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
References:
[1]

K. AboudolasM. Papageorgiou and E. Kosmatopoulos, Store-and-forward based methods for the signal control problem in large-scale congested urban networks, Transportation Research Part C: Emerging Technologies, 17 (2009), 163-174.  doi: 10.1016/j.trc.2008.10.002.  Google Scholar

[2]

R. E. Allsop, Estimating the traffic capacity of a signalized road junction, Transportation Research, 6 (1972), 245-255.  doi: 10.1016/0041-1647(72)90017-2.  Google Scholar

[3]

M. AndrewsK. KumaranK. RamananA. StolyarR. Vijayakumar and P. Whiting, Scheduling in a queuing system with asynchronously varying service rates, Probability in the Engineering and Informational Sciences, 18 (2004), 191-217.  doi: 10.1017/S0269964804182041.  Google Scholar

[4]

R. Brockett, Stabilization of motor networks, in Proceedings of the 34th IEEE Conference on Decision and Control, 1995, 1484–1488. doi: 10.1109/CDC.1995.480312.  Google Scholar

[5]

J. G. Dai and W. Q. Lin, Maximum pressure policies in stochastic processing networks, Operations Research, 53 (2005), 197-218.  doi: 10.1287/opre.1040.0170.  Google Scholar

[6]

E. J. Davison and U. Ozguner, Decentralized control of traffic networks, IEEE Transactions on Systems, Man, and Cybernetics, 13 (1983), 476-487.  doi: 10.1109/TAC.1983.1103296.  Google Scholar

[7]

M. Egerstedt and Y. Wardi, Multi-process control using queuing theory, in Proceedings of the 41st IEEE Conference on Decision and Control, 2002, 1991–1996. doi: 10.1109/CDC.2002.1184820.  Google Scholar

[8]

P. Giaccone, E. Leonardi and D. Shah, On the maximal throughput of networks with finite buffers and its application to buffered crossbars, in Proceedings of the 24th Annual Joint Conference of the IEEE Computer and Communications Societies, 2005,971–980. doi: 10.1109/INFCOM.2005.1498326.  Google Scholar

[9]

P. B. Hunt, D. I. Robertson, R. D. Bretherton and R. I. Winton, SCOOT - a Traffic Responsive Method of Coordinating Signals, Transport and Road Research Laboratory, UK, 1981. Google Scholar

[10]

H. Ishii and B. A. Francis, Stabilizing a linear system by switching control with dwell time, IEEE Trans. Automat. Control, 47 (2002), 1962-1973.  doi: 10.1109/TAC.2002.805689.  Google Scholar

[11]

M. J. NeelyE. Modiano and C. E. Rohrs, Dynamic power allocation and routing for time-varying wireless networks, IEEE Journal on Selected Areas in Communications, 23 (2005), 89-103.   Google Scholar

[12]

M. Pajic, S. Sundaram and G. J. Pappas, Stabilizability over Deterministic Relay Networks, in Proceedings of the 52nd IEEE Conference on Decision and Control, 2013. doi: 10.1109/CDC.2013.6760504.  Google Scholar

[13]

A. G. Sims and K. W. Dobinson, The Sydney coordinated adaptive traffic (SCAT) system philosophy and benefits, IEEE Transactions on Vehicular Technology, 29 (1980), 130-137.  doi: 10.1109/T-VT.1980.23833.  Google Scholar

[14]

A. L. Stolyar, MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic, Annals of Applied Probability, 14 (2004), 1-53.  doi: 10.1214/aoap/1075828046.  Google Scholar

[15]

L. Tassiulas, Adaptive back-pressure congestion control-based on local information, IEEE Transactions on Automatic Control, 40 (1995), 236-250.  doi: 10.1109/9.341781.  Google Scholar

[16]

L. Tassiulas and A. Ephremides, Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks, IEEE Transactions on Automatic Control, 37 (1992), 1936-1948.  doi: 10.1109/9.182479.  Google Scholar

[17]

M. van den Berg, A. Hegyi, B. De Schutter and H. Hellendoorn, A macroscopic traffic flow model for integrated control of freeway and urban traffic networks, in Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, 2774–2779. Google Scholar

[18]

P. Varaiya, Max pressure control of a network of signalized intersections, Transportation Research Part C: Emerging Technologies, 36 (2013), 177-195.  doi: 10.1016/j.trc.2013.08.014.  Google Scholar

[19]

T. Wongpiromsarn, T. Uthaicharoenpong, Y. Wang, E. Frazzoli and D. Wang, Distributed traffic signal control for maximum network throughput, in Proceedings of the 15th International IEEE Conference on Intelligent Transportation Systems, 2012,588–595. doi: 10.1109/ITSC.2012.6338817.  Google Scholar

[20]

