The network impacts of speed limits on travel time, emission

and safety

Hai YangChair Professor

Department of Civil and Environmental EngineeringThe Hong Kong University of Science and Technology

Clear Water Bay, Kowloon, Hong KongPR China

Drivers’ noncompliance of peed limit

Local impact of speed limit

System impact of speed limit

Tarko (2009) and Yang and Wang (2012)

Background of Research

Modeling drivers’ noncompliance behaviors of speed limits

Taking consideration of subjective travel time cost, the perceived crash risk and the perceived ticket cost

Formulate and examine drivers’ route choices and speed at user equilibrium (homogeneous or heterogeneous)

Optimal design of speed limits for enhancing safety and reducing emission and energy consumption.

Objectives

Speed is an essential factor in road safety Longer braking distances higher possibility of crash involvement Power functions (Maycock et al., 1998; Quimby et al., 1999) Exponential functions (Fildes et al. 1991; Kloeden et al., 1997,2001)

Speed variance another important factor Increased risk when speed is higher or slower than average

(Solomon 1964; Cirillo, 1968) Crash frequency at road section level increases with average speed

and speed level (Finch et al. 1994; Nilsson, 1982; Garber and Gadiraju, 1989)

Local impact of speed limit

Very limited attention has been paid to system-wide impact

Traffic reallocations effects (Lave and Elias 1994, 1997)

high speed traffic will shift from slower speed limit link to higher speed limit link, thus induced traffic reallocation effect.

Taylor 2000, Woolley et al. 2002, Madireddy et al. 2011

These three papers observed traffic reallocation and increased travel time due to reduced speed limit. But all three studies were carried out by virtue of microscopic traffic simulation tools.

System impact of speed limit

Accident analysis and preventionA.P. Tarko (2009)

Accident analysis and preventionAndrew P. Tarko

Speed s

Disutility u(s)

0 speed limit s *

optimal speed s

Time lossperception

Ticket riskperception

Crash riskperception

Notations

, , , ,w

v a r w a r fw W r R

v v f a A f

, ,0, , ,w

f r w r w w wr R

f f f d r R w W

Yang and Wang 2012, the obedient user case User equilibrium is conducted in a macroscopic network level and all users are

assumes to strictly obey speed limit rules.

UE can be achieved when all utilized routes have equal and minimum cost

Which is equivalent to:

Traffic equilibrium under speed limit

Figure 1. (a) speed-flow relationship (b) travel time-flow relationship (Source: Yang et al. 2012) with and without speed limit

, 0

,

a a aa a

a a a a a

t v vt v

t v v v C

* * *, ,, if 0, ,a a a r w r w w

a A

t v f r R w W

* * *, ,, if 0, ,a a a r w r w w

a A

t v f r R w W

0,min av

av fa A

t w dw

Major findings of Yang and Wang 2012

While the travel-time flow relationship is modified to be no longer differentiable and strictly increasing after an imposition of speed limit, the classic traffic assignment method still applies to find user equilibrium solutions.

The uniqueness of all link travel time at user equilibrium keeps unchanged, and the UE link flows are also unique if the speed limit on that link is not binding.

Traffic equilibrium under speed limit

Traffic equilibrium under speed limit

Traffic equilibrium under speed limit The non-obedient user case (heterogeneous users) Solomon in 1964 , Anna Hauer (1971) , Ezra Hauer (1971) , Lave (1985) also did regression

analysis based on analysis of 1981 and 1982 state cross-section data, and found that there is a strong relationship between the fatality rate and average speed.

speed variance between different user classes increases the risk of crash involvement compared with homogeneous user case

To make the risk function more conservative, we combined speed variance correlated risk with the risk function confirmed by meta-analysis conducted by Elvik et al. (2004).

2.70 avg

2.14( , ) ( ) ( ) ,( , ) ( ) ( ) ,c avg m avg m n m avg

a a a a ac avg m m avg avg n m avg

a a a a a

r s s s s s s sr s s s s s s s

, ,m nm m avg m c avg m m m ma

a a a a a a a a a a ama

lu s s r s s s s ss

avg m mm

s s v vm

mv v

Traffic equilibrium under speed limit The non-obedient user case (heterogeneous users)

, ,m nm m avg m c avg m m m ma

a a a a a a a a a a ama

lu s s r s s s s s

s

Traffic equilibrium under speed limit An artificial example With different speed limit set [60;60;70;80] and [60;60;60;90] for link 1 to 4, we

observed a different flow pattern and system utility.

Link Capacity Free flow time (min) Free flow speed (km/h) Length (km)

1 300 10.5 114 20

2 240 40 75 50

3 400 15 80 20

4 300 13.5 120 27

Demand OriginUser 1

OriginUser 2

Destination 1 12 200 2003 200 200

1 2

3

4

1

2

3

4

Traffic equilibrium under speed limit An artificial example The total utility dramatically dropped 42.65% from 5,068,354,436 to

2,906,566,466. Thus a proper assignment of speed limit scheme is crucial to the system

performance regarding to user travel time and travel risk.

congested

congested

User class 1 User class 2

Link Link Speed Link flow Link speed Link flow avg speed speed limit

1 39.6 365 39.6 200 39.6 60

2 66.0 35 66.0 200 66.0 60

3 66.6 200 69.6 200 68.1 60 Total utility

4 90.0 165 92.4 0 90.0 90 2.91+E9

User class 1 User class 2

Link Link Speed Link flow Link speed Link flow avg speed speed limit

1 42.5 316 42.5 231 42.5 60

2 63.6 84 63.6 169 63.6 60

3 69.6 200 69.6 200 69.6 70 Total utility

4 80.0 116 88.9 31 81.9 80 5.06+E9

Traffic equilibrium under speed limit Conclusion

The results show that users speed choice largely depends on alpha, beta, gamma value and the speed limit. The assignment of speed limit is vital for system performances.

The Sioux Falls Example proves that it is possible to set a speed limit scheme that balance travel time, crash risk and vehicle emission at the same time.

Thank you!