The impact of cordon design on the performance of road pricing schemes

Transport Policy 9 (2002) 209–220 www.elsevier.com/locate/tranpol

The impact of cordon design on the performance of road pricing schemes A.D. May*, R. Liu, S.P. Shepherd, A. Sumalee Institute for Transport Studies, University of Leeds, Leeds LS2 9JT, UK Received 1 February 2002; revised 1 June 2002; accepted 1 June 2002

Abstract Road pricing schemes are principally based on cordon-based pricing. Earlier studies have demonstrated that the performance of cordon schemes is critically dependent on cordon location. However, surveys of those designing such schemes indicate that they are opting for the simplest designs, in the interest of acceptability, and may well be overlooking designs which achieve greater economic benefit. A set of analytical procedures has been developed for identifying the locations for imposing charges and the charges at those points which are optimal in terms of economic efficiency. These are demonstrated on a simplified network of Cambridge. Tests on a larger network confirm that performance is very sensitive to cordon location. However, they also show that charging points selected by even a simple analytical procedure can achieve economic benefits around 50% higher than predefined cordons, and that relaxing the requirement to have uniform charges at all charging points can produce further substantial increases in economic benefits. q 2002 Elsevier Science Ltd. All rights reserved. Keywords: Pricing; Cordons; Optimisation; Urban networks

1. Background Road pricing has been proposed as a practical means of reducing the externalities arising from road use for almost four decades (Ministry of Transport, 1964). More recently, proposals have focused on three principal objectives of pricing: reducing congestion, improving the environment and generating revenue (May and Milne, 2000). While theoretical analyses have focused on the first-best, or system optimal strategy, in which all links in a network can be charged (Verhoef, 2000), practical (second-best) applications have considered four types of charging mechanism: charging to pass specific points or cordons in a network; and continuous charging based on distance travelled; time spent travelling; and time spent in congestion (May et al., 1998). Our own research has suggested that distance-based charging is likely to out-perform conventionally-developed cordon schemes (May and Milne, 2000), yet virtually all current proposals envisage the use of simple cordons (Greater London Authority, 2001; Edinburgh City Council, 2000). We have therefore focused our recent research on ways in which cordons might be designed to be more effective. * Corresponding author. Tel.: þ44-113-233-6610; fax: þ 44-113-2335334. E-mail address: [email protected] (A.D. May).

We use the term ‘cordon pricing’ to define any system in which charges are levied as vehicles pass points in the road network. These points can be isolated or, more commonly, grouped into continuous loops around defined areas, or screenlines between areas. An example of a complex cordon design is shown in Fig. 1 (May et al., 1996). Potentially, effectiveness can be measured in terms of contributions to the three objectives of efficiency, environmental protection and revenue generation. In most of what follows, we have focused solely on a conventional economic efficiency analysis of the benefits (Yang and Huang, 1998). In Section 2, we look at earlier evidence, from the London congestion charging study (MVA Consultancy, 1995), of the relative performance of different cordon designs. We then review recent research on the ways in which practitioners specify cordons. We use these, in a case study of a large scale network, to demonstrate that judgmentally specified cordons can differ markedly in their performance, and that simple mathematical approaches can be used to identify a limited set of charging points which perform much more effectively. We then outline a set of analytical procedures, which we have been developing, which promise to generate more effective second-best solutions (Shepherd et al., 2001a). Finally we consider the policy implications of our work to date, and outline the ways in which our analytical procedures can be further developed.

0967-070X/02/$ - see front matter q 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 9 6 7 - 0 7 0 X ( 0 2 ) 0 0 0 3 1 - 8

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Fig. 1. The design of London congestion charging scheme with three cordons and screenlines. Source: May et al. (1996).

