A Complex Network Methodology for Travel Demand Model Evaluation and Validation

  • Meead Saberi
  • Taha H. Rashidi
  • Milad Ghasri
  • Kenneth Ewe
Article

Abstract

Travel demand can be viewed as a weighted and directed graph where nodes are the origins and destinations and links represent the trips between nodes. This paper presents a network-theoretic methodology to evaluate and validate travel demand models. We apply the proposed method on three disaggregate travel demand models from Melbourne, Australia. Statistical properties of the modeled networks are compared against the observed networks over time. The new approach reveals the network structure and connectivity of the modeled trips that are not usually captured by traditional evaluation and validation methods. Results demonstrate the complexity involved in the development, evaluation, and validation of travel demand models, which calls for advanced evaluation techniques reflecting a wide range of attributes of the observed and modeled data, travelers, mobility patterns, and complex network characteristics.

Keywords

Travel demand modeling Evaluation Validation Complex networks Structure Connectivity 

Nomenclature

N

Number of nodes in the network

L

Number of edges in the network

T

Total number of trips

δ

Network connectivity (2 L/N 2 )

aij

Elements of the adjacency matrix

awij

Elements of the weighted adjacency matrix

Fi

Flux of a given node i

ki

Degree of a given node i

wij

Weight of a given edge between node i and node j

ci

Clustering coefficient of a given node i

bi

Betweenness centrality of a given node i

bij

Betweenness centrality of a given edge between node i and node j

F

Mean node flux in the network

k

Mean node degree in the network

w

Mean edge weight in the network

c

Mean clustering coefficient in the network

wc

Mean weighted clustering coefficient in the network

CV(F)

Coefficient of variation of node flux in the network

CV(k)

Coefficient of variation of node degree in the network

CV(w)

