# Transportation Models

• Dietmar P. F. Möller
Chapter
Part of the Simulation Foundations, Methods and Applications book series (SFMA)

## Abstract

This chapter begins, in Sect. 2.1, with a brief overview of the use of models in the transportation sector, several types of models used in transportation planning, and the specific evaluation methods used. Thereafter, the theory of traffic flow is introduced which enables investigation of the dynamic properties of traffic on road sections with regard to the respective variables defined at each point in space and time. Based on the mathematical equations derived, different transportation system scenarios are investigated in Sect. 2.2. Section 2.3 examines queuing theory, the mathematical study of waiting in lines or queues. Transportation system models incorporate queuing theory to predict, for example, queuing lengths and waiting times. Section 2.4 analyzes transportation systems with regard to existing demand and the potential impact of changes resulting from transportation planning and development projects. Traffic management has become a critical issue as the number of vehicles in metropolitan areas is nearing the existing road capacity, resulting in traffic congestion. In some areas, the volume of vehicles has met and/or exceeded road capacity. The methodological background of congestion is described in Sect. 2.5. Graph theory is introduced in Sect. 2.6. It is widely used to model and study transportation networks. Section 2.7 focuses on shortages occurring in transportation systems, so-called bottlenecks. The main consequence of a bottleneck is an immediate reduction in the capacity of the transportation system infrastructure. Section 2.8 describes a ProModel-based case study for a four-arm road intersection. Section 2.9 contains comprehensive questions from the transportation model area of concentration, and the final section includes references and suggestions for further reading.

## Keywords

Traffic Flow Transportation Planning Road Intersection Traffic Flow Model Markov Blanket
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

