Mohammadali Shirazi

A semiparametric negative binomial generalized linear model for modeling over-dispersed count data with a heavy tail: Characteristics and applications to crash data

Crash data can often be characterized by over-dispersion, heavy (long) tail and many observations with the value zero. Over the last few years, a small number of researchers have started developing and applying novel and innovative multi-parameter models to analyze such data. These multi-parameter models have been proposed for overcoming the limitations of the traditional negative binomial (NB) model, which cannot handle this kind of data efficiently. The research documented in this paper continues the work related to multi-parameter models. The objective of this paper is to document the development and application of a flexible NB generalized linear model with randomly distributed mixed effects characterized by the Dirichlet process (NB-DP) to model crash data. The objective of the study was accomplished using two datasets. The new model was compared to the NB and the recently introduced model based on the mixture of the NB and Lindley (NB-L) distributions. Overall, the research study shows that the NB-DP model offers a better performance than the NB model once data are over-dispersed and have a heavy tail. The NB-DP performed better than the NB-L when the dataset has a heavy tail, but a smaller percentage of zeros. However, both models performed similarly when the dataset contained a large amount of zeros. In addition to a greater flexibility, the NB-DP provides a clustering by-product that allows the safety analyst to better understand the characteristics of the data, such as the identification of outliers and sources of dispersion.

Sample-Size Guidelines for Recalibrating Crash Prediction Models: Recommendations for the Highway Safety Manual

The Highway Safety Manual (HSM) prediction models are fitted and validated based on crash data collected from a selected number of states in the United States. Therefore, for a jurisdiction to be able to fully benefit from applying these models, it is necessary to calibrate or recalibrate them to local conditions. The first edition of the HSM recommends calibrating the models using a one-size-fits-all sample-size of 30-50 locations with total of at least 100 crashes per year. However, the HSM recommendation is not fully supported by documented studies. The objectives of this paper are consequently: (1) to examine the required sample size based on the characteristics of the data that will be used for the calibration or recalibration process; and, (2) propose revised guidelines. The objectives were accomplished using simulation runs for different scenarios that characterized the sample mean and variance of the data. The simulation results indicate that as the ratio of the standard deviation to the mean (i.e., coefficient of variation) of the crash data increases, a larger sample-size is warranted to fulfill certain levels of accuracy. Taking this observation into account, sample-size guidelines were prepared based on the coefficient of variation of the crash data that are needed for the calibration process. The guidelines were then successfully applied to the two observed datasets. The proposed guidelines can be used for all facility types and both for segment and intersection prediction models.

A Procedure to Determine When Safety Performance Functions Should Be Recalibrated

ABSTRACT Crash prediction models or safety performance functions can be used for estimating the number of crashes and evaluating roadway safety. Developing a new model can be a difficult task and requires a significant amount of time and energy. To simplify the process, the Highway Safety Manual provides safety performance functions for conducting different types of safety analyses for several facilities. However, because data collected from a few selected states for a specific period of time were considered for fitting and validating these models, they are required to be calibrated to the conditions of the new jurisdiction, and as well need to be revisited for recalibration over time. Therefore, the analyst may need to know when or how often the models are recommended to be recalibrated. This article addresses this question and documents recommendations that are based on the general characteristics of data. The proposed procedure only requires (1) the total number of crashes, (2) the average traffic flow, and (3) the total segment length (or number of intersections) in the network. The method was validated with different empirical datasets collected in Texas and Michigan. The results show that the proposed procedure provides useful information about when recalibration is recommended.

Estimating the minimal revenue tolls in large-scale roadway networks using the dynamic penalty function method

The dynamic penalty function method is used to estimate a toll vector that guarantees the SO flows in the network.Numerical results show that this toll vector is a good estimation for the MinRev optimal solution.The proposed method is fast and memory effect for large-scale implementations.We used the method for sensitivity analysis on MinRev tolled links.More practical solutions were explored for two large networks using sensitivity analysis. Congestion toll pricing is an inexpensive management way to mitigate the traffic congestion and reduce the delay in the network. One of the models that were proposed for toll pricing is the minimum toll revenue (MinRev) problem. The objective of this model is to find link-tolls that simultaneously cause users to efficiently use the network and to minimize the total toll revenues to be collected. Although it can be written as a linear model, when applied to road networks in practice, this model is difficult to be solved optimally in a reasonable time, due to its large size. This paper proposes a method to approximately estimate the minimal revenue tolls in large-scale roadway networks. The method was implemented for four real network ranged from medium to large, and two large random networks. Implementation of this method indicated that this technique can find an approximate toll vector that is within 0.5% of the optimal solution after just a few seconds. Furthermore, this method allows to perform sensitivity or trade-off analysis between the total collected tolls, the number of tolled links and the desired network improvement, which could suggest implementing more practically efficient solutions with substantially fewer tolled links and even quicker solution time at a negligible additional network cost.

Solving the minimum toll revenue problem in real transportation networks

As a means to relieve traffic congestion, toll pricing has recently received significant attention by transportation planners. Inappropriate use of transportation networks is one of the major causes of network congestion. Toll pricing is a method of traffic management in which traffic flow is guided to proper time and path in order to reduce the total delay in the network. This article investigates a method for solving the minimum toll revenue problem in real and large-scale transportation networks. The objective of this problem is to find link tolls that simultaneously cause users to efficiently use the transportation network and to minimize the total toll revenues to be collected. Although this model is linear, excessive number of variables and constraints make it very difficult to solve for large-scale networks. In this paper, a path-generation algorithm is proposed for solving the model. Implementation of this algorithm for different networks indicates that this method can achieve the optimal solution after a few iterations and a proper CPU time.

Exploring the Need for Region-Specific Calibration Factors

States, or even large cities, may experience different crash rates in different regions or parts of the city. This variation can be attributed to differences in terrain, population, weather, and other unobserved characteristics. Hence, the variation can affect the calibration procedure and consequently the calibration factor when different crash rates are used for a large area. This study first investigated whether region-specific calibration factors were required and justified for large states, such as Texas and Michigan. Next, a procedure was proposed to determine if a specific region needed a different calibration factor from the one developed for the whole state. If it is determined that a separate factor is needed, the agency should derive a region-specific calibration factor with data that are collected within the region. The proposed procedure is based on the general characteristics of data at the network level: the total number of crashes, the mean value of traffic flow (average daily traffic or annual average daily traffic), and the total segment length (or the number of intersections). The procedure was validated for the two states mentioned and showed that the calculated calibration factor matched the factor proposed in the recommended decision-making procedure.

Using a Prospect Theory Approach to Studying the Car-Following Model

Car following is a fundamental traffic feature that has been widely studied in literature using vehicles’ speed and acceleration. This study investigates car following from an entirely different perspective, a psychological approach based on the Prospect Theory (PT). PT is a behavioral economic theory that explains human reaction under risk situations. Since car following can be regarded as a risk containing task that addresses the need for balancing safety with travel time reduction, PT is an ideal approach to model car following. Employing PT can provide a spectrum of probabilistic locations of following vehicles in contradiction with traditional methods that define the exact position. This study presents a sensitivity analysis in order to validate the results and calibrate PT’s parameters. The results reveal that PT generates similar probability distributions to the simulation scenarios that proxy the space headway in real situations.