Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

AN ESTIMATION OF THE APPLICABLE LONG-RUN ROAD PRICING CONSIDERED CAPITAL INVESTMENT AND THE DEGREE OF CONGESTIONS

Kyungwoo KANG Dongyong CHOI Professor Master candidate Transportation Engineering Transportation Engineering University of Hanyang University of Hanyang Sa-1dong, Sangrok-gu, Ansan Sa-1dong, Sangrok-gu, Ansan 425-791 KOREA 425-791 KOREA Fax : +82-31-406-6290 Fax : +82-31-406-6290 E-mail : [email protected] E-mail : [email protected]

Wookag KOOK Jongheun KIM Ph.D candidate Ph.D candidate Transportation Engineering Transportation Engineering University of Hanyang University of Hanyang Sa-1dong, Sangrok-gu, Ansan Sa-1dong, Sangrok-gu, Ansan 425-791 KOREA 425-791 KOREA Fax : +82-31-406-6290 Fax : +82-31-406-6290 E-mail : [email protected] E-mail : [email protected]

Abstract: In this paper, we estimated changeable road pricing while considering the capital and congestion degree, that could be applicable in the long term (Gangbyeon Expressway). We investigated traffic volume and speed(unit per 15 minutes, 2005. Jan. 10 - 2005. Jan. 14.). Then we determined congestion areas as when the average pass speed of vehicle is under 30km/h on Expressway occurred over 3 times a day. The 13 sections were investigated out of the total of 43 sections. These sections are between Nanji I.C. and the northern end of Sungsoo Bridge. As a result, there were some differences among each section(13 sections, average length : 1.38km), but we were able to estimate the range of road pricing which is 900 ～2,300won, that is in accordance with the degree of congestion.

Key Words : Road pricing, Degree of congestion, Rental price

1. INTRODUCTION

Recently, metropolitan transport problems are gathering serious topics not only in Korea but all around the world. We tried to solve the traffic congestion (caused by the increase of social activity and huge distribution transportation) with the expansion of infrastructures, but another cumulative causal process problems. After the new road constructed, the speed of vehicles were higher and therefore resulted in the improvement of traffic. But as the potential demand increased, the newly secured space was quickly filled by congestion. In other words, the cycle of congestion and accumulation keeps repeating and transit time worsens. This corresponds with Braess's paradox. Due to the limit of traffic volume handling, many countries are interested in demand management policies for regulation of traffic demand.

Demand management policies are divided various categories by many researchers, but A. D. Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

May(1986)1 categorized the policy into physical regulation, time regulation, financial control, institutional control. This paper is related with financial control(position of road pricing) which is one of the many demand management policies. In detail, raising marginal cost of road use higher than fixed cost can decrease traffic volume. We will estimate changeable road pricing considered Capital and congestion degree for applicable in the long term. The paper is structured as follows. Section 2 summarises the main theoretical and modeling feature of the road pricing. Section 3 presents the site map of data source and data collection method. Section 4 presents the estimation results of the applicable long-run road pricing. Section 5 summarises and discusses the main policy implications.

2. THE THEORETICAL AND MODELING OF THE ROAD PRICING

We will estimate proper road pricing for maximization of user's utilization degree and supply function considered user's personal labor and capital, effective utilization degree, total system capacity defined next equation (1).

ii = iii GGKLff ),,,( (1)

Li =labor of user i

Ki =capital of user i

Gi =effective utilization degree of user i G =total system capacity

Application of equation (2) (using an individual effective utilization degree(Gi ) and total system capacity( G )), degree of congestions are applied to supply function's element constraint formula make a Lagrange function and deduce constraint conditions for maximization of user's utility. ii = GKLff iii θ ),,,( (2)

n where, = θθ ∑ i GG ),( i=1 ii Max = GKLff iii ,,,( θ ) subject to; jj j = jjj θ =≠≥ K,,1,,),,,( njijXGKLff

i =≤ L,,1, niGG n (∑ i GKF ≤ 0), i=1 where,

X j =utility degree of user's i

1 May, A. D.(1986) Traffic Restraint, A review of the Alternative, Transportation Research, Vol. 20A Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