H. M. ZhangY. M. Nie and Z. S. Qian, Modelling network flow with and without link interactions: The cases of point queue, spatial queue and cell transmission model, Transportmetrica B: Transport Dynamics, 1 (2013), 33-51.   Google Scholar

show all references

References:
[1]

K. AboudolasM. Papageorgiou and E. Kosmatopoulos, Store-and-forward based methods for the signal control problem in large-scale congested urban networks, Transportation Research Part C: Emerging Technologies, 17 (2009), 163-174.  doi: 10.1016/j.trc.2008.10.002.  Google Scholar

[2]

R. E. Allsop, Estimating the traffic capacity of a signalized road junction, Transportation Research, 6 (1972), 245-255.  doi: 10.1016/0041-1647(72)90017-2.  Google Scholar

[3]

M. AndrewsK. KumaranK. RamananA. StolyarR. Vijayakumar and P. Whiting, Scheduling in a queuing system with asynchronously varying service rates, Probability in the Engineering and Informational Sciences, 18 (2004), 191-217.  doi: 10.1017/S0269964804182041.  Google Scholar

[4]

R. Brockett, Stabilization of motor networks, in Proceedings of the 34th IEEE Conference on Decision and Control, 1995, 1484–1488. doi: 10.1109/CDC.1995.480312.  Google Scholar

[5]

J. G. Dai and W. Q. Lin, Maximum pressure policies in stochastic processing networks, Operations Research, 53 (2005), 197-218.  doi: 10.1287/opre.1040.0170.  Google Scholar

[6]

E. J. Davison and U. Ozguner, Decentralized control of traffic networks, IEEE Transactions on Systems, Man, and Cybernetics, 13 (1983), 476-487.  doi: 10.1109/TAC.1983.1103296.  Google Scholar

[7]

M. Egerstedt and Y. Wardi, Multi-process control using queuing theory, in Proceedings of the 41st IEEE Conference on Decision and Control, 2002, 1991–1996. doi: 10.1109/CDC.2002.1184820.  Google Scholar

[8]

P. Giaccone, E. Leonardi and D. Shah, On the maximal throughput of networks with finite buffers and its application to buffered crossbars, in Proceedings of the 24th Annual Joint Conference of the IEEE Computer and Communications Societies, 2005,971–980. doi: 10.1109/INFCOM.2005.1498326.  Google Scholar

[9]

P. B. Hunt, D. I. Robertson, R. D. Bretherton and R. I. Winton, SCOOT - a Traffic Responsive Method of Coordinating Signals, Transport and Road Research Laboratory, UK, 1981. Google Scholar

[10]

H. Ishii and B. A. Francis, Stabilizing a linear system by switching control with dwell time, IEEE Trans. Automat. Control, 47 (2002), 1962-1973.  doi: 10.1109/TAC.2002.805689.  Google Scholar

[11]

M. J. NeelyE. Modiano and C. E. Rohrs, Dynamic power allocation and routing for time-varying wireless networks, IEEE Journal on Selected Areas in Communications, 23 (2005), 89-103.   Google Scholar

[12]

M. Pajic, S. Sundaram and G. J. Pappas, Stabilizability over Deterministic Relay Networks, in Proceedings of the 52nd IEEE Conference on Decision and Control, 2013. doi: 10.1109/CDC.2013.6760504.  Google Scholar

[13]

A. G. Sims and K. W. Dobinson, The Sydney coordinated adaptive traffic (SCAT) system philosophy and benefits, IEEE Transactions on Vehicular Technology, 29 (1980), 130-137.  doi: 10.1109/T-VT.1980.23833.  Google Scholar

[14]

A. L. Stolyar, MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic, Annals of Applied Probability, 14 (2004), 1-53.  doi: 10.1214/aoap/1075828046.  Google Scholar

[15]

L. Tassiulas, Adaptive back-pressure congestion control-based on local information, IEEE Transactions on Automatic Control, 40 (1995), 236-250.  doi: 10.1109/9.341781.  Google Scholar

[16]

L. Tassiulas and A. Ephremides, Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks, IEEE Transactions on Automatic Control, 37 (1992), 1936-1948.  doi: 10.1109/9.182479.  Google Scholar

[17]

M. van den Berg, A. Hegyi, B. De Schutter and H. Hellendoorn, A macroscopic traffic flow model for integrated control of freeway and urban traffic networks, in Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, 2774–2779. Google Scholar

[18]

P. Varaiya, Max pressure control of a network of signalized intersections, Transportation Research Part C: Emerging Technologies, 36 (2013), 177-195.  doi: 10.1016/j.trc.2013.08.014.  Google Scholar

[19]

T. Wongpiromsarn, T. Uthaicharoenpong, Y. Wang, E. Frazzoli and D. Wang, Distributed traffic signal control for maximum network throughput, in Proceedings of the 15th International IEEE Conference on Intelligent Transportation Systems, 2012,588–595. doi: 10.1109/ITSC.2012.6338817.  Google Scholar

