Investigating boundary effects of congestion charging in a single bottleneck scenario
Abstract
Many congestion charging projects charge traffic only within part of a day with predetermined congestion tolls. Demand peaks have been witnessed just around the time when the charge jumps up or down. Such peaks may not be desirable, in particular (a) when the resulting peaks are much higher than available capacities; (b) traffic speeding up to get into the charging zone causes more incidents just before the toll rises up to a higher level; or (c) traffic slowing down or parking on the roadside decreases road traffic throughput just before the toll falls sharply. We term these types of demand peaks ‘boundary effects’ of congestion charging. This paper investigates these effects in a bottleneck scenario and aims to design charging schemes that reduce undesired demand peaks. For this purpose, we observe and analyse the boundary effects utilising a bottleneck model under three types of toll profiles that are indicative of real charging schemes. The first type maintains a constant toll across the charging period, the second type allows the toll to increase from zero to a given maximum level and then decrease back to zero and the third type allows the toll to rise from zero to a given maximum level, remain at this level for a fixed period and then fall down to zero. This investigation shows that all three types of toll profiles can produce greater boundary peak demands than the bottleneck capacity. A significant contribution of this work is that instead of designing an optimal traffic congestion pricing scheme we analyse how existing sub-optimal congestion pricing schemes could be improved and suggest how observed problems may be overcome. Hence, we propose a set of extra requirements to supplement existing principles or requirements for design and implementation of congestion charging, which aim to reduce the adverse consequences of boundary effects. Concluding remarks are made on implications of this investigation for the improvement of existing congestion charging projects and for future research.
First published online 13 July 2015
Keyword : bottleneck models, congestion charging, boundary issues
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Arnott, R.; De Palma, A.; Lindsey, R. 1990. Economics of a bottleneck, Journal of Urban Economics 27(1): 111–130. http://dx.doi.org/10.1016/0094-1190(90)90028-L
Braid, R. M. 1989. Uniform versus peak-load pricing of a bottleneck with elastic demand, Journal of Urban Economics 26(3): 320–327. http://dx.doi.org/10.1016/0094-1190(89)90005-3
Carey, M.; Ge, Y. E. 2012. Comparison of methods for path flow reassignment for dynamic user equilibrium, Networks and Spatial Economics 12(3): 337–376. http://dx.doi.org/10.1007/s11067-011-9159-6
Carey, M.; Ge, Y. E. 2005. Convergence of a discretised traveltime model, Transportation Science 39(1): 25–38. http://dx.doi.org/10.1287/trsc.1030.0083
Carey, M.; Ge, Y. E. 2004. Efficient discretisation for link travel time models, Networks and Spatial Economics 4(3): 269–290. http://dx.doi.org/10.1023/B:NETS.0000039783.57975.f0
Carey, M.; Ge, Y. E. 2003. Comparing whole-link travel time models, Transportation Research Part B: Methodological 37(10): 905–926. http://dx.doi.org/10.1016/S0191-2615(02)00091-7
Chu, X. 1995. Endogenous trip scheduling: the Henderson approach reformulated and compared with the Vickrey approach, Journal of Urban Economics 37(3): 324–343. http://dx.doi.org/10.1006/juec.1995.1017
Daganzo, C. F. 1995a. A finite difference approximation of the kinematic wave model of traffic flow, Transportation Research Part B: Methodological 29(4): 261–276. http://dx.doi.org/10.1016/0191-2615(95)00004-W
Daganzo, C. F. 1995b. Properties of link travel time functions under dynamic loads, Transportation Research Part B: Methodological 29(2): 95–98. http://dx.doi.org/10.1016/0191-2615(94)00026-V