2. Evidence from London congestion charging study Between 1992 and 1995, consultants conducted, for the UK Department of Transport, one of the most comprehensive studies ever undertaken of the potential for road pricing, and the relative performance of a range of road pricing designs (MVA Consultancy, 1995; Richards et al., 1996). While that study initially considered continuous charging methods, it rapidly concluded that cordon-based schemes were likely to be more acceptable in the short term, and more feasible given current technology. However, it demonstrated that, while the concept of cordon pricing is simple, its application offers a wide range of options. Those tested in the study included a single cordon around Central London (the innermost ring in Fig. 1); a second and third cordon in Inner London; the addition of radial screenlines to charge orbital movements (Fig. 1); charges either inbound, outbound or both; charges varying by time of day; for the more complex schemes, variations in the ratio of charges

between cordons; and, for all of these, variations in the level of charge. In all, some 45 separate options were tested. Fig. 2 summarises the impact of 19 options, representing six charging structures and four charge levels, on economic efficiency. A simple, single cordon around Central London performs least well, and reaches an optimum level of performance at around £5 per crossing. This is broadly representative of the scheme now incorporated into the Mayor’s Transport Strategy (Greater London Authority, 2001). A second cordon in Inner London adds around 50% to the economic benefits, before taking account of the additional operating costs. Bi-directional charging on these cordons increases the benefits further, and produces results which are similar to those from three cordons with inbound charges. The best performing option is that shown in Fig. 1, with three cordons and four screenlines and bi-directional charging, which has benefits, at the levels of charge shown, of up to three times greater than those from the single cordon. Moreover, there is clear evidence that benefits would be even higher at higher levels of charge (May et al., 1996). Even allowing for the higher cost of operation, this most complex scheme has a net benefit three to four times greater than the simple single Central London cordon (Richards et al., 1996). It is interesting to note that the Mayor elected to forego these additional benefits in the interest of simplicity and public acceptability. The reasons for these differences can be traced back to three principal causes. Firstly, a single cordon intercepts fewer journeys, and thus excludes many which contribute significantly to congestion. Secondly, it imposes the same charge on all journeys which cross it, thus over-restraining short journeys and under-charging long ones. It is the overrestraint of some journeys which leads to the economic benefit falling at higher charges. Thirdly, and most importantly, it allows many journeys to escape the charge by rerouting around the cordon. In the case of London, the worst congestion is to be found just outside the central area, and the impact of a single cordon will be to relieve this

Fig. 2. 1991 Central and inner bi-directional cordon charging for different charging structures: economic benefits (£M per annum). Source: May et al. (1996).

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Fig. 3. 1991 Congestion charging: decrease in CO (%) versus economic benefit (£M per annum). Source: May et al. (1996).

congestion to the extent that radial journeys are reduced, but to aggravate it through traffic diversion. The more complex schemes, and particularly the screenlines, avoid this, and hence increase the benefits from congestion relief. Fig. 3 compares the performance of the 45 options in environmental terms with the efficiency impacts discussed earlier. The indicator shown is percentage reduction in carbon monoxide across Central and Inner London, but other environmental indicators showed similar effects. There is a close correlation between the performance against the two objectives, suggesting that those options which perform well in efficiency terms are also the best in reducing environmental impacts. The one exception is the few very high charge options, marked in the figure, where the charge level exceeds the efficiency optimum, but environmental benefits continue to rise.

Fig. 4 provides a similar comparison between traveller benefits and economic efficiency. Here economic benefits are separated into two elements: benefits to travellers and benefits to providers. The charges paid by travellers are received by providers, reducing the benefits for the former and increasing them for the latter. As expected, the traveller benefits are usually small or negative. What is clear, however, is that the impact on traveller benefits is very sensitive to cordon design. Some clusters of options, ringed in the figure, stand out as imposing much lower disbenefits, and in some cases small benefits, to travellers; in the main these are bi-directional cordons. Several important implications arise from these earlier London results, which are important as a context for the research reported below. A second cordon appears to add significantly to the benefits; similar results have been

Fig. 4. 1991 Congestion charging: traveller benefit versus economic benefit (£M per annum). Source: May et al. (1996).