[20]

H. M. ZhangY. M. Nie and Z. S. Qian, Modelling network flow with and without link interactions: The cases of point queue, spatial queue and cell transmission model, Transportmetrica B: Transport Dynamics, 1 (2013), 33-51.   Google Scholar

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
[1]

Qiang Fu, Yanlong Zhang, Yushu Zhu, Ting Li. Network centralities, demographic disparities, and voluntary participation. Mathematical Foundations of Computing, 2020, 3 (4) : 249-262. doi: 10.3934/mfc.2020011

[2]

Shipra Singh, Aviv Gibali, Xiaolong Qin. Cooperation in traffic network problems via evolutionary split variational inequalities. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020170

[3]

Yicheng Liu, Yipeng Chen, Jun Wu, Xiao Wang. Periodic consensus in network systems with general distributed processing delays. Networks & Heterogeneous Media, 2020  doi: 10.3934/nhm.2021002

[4]

Rajendra K C Khatri, Brendan J Caseria, Yifei Lou, Guanghua Xiao, Yan Cao. Automatic extraction of cell nuclei using dilated convolutional network. Inverse Problems & Imaging, 2021, 15 (1) : 27-40. doi: 10.3934/ipi.2020049

[5]

Pan Zheng. Asymptotic stability in a chemotaxis-competition system with indirect signal production. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1207-1223. doi: 10.3934/dcds.2020315

[6]

Editorial Office. Retraction: Honggang Yu, An efficient face recognition algorithm using the improved convolutional neural network. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 901-901. doi: 10.3934/dcdss.2019060

[7]

Yu-Jhe Huang, Zhong-Fu Huang, Jonq Juang, Yu-Hao Liang. Flocking of non-identical Cucker-Smale models on general coupling network. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1111-1127. doi: 10.3934/dcdsb.2020155

[8]

Ziang Long, Penghang Yin, Jack Xin. Global convergence and geometric characterization of slow to fast weight evolution in neural network training for classifying linearly non-separable data. Inverse Problems & Imaging, 2021, 15 (1) : 41-62. doi: 10.3934/ipi.2020077

[9]

Zuliang Lu, Fei Huang, Xiankui Wu, Lin Li, Shang Liu. Convergence and quasi-optimality of $ L^2- $norms based an adaptive finite element method for nonlinear optimal control problems. Electronic Research Archive, 2020, 28 (4) : 1459-1486. doi: 10.3934/era.2020077

[10]

Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323

[11]

Jian Zhang, Tony T. Lee, Tong Ye, Liang Huang. An approximate mean queue length formula for queueing systems with varying service rate. Journal of Industrial & Management Optimization, 2021, 17 (1) : 185-204. doi: 10.3934/jimo.2019106

[12]

Jakub Kantner, Michal Beneš. Mathematical model of signal propagation in excitable media. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 935-951. doi: 10.3934/dcdss.2020382

[13]

Yu Zhou, Xinfeng Dong, Yongzhuang Wei, Fengrong Zhang. A note on the Signal-to-noise ratio of $ (n, m) $-functions. Advances in Mathematics of Communications, 2020  doi: 10.3934/amc.2020117

[14]

Hui Zhao, Zhengrong Liu, Yiren Chen. Global dynamics of a chemotaxis model with signal-dependent diffusion and sensitivity. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2021011

[15]

Li-Bin Liu, Ying Liang, Jian Zhang, Xiaobing Bao. A robust adaptive grid method for singularly perturbed Burger-Huxley equations. Electronic Research Archive, 2020, 28 (4) : 1439-1457. doi: 10.3934/era.2020076

[16]

Ke Su, Yumeng Lin, Chun Xu. A new adaptive method to nonlinear semi-infinite programming. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021012

[17]

Tengfei Yan, Qunying Liu, Bowen Dou, Qing Li, Bowen Li. An adaptive dynamic programming method for torque ripple minimization of PMSM. Journal of Industrial & Management Optimization, 2021, 17 (2) : 827-839. doi: 10.3934/jimo.2019136

[18]

Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019

[19]

Wenbin Lv, Qingyuan Wang. Global existence for a class of Keller-Segel models with signal-dependent motility and general logistic term. Evolution Equations & Control Theory, 2021, 10 (1) : 25-36. doi: 10.3934/eect.2020040

[20]

Gang Bao, Mingming Zhang, Bin Hu, Peijun Li. An adaptive finite element DtN method for the three-dimensional acoustic scattering problem. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 61-79. doi: 10.3934/dcdsb.2020351

2019 Impact Factor: 1.053

Metrics

  • PDF downloads (168)
  • HTML views (216)
  • Cited by (2)

[Back to Top]