1. Bando M, Hasebe K, Nakayama A, Shibata A, Sugiyama Y (1995) Dynamical model of traffic congestion and numerical simulation. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 51(2):1035–1042Google Scholar
2. Bartholomew K, Ewing R (2009) Land use-transportation scenarios and future vehicle travel and land consumption: a meta-analysis. J Am Plann Assoc 75(1):13–27Google Scholar
3. Cascetta E (2009) Transportation systems analysis: models and applications. Springer, New York
4. Crommelin RW (1974) Employing intersection capacity utilization values to estimate overall level of service. Trans Res Board 44(10):11–14, Transportation Research Record, Washington, DCGoogle Scholar
5. CUTR (2007) Economics of travel demand management: comparative cost effectiveness and public investment, Center for Urban Transportation Research, at www.nctr.usf.edu/pdf/77704.pdf
6. D’Agostino RB, Stephens MA (1986) Eds.: Goodness-of-fit tests. Marcel Decker Publ.Google Scholar
7. Dagpunar J (1988) Principles of random variate generation. Clarendon, Oxford
9. Doboszcarek S, Forstall V (2013) Mathematical modeling by differential equations. http://www.norbertwiener.umd.edu/Education/m3cdocs/Presentation2.pdf
10. Dong X, Ben-Akiva M, Bowman J, Walker J (2006) Moving from trip-based to activity-based measures of accessibility. Transp Res A 40(2):163–180Google Scholar
11. Donoso P, Martinez F, Zegras C (2006) The Kyoto protocol and sustainable cities: potential use of clean-development mechanism in structuring cities for carbon-efficient transportation. Transp Res Rec 1983:158–166
12. Ellis D, Glover B, Norboge N (2012) Refining a methodology for determining the economic impacts of transportation improvements, University Transportation Center for Mobility at Texas A&M University. http://utcm.tamu.edu/publications/final_reports/Ellis_11-00-68.pdf
13. Evans M, Hastings N, Peacock B (2000) Statistical distributions. Wiley Publ., New YorkGoogle Scholar
14. Fishman GS (1973) Statistical analysis for queuing simulations. Management Science Vol. 20:363–369Google Scholar
15. Fishman GS (2006) Monte carlo: concepts, algorithms, and applications. Springer Publ., New YorkGoogle Scholar
16. Flynn MR, Kasimov AR, Nave J-C, Rosales RR, Seibold B (2009) Self-sustained nonlinear waves in traffic flow. Phys Rev E 79(5):056113. doi:, DOI:
17. Gupta D, Singla S, Singla P, Singh S (2013) Minimization of elapsed time in N × 3 flow shop scheduling problem, the processing time associated with probabilities including transportation time. Int J Innovat Eng Technol Special Issue ICAECE-2013, pp 38–42Google Scholar
18. Harris GA (2008) Bridging the data & information gap, project report no. AL-26-7262-01Google Scholar
19. Hogg RV, Craig AF (1995) Introduction to mathematical statistics. Prentice-Hall Publ., Englewood CliffsGoogle Scholar
20. Husch D (2003) Intersection capacity utilization. Trafficware, AlbanyGoogle Scholar
21. Immers LH, Logghe S (2002) Traffic flow theory, course H 111. Catholic University LeuvenGoogle Scholar
22. Jehle IA (2014) Simulation of a traffic light junction, student project work, TU Clausthal, GermanyGoogle Scholar
23. Kerner BS, Rehborn H (1997) Experimental properties of phase transitions in traffic flow. Phys Rev Lett 79:4030–4033Google Scholar
24. Kleijnen JPC (1974) Statistical techniques in simulation. Marcel Decker Publ, New York
25. Kockelman KM (2001) Modeling traffic’s flow-density relation: accommodation of multiple flow regimes and traveler types. Transportation 29(4):363–373
26. Lee H-T, Romer TF (2011) Automating the process of terminal area node-link model generation. J Guid Control Dyn 34(4):1228–1237
27. Lee R, Niemeier D, Parker T, Handy S (2012) Evaluation of operation and accuracy of available smart growth trip generation methodologies for use in California, Transportation Research Record. J Transport Res Board, Serial Issue Number 2307:120–131Google Scholar
28. Lima E, Chwif L, Baretto M (2008) Methodology for selecting the best suitable bottleneck detection method. In: Proceedings SCS 32nd conference on winter simulation. Society for Computer Simulation International, San Diego, pp 740–754Google Scholar
29. Lindsey CR, Verhoef ET (1999) Congestion modelling, Series Tinbergen Institute discussion papers, Number 99–091/3Google Scholar
30. Lindsey CR, van den Berg VAV, Verhoef ET (2012) Step tolling with bottleneck queuing congestion. J Urb Econ 72(1):46–59
31. Little JDC, Graves SC (2008) Little’s law, Chapter 5. In: Chhajed D, Loewe TJ (eds) Building intuition: insight from basis operations management models and principles. Springer Publ., pp 81–100Google Scholar
32. Litman T (2006) What’s it worth? Economic evaluation for transportation decision making, transportation association of Canada, (www.tac-atc.ca); at www.vtpi.org/worth.pdf
33. Litman T (2013) Congestion costing critique: critical evaluation of the urban mobility report. In: VTPI, (www.vtpi.org); at www.vtpi.org/UMR_critique.pdf
34. Moeller DPF, Haas R, Vakilzadian H (2013) Ubiquitous learning: teaching modeling and simulation (M&S) with technology. In: Vakilzadain H, Crosbie R, Huntsinger R, Cooper K (eds) Proceedings of the 2013 summer simulation multiconference GCMS 2013. Curran Publication, Red Hook, pp 125–132Google Scholar
35. Scheurer J, Horan E, Bajwa S (2009) Benchmarking public transport and land use integration in Melbourne and Hamburg: hints for policy makers. Presentation at 23rd AESOP 2009 congress, liverpoolGoogle Scholar
36. Small KA (1998) Project evaluation, Chapter 5. In: Gómez-Ibáñez JA, Tye W, Winston C (eds) Transportation policy and economics: a handbook in honor of John R. Meyer. www.brookings.edu, www.uctc.net/papers/379.pdf
37. Stahl WA (2002) Statistical data analysis (in German). Vieweg Publ. WiesbadenGoogle Scholar
38. Stopher PR, Greaves SP (2007) Household travel surveys: where are we going? Transp Res A 41(5):367–381Google Scholar
39. Sundarapandian V (2009) Queuing theory, Chapter 7. In: Probability, statistics and queuing theory. PHI Learning, New DelhiGoogle Scholar
40. Tan AC, Bowden RO (2004) The Virtual Transport System (VITS)—final report. Monograph, Transportation Research Board, Washington, DCGoogle Scholar
41. TDM Encyclopedia (2013) Transport model improvements: improving methods for evaluating the effects and value of transportation system changes; see http://www.vtpi.org/tdm/tdm125.htm
42. TDM Encyclopedia (2014) Victoria Transport Policy Institute, VictoriaGoogle Scholar
43. Transportation Research Board, see http://onlinepubs.trb.org/onlinepubs/sr/sr288.pdf
44. TRB (2007) Metropolitan Travel Forecasting: Current Practice and Future Direction, Special Report 288, Transportation Research Board (www.trb.org); at http://onlinepubs.trb.org/onlinepubs/sr/sr288.pdf
45. TRB (2012) The effect of smart growth policies on travel demand, capacity project C16, Strategic Highway Research Program (SHRP 2), (www.trb.org); http://onlinepubs.trb.org/onlinepubs/shrp2/SHRP2prepubC16.pdf
46. USDOT (2003) US Department of Transportation, Economic Analysis Primer, Office of Asset Management, FHWA, USDOT, 2003. www.fhwa.dot.gov/infrastructure/asstmgmt/primer.pdf
47. Wang Y, Zhao Q, Zheng D (2005) Bottlenecks in production networks: an overview. J Syst Sci Syst Eng 14:18ffGoogle Scholar
48. Yücesan E, Schruben LW (1998) Complexity of simulation models: a graph theoretic approach. Journal of Comput 10:94–108Google Scholar