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Optimal cordon-metering rates are obtained using Macroscopic Fundamental Diagrams in combination with flow conservation laws. A model-predictive control algorithm is also used so that time-varying metering rates are generated based on their forecasted impacts. Our scalable algorithm can do this for an arbitrary number of cordoned neighborhoods within a city. Unlike its predecessors, the proposed model accounts for the time-varying constraining effects that cordon queues impose on a neighborhood’s circulating traffic, as those queues expand and recede over time. The model does so at every time step by approximating a neighborhood’s street space occupied by cordon queues, and re-scaling the MFD to describe the state of circulating traffic that results. The model also differentiates between saturated and under-saturated cordon-metering operations. Computer simulations of an idealized network show that these enhancements can substantially improve the predictions of both, the trip completion rates in a neighborhood and the rates that vehicles cross metered cordons. Optimal metering policies generated as a result are similarly shown to do a better job in reducing the Vehicle Hours Traveled on the network. The VHT reductions stemming from the proposed model and from its predecessors differed by as much as 14%. 

Understanding mechanisms of coexistence is a central topic in ecology. Mathematical analysis of models of competition between two identical species moving at different rates of symmetric diffusion in heterogeneous environments show that the slower mover excludes the faster one. The models have not been tested empirically and lack inclusions of a component of directed movement toward favourable areas. To address these gaps, we extended previous theory by explicitly including exploitable resource dynamics and directed movement. We tested the mathematical results experimentally using laboratory populations of the nematode worm, Caenorhabditis elegans. Our results not only support the previous theory that the species diffusing at a slower rate prevails in heterogeneous environments but also reveal that moderate levels of a directed movement component on top of the diffusive movement allow species to coexist. Our results broaden the theory of species coexistence in heterogeneous space and provide empirical confirmation of the mathematical predictions.