F =conversion formula of total individual capital and public property

n n n iii i L ∑λ []−= GKLfX iii ∑αθ i +−+ μ ∑i GKFGG ),()(),,,( (3) i=1 i==11i i i i λ ,0,1( i <=−= GGX α = 0 for all i) ∂L i i μλ Ff =+−= 0 (4) K i P ∂Ki ∂L λi f i =−= 0 (5) Li ∂Li ∂L n i i +−= ff jj θλλ = 0 (6) Gi ∑ θ 1 ∂Gi j =1 n ∂L jj −= ∑ θ 2 μθλ Ff G =+ 0 (7) ∂G j =1

ii x /,∂∂= xff = GKx ii ,, θ n 1 θθ ∂∂= ∑Gi ),(/ θ2 = θ ∂∂ G)(/ i=1 n P ∂∂= ∑ KFF i ),(/ G / ∂∂= GFF i=1 Using equations (4) and (6), n i ff i +θ j ff j = 0)/()/( (8) G Kii 1∑ θ K j j =1 Also, using equations (4) and (7), n θ j j = FFff )/()/( (9) 2 ∑ θ K j PG j =1 Finally, using equations(8) and (9), i ff i + θθ FF = 0)/)(/()/( (10) G Kii 21 PG

We are able to know that if all users' coefficient of utilization and system capacity increase by the same ratio; congestion fixed and synonymous. Therefore we can represent the following equation (11); N 1∑ i θθ 2GG =+ 0 (11) i=1

Multiply equation (10) by Gi and then merge about all users, as a result next equation (12) n ( i i = )/()/ = GPFFGGff (12) ∑ G Kii i PG G i=1

= / FFP PGG , shadow pricing of public property

i ff i )/( is ratio of user i 's marginal supply of individual capital and marginal supply of G Kii Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007 public property, We should impose individualizational tax on each users for using effective public infrastructure along with equation (14). i = i ffP i )/( (13) G G Kii

At the same time, using equation (10), equation (14) will arrived. i PG −= θθ 21 FF PG −= θθ 21 )/()/)(/( PG (14) i PG : unit cost about public infrastructure capacity G

For the estimation of road pricing on transport networks, an empirical formula (equation (15)) was proposed by Anwar Shah (1992)2.

θ i = IGG i )( (15)

Truong Truong and David A Hensher3 defined equation (15), based on Answar Shah's empirical formula. Here, Ii < 1 stands for an ‘index of use’(of the road capacity) by user i , and θ is a ‘parameter indicating the degree of publicness of public infrastructure’. In the case of a road network, θ can be used to indicate the ‘degree of congestion’ on the road. To define the index of use, first, we assume that there is a minimum level of traffic density n0 at which (or below this level), the infrastructure remains a pure public good. When the infrastructure is a pure public good, the index of use by each user should be equal to 1(i.e. 100 percent utilization rate): Ii = 1 for ≤ nn 0 . Next, when traffic density exceeds this minimum level, > nn 0 , the ratio( 0 / nn ) can now be used to indicate the ‘relative index of use’. Since the infrastructure is now a semi-public or ‘congested’ public goods, each user's rate of utilization of the goods should be less than 1, and sum up to the same level as when there were only n0 users, I. e. i = 0 nnI < 1)/( for > nn 0 .

Capacity utilization level Gi (or the utilization index i /GG ) can also be defined as the following. Given any traffic density level n and with an average speed si achievable by each user at that density, the average traffic flow will be nsi . Comparing this with the potential maximum traffic flow of nsmax achievable if capacity utilization is 100 percent, i.e. when the speed achievable is a maximum at this density by all users, we can define the

‘capacity utilization ratio’ i GG )/( as being equal simply to this ratio of actual traffic flow over the potential maximum flows. We have i = i max = i //)/( ssnsnsGG max . From this, it can be seen that the capacity utilization ratio can be indicated by the ratio of the actual speed over the maximum potential speed, given any level of traffic density.

1) If there is no congestion θ = )0( , then i = i ssGG max = 1)/()/( , namely, every vehicle can travel at the potential maximum speed.