Daganzo, C. F. 1994. The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory, Transportation Research Part B: Methodological 28(4): 269–287. http://dx.doi.org/10.1016/0191-2615(94)90002-7
Doan, K.; Ukkusuri, S.; Han, L. 2011. On the existence of pricing strategies in the discrete time heterogeneous single bottleneck model, Transportation Research Part B: Methodological 45(9): 1483–1500. http://dx.doi.org/10.1016/j.trb.2011.05.019
Friesz, T. L.; Bernstein, D.; Smith, T. E.; Tobin, R. L.; Wie, B. W. 1993. A variational inequality formulation of the dynamic network user equilibrium problem, Operations Research 41(1): 179–191. http://dx.doi.org/10.1287/opre.41.1.179
Friesz, T. L.; Kim, T.; Kwon, C.; Rigdon, M. A. 2011. Approximate network loading and dual-time-scale dynamic user equilibrium, Transportation Research Part B: Methodological 45(1): 176–207. http://dx.doi.org/10.1016/j.trb.2010.05.003
Friesz, T. L.; Mookherjee, R. 2006. Solving the dynamic network user equilibrium problem with state-dependent time shifts, Transportation Research Part B: Methodological 40(3): 207–229. http://dx.doi.org/10.1016/j.trb.2005.03.002
Friesz, T. L.; Mookherjee, R.; Yao, T. 2008. Securitizing congestion: the congestion call option, Transportation Research Part B: Methodological 42(5): 407–437. http://dx.doi.org/10.1016/j.trb.2007.10.002
Ge, Y. E.; Carey, M. 2004. Travel time computation of link and path flows and first-in-first-out, in B. Mao, Z. Tian, Q. Sun, (Eds.). Proceedings of the 4th International Conference on Traffic and Transportation Studies, 2–4 August 2004, Dalian, China, 326–335.
Ge, Y. E.; Stewart, K.; Sun, B.; Ban, X. G.; Zhang, S. 2015. Investigating undesired spatial and temporal boundary effects of congestion charging, Transportmetrica B: Transport Dynamics. http://dx.doi.org/10.1080/21680566.2014.961044
Ge, Y. E.; Sun, B. R.; Zhang, H. M.; Szeto, W. Y.; Zhou, X. 2014. A comparison of dynamic user optimal states with zero, fixed and variable tolerances, Networks and Spatial Economics. http://dx.doi.org/10.1007/s11067-014-9243-9
Ge, Y. E.; Zhou, X. 2012. An alternative definition of dynamic user optimum on signalised road networks, Journal of Advanced Transportation 46(3): 236–253. http://dx.doi.org/10.1002/atr.207
Hau, T. D. 2006. Congestion charging mechanisms for roads, part I – conceptual framework, Transportmetrica 2(2): 87–116. http://dx.doi.org/10.1080/18128600608685658
Hendrickson, C.; Kocur, G. 1981. Schedule delay and departure time decisions in a deterministic model, Transportation Science 15(1): 62–77. http://dx.doi.org/10.1287/trsc.15.1.62
Laih, C.-H. 2004. Effects of the optimal step toll scheme on equilibrium commuter behaviour, Applied Economics 36(1): 59–81. http://dx.doi.org/10.1080/0003684042000177206
Laih, C.-H. 1994. Queueing at a bottleneck with single- and multi-step tolls, Transportation Research Part A: Policy and Practice 28(3): 197–208. http://dx.doi.org/10.1016/0965-8564(94)90017-5
Lighthill, M. J.; Whitham, G. B. 1955a. On kinematic waves. I. Flood movement in long rivers, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences 229: 281–316. http://dx.doi.org/10.1098/rspa.1955.0088
Lighthill, M. J.; Whitham, G. B. 1955b. On kinematic waves. II. A theory of traffic flow on long crowded roads, Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences 229: 317–345. http://dx.doi.org/10.1098/rspa.1955.0089
Lin, J.; Ge, Y. E. 2006. Impacts of traffic heterogeneity on roadside air pollution concentration, Transportation Research Part D: Transport and Environment 11(2): 166–170. http://dx.doi.org/10.1016/j.trd.2005.12.001
Lindsey, R. 2010. Reforming road user charges: a research challenge for regional science, Journal of Regional Science 50(1): 471–492. http://dx.doi.org/10.1111/j.1467-9787.2009.00639.x
Lindsey, R. 2006. Do economists reach a conclusion on road pricing? The intellectual history of an idea, Econ Journal Watch 3(2): 292–379.
