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 networktheoretic 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.
This is a preview of subscription content, log in to check access.
Abbreviations
 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})
 a _{ ij } :

Elements of the adjacency matrix
 a ^{w} _{ ij } :

Elements of the weighted adjacency matrix
 F _{ i } :

Flux of a given node i
 k _{ i } :

Degree of a given node i
 w _{ ij } :

Weight of a given edge between node i and node j
 c _{ i } :

Clustering coefficient of a given node i
 b _{ i } :

Betweenness centrality of a given node i
 b _{ ij } :

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
 d _{ T } :

Average shortest path
 wd _{ T } :

Average weighted shortest path
 φ :

Network diameter
 wφ :

Weighted network diameter
 ξ :

Network dissimilarity
References
Axhausen KW (2000) Activitybased modelling: Research directions and possibilities, New Look at MultiModal Modeling. Department of Environment, Transport and the Regions, London, Cambridge and Oxford
Axhausen K, Garling T (1992) Activitybased approaches to travel analysis: conceptual frameworks, models, and research problems. Transp Rev 12(4):323–341
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., P05001
Betty M (2013) The New Science of Cities. MIT press, Cambridge
Bowman JL, BenAkiva ME (2001) Activitybased disaggregate travel demand model system with activity schedules. Transp Res A 35:1–28
Breiman L (1996) Bagging Predictors. Mach Learn 24:123–140
Breiman L (2001) Random forests. Mach Learn 45:5–32
Breiman L, Cutler A (2004) Random Forests. Department of Statistics, University of California, Berkeley
Breiman L, Friedman JH, Olshen RA, Stone CI (1984) Classification and regression trees. Wadsworth Statistics/Probability. Chapman and Hall/CRC
Brockmann D, Hufnagel L, Geisel T (2006) The scaling laws of human travel. Nature 439:462–465
Castiglione J, Bradley M, Gliebe J (2015) ActivityBased Travel Demand Models: A Primer. No. SHRP 2 Report S2C46RR1
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 68:285–299
Colak S, Schneider CM, Wang P, González MC (2013) On the role of spatial dynamics and topology on network flows. New J Phys 15:113037
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 2526:126–135
Cherchi E, Cirillo C (2010) Validation and forecasts in models estimated from multiday travel survey. Transportation Research Record: Journal of the Transportation Research Board 2175:57–64
Do TMT, GaticaPereza D (2014) Where and what: Using smartphones to predict next locations and applications in daily life. Pervasive and Mobile Computing 12:79–91
Erath A, Lochl M, Axhausen K (2009) GraphTheoretical Analysis of the Swiss Road and Railway Networks Over Time. Networks and Spatial Economics 9(3):379–400
Faloutsos M, Faloutsos P, Faloutsos C (1999) On PowerLaw Relationships of the Internet Topology. In: In Conference of the ACM Special Interest Group on Data Communications (SIGCOMM). ACM Press, New York, pp 251–262
Fan Y, Khattak A (2008) Urban form, individual spatial footprints, and travel: examination of spaceuse behavior. Transp Res Rec 2082:98–106
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
Florian M, Nguyen S (1976) An application and validation of equilibrium trip assignment methods. Transp Sci 10(4):374–390
Flötteröd G, Chen Y, Nagel K (2012) Behavioral Calibration and Analysis of a LargeScale Travel Microsimulation. Networks and Spatial Economics 12(4):481–502
Ghasri M, Rashidi TH, Waller ST (2017) Developing a disaggregate travel demand system of models using data mining techniques. Transp Res A Policy Pract 105:138–153
González MC, Hidalgo CA, Barabási AL (2008) Understanding individual human mobility patterns. Nature 453:779–782
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 9–14
Hasan S, Schneider CM, Ukkusuri SV, González MC (2013) Spatiotemporal patterns of urban human mobility. J Stat Phys 151(1–2):304–318
Iqbal MS, Choudhury CF, Wang P, González MC (2014) Development of OriginDestination Matrices Using Mobile Phone Call Data. Transportation Research C 40:63–74
Jiang B, Yin J, Zhao S (2009) Characterizing the human mobility pattern in a large street network. Phys Rev E 80:1–11
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 computing
Liang X, Zheng X, Lv W, Zhu T, Xu K (2012) The scaling of human mobility by taxis is exponential. Physica A 391:2135–2144
Md K, Hine J (2012) Analysis of rural activity spaces and transport disadvantage using a multimethod approach. Transp Policy 19(1):105–120
Kang C, Ma X, Tong D, Liu Y (2012) Intraurban human mobility patterns: An urban morphology perspective. Physica A 391:1702–1717
Kelley R, Ideker T (2005) Systematic interpretation of genetic interactions using protein networks. Nat Biotechnol 23:561–566
Kim JW, Lee BH, Shaw MJ, Chang HL, Nelson M (2001) Application of decisiontree induction techniques to personalized advertisements on internet storefronts. Int J Electron Commer 5(3):45–62
Kullback S, Leibler RA (1951) On information and sufficiency. Ann Math Stat 22(1):79–86. https://doi.org/10.1214/aoms/1177729694
Kullback S (1959) Information Theory and Statistics. Wiley, New York; Chapman and Hall, London
Lam WHK, Huang HJ (2003) Combined Activity/Travel Choice Models: Time Dependent and Dynamic Versions. Network and Spatial Economics 3(3):323–347
