Modelling Road Pricing
TAG Unit 3.12.2

February 2007

Contents

1. Introduction

2. Segmentation

3. Representation of road pricing
3.2 Generalised cost
3.3 Point, Screenline and Cordon pricing
3.4 Distance pricing
3.5 Area licences
3.6 Marginal social cost (MSC) based pricing
3.7 Other elements of road pricing schemes

4. Network detail and assignment

5. Demand modelling

6. Other modelling considerations
6.1 Tiered modelling
6.2 Land use modelling
6.3 Reliability
6.4 Modelling packages of measures

7. Validation

8. Further information

9. References

10. Document provenance

11. Annex A: Segmentation and values of time for road pricing models
11.2 Segmentation
11.3 Values of time
11.4 Local values of time
11.5 Freight

12. Annex B: Modelling marginal social cost based prices
12.1 Introduction
12.2 Section 1 - calculation of marginal social costs and prices
12.3 Section 2 - methods for achieving equilibrium prices

13. Annex C: Core requirements for modelling road pricing
13.1 Introduction
13.2 General
13.3 Segmentation
13.4 Assignment
13.5 Demand modelling

1. Introduction

1.1.1 This Unit provides guidance on modelling requirements when projects include road pricing schemes. Where appropriate, it refers to guidance in other TAG Units, rather than repeating that guidance.

1.1.2 An overview of the modelling and appraisal issues, including scheme design issues, arising in the analysis of road pricing schemes can be found in Introduction to Modelling and Appraisal for Road Pricing (TAG Unit 2.12). Further detailed guidance for analysts may be found in:

• Designing Effective Road Pricing Schemes (TAG Unit 3.12.1), which discusses approaches to the design of effective road pricing schemes;
• Guidance on the issues arising when appraising road pricing schemes is provided in Appraisal of Road Pricing Schemes (TAG Unit 3.12.3); and
• Measuring the Social and Distributional Impacts of Road Pricing Schemes (TAG Unit 3.12.4) provides guidance on the use of social research methods to assess the social and distributional impacts of road pricing.

1.1.3 This Unit represents the current state of knowledge. This is a rapidly developing area where we are likely to learn from further development in modelling and design approaches and also from the practical implementation of road pricing schemes. This Unit will be revised and updated as further information becomes available or in light of any comments received during the application of the advice provided.

1.1.4 This Unit sets out the core requirements for the modelling of road pricing to support the development of a business case. A summary of the core requirements is given in Annex C.

1.1.5 As discussed in The Overall Approach: The Steps in the Process (TAG Unit 2.1), modelling is a key component of the study process and models should be used to inform the development of options. However, it will often be necessary to carry out preliminary analysis with a less than full suite of fit for purpose models. Where that course of action is taken, key decisions and detailed design should be revisited using the full suite of models when it becomes available.

1.1.6 Models should be sufficiently flexible to enable them to be used to explore a range of different strategies, including interventions other than road pricing. Flexibility is clearly needed during the early stages of the study process, when the precise form and location of the road pricing scheme is uncertain. It is also likely to be needed at later stages, to cater for changes in design (reflecting, for example, changes in views or circumstances) and sensitivity testing. The potential for models to be used for other purposes should also be kept in mind.

1.1.7 In some cases, simpler methods may be appropriate, while in other cases, more complex methods may be required. However, model simplification risks inadvertently biasing results, while increased complexity can lead to higher development costs and unsatisfactory model run times. Analysts should, therefore, provide a clear justification, based on the analytic requirements of the study in hand, for the use of models that are more or less complex than the core requirements. As a general guiding principle, models should be fit for the purpose, in that they should be capable of reflecting the outcome of road pricing schemes in a way which allows their impacts to be satisfactorily assessed.

1.1.8 Taken overall, with regard to road pricing, the model structure should be able to make allowance for all significant responses (these include frequency, change of time of travel, mode, destination and route) to pricing, and to allow for variations in response by purpose, person type and so on, as far as is useful and practical. It should also deal with secondary effects such as changed speeds for all classes of highway user (including buses), plus the likely effects on other modes of significant increases in demand (bus and rail overcrowding, for example).

