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Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections

Author

Listed:
  • Boon, Marko
  • Janssen, Guido
  • van Leeuwaarden, Johan
  • Timmerman, Rik

Abstract

Setting traffic light signals is a classical topic in traffic engineering, and important in heavy-traffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an elementary queueing model for one traffic light with cyclic signaling, we obtain heavy-traffic limits that capture the long-term queue behavior. We leverage the limit theorems to obtain sharp performance approximations for one queue in heavy traffic. We also consider optimization problems that aim for optimal division of green times among multiple conflicting traffic streams. We show that inserting heavy-traffic approximations leads to tractable optimization problems and close-to-optimal signal prescriptions.

Suggested Citation

  • Boon, Marko & Janssen, Guido & van Leeuwaarden, Johan & Timmerman, Rik, 2023. "Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 79-98.
    • Handle: RePEc:eee:transb:v:167:y:2023:i:c:p:79-98
    DOI: 10.1016/j.trb.2022.11.010
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    References listed on IDEAS

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    1. A. Oblakova & A. Al Hanbali & R. J. Boucherie & J. C. W. Ommeren & W. H. M. Zijm, 2019. "An exact root-free method for the expected queue length for a class of discrete-time queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 257-292, August.
    2. M. A. A. Boon & A. J. E. M. Janssen & J. S. H. Leeuwaarden & R. W. Timmerman, 2019. "Pollaczek contour integrals for the fixed-cycle traffic-light queue," Queueing Systems: Theory and Applications, Springer, vol. 91(1), pages 89-111, February.
    3. J. N. Darroch & G. F. Newell & R. W. J. Morris, 1964. "Queues for a Vehicle-Actuated Traffic Light," Operations Research, INFORMS, vol. 12(6), pages 882-895, December.
    4. Winands, E.M.M. & Adan, I.J.B.F. & van Houtum, G.J., 2011. "The stochastic economic lot scheduling problem: A survey," European Journal of Operational Research, Elsevier, vol. 210(1), pages 1-9, April.
    5. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    6. Sem Borst & Avi Mandelbaum & Martin I. Reiman, 2004. "Dimensioning Large Call Centers," Operations Research, INFORMS, vol. 52(1), pages 17-34, February.
    7. António Pacheco & Maria Lurdes Simões Simões & Paula Milheiro-Oliveira, 2017. "Queues with Server Vacations as a Model for Pretimed Signalized Urban Traffic," Transportation Science, INFORMS, vol. 51(3), pages 841-851, August.
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