2 Shah, A. (1992) Dynamics of Public Infrastructure, Industrial Productivity and Profitability, Review of Economics and Statistics 74, 28-36. 3 Truong Truong and David A Hensher (January 2003) Congestion Charging and the Optimal Provision of Public Infrastructure : Theory and Evidence. INSTITUTE OF TRANSPORT STUDIES Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

2) When there is some congestion on the road θ > )0( , capacity utilization ratio (and hence speed ratio) will depend on the index of use (relative traffic density / nn 0 ) as well as the θ degree of congestion. With i = 0 nnI < 1)/( and θ > 1, i 0 nnGG )/()/( <= 1 which gives :

0 )/( i ≤≤ GGGnn for θ ≤≤ )10( , as is equation (3).

3) When θ = 1, i = 0 )/( GnnG and i = 0 )/( snns max . This can be referred to as a situation when ‘public’ infrastructure good has become a completely rival or pure ‘private’ good. At this point, the actual traffic flow nsi reaches the maximum level 0sn msx , which is defined in the traditional literature as the maximum ‘capacity’ of the road. When θ = 1, any percentage decrease (or increase) in the level of speed for all vehicles.

Road space has become a pure private good, and one vehicle's ‘consumption’ of this space must be at the full expense of another's. Therefore, the rate at which road space is ‘consumed’ by all users (the traffic flow rate) must remain ‘constant’ at the maximum ‘capacity’ level, which is determined by the physical conditions of the road.

4) Finally, the case of θ > 1 and i < 0 )/( GnnG (or i < 0 )/( snns max ) can also be described as a situation when ‘public’ infrastructure good has become, not only a pure private good, but also with significant negative externality arising from the use of road space by one user on all others. The negative externality results in the aggregate utilization of road space by all users is now reduced rather than increased as a result of a marginal increase in traffic density. This means the resulting traffic flow will decrease and the travel time-traffic flow curve will become ‘backward bending’, a situation described in the traditional literature as one of ‘hyper-congestion’ or ‘bottleneck’ congestion.

From equation (15), we can now derive a formula for the congestion index. First, we substitute i = 0 nnI )/( into equation (15), and sum over all i 's, then taking the logarithm of both sides and re-arranging terms, we have : 1 ⎡ n ⎤ θ 1−= ⎢ln(∑ i − 0GnG )ln( ⎥ (16) nn 0 )/ln( ⎣ i=1 ⎦

Ii : index of use(of the road capacity) by user I, () n : average level of traffic density

Gi : Capacity utilization level θ : degree of congestion

n0 : minimum level of traffic density G : public infrastructure capacity

Transform formula (16) n 1−θ nn 0 = ∑ i 0GnG )/()()/( (17) i=1

Using (16)-(17), we can derive : Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

⎡ n ⎤ 21 ⎢ θθθ ∂∂= ∑Gi ⎥ []θ ∂∂ G)(//)(/)/( ⎣ i=1 ⎦ (18) n =− /(∑GG i ) i=1 θ −1 =− 0 /)/( nnn o

Equation (18) can apply to equation (14), we can obtain road pricing for optimum supply on transport infrastructure.

i θ −1 θ G = [ 0 ] G 0 = 0 G nPnnnPnnP )/()/()/()/(

i where, PG stand for willingness to pay(road pricing) about congestion of public infrastructure

3. SITE MAP AND DATA COLLECTION METHOD

We have established standards about various congestion situations while considering capital and density, and we will now investigate congestion areas on Gangbyeon Expressway for imposing road pricing, and analyze the examined areas by density. We used the data that was collected by video image detectors and CCTVs on Gangbyeon Expressway. This data contains vehicles' volume, speed, and density etc., and we used this for grasping feasible road pricing areas. In this paper, we investigated traffic volume and speed(unit per 15 minutes, 2005. Jan. 10 - 2005. Jan. 14.). Then we determined congestion areas as when the average pass speed of vehicle is under 30km/h on Expressway occurred over 3 times a day. The 13 sections were investigated out of the total of 43 sections. These sections are between Nanji I.C. and the northern end of Sungsoo Bridge as showed in figure 1. At the same time, table 1 shows the frequency of vehicles' average pass speed under 30km/h on Gangbyeon Expressway.