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Table 1 Potential design criteria for charging cordons Avoid adverse impacts The design should ensure the provision of sufficient alternative routes for drivers who want to bypass the charge area The design should avoid the dispersion of environmental or congestion problem to other areas The cordon should cover only the area having a good public transport service The design should leave the facilities for interchange outside the cordon (e.g. park and ride or parking facility) The design should ensure that all entry points to the charge area are charged or closed The design of the entry points should not be visually unattractive The design should place cordons at boundaries between land use types Gain public acceptance The cordon structure should be simple and easy to understand The charge structure should also be simple and easy to understand The charge should be at a level which is acceptable to the public The charge should be perceived as fair by the public The design should avoid the problem of local inequities (e.g. people just outside the cordon needing to access places just inside) The design should avoid the problem of commercial inequities (e.g. with the same type of business, one is just inside the cordon and the other is just outside the cordon) The design should aim at charging the traffic which contributes most to congestion and pollution The design should aim at charging the traffic which is of least benefit to the area The design should avoid charging the city’s residents The design should avoid charging people from low income areas of the city Practicality The number of charging points should be minimised to reduce capital costs The system should be designed to limit the scheme’s operating costs The design should avoid the types of road that cannot be tolled The design should avoid areas or locations that may cause technological or communication problems for the system The cordon should be located wholly inside the city authority area

As a first stage in answering this question, we considered it helpful to review past designs, and to ask those currently involved in developing road pricing schemes how they chose their cordon designs.

elsewhere (Shepherd et al., 2001a). It draws on experience in Singapore, Hong Kong, London and Norway (Holland and Watson, 1978; Harrison et al., 1986; Larsen and Ramjerdi, 1991; Menon, 2000; Greater London Authority, 2001). Unfortunately, none of these discusses in detail the basis on which cordons have been designed, and we have had therefore to infer the factors which have been considered. In doing so, we also returned to the criteria for design of road pricing schemes developed by Smeed (Ministry of Transport, 1964). We identified a number of potential design criteria, which could be grouped broadly under the three considerations of avoiding adverse impacts; gaining public acceptance; and satisfying practical constraints, as set out in Table 1. We had expected that cordon design criteria might also be dependent on the objectives of the scheme. However, as noted earlier, contributions to economic efficiency and environmental objectives are closely correlated, suggesting that a cordon design which performs well for one objective will be appropriate for the other. The one objective which does give rise to a different design approach is that of raising revenue for which, as evidenced by the Norwegian schemes, it is preferable to impose charges where the largest number of journeys can be intercepted (Larsen and Ramjerdi, 1991).

3.1. Literature review results

3.2. Survey results

reported elsewhere (Santos, 2002). Bi-directional charging is markedly preferable to inbound charging, in generating higher benefits and smaller traveller disbenefits, but performance is sensitive to the distribution of charges by direction and time of day. While a third cordon adds few further benefits, the introduction of screenlines does add further to the efficiency and environmental benefits, by controlling the growth of orbital movements. Generally, it is not apparent without significant testing which cordon configurations are likely to perform best. However, it appears that cordon designs which intercept more of the journeys which contribute to congestion, spread charges for longer journeys across a number of crossing points, and discourage orbital diversions, are likely to achieve higher efficiency and environmental benefits, and have a smaller adverse impact on travellers. This assessment prompts the question as to whether a more formal procedure can be developed for identifying better performing cordons.