1.1.9 Thus, as a core requirement, properly formulated variable demand and traffic assignment models are required to refine the preferred options and to support the business case. The variable demand model should include modules representing trip frequency, mode choice, macro time of day and trip distribution. The assignment model should include capacity restraint and junction simulation.

1.1.10 In some circumstances, it may be acceptable to omit some of these modules, but the decision to do so should start from the presumption that all are required. For example, for pricing schemes which do not vary appreciably by time of day, the choice of time of travel response could be dropped. However, the need to test a range of different options (see Introduction to Modelling and Appraisal for Road Pricing (TAG Unit 2.12)) suggests that a fully specified model meeting the core requirements will usually be required.

1.1.11 It may also be appropriate to include additional modules representing land use, vehicle occupancy, public transport supply, parking and exemptions from road pricing. The decision to include additional modules will depend on the study area, the objectives set for the project, and the nature of the schemes to be examined.

1.1.12 There are two key issues for the modelling of road pricing that are of particular importance. These are:

• enhanced segmentation definition, to ensure that variations in willingness to pay road prices are fully reflected in the modelling; and
• representation of road pricing, including capability to estimate marginal social cost based prices.

1.1.13 These requirements are discussed in some depth below. Analysts should note that some of the methods proposed to address these requirements are new and have not been widely applied. It may be necessary to modify or refine them to suit the needs of a specific study. Where this is the case, close liaison with the Department is recommended.

2. Segmentation

2.1.1 Advice on segmentation is given in Variable Demand Modelling - Scope of the Model (TAG Unit 3.10.2). The guidance given in that Unit represents a core requirement for modelling road pricing. The Unit notes that, for schemes specifically involving pricing, some additional segmentation by willingness-to-pay or income, and possibly also by trip distance, may be required. This section discusses segmentation in general terms; the specific requirements for segmentation of the assignment and demand models are discussed in the sections of this Unit dealing with those topics.

2.1.2 Segmentation is important for the modelling of road pricing because it enables the representation of the availability or level of service provided by transport modes (car availability for example, or crowding on public transport), and the variation in responsiveness to changes in conditions across travellers. The value of time of a traveller is a key determinant of the behaviour of a traveller in responding to road pricing. Research has shown that the assumptions made about the values of time have a significant impact on the model's performance. For example, variation of values of time with income and with purpose produce a greater level of diversion than using a single value of time for all car drivers. These are important second order effects. Inclusion of these aspects of value of time in the modelling assumptions is important if predictions about choices are to be reliable.

2.1.3 Segmentations by income and journey purpose are presented in Annex A, together with values of time for each segment. These segmentations and values of time have been obtained from national studies conducted on behalf of the Department for Transport. Use of the segmentation and associated values of time presented in this Annex is a core requirement for modelling unless more localised approaches are considered to be appropriate.

2.1.4 More localised approaches may be appropriate if there is good reason to believe that the study area is significantly different from the national average. Local segmentations and values of time should be derived from surveys of travellers who are expected to be within the catchment area of the road pricing scheme that is being tested.

2.1.5 Where the distribution by income and distance of trips in the study area is available, and significantly different from national, this information may be used to establish a local segmentation. Values of time for local segmentations may be estimated using the method given in the Annex.

2.1.6 It may be necessary to explore the differential impact of prices on behaviour, relative to fuel or parking costs, or the impact of different payment methods (cash, credit card, pre- or post-payment and so on). Where this is the case, stated preference studies may be undertaken to establish local values and distributions of values of time. Guidance on the use of, and analysis of the results from, stated preference studies is given in Mode Choice Models: Bespoke and Transferred (TAG Unit 3.11.3). For road pricing studies, if undertaken where the choice is between a price and time savings, there is a risk that there will be some form of strategic bias compounded by potential misperceptions of time spent in congested conditions. Care is required to ensure that this does not invalidate the results. Care is also required to ensure that resulting values of time are sufficiently robust for use in modelling.

3. Representation of road pricing

3.1.1 Road pricing schemes have many characteristics. These characteristics are discussed in detail in TAG Unit 2.12. The discussion below considers only those characteristics that need to represented in the modelling.