The average pass speed of vehicles under 30km/h on Expressway occurred over 3 times a day

Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

the frequency that vehicle's average pass speed is under 30km/h frequency of section under 30km/h

101 the northern end of Sungsan Bridge→the northern end of Yanghwa Bridge 4

102 the northern end of Yanghwa Bridge→the northern end of Seogang Bridge 3

103 the northern end of Seogang Bridge→the northern end of 3

104 the northern end of Mapo Bridge→the northern end of WonHou Bridge 6

105 the northern end of WonHou Bridge→the northern end of 4

106 the northern end of Hangang Bridge→the northern end of Dongjak Bridge 5 Gang 114 Nanji IC → the northern end of Sungsan Bridge 3 byeon 115 Sungsoo JC → the northern end of Sungsoo Bridge 20 Express way 201 Sungsoo JC → the northern end of Dongho Bridge 5

202 the northern end of Dongho Bridge→the northern end of 7

203 the northern end of Hannam Bridge→the northern end of 5

206 the northern end of WonHou Bridge→the northern end of Mapo Bridge 3

207 the northern end of Mapo Bridge→the northern end of Seogang Bridge 7

4. THE ESTIMATION RESULTS OF THE APPLICABLE LONG-RUN ROAD PRICING

To estimate the Road Pricing considering capital and congestion degree for applicable in the Long term while using deduced formulas, we need data about road system capacity. System capacity can be regarded as infra capacity or infra facilities' supply price. We apply the infra facilities' supply price to system capacity. This is because if we apply infra capacity to system capacity, we have some problems of changing currency concept. So we applied the infra facilities' supply price to system capacity instead. We derived the road construction cost of the analyzed sections from The Korea Transport Institute(KOTI)'s "The assumption result of capital stock on Road department". This treatise presents that road construction cost per unit area( km2 ) is 780 billion won in 1997. So we applied the length of the analyzed sections(17.96km) and width(35m, one way :8lane) to the data from the treatise of KOTI.

At a result, we derived capital of the analyzed sections(about 245.2 billion won, 1997). Then, we multiplied the capital of the analyzed sections by corporate bonds earning rate(4.69%, 2005). From this result, we deduced that the cost is the rental price(about 11.5 billion won) of the analyzed sections. The reason why we calculated the rental price is because the rental price construed an opportunity cost for the rental capital. We observed the data of traffic volume, speed, density per 15minutes, so we also applied the capital to the system capital per 15 minutes. Therefore, the rental price of Gangbyeon Expressway' Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007 analyzed sections is 11.5 billion won/(365*24*4)=328 thousand won.

We only used the data in which the congestion degree(θ ) is within the range of < θ < 10 . We didn't consider the data of the range of θ ≥ 0 , because in this case, the public infra goods change into purely private goods or negative exterior effect occurs to all the other users by user i. We estimated changeable road pricing considering the capital and congestion degree. Range of road pricing is 900~2,300 won in accordance with the degree of congestion (range : 0.06~0.54). Table 2 presents the classified degree of congestion and road pricing by each section.

Estimated of road pricing length θ congestion link section per section (degree of pricing number (unit::km) congestion) (won/km)

the northern end of Sungsan Bridge→the 101 1.65 0.06~0.53 800~2,200 northern end of Yanghwa Bridge

the northern end of Yanghwa Bridge→the 102 2.08 0.08~0.62 800~2,400 northern end of Seogang Bridge

the northern end of Seogang Bridge→the 103 1.37 0.05~0.58 800~2,700 northern end of Mapo Bridge

the northern end of Mapo Bridge→the 104 1.16 0.07~0.58 800~2,300 northern end of WonHou Bridge

the northern end of WonHou Bridge→the 105 1.36 0.06~0.50 800~1,700 northern end of Hangang Bridge

the northern end of Hangang Bridge→the 106 2.04 0.06~0.50 700~1,400 northern end of Dongjak Bridge

Nanji IC → the northern end of Sungsan 114 0.79 0.05~0.47 900~2,100 Bridge

Sungsoo JC → the norther n end of Sungsoo 115 0.56 0.06~0.46 1,300~3,000 Bridge

Sungsoo JC → the norther n end of Dongho 201 1.22 0.12~0.65 1,000~3,200 Bridge

the northern end of Dongho Bridge→the 202 1.34 0.05~0.57 900~2,400 northern end of Hannam Bridge Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

the northern end of Hannam Bridge→the 203 1.87 0.06~0.56 1,000~2,700 northern end of Banpo Bridge

the northern end of WonHou Bridge→the 206 1.16 0.06~0.51 800~1,800 northern end of Mapo Bridge

the northern end of Mapo Bridge→the 207 1.36 0.08~0.52 900~1,700 northern end of Seogang Bridge

total 17.96

We estimated degree of congestion and road pricing and as a result, we found that there are some differences among each section. We point out 201 section(Sungsoo J.C. → the northern end of Dongho Bridge) because the congestion is variously distributed and the degree of congestion is the highest in 201 section. Table 3 shows the degree of congestion and road pricing classified by speed on the 201 section.