Coefficient of variation of edge weight in the network

C

Network clustering coefficient

dT

Average shortest path

wdT

Average weighted shortest path

φ

Network diameter

Weighted network diameter

ξ

Network dissimilarity

References

  1. Axhausen KW (2000) Activity-based modelling: Research directions and possibilities, New Look at Multi-Modal Modeling. Department of Environment, Transport and the Regions, London, Cambridge and OxfordGoogle Scholar
  2. Axhausen K, Garling T (1992) Activity-based approaches to travel analysis: conceptual frameworks, models, and research problems. Transp Rev 12(4):323–341CrossRefGoogle Scholar
  3. Bazzani A, Giorgini B, Rambaldi S, Gallotti R, Giovannini L (2010). Statistical laws in urban mobility from microscopic GPS data in the area of Florence. J. Stat. Mech., P05001Google Scholar
  4. Betty M (2013) The New Science of Cities. MIT press, CambridgeGoogle Scholar
  5. Bowman JL, Ben-Akiva ME (2001) Activity-based disaggregate travel demand model system with activity schedules. Transp Res A 35:1–28CrossRefGoogle Scholar
  6. Breiman L (1996) Bagging Predictors. Mach Learn 24:123–140Google Scholar
  7. Breiman L (2001) Random forests. Mach Learn 45:5–32CrossRefGoogle Scholar
  8. Breiman L, Cutler A (2004) Random Forests. Department of Statistics, University of California, BerkeleyGoogle Scholar
  9. Breiman L, Friedman JH, Olshen RA, Stone CI (1984) Classification and regression trees. Wadsworth Statistics/Probability. Chapman and Hall/CRCGoogle Scholar
  10. Brockmann D, Hufnagel L, Geisel T (2006) The scaling laws of human travel. Nature 439:462–465CrossRefGoogle Scholar
  11. Castiglione J, Bradley M, Gliebe J (2015) Activity-Based Travel Demand Models: A Primer. No. SHRP 2 Report S2-C46-RR-1Google Scholar
  12. Chen C, Ma J, Susilo Y, Liu Y, Wang M (2016) The promises of big data and small data for travel behavior (aka human mobility) analysis. Transportation Research Part C: Emerging Technologies 68:285–299CrossRefGoogle Scholar
  13. Colak S, Schneider CM, Wang P, González MC (2013) On the role of spatial dynamics and topology on network flows. New J Phys 15:113037CrossRefGoogle Scholar
  14. Çolak S, Alexander LP, Alvim BG, Mehndiretta SR, González MC (2015) Analyzing Cell Phone Location Data for Urban Travel: Current Methods, Limitations and Opportunities. Transportation Research Records 2526:126–135CrossRefGoogle Scholar
  15. Cherchi E, Cirillo C (2010) Validation and forecasts in models estimated from multiday travel survey. Transportation Research Record: Journal of the Transportation Research Board 2175:57–64CrossRefGoogle Scholar
  16. Do TMT, Gatica-Pereza D (2014) Where and what: Using smartphones to predict next locations and applications in daily life. Pervasive and Mobile Computing 12:79–91CrossRefGoogle Scholar
  17. Erath A, Lochl M, Axhausen K (2009) Graph-Theoretical Analysis of the Swiss Road and Railway Networks Over Time. Networks and Spatial Economics 9(3):379–400CrossRefGoogle Scholar
  18. Faloutsos M, Faloutsos P, Faloutsos C (1999) On Power-Law Relationships of the Internet Topology. In: In Conference of the ACM Special Interest Group on Data Communications (SIGCOMM). ACM Press, New York, pp 251–262Google Scholar
  19. Fan Y, Khattak A (2008) Urban form, individual spatial footprints, and travel: examination of space-use behavior. Transp Res Rec 2082:98–106CrossRefGoogle Scholar
  20. Federal Highway Administration (2010) Travel Model Validation and Reasonableness Checking Manual. Second Edition. Last accessed July via 2016.https://www.fhwa.dot.gov/planning/tmip/publications/other_reports/validation_and_reasonableness_2010/fhwahep10042.pdf
  21. Florian M, Nguyen S (1976) An application and validation of equilibrium trip assignment methods. Transp Sci 10(4):374–390CrossRefGoogle Scholar
  22. Flötteröd G, Chen Y, Nagel K (2012) Behavioral Calibration and Analysis of a Large-Scale Travel Microsimulation. Networks and Spatial Economics 12(4):481–502CrossRefGoogle Scholar
  23. Ghasri M, Rashidi TH, Waller ST (2017) Developing a disaggregate travel demand system of models using data mining techniques. Transp Res A Policy Pract 105:138–153Google Scholar
  24. González MC, Hidalgo CA, Barabási AL (2008) Understanding individual human mobility patterns. Nature 453:779–782CrossRefGoogle Scholar
