Journal of Advaticed Transportation, Vol. 30, No. 3, pp. 45-56

Optimization of Tunnel Tolls in Land Use and Trans port PI an n i ng

William H.K. Lam Antonio C.K. Poon

R.J. Ye

The task of transport planning is to determine cost- effective methods of providing and improving mobility, which can include minimizing traffic congestion. A cost- effective solution to transport problems should consist of a land use pattern, a transport system an a set of road pricing policies that together bring demand and supply into balance in an efficient and equitable way. The conventional approach aimed to produce comprehensive, long-term plans for land use and transport in considerable detail, but tended to ignore the role of road pricing policy, thus ending up with solutions that might not be efficient or economical. This feature of sub- optimal road pricing policy is accentuated by the overall growth in car use, which has generated problems with the efficient use of road space. This paper presents a computer analysis system (or model) which will enable the analysis of coordinated tunnel toll pricing policies by optimising an "objective function" while satisfying the associated and other constraints. The possibility of integrating the optimal road pricing policies in the land use and transport planning are discussed. A case study based on Hong Kong data demonstrates the efficiency of optimizing tolls on two of the three harbour crossing tunnels in Hong Kong.

KEYWORDS Tunnel tolls, road pricing, land use and transport planning.

William H.K. Lam is an Associate Professor in the Department of Civil and Structural Engineering at the Hong Kong Polytechnic University, Hong Kong. Antonio C.K. Poonis the former Head of the Department of Applied Mathematics at the Hong Kong Polytechnic University. R.J. Ye is a Research Student in the Department of Civil and Structural Engineering at the Hoiig Kong Polytechnic University.

Received March 1994; I n revisal fonn Jaiiuaiy 1996.

46 W.H.K. Lam, A.C.K. Poon, R.J. Ye

Introduction

Transport affects the life of every resident of Hong Kong, not only directly in the daily journeys to work, school or other activities but also indirectly, by its influence on the economic activity and prosperity of the Territory. The development and maintenance of an efficient transport system has long been a central policy of Hong Kong Government.

Hong Kong is expanding rapidly. To accommodate this expansion, some two to three billion dollars have been invested every year for the construction of new highways and transport infrastructure. This investment is mainly made by the Government. There are a large number of potential projects to be chosen from, but there are practical constraints in terms of financial and construction industry capacities. Therefore, new transport infrastructure projects must be planned carefully so as to obtain the maximum benefits from the investment for the Territory.

However, it is necessary to consider the road pricing policies simultaneously when designing a road network. Otherwise, it may end with expensive but inefficient solution. Road pricing that as a way to reduce congestion, to provide a basis for investment decision, to assist traffic control, and so on, have been widely used. Distance licence used in Singapore (Holland and Watson, 1978); and electronic road pricing system has been examined in greater detail in Hong Kong (Dawson and Brown, 1985) and will be demonstrated fully in Singapore in the near future. The charging methods of road pricing can be divided into two categories, namely, direct and indirect method. Direct charges are road tolls, and petrol tax, while indirect charges are ALF (annual licence fee), FRT (first registration tax), and parking fee. In Hong Kong, various tolls are being charged to different vehicle types at different road tunnels.

This paper presents a road pricing optimization method which will enable the analysis of co-ordinated tunnel toll policies by optimizing an "objective function" while satisfying the associated and other constraints. Case study will be shown based on Hong Kong road network and planning data. We will use the optimization method to derive an optimal set of toll charges for the harbour crossing tunnels in Hong Kong. The case study will demonstrate the efticiency of optimizing tolls on two of the three harbour crossing tunnels. First, a review of the existing land use and transport planning approach will be briefly given together with the possibility of integrating road pricing policies and the proposed framework; second, formulation of the optimization method is described; third, the application of the optimization method will be presented in which the total network travel times are used as measure for evaluation

Optimization of Tunnel Tolls in the., . . 47

of the tunnel toll pricing policies in Hong Kong. Finally, conclusion is given together with recommendation for further study.

Background

In order to evaluate new infrastructure projects in Hong Kong, some transport models have been developed since 1973. The first Comprehensive Transport Study (CTS-1) was completed in 1976. The task of CTS-1 was to establish the analytical tools to evaluate transport proposals and to use these tools to devise a balanced programme of transport projects and transport policies. It has formed the basis of transport policy up to the present day. The planning horizon up to 1991. In 1986, the Government commissioned the Second Comprehensive Transport Study (CTS-2) to plan for the period up to 2001. This study provides a basis for the development of a long term transport strategy for Hong Kong for the next decade. The objectives of the study are: tirst, to project transport demand; second, to draw up a proposed transport infrastructure development programme; and third, to evaluate transport policy options.

