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1. Analytical Method to Approximate the Impact of Turning on the Macroscopic Fundamental Diagram

   https://doi.org/10.1177/0361198120933274  

   Xu, Guanhao; Yu, Zhengyao; Gayah, Vikash V. (September 2020, Transportation Research Record: Journal of the Transportation Research Board)

   null (Ed.)

   Network macroscopic fundamental diagrams (MFDs) have recently been shown to exist in real-world urban traffic networks. The existence of an MFD facilitates the modeling of urban traffic network dynamics at a regional level, which can be used to identify and refine large-scale network-wide control strategies. To be useful, MFD-based modeling frameworks require an estimate of the functional form of a network’s MFD. Analytical methods have been proposed to estimate a network’s MFD by abstracting the network as a single ring-road or corridor and modeling the flow–density relationship on that simplified element. However, these existing methods cannot account for the impact of turning traffic, as only a single corridor is considered. This paper proposes a method to estimate a network’s MFD when vehicles are allowed to turn into or out of a corridor. A two-ring abstraction is first used to analyze how turning will affect vehicle travel in a more general network, and then the model is further approximated using a single ring-road or corridor. This approximation is useful as it facilitates the application of existing variational theory-based methods (the stochastic method of cuts) to estimate the flow–density relationship on the corridor, while accounting for the stochastic nature of turning. Results of the approximation compared with a more realistic simulation that includes features that cannot be captured using variational theory—such as internal origins and destinations—suggest that this approximation works to estimate a network’s MFD when turning traffic is present. 

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2. Coordinated Perimeter Flow and Variable Speed Limit Control for Mixed Freeway and Urban Networks

   https://doi.org/10.1177/03611981211036677  

   Yocum, Rebeka; Gayah, Vikash V. (January 2022, Transportation Research Record: Journal of the Transportation Research Board)

   Recent studies have leveraged the existence of network macroscopic fundamental diagrams (MFD) to develop regional control strategies for urban traffic networks. Existing MFD-based control strategies focus on vehicle movement within and across regions of an urban network and do not consider how freeway traffic can be controlled to improve overall traffic operations in mixed freeway and urban networks. The purpose of this study is to develop a coordinated traffic management scheme that simultaneously implements perimeter flow control on an urban network and variable speed limits (VSL) on a freeway to reduce total travel time in such a mixed network. By slowing down vehicles traveling along the freeway, VSL can effectively meter traffic exiting the freeway into the urban network. This can be particularly useful since freeways often have large storage capacities and vehicles accumulating on freeways might be less disruptive to overall system operations than on urban streets. VSL can also be used to change where freeway vehicles enter the urban network to benefit the entire system. The combined control strategy is implemented in a model predictive control framework with several realistic constraints, such as gradual reductions in freeway speed limit. Numerical tests suggest that the combined implementation of VSL and perimeter metering control can improve traffic operations compared with perimeter metering alone. 

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3. City-wide traffic control: Modeling impacts of cordon queues

   https://doi.org/https://doi.org/10.1016/j.trc.2019.04.024  

   Ni, Wei; Cassidy, Michael (April 2020, Transportation research Part C Emerging technologies)

   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%. 

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4. On the impacts of roadway hierarchy on the network Macroscopic Fundamental Diagram

   Xu, Guanhao; Gayah, Vikash V. (January 2021, 100th Annual Meeting of the Transportation Research Board)

   null (Ed.)

   Relationships between average network productivity and accumulation or density aggregated 2 across spatially compact regions of urban networks—so called network Macroscopic Fundamental 3 Diagrams (MFDs)—have recently been shown to exist. Various analytical methods have been put 4 forward to estimate a network’s MFD as a function of network properties, such as average block 5 lengths, signal timings, and traffic flow characteristics on links. However, real street networks are 6 not homogeneous—they generally have a hierarchical structure where some streets (e.g., arterials) 7 promote higher mobility than others (e.g., local roads). This paper provides an analytical method 8 to estimate the MFDs of hierarchical street networks by considering features that are specific to 9 hierarchical network structures. Since the performance of hierarchical networks is driven by how 10 vehicles are routed across the different street types, two routing conditions— user equilibrium and 11 system optimal routing—are considered in the analytical model. The proposed method is first 12 implemented to describe the MFD of a hierarchical one-way limited access linear corridor and 13 then extended to a more realistic hierarchical two-dimensional grid network. For both cases, it is 14 shown that the MFD of a hierarchical network may no longer be unimodal or concave as 15 traditionally assumed in most MFD-based modeling frameworks. These findings are verified using 16 simulations of hierarchical corridors. Finally, the proposed methodology is applied to demonstrate 17 how it can be used to make decisions related to the design of hierarchical street network structures. 

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5. Cordon control with spatially-varying metering rates: a Reinforcement Learning approach

   https://doi.org/https://doi.org/10.1016/j.trc.2018.12.007  

   Ni, W. and (January 2019, Transportation research. Part C, Emerging technologies)

   The work explores how Reinforcement Learning can be used to re-time traffic signals around cordoned neighborhoods. An RL-based controller is developed by representing traffic states as graph-structured data and customizing corresponding neural network architectures to handle those data. The customizations enable the controller to: (i) model neighborhood-wide traffic based on directed-graph representations; (ii) use the representations to identify patterns in real-time traffic measurements; and (iii) capture those patterns to a spatial representation needed for selecting optimal cordon-metering rates. Input to the selection process also includes a total inflow to be admitted through a cordon. The rate is optimized in a separate process that is not part of the present work. Our RL-controller distributes that separately-optimized rate across the signalized street links that feed traffic through the cordon. The resulting metering rates vary from one feeder link to the next. The selection process can reoccur at short time intervals in response to changing traffic patterns. Once trained on a few cordons, the RL-controller can be deployed on cordons elsewhere in a city without additional training. This portability feature is confirmed via simulations of traffic on an idealized street network. The tests also indicate that the controller can reduce the network’s vehicle hours traveled well beyond what can be achieved via spatially-uniform cordon metering. The extra reductions in VHT are found to grow larger when traffic exhibits greater in-homogeneities over the network. 

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