# American Institute of Mathematical Sciences

June  2018, 13(2): 241-260. doi: 10.3934/nhm.2018011

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

 1 Dept of Civil and Environmental Engineering, Univ. of California, Berkeley, Berkeley, CA, USA 2 Dept. of Operations Research and Financial Engineering, Princeton University, Princeton, NJ, USA 3 TSS-Transport Simulation Systems, Barcelona, Spain 4 Dept of Civil and Environmental Engineering, Dept. of Electrical Engineering and Computer Science, Univ. of California, Berkeley, Berkeley, CA, USA

Received  May 2016 Revised  February 2018 Published  May 2018

Fund Project: This work was funded by the California Department of Transportation under the Connected Corridors program.

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.

Citation: Leah Anderson, Thomas Pumir, Dimitrios Triantafyllos, Alexandre M. Bayen. Stability and implementation of a cycle-based max pressure controller for signalized traffic networks. Networks & Heterogeneous Media, 2018, 13 (2) : 241-260. doi: 10.3934/nhm.2018011
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##### References:
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
Cb-MP demonstrated service rates that are consistent with a fully-actuated control system for similar cycle lengths
Cb-MP outperforms the actuated controller given high demand in terms of vehicle delay
While Cb-MP caused more vehicle stop events, stoppage times were similar to those observed using the actuated controller
Observed queues increase with cycle length using CbMP control
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