IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v100y2017icp82-92.html
   My bibliography  Save this article

Offset optimization in signalized traffic networks via semidefinite relaxation

Author

Listed:
  • Coogan, Samuel
  • Kim, Eric
  • Gomes, Gabriel
  • Arcak, Murat
  • Varaiya, Pravin

Abstract

We study the problem of selecting offsets of the traffic signals in a network of signalized intersections to reduce queues of vehicles at all intersections. The signals in the network have a common cycle time and a fixed timing plan. It is assumed that the exogenous demands are constant or periodic with the same period as the cycle time and the intersections are under-saturated. The resulting queuing processes are periodic. These periodic processes are approximated by sinusoids. The sinusoidal approximation leads to an analytical expression of the queue lengths at every intersection as a function of the demands and the vector of offsets. The optimum offset vector is the solution of a quadratically constrained quadratic program (QCQP), which is solved via its convex semidefinite relaxation. Unlike existing techniques, our approach accommodates networks with arbitrary topology and scales well with network size. We illustrate the result in two case studies. The first is an academic example previously proposed in the literature, and the second case study consists of an arterial corridor network in Arcadia, California.

Suggested Citation

  • Coogan, Samuel & Kim, Eric & Gomes, Gabriel & Arcak, Murat & Varaiya, Pravin, 2017. "Offset optimization in signalized traffic networks via semidefinite relaxation," Transportation Research Part B: Methodological, Elsevier, vol. 100(C), pages 82-92.
    • Handle: RePEc:eee:transb:v:100:y:2017:i:c:p:82-92
    DOI: 10.1016/j.trb.2017.01.016
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0191261516302648
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2017.01.016?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Wong, S. C., 1995. "Derivatives of the performance index for the traffic model from TRANSYT," Transportation Research Part B: Methodological, Elsevier, vol. 29(5), pages 303-327, October.
    2. Nathan H. Gartner & John D. C. Little & Henry Gabbay, 1975. "Optimization of Traffic Signal Settings by Mixed-Integer Linear Programming," Transportation Science, INFORMS, vol. 9(4), pages 321-343, November.
    3. Little, John D. C. & Kelson, Mark D. & Gartner, Nathan H., 1981. "MAXBAND : a versatile program for setting signals on arteries and triangular networks," Working papers 1185-81., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    4. Nathan H. Gartner & John D. C. Little & Henry Gabbay, 1975. "Optimization of Traffic Signal Settings by Mixed-Integer Linear Programming," Transportation Science, INFORMS, vol. 9(4), pages 344-363, November.
    5. R. E. Allsop, 1968. "Selection of Offsets to Minimize Delay to Traffic in a Network Controlled by Fixed-Time Signals," Transportation Science, INFORMS, vol. 2(1), pages 1-13, February.
    6. Nathan H. Gartner & Rahul Deshpande, 2009. "Harmonic Analysis and Optimization of Traffic Signal Systems," Springer Books, in: William H. K. Lam & S. C. Wong & Hong K. Lo (ed.), Transportation and Traffic Theory 2009: Golden Jubilee, chapter 0, pages 345-364, Springer.
    7. Wong, S. C., 1996. "Group-based optimisation of signal timings using the TRANSYT traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 30(3), pages 217-244, June.
    8. Andrew Korsak, 1973. "An Algorithm for Globally-Optimal Nonlinear-Cost Multidimensional Flows in Networks and Some Special Applications," Operations Research, INFORMS, vol. 21(1), pages 225-239, February.
    9. Muralidharan, Ajith & Pedarsani, Ramtin & Varaiya, Pravin, 2015. "Analysis of fixed-time control," Transportation Research Part B: Methodological, Elsevier, vol. 73(C), pages 81-90.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sadek, Bassel & Doig Godier, Jean & Cassidy, Michael J & Daganzo, Carlos F, 2022. "Traffic signal plans to decongest street grids," Transportation Research Part B: Methodological, Elsevier, vol. 162(C), pages 195-208.
    2. Wong, S. C. & Wong, W. T. & Leung, C. M. & Tong, C. O., 2002. "Group-based optimization of a time-dependent TRANSYT traffic model for area traffic control," Transportation Research Part B: Methodological, Elsevier, vol. 36(4), pages 291-312, May.