3. Judgmental approaches to cordon design

The review of the literature is reported more fully

The survey of practitioners focused on six UK local

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Table 2 Design criteria identified in the interviews Avoid adverse impacts The design should ensure the provision of sufficient alternative routes for drivers who want to bypass the charge area The design should avoid the dispersion of environmental or congestion problems to other areas The design should leave the facilities for interchange outside the cordon (e.g. park and ride or parking facility) The design should ensure that all entry points to the charge area are charged or closed The cordon boundaries should be associated with the controlled parking zone which can avoid the dispersion of parking demand around the fringe of cordon Gain public acceptance The cordon structure should be simple and easy to understand The charge structure should also be simple and easy to understand The charge should be at a level which is acceptable to the public The charge should be perceived as fair by the public Practicality The number of charging points should be minimised to reduce capital costs The cordon should be located wholly inside the city authority area

authorities which were active partners in the UK Charging Development Partnership, and were at differing stages in the development of road pricing proposals. It involved an initial questionnaire and a subsequent in-depth interview with a responsible transport planner which sought further information on key aspects of their proposed scheme. Full details are given by Sumalee (2001). Both questionnaire and interview were structured to cover in turn the context of the proposal, the objectives of the scheme, and the detailed design process. It became clear that the context and objectives generally had little impact on detailed design. Most respondents suggested that their schemes were being planned both to reduce congestion and environmental impact directly, and to generate revenue to finance other policy instruments. Road pricing was not seen as a solution in its own right, and therefore its design was not critically influenced by its objectives. The key elements in the design process were to avoid adverse impacts and to gain public acceptance; the practical aspects in Table 1 were generally less important. Table 2 lists, under the same three headings, the criteria which emerged from the survey. Under the heading of avoidance of adverse impacts, four of the seven criteria in Table 1 were identified; the issues of visual impact and land use boundaries were not considered important, and that of public transport availability was subsumed into the discussions of acceptability. One additional criterion, of avoiding fringe parking, was raised. The first four criteria in Table 1 under the heading of public acceptability were seen as important; conversely there was little direct discussion of local inequities. In contrast to the detailed list in Table 1, most respondents took the much more simple view that road pricing should be limited to the central area, even if traffic elsewhere contributed to congestion. In this way, issues of impact on residents, low income areas and those with inadequate public transport were avoided. Under the heading of practicality, only the concerns of limiting the number of crossings and keeping the cordon and its diversion routes within the city’s boundaries were retained.

In summary, the most frequent approach is to: † focus solely on the city centre, together with any major generators on its fringes; † place the cordon within the city centre ring road if one exists, or alternatively try to avoid charging routes which would allow drivers to avoid entering the area; † minimise the crossing points by using existing boundaries to movement, and keep the cordon as simple as possible; † check that all significant bypass routes are within the city’s jurisdiction; † ensure that on-street parking control extends beyond the cordon; † use a simple charge structure with uniform charges for all crossing points; and † keep the charge at a level sufficiently low to be acceptable. The considerations on location were seen as separate from those on charge level. While the surveys identified a clear preference for a simple approach, they also demonstrated that respondents were aware of the potential benefits of a more complex scheme. Typical among the responses was “at this stage we are trying to find a system that is just good enough to make this scheme work, rather than trying to find an optimal design which may not be possible to implement; but of course there is the possibility of extending the scheme to a more complex system subject to the success of the initial scheme”. Our work on the development of optimal designs needs to be seen in this context; it will not be applied initially, but it should help in identifying subsequent extensions of the first schemes. However, there is a case for at least identifying the nature of those possible extensions before committing to the initial scheme, to avoid undue abortive expenditure.

