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Generating the family of all traffic signal light cycles coordinated with pedestrian crosswalks

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Abstract

In this paper, the problem of setting traffic light cycles at crossroads and intersections is considered in order to reduce traffic congestion by minimizing total vehicle waiting time. In general, a signal light cycle should have the least number of phases. A method to determine the family \(\wp \) of all discrete cycle phasing systems with the minimum number of phases is presented. The aim is to detect from among all the components of \(\wp \) the most appropriate phasing sequence for traffic control corresponding to a current traffic situation, taking into account the activity of all pedestrian crosswalks at the intersection. The method is applied to both a typical and a complex multi-cross intersection. The problem, dealing with traffic movements and the conflicting relations that arise, is stated within the framework of graph theory.

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References

  1. Aho, A., Hopcroft, J., Ullmanm, J.: Data Structures and Algorithms. Addison-Wesley, Boston (1987)

    Google Scholar 

  2. Alexiou, D., Katsavounis, S.: Determining the minimum number of ware-houses and their space-size for storing compatible items, optimization theory, decision making, and operations research applications. In: Springer Proceedings in Mathematics & Statistics, pp. 189–198 (2013)

  3. Christofides, N.: Graph Theory. An Algorithmic Approach. Academic Press, New York (1975)

    MATH  Google Scholar 

  4. Diakaki, C., Papageorgiou, M., Aboudolas, K.: A multivariable regulator approach to traffic-responsive network-wide signal control. Control Eng. Pract. 10(2), 183–195 (2002)

    Article  Google Scholar 

  5. Garey, M.R., Johnson, D.S.: Computer Intractability: A Guide to the theory of NP-Completeness. Freeman, San Francisco (1979)

    Google Scholar 

  6. Harary, F.: Graph Theory. Addison Wesley, Boston (1969)

    Google Scholar 

  7. Jinwoo, L., Baher, A., Amer, S., Eui-Hwan, C.: Real-time optimization for adaptive traffic signal control using genetic algorithms. J. Intell. Transp. Syst. 9(3) (2005)

  8. Kouvelas, A., Aboudolas, K., Papageorgiou, M., Kosmatopoulos, E.B.: IEEE transactions on a hybrid strategy for real-time traffic signal control of urban road networks, intelligent transportation systems, vol. 12, no. 3 (2011)

  9. Leena, S., Sudhanshu, T., Himakshi, A.: Time optimization for traffic signal control using genetic algorithm. Int. J. Recent Trends Eng. 2(2). Academic Publisher, New York (2009)

  10. Michaels, J.G., Kenneth, H.R.: Application of Discrete Mathematics. McGraw-Hill Inc, New York (1991)

    Google Scholar 

  11. Mathew, T., Krishna R.: Traffic signal design-I, Chap. 41, NPTEL (2006). www.cdeep.iitb.ac.in/nptel/Civil%20Engineering/Transportation%20Engg%201/41-Ltexhtml/nptel_ceTEI_L41.pdf

  12. Opsut, R.J., Roberts, F.S.: I-Colorings. I-Phasings and I-intersection assignments for graphs, and their applications. Networks 13, 327–345 (1983b)

    Article  MathSciNet  MATH  Google Scholar 

  13. Raychaudhuri, A.: Optimal multiple interval assignments in frequency assignment and traffic phasing. Discrete Appl. Math. 40(3), 319–332 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  14. Roberts, F.S.: Some applications of graph theory. Department of Mathematics and DIMACS, Rutgers University, draft October 1 (2000). http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.76.5815&rep=rep1&type=pdf

  15. Stoffers, K.E.: Scheduling of traffic lights–a new approach. Transport. Res. 2, 199–234 (1968)

    Article  Google Scholar 

  16. Traffic Signal Design, Section 7, Phasing and Signal Groups, Department of Transportation, Minnesota (2013). http://www.dot.state.mn.us/trafficeng/publ/signaloperations/2013_Signal_Opt_and_Timing_Manual.pdf

  17. Traffic Signal Design, Section7, Phasing and Signal Group display sequence, Roads and Traffic (2011). http://www.rms.nsw.gov.au/documents/business-industry/partners-and-suppliers/guidelines/complementary-traffic-material/tsdsect7v12-i.pdf

  18. Traffic Signal Guidelines, 2004, Boston Transportation Department, Massachussets. https://www.cityofboston.gov/transportation/pdfs/traf_signal_oper_design_guide.pdf

  19. Traffic Signal Operation Handbook, Texas Transportation Institute, The Texas A&M University System, Research and Technology Implementation Office, Austin, Texas (2009). http://d2dtl5nnlpfr0r.cloudfront.net/tti.tamu.edu/documents/0-5629-P1.pdf

  20. Vogel, A., Goerick, C, von Werner, A.: Evolutionary Algorithms for Optimizing Traffic Signal Operation, ESIT 2000. Aachen, Germany, pp. 14–15 (2000)

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  1. Department of Spatial Planning and Development Engineering, School of Engineering, Aristotle University of Thessaloniki, 541 24, Thessaloniki, Greece

    Dimitra Alexiou

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  1. Dimitra Alexiou
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Correspondence to Dimitra Alexiou.

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Alexiou, D. Generating the family of all traffic signal light cycles coordinated with pedestrian crosswalks. Optim Lett 10, 473–484 (2016). https://doi.org/10.1007/s11590-015-0871-x

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  • DOI: https://doi.org/10.1007/s11590-015-0871-x

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