Robust perimeter control with cordon queues and heterogeneous transfer flows

Abstract

Accumulation-based Macroscopic Fundamental Diagram (MFD) model is widely employed to design perimeter control methods to improve traffic operation in urban networks. While the accumulation-based MFD assumes a low-scatter, non-linear relationship between region production and accumulation, the outflow relationship in formulating dynamics of multi-region networks requires simplifying assumptions. The existing perimeter control methods are grounded on accumulation-based MFD models where the number of transferring vehicles is approximated by the ratio of the instantaneous number of vehicles based on their destinations. Moreover, perimeter control may lead to more vehicles queuing at the region boundary (i.e. cordon queues) which add local impediments on traveling vehicles and impact the accuracy of well-defined MFDs. To address these shortcomings under time-varying conditions, this paper develops a robust perimeter control method based on the Sliding Mode Control to minimize total travel time in the entire network. To test the performance of the proposed control method, a trip-based MFD model is developed that accounts for cordon queues and various trip lengths of individual travelers. In this paper, two-region accumulation-based and trip-based MFD models are compared through numerical experiments. The results pinpoint the proposed robust perimeter control method can effectively alleviate congestion and improve network efficiency during traffic rush hours.