  25. Hamedmoghadam H, Steponavice I, Ramezani M, Saberi M (2017) A Complex Network Analysis of Macroscopic Structure of Taxi Trips. In Proceedings of the International Federation of Automatic Control (IFAC), Toulouse, France, July 9–14Google Scholar
  26. Hasan S, Schneider CM, Ukkusuri SV, González MC (2013) Spatio-temporal patterns of urban human mobility. J Stat Phys 151(1–2):304–318Google Scholar
  27. Iqbal MS, Choudhury CF, Wang P, González MC (2014) Development of Origin-Destination Matrices Using Mobile Phone Call Data. Transportation Research C 40:63–74CrossRefGoogle Scholar
  28. Jiang B, Yin J, Zhao S (2009) Characterizing the human mobility pattern in a large street network. Phys Rev E 80:1–11Google Scholar
  29. Jiang S, Yang Y, Fiore G, Ferreira J, Frazzoli E, González MC (2013) A review of urban computing for mobile phone traces: Current methods, challenges and opportunities. In Proceedings of the ACM SIGKDD international workshop on urban computingGoogle Scholar
  30. Liang X, Zheng X, Lv W, Zhu T, Xu K (2012) The scaling of human mobility by taxis is exponential. Physica A 391:2135–2144CrossRefGoogle Scholar
  31. Md K, Hine J (2012) Analysis of rural activity spaces and transport disadvantage using a multimethod approach. Transp Policy 19(1):105–120CrossRefGoogle Scholar
  32. Kang C, Ma X, Tong D, Liu Y (2012) Intra-urban human mobility patterns: An urban morphology perspective. Physica A 391:1702–1717CrossRefGoogle Scholar
  33. Kelley R, Ideker T (2005) Systematic interpretation of genetic interactions using protein networks. Nat Biotechnol 23:561–566CrossRefGoogle Scholar
  34. Kim JW, Lee BH, Shaw MJ, Chang HL, Nelson M (2001) Application of decision-tree induction techniques to personalized advertisements on internet storefronts. Int J Electron Commer 5(3):45–62CrossRefGoogle Scholar
  35. Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86.  https://doi.org/10.1214/aoms/1177729694 CrossRefGoogle Scholar
  36. Kullback S (1959) Information Theory and Statistics. Wiley, New York; Chapman and Hall, LondonGoogle Scholar
  37. Lam WHK, Huang HJ (2003) Combined Activity/Travel Choice Models: Time Dependent and Dynamic Versions. Network and Spatial Economics 3(3):323–347CrossRefGoogle Scholar
  38. Liu F, Janssens D, Cui JX, Wang YP, Wets G, Cools M (2014) Building a validation measure for activity-based transportation models based on mobile phone data. Expert Syst Appl 41(14):6174–6189CrossRefGoogle Scholar
  39. Newman M (2001) The structure of scientific collaboration networks. Proc Nat Acad Sci USA 98(2):404–409CrossRefGoogle Scholar
  40. Newman M (2010) Networks: an introduction. Oxford University Press, OxfordCrossRefGoogle Scholar
  41. Newman M, Park J (2003) Why social networks are different from other types of networks. Phys Rev E 68(3):036122CrossRefGoogle Scholar
  42. Noulas A, Scellato S, Lambiotte R, Pontil M, Mascolo C (2012) A Tale of Many Cities: Universal Patterns in Human Urban Mobility. PLoS One 7(5):e37027.  https://doi.org/10.1371/journal.pone.0037027 CrossRefGoogle Scholar
  43. Patuelli R, Reggiani A, Gorman S, Nijkamp P, Bade FJ (2007) Network Analysis of Commuting Flows: A Comparative Static Approach to German Data. Networks and Spatial Economics 7(4):315–331CrossRefGoogle Scholar
  44. Peng C, Jin X, Wong K-C, Shi M, Liò P (2012) Collective Human Mobility Pattern from Taxi Trips in Urban Area. PLoS One 7:e34487CrossRefGoogle Scholar
  45. Raney B, Cetin N, Vollmy A, Vrtic M, Axhausen K, Nagel K (2003) An Agent-Based Microsimulation Model of Swiss Travel: First Results. Networks and Spatial Economics 3(1):23–41CrossRefGoogle Scholar
  46. Roorda MJ, Miller EJ, Habib KMN (2008) Validation of TASHA: A 24-H activity scheduling microsimulation model. Transp Res A Policy Pract 42(2):360–375CrossRefGoogle Scholar
  47. Roth C, Kang SM, Batty M, Barthélemy M (2011) Structure of urban movements: polycentric activity and entangled hierarchical flows. PLoS One 6:e15923CrossRefGoogle Scholar
  48. Rual JF, Venkatesan K, Hao T, Hirozane-Kishikawa T, Dricot A, Li N, Berriz GF, Gibbons FD, Dreze M, Ayivi-Guedehoussou N, Klitgord N, Simon C, Boxem M, Milstein S, Rosenberg J, Goldberg DS, Zhang LV, Wong SL, Franklin G, Li S, Albala JS, Lim J, Fraughton C, Llamosas E, Cevik S, Bex C, Lamesch P, Sikorski RS, Vandenhaute J, Zoghbi HY, Smolyar A, Bosak S, Sequerra R, Doucette-Stamm L, Cusick ME, Hill DE, Roth FP, Vidal M (2005) Towards a proteome-scale map of the human protein–protein interaction network. Nature 437(7062):1173–1178CrossRefGoogle Scholar