4. Theoretical approaches 4.1. The CORDON and LOCATE methods Methods for specifying optimal charges where all links

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in a transport network can be included (the ‘first best’ problem) are readily available (Sheffi, 1985), and we use these to compute our first best system optimal tolls. However, those which cater for charging at a limited number of points, such as across cordons, are much less well developed. The mathematical approach adopted in this study builds directly on work by Verhoef (1998, 2000). The approach is logically divided into two stages, the definition of optimal charge levels for a given set of locations and the prediction of optimal toll locations. The CORDON process associated with SATURN was developed in order to solve the problem of optimal charge levels. SATURN is a steady-state equilibrium assignment model, which predicts route choice and traffic flows on a road network based on the generalised costs of travel, taking account of delays due to capacity constraints (Van Vliet, 1982). It includes an assignment sub-model, which estimates driver route choices using Wardrop user optimum equilibrium assumptions (Wardrop, 1952). In its conventional form, the model assumes fixed road travel demand. However, the capability exists to introduce variable demand through the SATEASY elastic assignment algorithm. The tests reported here use SATEASY, and thus reflect the potential for changes in the costs of using the road network to result in changes in levels of use. No attempt is made, however, to distinguish between changes resulting from trip suppression, rescheduling and changes in mode. The detailed impacts of these changes are thus omitted from the calculation of economic benefits. The CORDON process for the first stage is to maximise the given objective function, based on social welfare, subject to the constraint of only using a given set of tolled links. It is assumed that the regulator sets the tolls so as to maximise social welfare W, defined as total benefits minus total costs1: Max WðF; TÞ ¼

X ð Ti i

0

Di ðxÞdx 2

X

Fp ·cp

p

where Fp are path flows, cp path costs, Di the inverse demand function and Ti the number of users between OD pair i. The method involves setting the maximisation problem up as a standard Lagrangian with the constraint that each relevant path be in Wardrop equilibrium. The first derivatives are used to form a set of equations with dimension determined by the number of paths plus the number of chargeable links considered. These equations are solved using singular value decomposition (SVD). Solving these first order conditions results in a prediction for the optimal toll levels for each chargeable link. These predictions can be tested with the SATURN model and the process is repeated until the method converges. The LOCATE process is an extension of CORDON developed to solve the problem of choosing optimal toll 1

Note that operating costs can be added by including a cost per toll point.

locations. The process involves building up a list of toll points incrementally, by choosing links one by one on the basis of a location index. A location index is an approximation of the welfare gain that would result from placing an optimal charge in a particular location. It makes use of the predicted toll from the first iteration of the CORDON process combined with the shadow prices associated with the link(s) considered. Although previously selected toll points are always included, the charge levels are allowed to vary each time an additional link is added. Those interested in the details of the CORDON process and the LOCATE process should refer to Shepherd et al. (2001a, b), respectively. Unfortunately at the time of writing the CORDON method had not been applied successfully to a larger scale network. The method requires perfect convergence of the assignment problem as any convergence errors at the path level are magnified by the Lagrange multipliers and hence upset the prediction of the optimal tolls. It may also be the case that as the dimension of the problem is increased then the solution of the simultaneous equations fails—the equations becoming ill-conditioned. An alternative method, GACHARGE, has been developed to tackle this problem, based on the idea of genetic algorithms (GA) (Michalewicz, 1994; Gen and Cheng, 2000). Section 4.3 explains the detail of the GACHARGE method. The LOCATE process fails to identify the optimal toll locations in cases where the optimal toll location in an early iteration is not the optimal toll location in later iterations. This is due to failure to deselect a toll location selected previously. The GALOCATE method has been developed as an alternative to LOCATE, again based on the idea of GA. The detail of GALOCATE is explained in Section 4.2. 4.2. A genetic algorithms based approach to solve the optimal toll location problem (GALOCATE) The basic idea of the GA approach is to code the decision variables of the problem as a finite string (called ‘chromosome’) and calculate the fitness (objective function) of each string. Chromosomes with a high fitness level have a higher probability of survival. The surviving chromosomes then reproduce and form the chromosomes for the next generation through the ‘crossover’ and ‘mutation’ process. The GA based approach applied here, termed GALOCATE, uses location indices, based on predictions of welfare gains that would result from placing optimal charges in particular locations, as suggested by Verhoef (2000), as its fitness indicator for each chromosome. Each chromosome in GALOCATE represents a set of tolled links in a network. The traditional structure of the chromosome in GA is a binary-bit string. In this application, the length of the chromosome represents the number of toll points required, and the number in each bit identifies the link to be tolled.

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Fig. 5. Representation of chromosome in GACHARGE.

