The impact of speed limits on traffic equilibrium and system performance in networks Hai Yang Chair Professor Department of Civil and Environmental Engineering, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, PR China

OUTLINE Introduction Impact of speed limit at a macroscopic network level –Travel time-flow relationship –Traffic equilibrium and system performance Comparison of speed limits and road pricing for traffic regulation Conclusion

Reference Yang, H., Wang, X.L. and Yin, Y.F. (2012) The impact of speed limits on traffic equilibrium and system performance in networks. Transportation Research 46B, No.10,

1. INTRODUCTION

Main Objectives of Speed Limit Enhance safety –High speed leads to high risk of crash involvement (i.e. Solomon 1964, Cirillo 1968, Garber and Graham 1990, Ashenfelter and Greenstone 2002 ) –The severity of injuries is an increasing function of speed (Joksch 1975) Reduce fuel consumption –1974, U.S. 55 mph speed limit on highways  reduce gasoline and diesel fuel consumption during energy crisis Reduce vehicle emissions –2003, southern Switzerland, 80 Km/h on some motorways  reduce ozone level –2003, Rotterdam, 80 Km/h on urban motorways  reduce ozone levels

Taylor (2000), Woolley et al. (2002) and Madireddy et al. (2011) –Microscopic simulation of the network impact of speed limit –Traffic reallocation is observed and travel time is reported to increase with reduced speed limits but not in a direct proportion to the change of speed limits Network Impact of Speed Limit

2. IMPACT OF SPEED LIMIT

Travel Time – Flow Relationship with a Speed Limit C Traffic volume v t0t0 Travel time t Normal flow Forced flow C Traffic volume v Speed s

Travel Time Function with a Speed Limit Continuous, convex and increasing but no longer differentiable and strictly increasing C Traffic volume v t0t0 Travel time t

Link-specific Speed Limit Law

User Equilibrium under Speed Limit

Uniqueness of UE Solutions

Appearance of Non-unique Link Flows on Links with Binding Speed Limit The Parallel Network

Appearance of Non-unique Link Flows on Links with Binding Speed Limit

Appearance of Non-unique Link Flows on Links with Binding Speed Limit: The General Network

Pareto-improvement in total travel time and vehicular emissions with a speed limit law: A Numerical Example

3. SPEED LIMIT V.S. PRICING FOR TRAFFIC REGULATION

Comparison of Speed Limits and Road Pricing for Traffic Regulation: Speed Limits VS Non-negative Toll Charge

Comparison of speed limits and road pricing for traffic regulation Speed Limits VS Non-negative Link Tolls

Comparison of speed limits and road pricing for traffic regulation Speed Limits VS Non-negative Link Tolls The difference of total network emissions under the speed limit and the toll charge schemes depends on the target link flow pattern and the link emission functions.

Speed Limits VS Non-negative Link Tolls PolicyScheme Individual travel cost /min Link travel time /min Total time/min Link emission Total emission No policy link tolls(18,0)$ speed limit (90.0,187.5) Km/h

Comparison of speed limits and road pricing for minimum traffic emissions Speed Limits VS Negative Link Tolls (Subsidy) Policy Optimal scheme Link flowTotal time Total emission No policy interventionN/A (1.0,1.0)2900 Minimize emission through toll and subsidy* (3.32, 3.32) Minimize emission through speed limit (1.0,1.0) * If only non-negative tolls are allowed, then no emission reduction can be achieved.

Conclusion The standard traffic assignment method still applies. The uniqueness of link travel times at user equilibrium (UE) remains valid, and the UE flows on links with non-binding speed limit are still unique. For other links with binding speed limits, a polyhedron which contains all UE link flows on these links are explicitly given, and the uniqueness of UE link flows can be determined by solving a linear system of equalities and inequalities. Although from different perspectives for regulating traffic flows with a different mechanism, a speed limit law can play the same role as a positive toll scheme and overwhelm some negative (rebate) toll schemes under certain conditions for network flow management.