The price of uncertainty in pavement infrastructure management planning: An integer programming approach

Currently there is a true dichotomy in the pavement maintenance and rehabilitation (M&R) literature. On the one hand, there are integer programming-based models that assume that parameters are deterministically known. On the other extreme, there are stochastic models, with the most popular class being based on the theory of Markov decision processes that are able to account for various sources of uncertainties observed in the real-world. In this paper, we present an integer programming-based alternative to account for these uncertainties. A critical feature of the proposed models is that they provide – a priori – probabilistic guarantees that the prescribed M&R decisions would result in pavement condition scores that are above their critical service levels, using minimal assumptions regarding the sources of uncertainty. By construction of the models, we can easily determine the additional budget requirements when additional sources of uncertainty are considered, starting from a fully deterministic model. We have coined this additional budget requirement the price of uncertainty to distinguish from previous related work where additional budget requirements were studied due to parameter uncertainties in stochastic models. A numerical case study presents valuable insights into the price of uncertainty and shows that it can be large.     

A chance-constrained based stochastic dynamic traffic assignment model: Analysis, formulation and solution algorithms

This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).     

Distribution-free travel time reliability assessment with probability inequalities

An assumption that pervades the current transportation system reliability assessment literature is that probability distributions of the sources of uncertainty are known explicitly. However, this distribution may be unavailable (inaccurate) in reality as we may have no (insufficient) data to calibrate the distribution. In this paper we relax this assumption and present a new method to assess travel time reliability that is distribution-free in the sense that the methodology only requires that the first N moments (where N is a user-specified positive integer) of the travel time to be known and that the travel times reside in a set of bounded and known intervals. Because of our modeling approach, all sources of uncertainty are automatically accounted for, as long as they are statistically independent. Instead of deriving exact probabilities on travel times exceeding certain thresholds via computationally intensive methods, we develop semi-analytical probability inequalities to quickly (i.e. within a fraction of a second) obtain upper bounds on the desired probability. Numerical experiments suggest that the inclusion of higher order moments can potentially significantly improve the bounds. The case study also demonstrates that the derived bounds are nontrivial for a large range of travel time values.     

Incorporating equity into the transit frequency-setting problem

This paper and the proposed formulation contribute to an apparent gap in transit research design by integrating equity considerations into the transit frequency-setting problem. The proposed approach provides a means to design transit service such that equitable access to basic amenities (e.g., employment, supermarkets, medical services) is provided for low-income populations or disadvantaged populations. The overarching purpose is to improve access via transit to basic amenities to: (1) reduce the disproportionate burden faced by transit dependent populations; and (2) create a more feasible transportation option for low-income households as an opportunity to increase financial security by reducing dependence on personal autos. The formulation is applied to data from a mid-sized US metropolitan area. The example application illustrates the formulation successfully increases access to employment opportunities for residents in areas with high percentages of low-income persons, as well as demonstrates the importance of considering uncertainty in the locations of populations and employment.