3.1.2 The form of road pricing to be considered will affect the way in which it is represented in modelling. While the form of road pricing has a substantial effect on the way it is represented on the modelled highway network used for assignment, the way it is included in the formulation of generalised cost is common to all. In addition, in most cases (circumstances where this may not be necessary are discussed in section 4 below), the basic components of generalised cost (time, distance, road price, and other money costs) are skimmed from the network used in assignment and used to construct generalised costs for use in the demand model. Therefore, this section discusses the representation of road pricing in generalised cost in general terms, then goes on to discuss its representation on the modelled highway network for each of the principal forms of road pricing.

3.2 Generalised cost

3.2.1 The generalised cost of travel - usually a linear weighted sum of journey time and other journey costs - is the key determinant of people's travel choices in most transport models. The concept of generalised cost is discussed in Variable Demand Modelling - Scope of the Model (TAG Unit 3.10.2). By including road prices in the formulation of generalised costs, transport models can estimate the impact of road pricing on traveller behaviour. Most transport models measure generalised cost in time units, so the usual approach to incorporating road prices in generalised costs is to divide the price by the appropriate value of time and add it to the other components of generalised cost.

3.2.2 Within the assignment model, it is important to allow for vehicle occupancy. For example:

G_car = T + D*VOC/(occ*VOT) + RP/(occ*VOT)

where T is the journey time spent in the car, VOC is the vehicle operating cost per km for a journey of D km, occ is the number of people in the car (who are assumed to share the cost), VOT is the appropriate value of time, and RP is the road price for the journey.

3.2.3 If the demand model does not distinguish between car drivers and car passengers, the same formulation of generalised cost may be used for car users. However, if the model has been extended beyond the core requirement to distinguish between car drivers and car passengers, some assumptions will need to be made about the distribution of costs between drivers and passengers. In the National Transport Model, it is assumed that car drivers perceive their costs in full (though, as usual, non-work drivers are assumed to perceive only fuel costs), while passengers are assumed to perceive 'guilt' equivalent to half the money costs of the journey, in addition to the time costs. Analysts will need to consider whether this assumption is suitable for their study, or whether an alternative assumption is appropriate. In either case, the assumption adopted should be clearly stated and justified in model documentation.

3.3 Point, screenline and cordon pricing

3.3.1 These forms of pricing are probably the easiest to represent in modelling. Each link in the highway network that is to be priced is assigned a price. For screenline and cordon pricing, the price on all links will usually be the same, though it may, in principle, vary from link to link and some links may be unpriced. Prices may be represented as applying in one direction only, or in both directions. Prices will usually be set outside the model.

3.4 Distance pricing

3.4.1 For distance based pricing, each link to be priced must be identified and assigned a price depending on the link length. The price for each link is dependent only on the link length - it is unaffected by the link flow or other model outputs. Thus, the price may be estimated within the assignment model, or it may be set outside the model - both approaches are acceptable. The rate per unit distance may be the same for all links, or it may vary from link to link.

3.5 Area licences

3.5.1 Area licences, as implemented in the London Congestion Charging scheme, are more difficult to model, for two reasons. First, one payment allows the vehicle to be used for as many journeys as the driver wishes. This means that the cost per journey is difficult to estimate. Second, a payment (possibly at a lower rate than for those entering the area) is levied on vehicles based within the priced area if they use the roads, even though they may not cross the cordon.

3.5.2 Modelling area licence schemes also depends on the form of the assignment and demand models. The following paragraphs outline an approach that has proved successful, but the precise method adopted will need to be tailored to the model structure that is available.

3.5.3 An area licence scheme can be modelled by a combination of an inbound cordon price applied to trips generated outside the charged area ('non-residents') and a penalty price applied to all trips generated within the charged area ('residents'). To facilitate this, it is necessary to segment the demand and supply models into residents and non-residents. The need for this segmentation, which is in addition to the segmentation required as part of the core requirement - see Segmentation, above - is explained below.

3.5.4 It is reasonable to assume that most trips are part of a daily 'tour', comprising, as a minimum, an outbound and return trip. Therefore, the price of an area licence should be 'shared' across all the trips in a typical daily tour. Ignoring non-home based trips would lead to a halving of the price to obtain the price per trip. However, an allowance for non-home based trips should be made.

3.5.5 The resulting price per trip is suitable for use as an in-bound only cordon charge, applicable to non-residents only, for use in the assignment model. Used in this way, it will ensure that alternative routes for through trips are appropriately priced and hence ensure that diversion is correctly modelled. Costs skimmed from the network for through trips will also be suitable for use in demand modelling and in appraisal.