The candidate list of chargeable links has to be prepared in advance by assigning a number to each candidate link. For the selection process, the roulette wheel and elitism approaches are adopted. All chromosomes in a generation are placed in a virtual roulette wheel. The probability of a chromosome being selected is proportional to its fitness function, which is the value of the location indices. The elitism method first copies the best chromosome (or a few best chromosomes) to the new generation. Elitism can very rapidly increase the performance of GA because it avoids losing the best solution. 4.3. A genetic algorithms based approach for optimising charge levels for a given set of locations (GACHARGE) The GACHARGE approach is to maximise the given objective function, based initially on social welfare, subject to the constraint of only using a given set of tolled links. It is assumed that the regulator sets the tolls so as to maximise social welfare, defined as total benefits minus total costs. In GACHARGE, the chromosome represents the toll levels on predefined tolled links.

215

This section will concentrate on the design of the chromosome structure within the GA for the problem of optimising charge levels. Let t be the number of predefined chargeable links and let r be the predefined maximum charge level. Each chromosome represents a set of charge levels for the t-tolled links in binary format. The structure of the chromosome is therefore a matrix A with t columns and k rows where k is determined by the number of digits required to represent the maximum toll in binary format. Fig. 5 shows an example chromosome (A matrix) for four chargeable links. The toll on each link is defined by the binary number in each column which in this case are 13, 14, 12, and 11 s, respectively. For the realistic case study presented in Section 6 the maximum toll was 3000 s represented by 11 rows in the chromosome.

5. Application to a network of Cambridge The MINICAM network is a broadly symmetrical ringradial network, based loosely on conditions in Cambridge (Fig. 6). The network is relatively large consisting of 184 links (with non-linear cost functions) and 16 origindestination zones. The demand function is common for all OD pairs being non-linear with constant elasticity. The generalised costs considered in the tests are based on time only and resulted in 281 paths at equilibrium in the base, no toll case. Because only time is considered, tolls are expressed in seconds. The 16 zones in the network are symmetrically located in

Fig. 6. MINICAM network of Cambridge with three cordons.

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Table 3 Optimal uniform charges and benefits for the symmetric demand of MINICAM network Cordon

Optimal uniform charge (s)

Benefit (1000 s)

Inner Intermediate Outer

200 210 180

136 109 45

three main areas: city centre (with four zones), urban area (six zones) and external (four zones). The base matrix, which has been calibrated to traffic conditions in Cambridge, is also near symmetrical with demand to/from zones in the same area equal or close to equal. This has resulted in symmetric link flow distributions across the network, in particular equal demand along the radials which carried the majority of the traffic. Three closed cordons, an outer, intermediate and an inner cordon were tested with both uniform and variable charges. In addition the CORDON, LOCATE and GALOCATE processes were applied to test the optimal charge levels and locations. Table 3 shows the optimal uniform charges and resulting benefits (in seconds) for the three cordons. The inner cordon is the best solution with a uniform charge of 200 s. Fig. 7 shows a benefit contour plot for the intermediate cordon where the charges are allowed to vary in pairs. It also depicts the optimisation path taken by the CORDON process when all four charges are allowed to vary. The optimisation process confirms the optimal solution is in this case to apply uniform charges of 200 s

around the cordon. This result is as expected due to the equal demand levels on all inbound radials. The LOCATE and GALOCATE approaches were used to identify the best four chargeable links from a possible 112 candidate links. Both the LOCATE and GALOCATE approach confirmed the inner cordon as the optimal location for a set of four chargeable links. In this case the judgmental approach coincides with the theoretical optimum, but the network and demand structure will have simplified the choice process. In an attempt to explore these issues further the demand matrix was varied so that demand levels along the radials were not equal in the no toll equilibrium which is probably closer to a real situation. Initial results show that the CORDON process gives a 12% increase in benefits for the intermediate cordon when charges were allowed to vary. However, the LOCATE process failed to select the best four links. The cause of the problem is that LOCATE does not allow a location, once selected, to be de-selected. This difficulty was not experienced with symmetrical demand.

