چكيده به لاتين
Abstract:
Paratransit systems play a remarkable role in passenger and freight movements. The determination of efficient routes for paratransit vehicles can decrease their operational costs and increase the utility of these systems.
Travel time is one of the most important factors affecting paratransit vehicle routing. In previous studies in the field of paratransit vehicle routing, travel times were treated as deterministic variables or independent random variables. However, as evidenced by empirical studies, there exists significant correlation between travel time variables.
Ignoring correlations among travel times may lead to the inaccurate estimation of operational costs of a paratransit system. This, in turn, can result in inefficient routes for paratransit vehicles. Accordingly, this study aims to address the paratransit vehicle routing when travel times are correlated random variables. To this end, a framework is proposed. The framework comprises six elements including 1) mathematical modeling of the routing problem, 2) modeling travel time variability, 3) modeling the dependency structure between random travel times, 4) estimating the path travel time distribution, 5) estimating on-time performance and 6) solving the mathematical model.
The results of this study show that travel time variability can be best described by mixture probability distributions. Furthermore, among single-component distributions, the burr distribution and the lognormal distribution provide the best fit to travel time data. According to the results of this study, there exists a significant correlation between travel times. In addition, the results of the present study reveal that the dependency structure between random travel times can be modeled accurately by multivariate mixture distributions, copula functions, vine copulas and non-parametric Bayesian networks.
To examine the effect of ignoring correlations between travel times, the vehicle routing problem with time windows is considered. The problem is solved under two cases: a) considering the correlation between travel times and b) ignoring correlation. The results show that ignoring correlation can lead to considerable error in estimating the on-time performance of a paratransit system. This, in turn, results in inefficient routes for paratransit vehicles when the correlation between travel times is ignored.
Keywords: Paratransit systems, Routing, Travel time reliability, correlated travel times.