Liu F, Janssens D, Cui JX, Wang YP, Wets G, Cools M (2014) Building a validation measure for activitybased transportation models based on mobile phone data. Expert Syst Appl 41(14):6174–6189
Newman M (2001) The structure of scientific collaboration networks. Proc Nat Acad Sci USA 98(2):404–409
Newman M (2010) Networks: an introduction. Oxford University Press, Oxford
Newman M, Park J (2003) Why social networks are different from other types of networks. Phys Rev E 68(3):036122
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
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):315–331
Peng C, Jin X, Wong KC, Shi M, Liò P (2012) Collective Human Mobility Pattern from Taxi Trips in Urban Area. PLoS One 7:e34487
Raney B, Cetin N, Vollmy A, Vrtic M, Axhausen K, Nagel K (2003) An AgentBased Microsimulation Model of Swiss Travel: First Results. Networks and Spatial Economics 3(1):23–41
Roorda MJ, Miller EJ, Habib KMN (2008) Validation of TASHA: A 24H activity scheduling microsimulation model. Transp Res A Policy Pract 42(2):360–375
Roth C, Kang SM, Batty M, Barthélemy M (2011) Structure of urban movements: polycentric activity and entangled hierarchical flows. PLoS One 6:e15923
Rual JF, Venkatesan K, Hao T, HirozaneKishikawa T, Dricot A, Li N, Berriz GF, Gibbons FD, Dreze M, AyiviGuedehoussou 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, DoucetteStamm L, Cusick ME, Hill DE, Roth FP, Vidal M (2005) Towards a proteomescale map of the human protein–protein interaction network. Nature 437(7062):1173–1178
Saberi M, Mahmassani H, Brockmann D, Hosseini A (2016) A Complex Network Perspective for Characterizing Urban Travel Demand Patterns: Graph Theoretical Analysis of LargeScale OriginDestination Demand Networks. Transportation 44(6):1383–1402
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 66:154166.
Schintler L, Kulkarni R, Gorman S, Stough R (2007) Using RasterBased GIS and Graph Theory to Analyze Complex Networks. Networks and Spatial Economics 7(4):301–313
Sammour G, Bellemans T, Vanhoof K, Janssens D, Kochan B, Wets G (2012) The usefulness of the sequence alignment methods in validating rulebased activitybased forecasting models. Transportation 39(4):773–789
Schneider CM, Belik V, Couronné T, Smoreda Z, González MC (2013) Unravelling daily human mobility motifs. J R Soc Interface 10:1–8
Schonfelder A, Axhausen KW (2003) Activity spaces: measures of social exclusion? Transp Policy 10(4):273–286
Siganos G, Faloutsos M, Faloutsos P, Faloutsos C (2003) Power laws and the ASlevel internet topology. IEEE/ACM Trans Networking 11(4):514–524
Simini F, González MC, Maritan A, Barabási AL (2012) A universal model for mobility and migration patterns. Nature 484:96–100
Song C, Koren T, Wang P, Barabási A (2010) Modelling the scaling properties of human mobility. Nat Phys 6:818–823
Thiemann C, Theis F, Grady D, Brune R, Brockmann D (2010) The Structure of Borders in a Small World. PLoS One 5(11):e15422
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 58:162–177
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/s1106701793701
Vovsha P, Bradley M, Bowman J (2004) Activitybased travel forecasting models in the United States: Progress since 1995 and Prospects for the Future. In the EIRASS Conference on Progress in ActivityBased Analysis, May 28–31, Vaeshartelt Castle, Maastricht
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
Watts DJ (2003) Six degrees. In: The science of a connected age. W. W. Norton & Co. Inc, New York
Wegmann F, Everett J (2008) Minimum Travel Demand Model Calibration and Validation Guidelines for State of Tennessee. Center for Transportation Research, University of Tennessee, Knoxville
Widhalm P, Yang Y, Ulm M, Athavale S, González MC (2015) Discovering urban activity patterns in cell phone data. Transportation 42(4):597–623
WoolleyMeza 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 84:589–600
Wu CH, Ho JM, Lee DT (2004) Traveltime prediction with support vector regression. IEEE Trans Intell Transp Syst 5(4):276–281
Xie F, Levinson D (2009) Modeling the Growth of Transportation Networks: A Comprehensive Review. Networks and Spatial Economics 9(3):291–307
Yook SH, Jeong H, Barabasi AL (2002) Modeling the Internet's largescale topology. Proceedings of the National Academy of Science of the United States (PNAS) 99(22):13382–13386
Author information
Affiliations
Corresponding author
Appendix A
Appendix A
The node degree k is the number of links connected to a node in a network where a_{ij} are elements in the adjacency matrix.
The node flux F is the number of trips starting or ending at a node where w_{ij} represents the weight or the number of trips between each pair of nodes.
The clustering coefficient c for node i is calculated as the number of triangles in the graph that pass through a node.
The network clustering coefficient C is a global measure of the extent to which nodes in a network are clustered. C is calculated as a ratio of the number of triangles to the number of connected triples of nodes, expressed as:
Rights and permissions
About this article
Cite this article
Saberi, M., Rashidi, T.H., Ghasri, M. et al. A Complex Network Methodology for Travel Demand Model Evaluation and Validation. Netw Spat Econ 18, 1051–1073 (2018). https://doi.org/10.1007/s110670189397y
Published:
Issue Date:
Keywords
 Travel demand modeling
 Evaluation
 Validation
 Complex networks
 Structure
 Connectivity