3.5.6 Route choice is not an issue for non-residents ending their trip within the licence area, since all cordon crossings will be priced the same. However, using the price per trip as an in-bound only charge will mean that the price per trip will not be included in the costs skimmed from the network for outbound trips by non-residents. It will, therefore, be necessary to allow for this when generating costs to be used in the demand model or the appraisal.

3.5.7 The price per trip will also be suitable for use in the demand model and in appraisal as a penalty price for all trips made by residents, whether they cross the cordon or not. Costs skimmed from the network for these trips will not include the price per trip, since that is applicable only to trips made by non-residents.

3.6 Marginal social cost (MSC) based pricing

3.6.1 MSC based pricing may not be practical to implement, but it provides a useful benchmark against which to gauge the efficiency of more practical schemes. However, MSC based pricing presents a significantly different challenge for modelling.

3.6.2 MSC based prices are related to the flow on a link. Thus, the challenge is to identify the price that is consistent with the flow on each link in the priced network. Prices cannot be estimated outside the model and input as is the case for other forms of pricing. They must be estimated within the model.

3.6.3 The estimation process will require an iterative procedure, iterating between price setting and model responses to the price. An approach that has proved successful in tests using the National Transport Model is outlined in Annex B.

3.6.4 Annex B assumes that MSC based prices will reflect three elements of external costs: the congestion impact of vehicles in delaying other vehicles; the impact on fuel consumption; and environmental costs. In some cases, particularly for local pricing schemes, it may only be necessary to consider the congestion element of the external cost. The use of approaches that focus upon the marginal external congestion costs to determine prices is discussed further in Designing Effective Road Pricing Schemes (TAG Unit 3.12.1).

3.7 Other elements of road pricing schemes

3.7.1 Road pricing schemes may include prices that vary by vehicle class and/or by time of day. They may also include exemptions and discounts. It will often be desirable to represent these elements of the design of a road pricing scheme in modelling.

3.7.2 Pricing (or exemption) by vehicle type can be accommodated in models, provided the assignment model is appropriately segmented. However, modelling is unlikely to be sufficiently sensitive to enable more subtle vehicle typologies (by vehicle emissions group, for example) to be distinguished.

3.7.3 The ability to test pricing by time of day will be limited by the modelling of time of day effects. The core requirement is for the morning and evening peak and the interpeak periods to be modelled. If a time of day model is implemented, this will allow transfers between these broad time periods to be modelled.

3.7.4 Exemptions need to be considered against the objective of a scheme, which is to tackle congestion. It is therefore suggested that the starting assumption should be that any vehicle that contributes to congestion should be covered by the scheme. Where exemptions cannot be avoided, their impact on the effectiveness of the scheme must be carefully and thoroughly analysed.

3.7.5 Exemptions can take many forms. Some may have a significant effect on the impact of road pricing, others may be negligible. Where exemptions are expected to have a significant effect, they should be represented in modelling, to the extent that it is possible to do so. The following paragraphs outline some examples of exemptions that can be represented in modelling relatively easily.

3.7.6 Exemptions (including discounts) applying to specific user groups can be represented by appropriate segmentation. However, this is only likely to be worthwhile if the user group is quite large. Exemptions for small user groups may be excluded from some or all modules of the model. For example, they may be excluded from the variable demand modelling (thus implying a fixed matrix) but added into the matrix to be assigned to the network. Or they may be preloaded to the network if their routeing is expected to be fixed.

3.7.7 Exemptions (or discounts) may apply to certain geographical areas. Again, segmentation will allow a separate pricing structure to be established for the exempt locations. Discounts for those within the boundary of an area licence scheme can be relatively easily dealt with (at least approximately) by adjusting the penalty price to be charged for trips generated within the boundary.

4. Network detail and assignment

4.1.1 A good representation of the highway network is required, to provide robust estimates of the impact of re-routeing on traffic flows and speeds on priced routes and alternatives. The assignment model must be capable of reflecting the possibility of reallocating road capacity between different types of user.

4.1.2 The core requirement is for highway assignment (choice of route) to be dealt with by means of conventional network procedures. Further guidance on highway assignment can be found in Transport Models, (TAG Unit 3.1.2) and in DMRB 12.2.1, Traffic Appraisal in Urban Areas.

4.1.3 The likelihood that road pricing will result in differential re-routing must be considered carefully. For some cordon or area licensing schemes, it may be clear that there is little or no through traffic currently passing through the proposed priced area, or that the charge will be sufficiently high that almost all through traffic will be diverted to routes avoiding the proposed priced area. Where that is the case, standard highway assignment techniques will be satisfactory. However, where differential re-routeing is considered likely, it will be important to ensure that it is satisfactorily represented.

4.1.4 To ensure that differential re-routeing responses are satisfactorily represented, the highway assignment model must be segmented by user class, with a separate value of time for each user class. The core requirement for assignment segmentation is to ensure that the number of user classes is sufficient to represent the heterogeneity of values of time. It is recognised that, for practical reasons, the number of user classes is likely to be smaller than the number of segments used in demand modelling. However, it will usually be helpful for the user classes to be consistent with the segmentation adopted in the variable demand model. A user class structure based on vehicle class (lights and heavies), journey purpose (business and other), and, for those purposes representing a major proportion of trips within a modelled period (usually 'other'), by income has proved to be practical in past studies. Further guidance on segmentation is given above, under Segmentation.

4.1.5 Diversion could be a significant response where there are feasible alternative routes. If this is to be predicted realistically, it is important that the model represents realistically both the levels of congestion prevailing on the surrounding network and the journey times through it. Thus, it is a core requirement to employ an adequate representation of the network containing the alternative routes, including the effective capacity of minor roads, and of the prevailing levels of traffic on these roads. Zone size should be consistent with the level of network detail. The need to represent adequately the responses of short trips may dictate the use of relatively small zones (and correspondingly detailed networks) in key locations.

4.1.6 The use of a simplified model of the road network which does not take into account delays at all key junctions, including those on secondary routes, may tend to overestimate the amount of diverted traffic for a given price level. The core requirement is to model junction delays (including flow metering and, where necessary, blocking back) at all junctions likely to be affected by diverted traffic and, where there is doubt, include more, rather than less, junction modelling. Clearly, a capacity restraint mechanism is a core requirement. Further guidance on assignment modelling is given in Chapter 4 of Traffic Appraisal in Urban Areas, DMRB 12.2.1.

4.1.7 The ease and cost of parking will affect traveller response to road pricing: fiscal aspects of company provision are also relevant here. It is unlikely that road pricing can be considered without some attention given to parking policy and parking charges. In some road pricing systems, parking could be subsumed in the road price. Capacity effects in parking supply will lead to increased search times (and hence greater congestion) and, potentially, longer walking times: these impact on demand through changes in generalised cost. Where parking policy is expected to be an important issue, consideration should be given to going beyond the core requirement by representing parking in the model.

4.1.8 The journey time impacts of road pricing will affect on-street public transport journey times as well as those of private vehicles. These changes in public transport journey times must be taken into account in the appraisal of road pricing schemes. However, these changes will also make public transport more attractive, thus affecting mode choice. Where this seems likely to be a significant effect, consideration should be given to the inclusion of a public transport network. Clearly, journey times in the public transport network will need to be consistent with those on the highway network. Thus, some linkage between the highway and public transport networks will be required.

4.1.9 A public transport network will also be required where complementary measures are expected to include improvements to public transport. Where public transport networks are required, they should include a level of detail appropriate to model the likely modal switching expected. In some cases, a public transport assignment model and/or a public transport sub mode choice model may be required. Further guidance on this is provided in Road Traffic and Public Transport Assignment Modelling (TAG Unit 3.11.2).

5. Demand modelling

5.1.1 Where road pricing is envisaged, there is a wide variety of possible responses that travellers (and non-travellers) could make in the face of such prices. For those travellers already using the road in question the choices are to:

• Pay the price and continue travelling as before.
• Change to a route with no (or a lower) price.
• Change to a destination to avoid (or reduce) price.
• Change to a time of travel when there are no (or lower) prices.
• Change mode of travel (including to car passenger).
• Change trip frequency or decide not to travel at all.
• Any combination of these responses.

5.1.2 The extent to which these responses are represented in the model will be conditioned by the particular application in question, but most are likely to be required. Detailed guidance on variable demand modelling is given in Variable Demand Modelling, (TAG Unit 3.10). This represents the core requirement for modelling for road pricing.