  49. Saberi M, Mahmassani H, Brockmann D, Hosseini A (2016) A Complex Network Perspective for Characterizing Urban Travel Demand Patterns: Graph Theoretical Analysis of Large-Scale Origin-Destination Demand Networks. Transportation 44(6):1383–1402CrossRefGoogle Scholar
  50. Saberi M, Ghamami M, Gu Y, Shojaei MHS, Fishman E (2018) Understanding the impacts of a public transit disruption on bicycle sharing mobility patterns: A case of Tube strike in London. Journal of Transport Geography 66:154-166.Google Scholar
  51. Schintler L, Kulkarni R, Gorman S, Stough R (2007) Using Raster-Based GIS and Graph Theory to Analyze Complex Networks. Networks and Spatial Economics 7(4):301–313CrossRefGoogle Scholar
  52. Sammour G, Bellemans T, Vanhoof K, Janssens D, Kochan B, Wets G (2012) The usefulness of the sequence alignment methods in validating rule-based activity-based forecasting models. Transportation 39(4):773–789CrossRefGoogle Scholar
  53. Schneider CM, Belik V, Couronné T, Smoreda Z, González MC (2013) Unravelling daily human mobility motifs. J R Soc Interface 10:1–8CrossRefGoogle Scholar
  54. Schonfelder A, Axhausen KW (2003) Activity spaces: measures of social exclusion? Transp Policy 10(4):273–286CrossRefGoogle Scholar
  55. Siganos G, Faloutsos M, Faloutsos P, Faloutsos C (2003) Power laws and the AS-level internet topology. IEEE/ACM Trans Networking 11(4):514–524CrossRefGoogle Scholar
  56. Simini F, González MC, Maritan A, Barabási AL (2012) A universal model for mobility and migration patterns. Nature 484:96–100CrossRefGoogle Scholar
  57. Song C, Koren T, Wang P, Barabási A (2010) Modelling the scaling properties of human mobility. Nat Phys 6:818–823CrossRefGoogle Scholar
  58. Thiemann C, Theis F, Grady D, Brune R, Brockmann D (2010) The Structure of Borders in a Small World. PLoS One 5(11):e15422CrossRefGoogle Scholar
  59. Toole JL, Colak S, Sturt B, Alexandre L, Evsukoff A, González MC (2015) The Path Most Travelled: Travel Demand Estimation Using Big Data Resources. Transportation Research C 58:162–177CrossRefGoogle Scholar
  60. Viljoen N, Joubert J (2017) The Road most Travelled: The Impact of Urban Road Infrastructure on Supply Chain Network Vulnerability. Networks and Spatial Economics.  https://doi.org/10.1007/s11067-017-9370-1
  61. Vovsha P, Bradley M, Bowman J (2004) Activity-based travel forecasting models in the United States: Progress since 1995 and Prospects for the Future. In the EIRASS Conference on Progress in Activity-Based Analysis, May 28–31, Vaeshartelt Castle, MaastrichtGoogle Scholar
  62. Wang P, Hunter T, Bayen A, Schechtner K, González MC (2012) Understanding Road Usage Patterns in Urban Areas. Sci Rep 2.  https://doi.org/10.1038/srep01001
  63. Watts DJ (2003) Six degrees. In: The science of a connected age. W. W. Norton & Co. Inc, New YorkGoogle Scholar
  64. Wegmann F, Everett J (2008) Minimum Travel Demand Model Calibration and Validation Guidelines for State of Tennessee. Center for Transportation Research, University of Tennessee, KnoxvilleGoogle Scholar
  65. Widhalm P, Yang Y, Ulm M, Athavale S, González MC (2015) Discovering urban activity patterns in cell phone data. Transportation 42(4):597–623CrossRefGoogle Scholar
  66. Woolley-Meza O, Thiemann C, Grady D, Lee JJ, Seebens H, Blasius B, Brockmann D (2011) Complexity in human transportation networks: A comparative analysis of worldwide air transportation and global cargo ship movements. Eur Phys J B 84:589–600CrossRefGoogle Scholar
  67. Wu CH, Ho JM, Lee DT (2004) Travel-time prediction with support vector regression. IEEE Trans Intell Transp Syst 5(4):276–281CrossRefGoogle Scholar
  68. Xie F, Levinson D (2009) Modeling the Growth of Transportation Networks: A Comprehensive Review. Networks and Spatial Economics 9(3):291–307CrossRefGoogle Scholar
  69. Yook SH, Jeong H, Barabasi AL (2002) Modeling the Internet's large-scale topology. Proceedings of the National Academy of Science of the United States (PNAS) 99(22):13382–13386CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Research Centre for Integrated Transport Innovation, School of Civil & Environmental EngineeringUniversity of New South WalesSydneyAustralia
  2. 2.Australian Road Research Board (AARB)MelbourneAustralia

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