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). i i f= f(,,,) Li K i G i G (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. i i f= f(,,,) Li K i G i θ (2) n where, θ= θ (,)∑GGi i=1 i i Max f= f(,,, Li K i G i θ ) subject to; j j j f= f( Lj , K j , G j ,θ )≥ X , j ≠ i , j = 1,K , n Gi ≤ G, i = 1,L , n n FKG(∑ i , )≤ 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 i i i i L =∑λ []X − f(,,,)()(,) Li K i G i θ+∑ α GGFKGi − + μ ∑i (3) i=1 i==11i i i i (λ = − 1,XGG = 0, i < α = 0 for all i) ∂L = −λi fi + μ F = 0 (4) K i P ∂Ki ∂L = −λi f i = 0 (5) Li ∂Li ∂L n = −λi fi + λj f j θ = 0 (6) Gi ∑ θ 1 ∂Gi j =1 n ∂L j j = −∑λfθ θ2 + μ FG = 0 (7) ∂G j =1 i i fx = ∂ f/, ∂ x x= Ki,, G i θ n θ1 = ∂ θ / ∂ (∑Gi ), θ2 = ∂θ /() ∂ G i=1 n FFKP = ∂/ ∂ (∑ i ), FFGG = ∂/ ∂ i=1 Using equations (4) and (6), n (fi / f i )+θ (fj / f j )= 0 (8) GiK i 1∑ θ K j j =1 Also, using equations (4) and (7), n θ (/)(/)fj fj = F F (9) 2 ∑ θ K j GP j =1 Finally, using equations(8) and (9), (fi / f i )+ (θ / θ )(FF / )= 0 (10) GiK i 1 2 GP 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 θ1∑GGi + θ2 = 0 (11) i=1 Multiply equation (10) by Gi and then merge about all users, as a result next equation (12) n (fi /)(/) fi G= G F F= GP (12) ∑ GiK i i GP G i=1 PFFGGP= / , shadow pricing of public property (/)fi f i is ratio of user i 's marginal supply of individual capital and marginal supply of GiK i 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). Pi = (/) fi f i (13) G GiK i At the same time, using equation (10), equation (14) will arrived. i PG = −(θ1 / θ 2 )(FFGP / )= − (θ1 / θ 2 )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 GGIi = ()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 n≤ n0 . Next, when traffic density exceeds this minimum level, n> n0 , the ratio( n0 / n ) 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. Ii = ( n0 / n )< 1 for n> n0 . Capacity utilization level Gi (or the utilization index GGi / ) 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’ (/)GGi as being equal simply to this ratio of actual traffic flow over the potential maximum flows. We have (/)//Gi G= nsi nsmax = si smax . 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 (Gi / G )= ( si / smax )= 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 n/ n0 ) as well as the θ degree of congestion.