On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites

Incorporating weather into regionwide safety planning prediction models

Predicting safety on roadways is standard practice for road safety professionals and has a corresponding extensive literature. The majority of safety prediction models are estimated using roadway segment and intersection (microscale) data, while more recently efforts have been undertaken to predict safety at the planning level (macroscale). Safety prediction models typically include roadway, operations, and exposure variables—factors known to affect safety in fundamental ways. Environmental variables, in particular variables attempting to capture the effect of rain on road safety, are difficult to obtain and have rarely been considered. In the few cases weather variables have been included, historical averages rather than actual weather conditions during which crashes are observed have been used. Without the inclusion of weather related variables researchers have had difficulty explaining regional differences in the safety performance of various entities (e.g. intersections, road segments, highways, etc.) As part of the NCHRP 8-44 research effort, researchers developed PLANSAFE, or planning level safety prediction models. These models make use of socio-economic, demographic, and roadway variables for predicting planning level safety. Accounting for regional differences - similar to the experience for microscale safety models - has been problematic during the development of planning level safety prediction models. More specifically, without weather related variables there is an insufficient set of variables for explaining safety differences across regions and states. Furthermore, omitted variable bias resulting from excluding these important variables may adversely impact the coefficients of included variables, thus contributing to difficulty in model interpretation and accuracy. This paper summarizes the results of an effort to include weather related variables, particularly various measures of rainfall, into accident frequency prediction and the prediction of the frequency of fatal and/or injury degree of severity crash models. The purpose of the study was to determine whether these variables do in fact improve overall goodness of fit of the models, whether these variables may explain some or all of observed regional differences, and identifying the estimated effects of rainfall on safety. The models are based on Traffic Analysis Zone level datasets from Michigan, and Pima and Maricopa Counties in Arizona. Numerous rain-related variables were found to be statistically significant, selected rain related variables improved the overall goodness of fit, and inclusion of these variables reduced the portion of the model explained by the constant in the base models without weather variables. Rain tends to diminish safety, as expected, in fairly complex ways, depending on rain frequency and intensity.

Forecasting crashes at the planning level: Simultaneous negative binomial crash model applied in Tucson, Arizona

At least two important transportation planning activities rely on planning-level crash prediction models. One is motivated by the Transportation Equity Act for the 21st Century, which requires departments of transportation and metropolitan planning organizations to consider safety explicitly in the transportation planning process. The second could arise from a need for state agencies to establish incentive programs to reduce injuries and save lives. Both applications require a forecast of safety for a future period. Planning-level crash prediction models for the Tucson, Arizona, metropolitan region are presented to demonstrate the feasibility of such models. Data were separated into fatal, injury, and property-damage crashes. To accommodate overdispersion in the data, negative binomial regression models were applied. To accommodate the simultaneity of fatality and injury crash outcomes, simultaneous estimation of the models was conducted. All models produce crash forecasts at the traffic analysis zone level. Statistically significant (p-values < 0.05) and theoretically meaningful variables for the fatal crash model included population density, persons 17 years old or younger as a percentage of the total population, and intersection density. Significant variables for the injury and property-damage crash models were population density, number of employees, intersections density, percentage of miles of principal arterial, percentage of miles of minor arterials, and percentage of miles of urban collectors. Among several conclusions it is suggested that planning-level safety models are feasible and may play a role in future planning activities. However, caution must be exercised with such models.

Differences in the performance of safety performance functions estimated for total crash count and for crash count by crash type

In recent years the development and use of crash prediction models for roadway safety analyses have received substantial attention. These models, also known as safety performance functions (SPFs), relate the expected crash frequency of roadway elements (intersections, road segments, on-ramps) to traffic volumes and other geometric and operational characteristics. A commonly practiced approach for applying intersection SPFs is to assume that crash types occur in fixed proportions (e.g., rear-end crashes make up 20% of crashes, angle crashes 35%, and so forth) and then apply these fixed proportions to crash totals to estimate crash frequencies by type. As demonstrated in this paper, such a practice makes questionable assumptions and results in considerable error in estimating crash proportions. Through the use of rudimentary SPFs based solely on the annual average daily traffic (AADT) of major and minor roads, the homogeneity-in-proportions assumption is shown not to hold across AADT, because crash proportions vary as a function of both major and minor road AADT. For example, with minor road AADT of 400 vehicles per day, the proportion of intersecting-direction crashes decreases from about 50% with 2,000 major road AADT to about 15% with 82,000 AADT. Same-direction crashes increase from about 15% to 55% for the same comparison. The homogeneity-in-proportions assumption should be abandoned, and crash type models should be used to predict crash frequency by crash type. SPFs that use additional geometric variables would only exacerbate the problem quantified here. Comparison of models for different crash types using additional geometric variables remains the subject of future research.

