Adaptive traffic signal control with equilibrium constraints under stochastic demand. (October 2018)

• Record Type: Journal Article
• Authors: Huang, Wei; Li, Lubing; Lo, Hong K.
• Is Part Of: Transportation research. Volume 95(2018)
• Page Start: 394
• Page End: 413
• Publication Date: 2018-10
• Subjects: Network design -- Adaptive signal control -- Control buffer -- Reliability -- Demand uncertainty; Transportation -- Periodicals; Transportation -- Technological innovations -- Periodicals; 388.011
• DOI: 10.1016/j.trc.2018.07.018
• Languages: English
• ISSNs: 0968-090X

Abstract

Highlights: A reliable network signal design problem under demand uncertainty is proposed. The network signal design problem is formulated as a two-stage stochastic program. A travel time budget equilibrium model that captures travelers' risk attitude is formulated. A service reliability-based gradient projection algorithm is developed. The stage-one base control plan optimizes long-term network equilibrium performance. The stage-two recourse decisions adaptively respond to short-term demand variations. Abstract: This study develops a methodology to model transportation network design with signal settings in the presence of demand uncertainty. It is assumed that the total travel demand consists of commuters and infrequent travellers. The commuter travel demand is deterministic, whereas the demand of infrequent travellers is stochastic. Variations in demand contribute to travel time uncertainty and affect commuters' route choice behaviour. In this paper, we first introduce an equilibrium flow model that takes account of uncertain demand. A two-stage stochastic program is then proposed to formulate the network signal design under demand uncertainty. The optimal control policy derived under the two-stage stochastic program is able to (1) optimize the steady-state network performance in the long run, and (2) respond to short-term demand variations. In the first stage, a base signal control plan with a buffer against variability is introduced to control the equilibrium flow pattern and the resulting steady-state performance. In the second stage, after realizations of the random demand, recourse decisions of adaptive signal settings are determined to address the occasional demand overflows, so as to avoid transient congestion. The overall objective is to minimize the expected total travel time. To solve the two-stage stochastic program, a concept of service reliability associated with the control buffer is introduced. A reliability-based gradient projection algorithm is then developed. Numerical examples are performed to illustrate the properties of the proposed control method as well as its capability of optimizing steady-state performance while adaptively responding to changing traffic flows. Comparison results show that the proposed method exhibits advantages over the traditional mean-value approach in improving network expected total travel times.