Lindsey, C. R.; Van den Berg, V. A. C.; Verhoef, E. T. 2012. Step tolling with bottleneck queuing congestion, Journal of Urban Economics 72(1): 46–59. http://dx.doi.org/10.1016/j.jue.2012.02.001
Lo, H. K.; Szeto, W. Y. 2002. A cell-based variational inequality formulation of the dynamic user optimal assignment problem, Transportation Research Part B: Methodological 36(5): 421–443. http://dx.doi.org/10.1016/S0191-2615(01)00011-X
Long, J.; Gao, Z.; Szeto, W. Y. 2011. Discretised link travel time models based on cumulative flows: formulations and properties, Transportation Research Part B: Methodological 45(1): 232–254. http://dx.doi.org/10.1016/j.trb.2010.05.002
LTA. 2013. ONE.MOTORING Services. Land Transport Authority (LTA). Available from Internet: http://www.onemotoring.com.sg/publish/onemotoring/en/imap.html
Mahmassani, H.; Herman, R. 1984. Dynamic user equilibrium departure time and route choice on idealized traffic arterials, Transportation Science 18(4): 362–384. http://dx.doi.org/10.1287/trsc.18.4.362
Mounce, R.; Carey, M. 2011. Route swapping in dynamic traffic networks, Transportation Research Part B: Methodological 45(1): 102–111. http://dx.doi.org/10.1016/j.trb.2010.05.005
Newell, G. F. 1993a. A simplified theory of kinematic waves in highway traffic, part I: general theory, Transportation Research Part B: Methodological 27(4): 281–287. http://dx.doi.org/10.1016/0191-2615(93)90038-C
Newell, G. F. 1993b. A simplified theory of kinematic waves in highway traffic, part II: queueing at freeway bottlenecks, Transportation Research Part B: Methodological 27(4): 289–303. http://dx.doi.org/10.1016/0191-2615(93)90039-D
Newell, G. F. 1993c. A simplified theory of kinematic waves in highway traffic, part III: multi-destination flows, Transportation Research Part B: Methodological 27(4): 305–313. http://dx.doi.org/10.1016/0191-2615(93)90040-H
Newell, G. F. 1988. Traffic flow for the morning commute, Transportation Science 22(1): 47–58. http://dx.doi.org/10.1287/trsc.22.1.47
Nie, Y. 2012. Transaction costs and tradable mobility credits, Transportation Research Part B: Methodological 46(1): 189–203. http://dx.doi.org/10.1016/j.trb.2011.10.002
Ramadurai, G.; Ukkusuri, S. V.; Zhao, J.; Pang, J.-S. 2010. Linear complementarity formulation for single bottleneck model with heterogeneous commuters, Transportation Research Part B: Methodological 44(2): 193–214. http://dx.doi.org/10.1016/j.trb.2009.07.005
Richards, P. I. 1956. Shock waves on the highway, Operations Research 4(1): 42–51. http://dx.doi.org/10.1287/opre.4.1.42
Salmon, F. 2010. The Congestion Pricing Debate. 4 June 2010. Available from Internet: http://blogs.reuters.com/felixsalmon/2010/06/04/the-congestion-pricing-debate-cont
Seik, F. T. 1997. An effective demand management instrument in urban transport: the area licensing scheme in Singapore, Cities 14(3): 155–164. http://dx.doi.org/10.1016/S0264-2751(97)00055-3
Small, K. A. 1982. The scheduling of consumer activities: work trips, The American Economic Review 72(3): 467–479.
Small, K. A.; Verhoef, E. T. 2007. The Economics of Urban Transportation. Routledge. 296 p.