Expected safety performance of rural signalized intersections in South Korea

Understanding the expected safety performance of rural signalized intersections is critical for (a) identifying high-risk sites where the observed safety performance is substantially worse than the expected safety performance, (b) understanding influential factors associated with crashes, and (c) predicting the future performance of sites and helping plan safety-enhancing activities. These three critical activities are routinely conducted for safety management and planning purposes in jurisdictions throughout the United States and around the world. This paper aims to develop baseline expected safety performance functions of rural signalized intersections in South Korea, which to date have not yet been established or reported in the literature. Data are examined from numerous locations within South Korea for both three-legged and four-legged configurations. The safety effects of a host of operational and geometric variables on the safety performance of these sites are also examined. In addition, supplementary tables and graphs are developed for comparing the baseline safety performance of sites with various geometric and operational features. These graphs identify how various factors are associated with safety. The expected safety prediction tables offer advantages over regression prediction equations by allowing the safety manager to isolate specific features of the intersections and examine their impact on expected safety. The examination of the expected safety performance tables through illustrated examples highlights the need to correct for regression-to-the-mean effects, emphasizes the negative impacts of multicollinearity, shows why multivariate models do not translate well to accident modification factors, and illuminates the need to examine road safety carefully and methodically. Caveats are provided on the use of the safety performance prediction graphs developed in this paper.

Railway junction traffic control by heuristic methods

Traffic conflicts at railway junctions are very conmon, particularly on congested rail lines. While safe passage through the junction is well maintained by the signalling and interlocking systems, minimising the delays imposed on the trains by assigning the right-of-way sequence sensibly is a bonus to the quality of service. A deterministic method has been adopted to resolve the conflict, with the objective of minimising the total weighted delay. However, the computational demand remains significant. The applications of different heuristic methods to tackle this problem are reviewed and explored, elaborating their feasibility in various aspects and comparing their relative merits for further studies. As most heuristic methods do not guarantee a global optimum, this study focuses on the trade-off between computation time and optimality of the resolution.

Optimal traffic control at railway junctions

Conflict occurs when two or more trains approach the same junction within a specified time. Such conflicts result in delays. Current practices to assign the right of way at junctions achieve orderly and safe passage of the trains, but do not attempt to reduce the delays. A traffic controller developed in the paper assigns right of way to impose minimum total weighted delay on the trains. The traffic flow model and the optimisation technique used in this controller are described. Simulation studies of the performance of the controller are given.

Fuzzy logic traffic control at a road junction with time-varying flow rates

Fuzzy logic has been applied to control traffic at road junctions. A simple controller with one fixed rule-set is inadequate to minimise delays when traffic flow rate is time-varying and likely to span a wide range. To achieve better control, fuzzy rules adapted to the current traffic conditions are used.

Hierarchical fuzzy logic traffic control at a road junction

Traffic control at road junctions is one of the major concerns in most metropolitan cities. Controllers of various approaches are available and the required control action is the effective green-time assigned to each traffic stream within a traffic-light cycle. The application of fuzzy logic provides the controller with the capability to handle uncertain natures of the system, such as drivers’ behaviour and random arrivals of vehicles. When turning traffic is allowed at the junction, the number of phases in the traffic-light cycle increases. The additional input variables inevitably complicate the controller and hence slow down the decision-making process, which is critical in this real-time control problem. In this paper, a hierarchical fuzzy logic controller is proposed to tackle this traffic control problem at a 2-way road junction with turning traffic. The two levels of fuzzy logic controllers devise the minimum effective green-time and fine-tune it respectively at each phase of a traffic-light cycle. The complexity of the controller at each level is reduced with smaller rule-set. The performance of this hierarchical controller is examined by comparison with a fixed-time controller under various traffic conditions. Substantial delay reduction has been achieved as a result and the performance and limitation of the controller will be discussed.

Markov modelling of the IEEE 802.11 DCF for real-time applications with periodic traffic

Popular wireless network standards, such as IEEE 802.11/15/16, are increasingly adopted in real-time control systems. However, they are not designed for real-time applications. Therefore, the performance of such wireless networks needs to be carefully evaluated before the systems are implemented and deployed. While efforts have been made to model general wireless networks with completely random traffic generation, there is a lack of theoretical investigations into the modelling of wireless networks with periodic real-time traffic. Considering the widely used IEEE 802.11 standard, with the focus on its distributed coordination function (DCF), for soft-real-time control applications, this paper develops an analytical Markov model to quantitatively evaluate the network quality-of-service (QoS) performance in periodic real-time traffic environments. Performance indices to be evaluated include throughput capacity, transmission delay and packet loss ratio, which are crucial for real-time QoS guarantee in real-time control applications. They are derived under the critical real-time traffic condition, which is formally defined in this paper to characterize the marginal satisfaction of real-time performance constraints.

