Skip to main content

Abstract

In this chapter is mainly devoted to the capacity allocation problem as one of the most significant for road network topology optimization. A brief review on problems concerning network design and relevant fields is given in the Sect. 6.1. Capacity allocation control for a general topology network in the form of a mathematical problem is formulated in the Sect. 6.2. The Sect. 6.3 is devoted to solving the capacity allocation problem for a single-commodity linear network of non-interfering routes. The solution is obtained explicitly that allows to make practically substantial conclusions. The Sect. 6.4 addresses the problem of optimal capacity allocation control under multi-modal traffic flows. The multi-modality influence on optimal control strategy for capacity allocation is also discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Migdalas A (1995) Bilevel programming in traffic planning: models, methods and challenge. J Glob Optim 7(4):381–405

    Article  MathSciNet  Google Scholar 

  2. Stackelberg H (1952) The theory of the market economy. Oxford University Press, London

    Google Scholar 

  3. Mazalov VV (2014) Mathematical game theory and applications. Wiley

    Google Scholar 

  4. Simaan M, Cruz JB Jr (1973) On the Stackelberg strategy in nonzero-sum games. J Optim Theory Appl 11:533–555

    Article  MathSciNet  Google Scholar 

  5. Cascetta E, Gallo M, Montella B (2006) Models and algorithms for the optimization of signal settings onurban networks with stochastic assignment. Ann Oper Res 144(1):301–328

    Article  MathSciNet  Google Scholar 

  6. Chiou S (2008) A hybrid approach for optimal design of signalized road network. Appl Math Model 32(2):195–207

    Article  Google Scholar 

  7. Meneguzzer C (1995) An equilibrium route choice model with explicit treatment of the effect of intersections. Transp Res Part B 29(5):329–356

    Article  Google Scholar 

  8. Wey WM (2000) Model formulation and solution algorithm of traffic signal control in an Urban network. Comput Environ Urban Syst 24(4):355–377

    Article  Google Scholar 

  9. Wong SC, Yang C (1999) An iterative group-based signal optimization scheme for traffic equilibrium networks. J Adv Transp 33(2):201–217

    Article  Google Scholar 

  10. Farahani RZ, Miandoabchi E, Szeto WY, Rashidi H (2013) A review of Urban transportation network design problems. Eur J Oper Res 229:281–302

    Article  MathSciNet  Google Scholar 

  11. Daganzo CF, Sheffi Y (1977) On stochastic models of traffic assignment. Transp Sci 11(3):253–274

    Article  Google Scholar 

  12. Chen M, Alfa AS (1991) A network design algorithm using astochastic incremental traffic assignment approach. Transp Sci 25(3):215–224

    Article  Google Scholar 

  13. Drezner Z, Wesolowsky GO (1997) Selecting an optimum configuration of one-way and two-way routes. Transp Sci 31(4):386–394

    Article  Google Scholar 

  14. LeBlanc LJ, Boyce DE (1986) A bilevel programming algorithm for exact solution of the network design problem with user-optimal flows. Transp Res Part B 20(3):259–265

    Article  MathSciNet  Google Scholar 

  15. Long J, Gao Z, Zhang H, Szeto WY (2010) A turning restriction design problem in Urban road networks. Eur J Oper Res 206(3):569–578

    Article  MathSciNet  Google Scholar 

  16. Gao Z, Sun H, Zhang H (2007) A globally convergent algorithm for transportation continuous network design problem. Optim Eng 8(3):241–257

    Article  MathSciNet  Google Scholar 

  17. Gao Z, Wu J, Sun H (2005) Solution algorithm for the bi-level discrete network design problem. Transp Res Part B 39(6):479–495

    Article  Google Scholar 

  18. Zhang H, Gao Z (2009) Bilevel programming model and solution method for mixed transportation network design problem. J Syst Sci Complex 22:446–459

    Article  MathSciNet  Google Scholar 

  19. Lo HK, Szeto WY (2009) Time-dependent transport network design under cost-recovery. Transp Res Part B 43(1):142–158

    Article  Google Scholar 

  20. Szeto WY, Jaber X, O’Mahony M (2010) Time-dependent discrete network design frameworks considering land use. Comput-Aided Civil Infrastruct Eng 25(6):411–426

    Article  Google Scholar 

  21. Szeto WY, Lo HK (2008) Time-dependent transport network improvement and tolling strategies. Transp Res Part A 42(2):376–391

    Google Scholar 

  22. Marcotte P, Marquis G (1992) Efficient implementation of heuristics for the continuous network design problem. Ann Oper Res 34(1):163–176

    Article  Google Scholar 

  23. Marcotte P (1986) Network design problem with congestion effects: a case of bilevel programming. Math Program 34(2):142–162

    Article  MathSciNet  Google Scholar 

  24. Suh S, Kim T (1992) Solving nonlinear bilevel programming models of the equilibrium network design problem: a comparative review. Ann Oper Res 34(1):203–218

    Article  MathSciNet  Google Scholar 

  25. Ziyou G, Yifan S (2002) A reserve capacity model of optimal signal control with user-equilibrium route choice. Transp Res Part B 36(4):313–323

    Article  Google Scholar 

  26. Mathew TV, Sharma S (2009) Capacity expansion problem for large Urban transportation networks. J Transp Eng 135(7):406–415

    Article  Google Scholar 

  27. Miandoabchi E, Farahani RZ (2010) Optimizing reserve capacity of Urban road networks in a discrete network design problem. Adv Eng Softw 42(12):1041–1050

    Article  Google Scholar 

  28. Poorzahedy H, Rouhani OM (2007) Hybrid meta-heuristic algorithms for solving network design problem. Eur J Oper Res 182(2):578–596

    Article  MathSciNet  Google Scholar 

  29. Wardrop JG (1952) Some theoretical aspects of road traffic research. Proc Inst Civil Eng 2:325–378

    Google Scholar 

  30. Sheffi Y (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall Inc., Englewood Cliffs, NJ

    Google Scholar 

  31. Patriksson M (2015) The traffic assignment problem: models and methods. Dover Publications Inc., Mineola, NY

    Google Scholar 

  32. Ben-Ayed O, Boyce DE, Blair CE III (1988) Ageneral bilevel linear programming formulation of the network design problem. Transp Res Part B 22(4):311–318

    Article  Google Scholar 

  33. Luo Z, Pang J, Ralph DC (1996) Mathematical programs with equilibrium constraints. Cambridge University Press, Cambridge

    Book  Google Scholar 

  34. LeBlanc LJ, Morlok EK, Pierskalla WP (1975) An efficient approach to solving the road network equilibrium traffic assignment problem. Transp Res 9:309–318

    Article  Google Scholar 

  35. Krylatov AY (2017) Optimal strategies for road network’s capacity allocation. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 13(2):182–192

    MathSciNet  Google Scholar 

  36. Krylatov AY (2014) Optimal strategies for traffic management in the network of parallel routes. Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2:121–130

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Krylatov .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Krylatov, A., Zakharov, V., Tuovinen, T. (2020). Topology Optimization of Road Networks. In: Optimization Models and Methods for Equilibrium Traffic Assignment. Springer Tracts on Transportation and Traffic, vol 15. Springer, Cham. https://doi.org/10.1007/978-3-030-34102-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34102-2_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34101-5

  • Online ISBN: 978-3-030-34102-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics