Robust controls for traffic networks: The near-Bayes near-Minimax strategy

Traffic signals allocate scarce capacity at roadway junctions and, as such, influence the level of service both locally and in the corresponding traffic network. This paper addresses the problem of determining robust signal controls in a traffic network which (a) consider the interdependency of signal controls and traffic flow patterns and (b) account for the variability or uncertainty in the origin-destination demands. The approach taken is to model the uncertainty in terms of constraints on the possible origin-destination (OD) demands concurrently with the signal controls to produce a " best" strategy that accounts for this uncertainty. To develop this strategy solutions for two extreme cases are considered. One is the Bayes case in which we assume a probability density on the possible OD matrices. The second is the Minimax solution which seeks to minimize the worst possible costs that may occur. The strategy employed is a compromise between the Bayes and the Minimax solutions and is termed the near-Bayes near-Minimax (NBNM) strategy. It is designed to provide performance that is close to the best that can be obtained under Bayes conditions, yet does not depart too far from the most beneficial controls under the most costly origin-destination demands. As such, this is a conservative approach whose controls can provide robust or risk-averse performance. Application of the methodology is illustrated in three case studies.