degree of congestion and road pricing classified by speed on 201 section. speed (km/h) degree of congestion road pricing(won)

10 0.65 3,200

20 0.43 1,500

30 0.32 1,300

40 0.25 1,200

50 0.18 1,200

60 0.10 1,000

The range of the degree of congestion(θ ) is 0.12～0.65 as shown as in figure 2. When the vehicles' speed is low, the degree of congestion is high and when the vehicles' speed is high, the degree of congestion is low. So we can see that the speed and degree of congestion are in inverse proportion.

Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007

degree of congestion and speed
road pricing and speed

The range of the road pricing is 1,000~3,200 won as shown as in figure 3. We are able to know that when the vehicles' speed is low and the congestion is high, the individual i allotment( PG ) increases. Due to the fact above, we conclude that when the vehicles' speed is low, the degree of congestion changes rapidly. And when the elasticity of road pricing and the vehicles' speed is high, the degree of congestion and road pricing's elasticity is low.

5. DISCUSSION AND POLICY IMPLICATIONS

In this paper, we estimated changeable road pricing while considering the capital and congestion degree, that could be applicable in the long term (Gangbyeon Expressway). At first, we tried to estimate road pricing while considering labor(private goods) and capital, but the formulas by the Lagrange function progressed regardlessly of labor. So, road pricing was estimated by only considering capital and congestion degree for applicable in the long term.

The purpose of this paper is to estimate the cost of road pricing by changing density, while considering the traffic situation. As a result, there were some differences among each section(13 sections, average length : 1.38km), but we were able to estimate the range of road pricing which is 900～2,300won, that is in accordance with the degree of congestion. We found that when the traffic speed is low, the variation of road pricing is rapidly grows higher.

Because estimated road pricing is variable by the degree of congestion, this estimation has a rational and efficient merit, theoretically. But transport policies must be predictable to users. As we investigated the speed of road passing, we found that when the vehicle's speed remains higher than the marginal speed, we reduce the road pricing and when the vehicle's speed remains under the marginal speed we pull up the road pricing. So, if the users can predict the traffic situation, and we can maximize the congestion easement. Also, it is important that if adopting transport policies are feasible or not. This is because transport policies are operated on the assumption that they will be applied to reality.

For this paper to have a realistic possibility, it should be content with the next two preconditions.

First of all, electronic road user charging is necessary. Throughout the world, there is so far no case that electronic road user charging system was selected across the board, but if we will use the toll booth system on road pricing of Gangbyeon Expressway, there will be no point in charging. If the toll booth system is adopted on Gangbyeon Expressway, it is true that this brings on the bigger congestion according to speed reduction of vehicles and shock wave effect. If electronic road user charging system is selected on Gangbyeon Expressway, there will be less speed reduction of vehicles, and therefore drivers can use the road on cheerful surroundings and we can minimize the social welfare loss.

Second, public relations is necessary for successful road pricing charging. When Gangbyeon Expressway first opened, it was free road. It can be expected that users will be discontented with the fact that Gangbyeon Expressway will be a toll road. If the government promotes sufficient public relations(starting time, reason, etc.), the rejection will be minimized and it Proceedings of the Eastern Asia Society for Transportation Studies, Vol.6, 2007 will shape public opinions. We can know through the congestion pricing of London, that using the sufficient public relations is a successful way to congestion pricing charging.

This paper does not consider the interrupted flow-traffic conditions. However, if we investigate the realtime using hereafter ITS technology and system capacity presented in this paper, it will be solvable. Also, more studies should be conducted on this issue. Furthermore, if we consider the elasticity(fare-traffic volume) to forecasting the road situation to drivers, like Singapore's case, not only will we be able to improve the forecasting possibility satisfactorily, but also rules will established and they will minimize future problems.

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