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Stability and implementation of a cycle-based max pressure controller for signalized traffic networks

This work was funded by the California Department of Transportation under the Connected Corridors program.
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  • Intelligent use of network capacity via responsive signal control will become increasingly essential as congestion increases on urban roadways. Existing adaptive control systems require lengthy location-specific tuning procedures or expensive central communications infrastructure. Previous theoretical work proposed the application of a max pressure controller to maximize network throughput in a distributed manner with minimal calibration. Yet this algorithm as originally formulated has unpractical hardware and safety constraints. We fundamentally alter the formulation of the max pressure controller to a setting where the actuation can only update once per multiple time steps of the modeled dynamics. This is motivated by the case of a traffic signal that can only update green splits based on observed link-counts once per "cycle time" of 60-120 seconds. Furthermore, we extend the domain of allowable actuations from a single signal phase to any convex combination of available signal phases to model intra-cycle signal changes dictated by pre-selected cycle green splits. We show that this extended max pressure controller will stabilize a vertical queueing network given restrictions on admissible demand flows that are slightly stronger than those suggested in the original formulation of max pressure. We ultimately apply our cycle-based extension of max pressure to a simulation of an existing arterial network and provide comparison to the control policy that is currently deployed at the modeled location.

    Mathematics Subject Classification: Primary: 90B15, 93C99; Secondary: 90B20.

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  • Figure 1.  The chosen network was calibrated to represent realistic demands and physical parameters observed on a stretch of Black Mountain Road near the I-15 freeway in San Diego, California

    Figure 2.  Cb-MP demonstrated service rates that are consistent with a fully-actuated control system for similar cycle lengths

    Figure 3.  Cb-MP outperforms the actuated controller given high demand in terms of vehicle delay

    Figure 4.  While Cb-MP caused more vehicle stop events, stoppage times were similar to those observed using the actuated controller

    Figure 5.  Observed queues increase with cycle length using CbMP control

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