5.1.3 As discussed above under Segmentation, segmentation to represent the distribution of traveller values of time is important for road pricing applications. Guidance on segmentation for demand models is given in Variable Demand Modelling - Scope of the Model (TAG Unit 3.10.2). Segmentation to reflect the variation in value of time with income is a core requirement for modelling for road pricing.

5.1.4 Note that Variable Demand Modelling - Key Processes (TAG Unit 3.10.3) recommends that macro time period choice (that is, choice between broad time periods, such as the peak and interpeak periods) should be considered when strong cost differentials between time periods are expected to develop or change. This is obviously the case where different road prices are proposed for the peak and inter peak or off-peak periods. In these cases it is obviously important to choose the modelled time periods to facilitate the modelling of the differential costs. The time period model should also fully reflect the effects of changing congestion levels within each modelled time period.

5.1.5 For some studies, mode switching may be an important alternative. This will depend on the availability of alternatives, the generalised costs of alternative modes and personal perceptions of alternative modes. Where mode switching is likely to have a significant impact on public transport, provision of a public transport network model should be considered - see Network detail and assignment above. Further guidance on mode choice modelling may be found in Specification, Development and Use of Models for Major Public Transport Schemes, (TAG Unit 3.11).

5.1.6 Modelling for the Road Pricing Feasibility Study suggested that increased car sharing is a potentially important response to road pricing. Analyses using the National Transport Model (NTM) showed that reductions in car driver trips were accompanied by large increases in car passenger trips. Monitoring of the London Congestion Charging scheme has also shown some increases in average occupancies of cars that still enter the charging zone. Analysts should, therefore, consider whether to extend their model beyond the core requirement to include the means to model changes in car occupancy. The NTM models car drivers and car passengers as separate 'modes'. The main problem this poses is what to include in the generalised cost of car passengers. Clearly, they perceive the same car journey times as car drivers, though their access and egress times may be different. However, it is unclear whether they perceive car money costs and, if so, what weight they give to them. The approach adopted in the National Transport Model has been outlined in the discussion of generalised cost - see Representation of road pricing, above.

5.1.7 It is important that the assignment and demand models are iterated to an acceptable degree of convergence, otherwise the scale of response cannot be accurately predicted. Variable Demand Modelling - Convergence, Realism and Sensitivity TAG Unit 3.10.4) recommends the use of the 'demand-supply gap' statistic as a measure of convergence and provides guidance on what is an acceptable level of convergence. Convergence in line with this guidance is a core requirement.

6. Other modelling considerations

6.1 Tiered modelling

6.1.1 The concept of operating forecasting models at different spatial levels, essentially to ease the computational burden, has been a feature of a number of models. The weaknesses inherent in aggregation of the supply representation can be reduced by taking a tiered approach to model formulation. In this configuration, the upper tier is the demand model with a spatially aggregate supply representation. The lower tier is a detailed network assignment model. The linkages need to ensure that the detailed model characteristics can be compressed to form the supply representation for the upper tier model, where travel demand forecasts are estimated. Demand forecasts from the upper tier model can in turn be disaggregated to the level of the detailed model zoning system, allowing their detailed routing implications to be tested and understood.

6.1.2 However, it is clear is that the problems of operating at different spatial levels have not been satisfactorily resolved. The use of two tiers of modelling - as for example where a high-level strategic model is coupled with a spatially detailed network model - can lead to inconsistent estimates of the scale of expected diversion from a given level of toll unless the speed/flow relationships embodied in the different levels are internally consistent and there is some degree of iteration between the layers.

6.1.3 The key difficulty is deriving a simplified representation of the detailed highway supply model that retains the realism and responsiveness of the detailed version. Recent work has suggested that satisfactory results may be obtained by:

• Using the detailed model's network structure (pattern of links and nodes) in the simplified model;
• Deriving speed/flow relationships for each link in the simplified model to represent the relationship between the sum of link transit and junction delays and link flows for the corresponding link in the detailed model;
• Confirming that the simplified representation is satisfactory by 'validating' it against the speeds and flows estimated by the detailed model;
• Revisiting this process whenever significant changes are made to either the network or the pattern of demand; and
• Checking that the gap between demand estimated by the simplified model and supply estimated by the detailed model is satisfactorily converged.