An enhanced explicit rate algorithm for ABR traffic control in ATM networks

A high performance, low computational complexity rate-based flow control algorithm which can avoid congestion and achieve fairness is important to ATM available bit rate service. The explicit rate allocation algorithm proposed by Kalampoukas et al. is designed to achieve max–min fairness in ATM networks. It has several attractive features, such as a fixed computational complexity of O(1) and the guaranteed convergence to max–min fairness. In this paper, certain drawbacks of the algorithm, such as the severe overload of an outgoing link during transient period and the non-conforming use of the current cell rate field in a resource management cell, have been identified and analysed; a new algorithm which overcomes these drawbacks is proposed. The proposed algorithm simplifies the rate computation as well. Compared with Kalampoukas's algorithm, it has better performance in terms of congestion avoidance and smoothness of rate allocation.

Traffic and climate change impacts on water quality : measuring build-up and wash-off of heavy metals and petroleum hydrocarbons

Understanding the impacts of traffic and climate change on water quality helps decision makers to develop better policy and plans for dealing with unsustainable urban and transport development. This chapter presents detailed methodologies developed for sample collection and testing for heavy metals and total petroleum hydrocarbons, as part of a research study to investigate the impacts of climate change and changes to urban traffic characteristics on pollutant build-up and wash-off from urban road surfaces. Cadmium, chromium, nickel, copper, lead, iron, aluminium, manganese and zinc were the target heavy metals, and selected gasoline and diesel range organics were the target total petroleum hydrocarbons for this study. The study sites were selected to encompass the urban traffic characteristics of the Gold Coast region, Australia. An improved sample collection method referred to as ‘the wet and dry vacuum system’ for the pollutant build-up, and an effective wash-off plan to incorporate predicted changes to rainfall characteristics due to climate change, were implemented. The novel approach to sample collection for pollutant build-up helped to maintain the integrity of collection efficiency. The wash-off plan helped to incorporate the predicted impacts of climate change in the Gold Coast region. The robust experimental methods developed will help in field sample collection and chemical testing of different stormwater pollutants in build-up and wash-off.

Generation evolution in GA application on railway traffic control

This paper presents a Genetic Algorithms (GA) approach to resolve traffic conflicts at a railway junction. The formulation of the problem for the suitable application of GA will be discussed and three neighborhoods have been proposed for generation evolution. The performance of the GA is evaluated by computer simulation. This study paves the way for more applications of artificial intelligence techniques on a rather conservative industry.

An event-based traffic flow model for traffic control at railway junctions

This paper introduces an event-based traffic model for railway systems adopting fixed-block signalling schemes. In this model, the events of trains' arrival at and departure from signalling blocks constitute the states of the traffic flow. A state transition is equivalent to the progress of the trains by one signalling block and it is realised by referring to past and present states, as well as a number of pre-calculated look-up tables of run-times in the signalling block under various signalling conditions. Simulation results are compared with those from a time-based multi-train simulator to study the improvement of processing time and accuracy.

Development of a composite line source emission model for traffic interrupted microenvironments and its application in particle number emissions at a bus station

A composite line source emission (CLSE) model was developed to specifically quantify exposure levels and describe the spatial variability of vehicle emissions in traffic interrupted microenvironments. This model took into account the complexity of vehicle movements in the queue, as well as different emission rates relevant to various driving conditions (cruise, decelerate, idle and accelerate), and it utilised multi-representative segments to capture the accurate emission distribution for real vehicle flow. Hence, this model was able to quickly quantify the time spent in each segment within the considered zone, as well as the composition and position of the requisite segments based on the vehicle fleet information, which not only helped to quantify the enhanced emissions at critical locations, but it also helped to define the emission source distribution of the disrupted steady flow for further dispersion modelling. The model then was applied to estimate particle number emissions at a bi-directional bus station used by diesel and compressed natural gas fuelled buses. It was found that the acceleration distance was of critical importance when estimating particle number emission, since the highest emissions occurred in sections where most of the buses were accelerating and no significant increases were observed at locations where they idled. It was also shown that emissions at the front end of the platform were 43 times greater than at the rear of the platform. Although the CLSE model is intended to be applied in traffic management and transport analysis systems for the evaluation of exposure, as well as the simulation of vehicle emissions in traffic interrupted microenvironments, the bus station model can also be used for the input of initial source definitions in future dispersion models.