6. Application to a large scale network Again SATURN has been used, but in this case, with a realistic but coarse network of a medium sized European city for the morning peak hour with 350 links and 25 zones. Fig. 8 shows the network and four cordon charging designs resulting from applying the judgmental approach. The inner cordons are designed to protect the historical centre, the

Fig. 7. Contour of the benefits for the intermediate cordon with symmetrical trip matrix for pairs of charges (in seconds).

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Fig. 8. The large scale network.

outer cordons makes use of the outer ring-road and the natural boundary formed by the coast. In order to display the effect of variable charges and alternative locations two other theoretical approaches were adopted. The first simply takes the first-best system optimal tolls (when all links may be charged; Sheffi, 1985) derived automatically by SATURN and selects the highest 10 charges only. These top 10 charges and their locations are shown in Fig. 9. The second method, used to display the effect of varying charges around a cordon, is to apply the GACHARGE approach described earlier. GACHARGE was applied to the inner 1 and outer 1 cordons. A number of comparisons can be made with the four judgmental cordons, the top 10 links and the GACHARGE results. These are as follows: (a) compare the benefits for optimal uniform charges for the four cordons; (b) compare the benefit for the top 10 links with variable charges; (c) restrict the charges for the top 10 links to be uniform; (d) allow two charge levels to be applied to the top 10 links depending on location as shown in Fig. 9 by the circles and rectangles; (e) compare the benefit with the variable charges developed by GACHARGE. Fig. 10 shows the total benefits as the uniform charges are varied for the four cordons and the top 10 links (restricted to uniform charges). The optimal uniform

charges vary between £0.50 and £2.25 and the best of the judgmental cordons is the outer 1 cordon giving a benefit of £6.2k for a single peak hour. The top 10 links with uniform charge (£0.80) increase the benefit further to £9.0k per peak period which shows that closed cordons are not necessarily optimal in terms of location. However, it is worth noting that the performance of the top 10 links is much more sensitive to mis-specification of charge level than is outer cordon 1. Table 4 shows the test results in more detail. In particular, benefits are compared to the first best solution derived by SATURN when all links may be tolled. It can be seen that the judgmental cordons can achieve between 8 and 17% of the first best solution. Allowing the location to vary (top 10 links) increases the benefit to 24% of first best, while allowing the charges to vary as shown in Fig. 9 increases the benefit further to 41% of first best. It is unlikely that such variable charges would be implemented in practice, though a two zone system may well be adopted, as is being considered in the Dutch vehiclekm based charging proposal (Bovy, 2000). The top 10 links were assigned to two zones, as shown in Fig. 9, and the optimal combination of charges was found to be £0.50 and £2.00 for the inner and outer zones, respectively. This system of charges provided 32% of the first best solution which is mid-way between the uniform and variable solution for these links. The top 10 results demonstrate the benefit of being able to implement more complex charging structures. GACHARGE was used to find the optimal variable

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Fig. 9. The top 10 links with the highest marginal cost tolls in the large scale network.

charges around the outer 1 and inner 1 cordons. Applying these variable charges gives a benefit of 20 and 10% of first best, which represent improvements over uniform charges of 20 and 21% for the outer 1 and inner 1 cordons, respectively. It should be noted that the benefits discussed earlier are before any implementation and operating costs have been considered. In practice the equipment and operational cost of the system, which depends on the number of toll points,

should be deducted from these gross benefits to give a net benefit. The equipment and operational costs have been estimated to be £183,400 per toll point and £85,300 per toll point per annum, respectively, (Oscar Faber Consultancy, 2001). If we assume a 30 year life, a discount rate of 6% and 1000 peak hours per year then this is approximately equivalent to £100 per toll point per peak-hour for implementation and operating costs. The four cordons have 9, 7, 16 and 20 toll points, respectively, which implies

Fig. 10. Total benefit (£k) per peak hour for the large scale network with different charging regimes.

costs of £900, £700, £1600 and £2000 per peak hour as shown in Table 4. The top 10 cordon would incur £1000 costs. These costs are relatively low and all test results imply that the costs can be met in full. However, if we were to assume similar costs per toll point for the first best solution then the costs would be in the order of £35,000 per peak hour which would result in net benefits significantly lower than those from the top 10 and outer 1 cordon with uniform and varied charges.

