The k-th order mean-deviation model for route choice under uncertainty

Abstract

This study introduces the k-th order mean-deviation model for optimizing route choice within large, stochastic, and time-variant networks. This model addresses the limitations of the traditional mean-standard deviation approach by better handling extreme outcomes in travel times. It features an objective function called the “travel time budget”, which combines the average path travel time with a safety margin. This margin is defined by a trade-off coefficient and a selected deviation measure (total or semi) of the travel time. The model is divided into three variations: 1) The mean-total deviation (MTD) model for symmetric travel time distributions, 2) The mean-upper-semi-deviation (MUSD) model for asymmetric distributions prioritizing upper semi-deviations, suitable for risk-averse travelers, and 3) The mean-lower-semi-deviation (MLSD) model for asymmetric distributions focusing on lower semi-deviations, preferred by risk-prone individuals. We explore these models’ alignment with the stochastic dominance (SD) rule and develop a solution methodology based on SD principles. Numerical experiments in two real-world transportation networks demonstrate the models’ effectiveness and show how the choice of deviation affects route selection decisions.