Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points Erik T. Verhoef * ,1 Department of Spatial Economics, Free University Amsterdam, De Boelelaan 1105, 1081 HV Amsterdam, Netherlands Received 19 October 2000; received in revised form 8 June 2001; accepted 15 June 2001 Abstract This paper considers the second-best problem where not all links of a congested transportation network can be tolled. This paper builds on earlier work, in which the second-best tax rule for this problem was derived for general static networks, so that the solution presented is valid for any graph of the network, and for any set of tolling points available on that network. An algorithm is presented for finding second-best tolls, based on this general solution. A simulation model is used for studying its performance for various archetype pricing schemes: a toll-cordon, area licences, parking policies in the city centre, pricing of a single major highway, and pay-lanes and ‘free-lanes’ on major highways. Furthermore, an exploratory analysis is given of a method for selecting the optimal location of toll points when not all links can be tolled. Ó 2002 Elsevier Science Ltd. All rights reserved. JEL classification: R41; R48; D62 Keywords: Congestion; Road pricing; Networks; Second-best 1. Introduction Second-best issues in transport regulation have received ample attention in the recent literature. This is often motivated by the observation that the first-best policy for a congested road network – tolls equal to marginal external costs on each individual link – is a rather theoretical construct. Transport regulators often consider second-best solutions only, in which not every single link of a Transportation Research Part B 36 (2002) 707–729 www.elsevier.com/locate/trb * Tel.: +31-20-4446094; fax: +31-20-4446004. E-mail address: everhoef@econ.vu.nl (E.T. Verhoef). 1 The author is affiliated to the Tinbergen Institute, Keizersgracht 482, 1017 EG Amsterdam. The research of the author has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. 0191-2615/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0191-2615(01)00025-X