STA. 2013. Congestion taxes in Stockholm and Gothenburg. Swedish Transport Agency (STA). Available from Internet: http://www.transportstyrelsen.se
Szeto, W. Y.; Lo, H. K. 2004. A cell-based simultaneous route and departure time choice model with elastic demand, Transportation Research Part B: Methodological 38(7): 593–612. http://dx.doi.org/10.1016/j.trb.2003.05.001
Teodorović, D.; Triantis, K.; Edara, P.; Zhao, Y.; Mladenović, S. 2008. Auction-based congestion pricing, Transportation Planning and Technology 31(4): 399–416. http://dx.doi.org/10.1080/03081060802335042
TfL. 2013. Congestion Charge. Transport for London (TfL). Available from Internet: http://www.tfl.gov.uk/roadusers/congestioncharging
TfL. 2008. Central London Congestion Charging: Impacts Monitoring. Sixth Annual Report. Transport for London (TfL). 227 p. Available from Internet: https://www.tfl.gov.uk/cdn/static/cms/documents/central-london-congestion-charging-impacts-monitoring-sixth-annual-report.pdf
Tian, L.-J.; Yang, H.; Huang, H.-J. 2013. Tradable credit schemes for managing bottleneck congestion and modal split with heterogeneous users, Transportation Research Part E: Logistics and Transportation Review 54: 1–13. http://dx.doi.org/10.1016/j.tre.2013.04.002
Tsekeris, T.; Voß, S. 2009. Design and evaluation of road pricing: state-of-the-art and methodological advances, Netnomics: Economic Research and Electronic Networking 10(1): 5–52. http://dx.doi.org/10.1007/s11066-008-9024-z
Van den Berg, V. A. C. 2014. Coarse tolling with heterogeneous preferences, Transportation Research Part B: Methodological 64: 1–23. http://dx.doi.org/10.1016/j.trb.2014.03.001
Van den Berg, V. A. C. 2012. Step-tolling with price-sensitive demand: why more steps in the toll make the consumer better off, Transportation Research Part A: Policy and Practice 46(10): 1608–1622. http://dx.doi.org/10.1016/j.tra.2012.07.007
Van den Berg, V.; Verhoef, E. T. 2011. Congestion tolling in the bottleneck model with heterogeneous values of time, Transportation Research Part B: Methodological 45(1): 60–78. http://dx.doi.org/10.1016/j.trb.2010.04.003
Vickrey, W. 1992. Principles of Efficient Congestion Pricing. Available from Internet: http://www.vtpi.org/vickrey.htm
Vickrey, W. S. 1969. Congestion theory and transport investment, The American Economic Review 59(2): 251–260.
Xiao, F.; Qian, Z.; Zhang, H. M. 2013. Managing bottleneck congestion with tradable credits, Transportation Research Part B: Methodological 56: 1–14. http://dx.doi.org/10.1016/j.trb.2013.06.016
Xiao, F.; Qian, Z.; Zhang, H. M. 2011. The morning commute problem with coarse toll and nonidentical commuters, Networks and Spatial Economics 11(2): 343–369. http://dx.doi.org/10.1007/s11067-010-9141-8
Xiao, F.; Shen, W.; Zhang, H. M. 2012. The morning commute under flat toll and tactical waiting, Transportation Research Part B: Methodological 46(10): 1346–1359. http://dx.doi.org/10.1016/j.trb.2012.05.005
Yang, H.; Huang, H.-J. 2005. Mathematical and Economic Theory of Road Pricing. Elsevier Science. 486 p.
Yang, H.; Huang, H.-J. 1997. Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory, Transportation Research Part B: Methodological 31(6): 425–440. http://dx.doi.org/10.1016/S0191-2615(97)00005-2
Yang, H.; Wang, X. 2011. Managing network mobility with tradable credits, Transportation Research Part B: Methodological 45(3): 580–594. http://dx.doi.org/10.1016/j.trb.2010.10.002
Yao, T.; Friesz, T. L.; Wei, M. M.; Yin, Y. 2010. Congestion derivatives for a traffic bottleneck, Transportation Research Part B: Methodological 44(10): 1149–1165. http://dx.doi.org/10.1016/j.trb.2010.03.002
Zhang, H. M.; Ge, Y. E. 2004. Modeling variable demand equilibrium under second-best road pricing, Transportation Research Part B: Methodological 38(8): 733–749. http://dx.doi.org/10.1016/j.trb.2003.12.001
Zhang, H. M.; Nie, Y.; Qian, Z. 2013. Modelling network flow with and without link interactions: the cases of point queue, spatial queue and cell transmission model, Transportmetrica B: Transport Dynamics 1(1): 33–51. http://dx.doi.org/10.1080/21680566.2013.785921