For the purpose of strategic land use development planning, a Land Use Transport Optimization (LUTO) model was developed (Choi, 1986) for solving the problem of a joint optimization of a land use plan and a transportation development plan.

These LUTO and CTS models have been being used for the strategic land use and transport development planning in Hong Kong (Choi, 1986; Leung and Lam, 1991). Since the task of transport planning is to determine cost-effective solutions for minimizing traffic congestion, a cost-effective solution to the transport problems should consist of a land use pattern, a transport system and a set of pricing policies that together bring demand and supply into balance. However, the road pricing policies considered for studies be seen as some fixed parameters in the models, and ignored the role of pricing policy as an alternative to transport investment. This paper examines how road pricing policies to be integrated in the land use and transport planning. Tunnel tolls are chosen as the control measures of road pricing policies because they have been used in Hong Kong and would affect the traffic condition directly. In the previous related studies, Beckman (1965) commented that "tolls are economically optimal if they induce and efficient use of the available road capacity". Dafermos and Sparrow (197 1) showed that by the means of congestion tolls, we can force individuals to choose their travel paths

48 W.H.K. Lam, A.C.K. Poon, R.J. Ye

leading to a system optimal resource allocation and toll patterns for a simple network with two paths. Similarly, Lam (1988) also demonstrated how road tolls affect the decision of transport investment and the role of road pricing in network design.

Land Use and Transport Planning

In countries where there is heavy concentration of urban population, the integration of land use and transport planning becomes important. While land use planning consists of identifying and selecting potential development areas to meet the expected land requirements, transport planning consists of identifying and selecting potential transport systems to meet the expected travel demand. The primary dependence of land use planning criteria is on the availability of transport infrastructure on the one hand, and the dependence on travel demand on land use pattern on the other hand. The inter-dependence necessitates integration of the land use and transport planning processes.

It is recognised that the conventional approach is a valid tool to be employed in situations where there are relatively few and fairly obvious land use alternatives to be examined and where the scale of demands is close to the capacity available in defined development areas. However, under a converse situation where there is a large number of alternative development possibilities and there is a choice to be made from various feasible transport links, the possible land use - transport plans may become virtually infinite. Under such circumstances, the conventional approach has severe practical limitations in that only a few land use options and a few alternative transport networks can be evaluated.

Faced with the problems associated with a conventional approach as outlined above it was suggested that a fresh look should be taken at how alternative land use - transport strategies might be more rationally derived on an integrated basis, as conceptualized by Fig. 1 .

The land use transport optimization (LUTO) model takes the options of ’modifying land use plan’ and ’modifying transport network’ and enables the simultaneous selection of land development areas and new transport links by optimizing an objective fiinction consisting of both land development costs and transport costs. But road pricing policies were assumed as tixed planning parameters in the LUTO model. As shown in Fig. 2, we are now proposing to incorporate the option of ’modifying road pricing policies’ in the land use and transport planning. This will

Optimization of Tunnel To10 in the.. . .

c

TRANSPORT NETWORK TRANSPORT

MODEL

49

TRANSPORT NETWORK - - - - - - - - -

- 1 I I I I I

-I I

EVALUATE

OF LAND USE- TRANSPORT

ON INITIAL I MODIFIED

NETWORK SYSTEM

. - - - - - - -- ----- INADEQUATE PERFORMANCE

I I I I I - -

I I

ADEQUATE PERFORMANCE

FINAL LAND USE-TRANSPORT

FIRST RUN OF MODEL

SUBSEQUENT ITERATIVE RUNS OF MODEL

----- => FINAL RESULTS

Figure 1. Integrated Land Use and Transport Planning

lead to a more efficient solution - to make more economic use of the transport system.