2.19a

2.72

5.81

10.96

7.99

2.10 3.99 4.57 1.96 14.50

a

An approximation given the coarseness of the network.

100.0 37.19 35.00a NA

9.7 3.62 0.90 Varied

19.9 7.41 1.60

32.2 11.96 1.00

£0.50 and £2.00 for inner and outer set Varied

24.2 8.99 1.00 £0.80

8.1 12.6 16.6 10.6 40.7 £0.50 £0.75 £2.25 £0.75 Varied

Inner 1 cordon Inner 2 cordon Outer 1 cordon Outer 2 cordon Top 10 links with varied charges Top 10 links with uniform charge Top 10 links with two level charges Outer 1 cordon with varied charges (GA) Inner 1 cordon with varied charges (GA) First-best condition

3.00 4.69 6.17 3.96 15.50 0.90 0.70 1.60 2.00 1.00

Optimal toll

Cost of implementation/operation per peak hour (£k)

219

7. Conclusions and implications for further research

Cordon

Table 4 Optimal toll, costs and benefits per morning peak hour for the large scale network

Gross total benefit per peak hour (£k)

% of gross total benefit compared to first-best

Net benefit per peak hour (£k)

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Cordon-based pricing appears likely to remain the preferred method of implementing road pricing in the medium term. The detailed studies for London, and similar studies elsewhere, have demonstrated that the performance of cordon pricing depends critically on the locations chosen for the cordons. While the London study suggests that the relative merits of different cordons are likely to be similar in terms of their efficiency and environmental impacts, their distributional impacts appear to be sensitive to different aspects of cordon design. While such analytical studies have investigated a wide range of designs, our surveys with practitioners indicate that they are focused on a much simpler set of design options, prompted largely by considerations of acceptability of the initial schemes. While this is understandable, there is a real danger that simple designs will produce substantially lower benefits, and may impose unnecessarily adverse distributional impacts. Our research is focused, not so much on the early design decisions, but on helping to ensure that subsequent schemes can be designed to be more effective. Two analytical methods, CORDON and LOCATE, have been developed to identify the optimal levels of charge at predefined charging points, and the optimal locations for such charging points. Versions of both methods, using genetic algorithms to facilitate the analysis, have also been generated. The methods have been shown to work in a simplified network of Cambridge, for which the optimum (inner) cordon location was identified, and optimal toll levels specified. However, they still require further testing on more complex and less symmetrical networks. A related set of tests on a large scale network have confirmed the initial assumption that simple cordons may be suboptimal. The four cordons tested varied substantially in their performance, with the best producing double the benefits of the worst. Relaxing the requirement for a closed cordon, and instead identifying the 10 most effective charging points, with a uniform charge, added around 50% to the benefits of the best cordon. Further relaxing the requirement for uniform charges at all points increased benefits by around 20% on the cordons and by over 60% on the top 10 links. It is clear from these results that there is the potential for very substantial improvements in the performance of

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cordon-based pricing as a means of improving network efficiency. It is probable that there will be similarly large improvements in environmental performance. Further work is needed to ensure that the newly developed methods are fully effective, and to test the distributional impacts of the designs which they generate.

Acknowledgments The research reported here was supported financially by the UK Engineering and Physical Sciences Research Council and the Department of Transport, Local Government and the Regions. We are grateful to both of these bodies for their support. We also acknowledge the contributions of Erik Verhoef and our colleagues Dave Milne and David Watling. The conclusions, however, are the authors’ own.

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