Road pricing modeling for hyper-congestion Hong K. Lo a, * , W.Y. Szeto b,1 a Department of Civil Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China b Department of Civil, Structural, and Environmental Engineering, Trinity College, University of Dublin, Dublin 2, Ireland Received 7 November 2003; received in revised form 25 August 2004; accepted 22 February 2005 Abstract Recently there has been a resurgence in the interest of road pricing. Most studies adopt the static mod- eling paradigm, typically using either separable monotone or backward-bending link travel time functions for the analysis. In this study, through the shockwave analysis, we show that separable backward-bending functions are not appropriate for modeling hyper-congestion and hence road pricing. In the absence of queue spillback, link travel time is a monotone increasing function of inflow. However, in the presence of queue spillback, we show that the static paradigm even with a monotone travel time function cannot adequately portray the congestion phenomenon. In some cases, the tolls determined by the static paradigm can be even detrimental, worsening rather than alleviating the congestion problem. In the end, to model congested networks properly, perhaps one has no other choices but to adopt a modeling paradigm that faithfully captures both the temporal as well as the spatial dimensions of traffic queuing. Ó 2005 Elsevier Ltd. All rights reserved. 1. Introduction The concept of road pricing needs no introduction. It is supported by a long history of economic and transportation analyses (for example, see Hau, 2005a,b), pointing to its potential 0965-8564/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.tra.2005.02.019 * Corresponding author. Tel.: +852 2358 8742; fax: +852 2358 1534. E-mail addresses: cehklo@ust.hk (H.K. Lo), ceszeto@yahoo.com.hk (W.Y. Szeto). 1 Tel.: +353 1 6083646; fax: +353 1 6773072. www.elsevier.com/locate/tra Transportation Research Part A 39 (2005) 705–722