Alpha-fair large-scale urban network control: A perimeter control based on a macroscopic fundamental diagram

Abstract

This paper introduces a novel α-fair perimeter control (AFPC) scheme for a multi-region urban network based on the macroscopic fundamental diagram (MFD) modeling approach. The goal is to optimize the allocation of available region resources (i.e., available capacity) through perimeter control by metering the flow that transfers between any two neighbor regions while also considering the impacts (i.e., accumulation, average speed and queue) of such decision on road users in the regions. Regional traffic state dynamics are modeled using a multi-region MFD approach while queuing dynamics at a regional perimeter border, caused by control, are modeled using a point queue model. Based on regional average speed, a utility measure for each region is defined. Weights corresponding to regions are assigned dynamically to reflect the prevailing state of regional queues. The problem is then formulated based on these utilities with a novel perimeter control model that identifies the inflows between any two neighboring regions. The unique feature of the developed AFPC model is its ability to find a balanced trade-off between efficiency (i.e., travel time savings) and fairness in the distribution of both resources and impacts. The performance of the proposed model is compared with the no control base scenario as well as four other control scenarios. The results indicate that our proposed approach outperforms other control scenarios in terms of fairness while not degrading efficiency. The sensitivity analysis of a range of α values illustrates the wide spectrum of fair-centered yet efficient solutions that can be successfully achieved. Thus, by manipulating α values and regions’ weights, the AFPC framework can be tweaked to meet the specific fairness and efficiency aspirations of a network while also tailoring the specific regions’ need.