the development of peritoneal carcinomatosis associated with malignant ascites formation, the characteristic feature of advanced ovarian cancer at diagnosis. In both experimental and clinical studies, VEGF levels have been inversely correlated with survival. Moreover, VEGF inhibition has been shown to inhibit tumor growth and ascites production and to suppress tumor invasion and metastasis. These findings have laid the basis for the clinical evaluation of agents targeting VEGF signaling pathway in patients with ovarian cancer. In this review, we will focus on VEGF involvement in the pathophysiology of ovarian cancer and its contribution to the disease progression and dissemination

Estimation of mean and covariance of stochastic multi-class OD demands from classified traffic counts

This paper proposes a new model to estimate the mean and covariance of stochastic multi-class (multiple vehicle classes) origin-destination (OD) demands from hourly classified traffic counts throughout the whole year. It is usually assumed in the conventional OD demand estimation models that the OD demand by vehicle class is deterministic. Little attention is given on the estimation of the statistical properties of stochastic OD demands as well as their covariance between different vehicle classes. Also, the interactions between different vehicle classes in OD demand are ignored such as the change of modes between private car and taxi during a particular hourly period over the year. To fill these two gaps, the mean and covariance matrix of stochastic multi-class OD demands for the same hourly period over the year are simultaneously estimated by a modified lasso (least absolute shrinkage and selection operator) method. The estimated covariance matrix of stochastic multi-class OD demands can be used to capture the statistical dependency of traffic demands between different vehicle classes. In this paper, the proposed model is formulated as a non-linear constrained optimization problem. An exterior penalty algorithm is adapted to solve the proposed model. Numerical examples are presented to illustrate the applications of the proposed model together with some insightful findings on the importance of covariance of OD demand between difference vehicle classes.Department of Civil and Environmental Engineerin