A Mean-Variance Model for Route Guidance in Advanced Traveler Information Systems

Abstract

T raditional models of route generation are based on choosing routes that minimize expected travel-time between origin and destination. Such approaches do not account for the fact that travelers often incorporate travel-time variability within their decision making. Thus, a route with lower travel-time variability is preferred by some travelers, even if such a route is not one with the lowest mean travel-time. Such traveler behavior is best captured by a multiobjective model in which the choice of a route is based on the mean as well as the variance of the path travel-time. Our route-planning model is intended to help travelers make choices that reflect their decision-making process better. We formulate a network flow multiobjective model in which one of the objectives (expectation) is linear, whereas, the other (variance) is quadratic. In order to present the user with a series of options, we solve a series of parametric 0-1 quadratic integer programs. By utilizing the network structure of the problem, we devise an effective algorithm in which the 0-1 quadratic program is solved by using a continuous relaxation together with an enumeration of some selected paths. Finally, we note that the data requirements for the model can be easily satisfied in practice.

Hybrid Vehicle-Centric Route Guidance 1

“…Sen et al [55], for example, presents a formulation which incorporates both travel time and travel time variance into the objective function. This formulation relies on a series of parametric 0-1 quadratic integer programs.…”

On the Quadratic Shortest Path Problem

“…In this case, the quadratic part of the objective function is determined by the covariance matrix of the coefficient's probability distributions. In [12] the authors develop a multi-objective model to minimize both the expected travel time of a path and its variance. Then they solve the multi-objective optimization problem by combining the linear and quadratic objective functions into a single quadratic shortest path problem.…”

An Investigation of Measurement for Travel Time Variability

“…The variance of travel times within a time period over consecutive days was employed as an indicator of uncertainty. With the concept of multi-objective approach, Sen and Pillai (2001) developed a mean-variance model for optimizing route guidance problems. The tradeoff between the mean and variability of travel time was discussed.…”