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

Abstract

This paper proposes a new model to estimate the mean and covariance of stochastic multi-class (multiple vehicle classes) origindestination (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.

Statistical inference of probabilistic origin-destination demand using day-to-day traffic data

“…Compared to the framework by Shao et al [67,68], we argue that the IGLS-based formulation is statistical interpretable and more computationally efficient to solve on large-scale networks. As shown in Del Pino [23], each iteration in the IGLS resembles one gradient descent step in the Newton-Raphson algorithm.…”

“…Shao et al [67,68] proposed a generalized least square formulation to estimate the mean and variance of O-D demand that follows the MVN. The formulation is a bi-level optimization problem.…”

Implementation Flexibility of Multiperiod Rail Line Design with Consideration of Uncertainties in Population Distribution

“…This function is referred to as the stochastic population distribution function. Besides, the stochastic population distribution function is assumed as a nondecreasing function with respect to its mean value [9,14].…”

“…With the IIA assumption of population distribution, uncertainties of population distribution cannot be fully explored. Uncertainties of population distribution can be classified into variations of population distribution year by year and spatial-temporal correlation of population distribution [8][9][10]. The year-by-year variations of population distribution can be captured by a stochastic variable of annual population growth rate, with its mean value and standard deviation [9,11,12].…”

“…Uncertainties of population distribution can be classified into variations of population distribution year by year and spatial-temporal correlation of population distribution [8][9][10]. The year-by-year variations of population distribution can be captured by a stochastic variable of annual population growth rate, with its mean value and standard deviation [9,11,12]. The spatial-temporal correlation of population distribution can be described by the spatial and temporal correlation coefficient of population densities [8,9,13].…”