The integration of transport investment and pricing planning is a new avenue of research. In this paper, an optimization framework is proposed to formulate the co-ordination plan of transport investment and pricing policy. A main characteristic of the integrated process is the relation between the supply of transport capacity and the effect of pricing policy on travel demand. The primary problems are to determine that which transport links of the maximal network are to be retained and what levels of pricing policies are to be adopted, so as to best co-ordinate the transport investment and policy control according to certain planning goals. The desired solution, in the form of the optima1 set of pricing policies and transport links, would be obtained by minimizing an objective function while satisfying the following constraints:

50 W.H.K. Lam, A.C.K. Poon, R.J. Ye

MODIFIED

NETWORK

LAND USE- TRANSPORT PERFORMANCE OBJECTIVES

I

I

MODIFY

LAND USE

- - k -

INITIALLY ASSUMED LAND USE DISTRIBUTION

OTHER PLANNING PARAMETERS & I , . c CONSTRAINTS 0

0 0

0 I INITIAL 0

TRANSPORT NETWORK

MODEL I

OF LAND USE- - _---------------- SYSTEM

INADEQUATE PERFORMANCE - TRANSPORT

FINAL LAND USE-TRANSPORT PLAN 6 ROAD

FIRST RUN OF MODEL

SUBSEQUENT ITERATIVE RUNS OF MODEL

-_ - - - -> FINAL RESULTS

Figure 2. Integration of Road Pricing Policies in Land Use and Transport Planning

(1) Maximal network identified by sub regional studies, (2) Feasible range of pricing policy, and (3) Acceptable level of service on transport facilities.

The economic objective function is adopted in this paper. The total network travel time (and/or total network travel cost) will be minimized. The optimization framework consists of iteratively solving a network optimization problem with constant trip matrix and solving a road pricing policy optimization problem with tixed road network. The entire process will be repeated until no further improvement to the objective function is possible.

In this paper, the land use pattern and road network will be held fixed in the optimization process. The optimization method used in this paper will enable all feasible toll pricing policies to be tested, in contrast to the conventional process whereby the preferred pricing policies are selected by testing only a limited number of alternatives.

Optimization of Tunnel Tolls in Land Use.. . . 51

Optimization Method

Given a road network with n toll links, let xi denote the percentage increase (or decrease if negative) of the charge of the ith toll link with respect to a reference charge t?. Hence for each (xl, ..., x,,), there corresponds a pricing policy in which the toll charge of the ith toll link is given by ti = (1 + xi ) t?. For each pricing policy ( x ~ , ..., x"), let c(xl, ..., x,,) be the total network travel time corresponding to it. In this paper, such time is computed by the LUTO model. The objective is to find an optimal pricing policy (x;, ..., x:) such that c(x7, ..., x,) IS a minimum .

Let us select m pricing policies (xi ,..., xz), j = 1 , ..., m and compute their network travel times c(x4 ,..., xi), j = 1, ..., m. We have a set of m points in R"+I,

* .

{((xi ,... ,X;J, c~x i , ..., xi>> I j = 1, ... , mi. Theoretically, this set should lie on a convex bow in the steady-state

situation that each driver is on his own minimum cost route (Van Vuren and Van Vliet 1992). We try, therefore, to approximate this bow with the simplest bow-like surface, namely, a quadratic surface

The coefficients a&, pi and y are so determined that the sum of and square error (SEE) at the m selected points is the least, i.e. cluk,

y render

j j j 2 m

j = 1 SSE = 1 [f (x:, ..., xn) - c ( x ~ , ..., xJ]

a minimum. Such least square fit is a standard procedure in linear algebra.

If the error percentage as reflected by the ratio of sum of square error and the sum of square data is reasonably small, we may assume that f(xl, ..., x,,) is an acceptable approximation of c(xl, ..., x,,). If this is the case, the problem is reduced to finding the minimum of a quadratic function which is a easy task.

The strength of this method lies on the fact that the number of evaluation of c(x,, ..., x,,), which is very time consuming, is fixed at m. Its weakness lies, of course, with the fact that the distribution of the data points may not be as bow-shape as expected.

52 W.H.K. Lnm, A.C.K. Poon, R.J. Ye

Case Study

We used the 2001 LUTO planning data and road network with three toll links crossing the harbour; namely, the Cross Harbour Tunnel (XHT) the Western Harbour Crossing (WHX), and the Eastern Harbour Crossing (EHX).

