Abstract
It is widely acknowledged that, to create models for transportation planning that recognize the essential dynamic character of passenger network flows, one must consider two time scales: the so-called within-day time scale and the day-to-day time scale. Substantial progress has been made in modelling within-day dynamic flows for fixed trip matrices; one of the most widely acknowledged models for this purpose is the dynamic user equilibrium model proposed by Friesz et al. (1993) and studied by Xu et al. (1999), Wu et al. (1998), Friesz et al. (2001), Bliemer and Bovy (2003), and Friesz and Mookherjee (2006). In this chapter we propose two day-to-day models of demand growth compatible with a differential variational inequality formulation of the Friesz et al. (1993) model. The first of these employs dynamics inspired by evolutionary game theory, while the second uses the perspective of preferential attachment familiar from the network science and social network literature to create a model of demand growth. Additionally, numerical experiments to compare and contrast the two proposed theories of demand growth are described, along with hypotheses that one might address via such experiments.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bianconi G, Barabási A (2001) Competition and multiscaling in evolving networks. Europhys Lett 54(4):436–442
Bliemer M, Bovy P (2003) Quasi-variational inequality formulation of the multiclass dynamic traffic assignment problem. Transp Res Part B 37(6):501–519
Bryson AE, Ho YC (1975) Applied optimal control. Hemisphere Publishing Company
Chung F, Lu L (2004) The average distance in a random graph with given expected degrees. Internet Math 1(1):91–113
Erdos P, Renyi A (1959) On random graphs. Publicationes Mathematicae Debrecen 6 (290)
Friesz TL, Mookherjee R (2006) Solving the dynamic network user equilibrium problem with state-dependent time shifts. Transp Res Part B 40:207–229
Friesz TL, Bernstein D, Smith T et al. (1993) A variational inequality formulation of the dynamic network user equilibrium problem. Oper Res 41:80–91
Friesz T, Bernstein D, Suo Z et al. (2001) Dynamic network user equilibrium with state-dependent time lags. Netw Spatial Econ 1:319–347
Hofbauer J, Sigmund K (1998) Evolutionary games and replicator dynamics. Cambridge University Press
Molloy M, Reed B (1998) The size of the giant component of a random graph with a given degree sequence. Comb Probab Comput 7(03):295–305
Newman M, Strogatz S, Watts D (2001) Random graphs with arbitrary degree distributions and their applications. Phys Rev E 64(2):26118
Smith T (1983) A cost-efficiency approach to the analysis of congested spatial-interaction behavior. Environ Plann A 15:435–464
Strauss D (1986) On a general class of models for interaction. SIAM Rev 28(4):513–527
Wu J, Chen Y, Florian M (1998) The continuous dynamic network loading problem: a mathematical formulation and solution method. Transp Res Part B 32(3):173–187
Xu Y, Wu J, Florian M et al. (1999) Advances in the continuous dynamic network loading problem. Transport Sci 33(4):341–353
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Friesz, T.L., Kwon, C., Bernstein, D. (2009). Evolutionary and Preferential Attachment Models of Demand Growth. In: Reggiani, A., Nijkamp, P. (eds) Complexity and Spatial Networks. Advances in Spatial Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01554-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-01554-0_11
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-01553-3
Online ISBN: 978-3-642-01554-0
eBook Packages: Business and EconomicsEconomics and Finance (R0)