    3. Zhou, Xuesong, 2017. "Recasting and optimizing intersection automation as a connected-and-automated-vehicle (CAV) scheduling problem: A sequential branch-and-bound search approach in phase-time-traffic hypernetworkAuthor-N," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 479-506.
    4. Yu, Chunhui & Ma, Wanjing & Yang, Xiaoguang, 2020. "A time-slot based signal scheme model for fixed-time control at isolated intersections," Transportation Research Part B: Methodological, Elsevier, vol. 140(C), pages 176-192.
    5. Rey, David & Levin, Michael W., 2019. "Blue phase: Optimal network traffic control for legacy and autonomous vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 130(C), pages 105-129.
    6. Pillai, Rekha S. & Rathi*, Ajay K. & L. Cohen, Stephen, 1998. "A restricted branch-and-bound approach for generating maximum bandwidth signal timing plans for traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 32(8), pages 517-529, November.
    7. Chow, Andy H.F. & Lo, Hong K., 2007. "Sensitivity analysis of signal control with physical queuing: Delay derivatives and an application," Transportation Research Part B: Methodological, Elsevier, vol. 41(4), pages 462-477, May.
    8. Wong, S. C. & Yang, Chao & Lo, Hong K., 2001. "A path-based traffic assignment algorithm based on the TRANSYT traffic model," Transportation Research Part B: Methodological, Elsevier, vol. 35(2), pages 163-181, February.
    9. Wong, C. K. & Wong, S. C., 2003. "Lane-based optimization of signal timings for isolated junctions," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 63-84, January.
    10. Le, Tung & Vu, Hai L. & Walton, Neil & Hoogendoorn, Serge P. & Kovács, Péter & Queija, Rudesindo N., 2017. "Utility optimization framework for a distributed traffic control of urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 539-558.
    11. Little, John D. C. & Kelson, Mark D. & Gartner, Nathan H., 1981. "MAXBAND : a versatile program for setting signals on arteries and triangular networks," Working papers 1185-81., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    12. Lee, Seunghyeon & Wong, S.C. & Varaiya, Pravin, 2017. "Group-based hierarchical adaptive traffic-signal control Part II: Implementation," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 376-397.
    13. Lee, Seunghyeon & Wong, S.C. & Varaiya, Pravin, 2017. "Group-based hierarchical adaptive traffic-signal control part I: Formulation," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 1-18.
    14. Yao, Zhihong & Zhao, Bin & Qin, Lingqiao & Jiang, Yangsheng & Ran, Bin & Peng, Bo, 2020. "An efficient heterogeneous platoon dispersion model for real-time traffic signal control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    15. Lee, Seunghyeon & Wong, S.C., 2017. "Group-based approach to predictive delay model based on incremental queue accumulations for adaptive traffic control systems," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 1-20.
    16. Xingmin Wang & Zachary Jerome & Zihao Wang & Chenhao Zhang & Shengyin Shen & Vivek Vijaya Kumar & Fan Bai & Paul Krajewski & Danielle Deneau & Ahmad Jawad & Rachel Jones & Gary Piotrowicz & Henry X. L, 2024. "Traffic light optimization with low penetration rate vehicle trajectory data," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    17. Lo, Hong K., 1999. "A novel traffic signal control formulation," Transportation Research Part A: Policy and Practice, Elsevier, vol. 33(6), pages 433-448, August.
    18. Giulio Cantarella & Antonino Vitetta, 2006. "The multi-criteria road network design problem in an urban area," Transportation, Springer, vol. 33(6), pages 567-588, November.
    19. Kouvelas, Anastasios & Saeedmanesh, Mohammadreza & Geroliminis, Nikolas, 2017. "Enhancing model-based feedback perimeter control with data-driven online adaptive optimization," Transportation Research Part B: Methodological, Elsevier, vol. 96(C), pages 26-45.
    20. Yuan, Tianchen & Ioannou, Petros A., 2023. "Coordinated Traffic Flow Control in a Connected Environment," Institute of Transportation Studies, Working Paper Series qt6q67f9z4, Institute of Transportation Studies, UC Davis.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:100:y:2017:i:c:p:82-92. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.