Table 1. Tolls in Equivalent Minutes

Cross Harbour Tunnel (XHT)

Western Harbour Crossing (WHX)

Eastern Harbour Crossing (EHX)

Toll in equivalent in i nut es

Private Goods

Veh icl e

21.0 I 56.0

9.0 I 27.0

We used them as the reference charges but only the proportions of change of toll charge on XHT and WHX, x i and x2 respectively, are considered as decision variables. Forty-nine toll pricing policies were selected as follows with & 30% intervals from the reference charges,

{(XI, x?) I xi = -0.9, -0.6, -0.3, 0.0, 0.3, 0.6, 0.9)

where

x1 = proportion of change of toll charge on the Cross Harbour Tunnel, x., = proportion of change of toll charge on the Western Harbour

Crossing.

Their corresponding total network times in hundred equivalent

These data points shown in Fig. 3 appear to be a convex profile and minutes were computed by LUTO and are shown in the Table 2.

were best titted by the following quadratic surface.

f(xi, x?) = 24009.7 x: - 35775.7 x I x2 + 42980.4 x; -3716.6 X I + 34652.1 X? + 819562 (3)

Table 2. Total Network Travel Time vs. Proportion of Change of Toll Charge on Crossing Harbour Tunnel (xl) and on Western Harbour Crossing (x2)

Total network travel time in hundred

vehicle-minutes

Proportion of change of toll on the Cross Harbour Tunnel

X1

-0.9 -0.6 -0.3 0.0 0.3 0.6 0.9

-0.9

-0.6

Western -0.3 Harbour crossing x2 0.0

0.3

0.6

0.9

2 5 5 h

811685 810710 815927 825031 840497 865978 865753

814753 806956 805467 810582 820902 834869 860726

830139 816464 809257 807011 811026 822342 836818

849734 837254 823857 815627 812979 817000 830135

884400 859917 843881 836305 827738 827578 830361

904913 891897 879338 861283 849713 847368 851521

904913 901005 898683 888375 878730 878393 884436

-. 2

3 5

54 W.H.K. Lam, A.C.K. Poon, R.J. Ye

x,

950000

850000

Figure 3. Total Network Travel Time vs. Proportion of Change of Toll Charge on XHT (Xl) and on WHX (X2)

The ratio of the sum of the square error and the sum of the square data was found to be 0.0001. The optimal value of f(xl, x2) was attained at x1 = -0.3231 and xz = -0.5376 which yields a c(xl, xz) value of 804233. The minimum of c(xl,x2) in a lattice search was found to be 804764 attained at x I = -0.4 and x2 = -0.5. When x1 is fixed at 0, the lattice search optimal c(x,, x2) value is 807008 attained at x2 = -0.4. When x2 is fixed at 0, the lattice search optimal c(xl, x2) value is 812310 attained at x1 = 0.2.

Conclusions

With the use of the proposed framework, it would ensure that the decisions on transport investment will be compatible with pricing policy control in the strategic planning as the optimal set of pricing policies derived from the proposed system could be served as guidelines for long- term policy planning.

The facts illustrated by the example are the important ones from the viewpoint of land use and transport planning. The control measure such as toll pricing can reduce the total network travel time because each road user chooses his own minimum cost route. The example demonstrates that an optimal toll on only one of the several parallel roads is less

Optimization of Tunnel Toils in Land Use.. . 55

efficient and the total network travel time would be smaller in the case where optimal tolls are charged on two of the three harbour crossing tunnels. The imposition of an appropriate set of tunnel tolls can reduce not only the total network travel time, but also the road congestion. It is therefore necessary to consider the road pricing policies simultaneously when planning land use and transport network. Otherwise, it may end with expensive but inefficient solution.

On the other hand, the system objective should be carefully determined at different objectives would result from different tunnel toll pricing policies. These phenomena should be further illustrated for cases of (1) maximizing toll revenue, (2) minimizing total marginal cost of travel, and (3) minimizing total vehicular emissions.

Finally, a systematic optimization method is proposed to enable the simultaneous selection of the best set of tunnel tolls by optimizing an objective function while satisfying the associated and other constraints.

Acknowledgements

This research was funded by the Hong Kong Research Grant Council under Project No. 340.917. The views presented in this paper are those of the authors only.

References

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Dafermos, S . and Sparrow, F.T. (197 1). "Optimal resource allocation and toll patterns in user-optimized transport network", Journal of Transport Economics and Policy, 5 (2), pp. 198-200.

Dawson, J.A.L. and Brown, F.N. (1985). "Electronic road pricing in Hong Kong: 1. A fair way to go?", Traftic Engineering and Control,

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26 (1 l ) , pp. 522-529.

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