6.1.4 With ever-increasing computation power, the need to operate at more than one spatial tier is reducing. Where this allows the use of tiered modelling to be avoided, it removes a major source of difficulty. However, it remains an obstacle for applying transport models in large areas. In addition, tiered models offer the potential advantage of fast turnaround for strategy testing, suggest that they will continue to be attractive to those carrying out major studies.

6.1.5 Tiered modelling is not a core requirement. However, if a tiered modelling approach is being considered, it is a core requirement that the demand estimated by the higher tier model and supply estimated by the detailed model meets the Department's published guidelines for acceptable demand-supply convergence (see Variable Demand Modelling - Convergence, Realism and Sensitivity (TAG Unit 3.10.4)). There must always be a check that the demand response to a particular price predicted by the upper level is consistent with that predicted at the lower level, and especially that the aggregate speed-flow relationship of the higher level is fully compatible with that governing the network model.

6.2 Land use modelling

6.2.1 Patterns of land use are an important driver for transport demand. It is standard practise, therefore, to take account of changes in land use when using a transport model for forecasting. It is also generally accepted that transport impacts on land use, both in terms of the way existing developments are used and the pressures for new development. While transport models reflect some of these 'feedback' effects, a land use module is needed if all effects are to be captured.

6.2.2 Land use models can be used to estimate changes in the distribution of employment in an area, as a result of a transport scheme. Changes in employment location are an input to the analysis of impacts on productivity - see Transport, Wider Economic Benefits and Impacts on GDP (DfT, June, 2006). However, tests have shown that changes in generalised cost, rather than changes in employment location, are the dominant factor in estimating employment densities and hence in forecasting changes in productivity due to agglomeration effects. Changes in employment location are also needed to calculate changes in productivity due to moves to more productive jobs, but experience to date suggests that agglomeration effects tend to be substantially larger than effects due to moves to more productive jobs. Thus, omitting modest changes in employment will not result in serious inaccuracy. So a land use model may be of value in the assessment of the productivity effects of schemes if one is available, but should not be developed solely for this purpose.

6.2.3 Land use modelling is not a core requirement. It may be appropriate for major schemes which are intended to have land use and/or economic impacts, or where there is public or political concern that schemes may have unintended land use and/or economic impacts. Where there are concerns about unintended land use and/or economic impacts, land use modelling may help to put those concerns in context, relative to long term underlying trends. Where this is the case, consideration should be given to the need to go beyond the core requirement to include a land use model when designing models for road pricing studies. Business cases should provide a reasoned justification for the decision reached, whether it is to include or exclude a land use model. Where a land use model is to be included, analysts should discuss their proposals with the Department.

6.2.4 Land use modelling may also contribute to the supporting analyses as well as to the core transport modelling and economic assessment tasks. It can enhance the analysis of the distributional impacts of road pricing both in space and across social groups and can help in the assessment of the extent to which the scheme contributes to policy objectives. For example, if policies are to support the economic vitality of core city centres as employment and retail centres, land use modelling may help to show whether road pricing, together with the complementary measures proposed, will support those policies.

6.3 Reliability

6.3.1 In many studies of road usage the issue of reliability is seen as critical. Unfortunately, modelling reliability and its impact on behaviour is not well developed. Relationships between the reliability of journeys and network characteristics (link geometry, junction design, traffic levels and so on) are very poorly understood.

6.3.2 For urban networks, simple relationships between the standard deviation of link transit time (the commonly accepted measure of reliability for highway modelling) and link capacity and traffic volume have been derived for suburban networks. Relationships of this kind were used in APRIL, developed in the early 1990s for the London Congestion Charging Research Programme. Further work on the database used in this study and on data collected in Leeds has been re-analysed and is reported in The Variability of Urban Travel Times (Black and others, 2004). It may be possible to incorporate these into traffic assignment models. Analysts interested in incorporating reliability into urban models should discuss this with the Department.

6.3.3 For inter-urban networks, work in the UK has focussed on the impact of incidents on motorways. This work is unlikely to be suitable for use in traffic assignment models, though it may be used in the appraisal of road pricing schemes. By estimating the number of incidents and their impact on reliability with and without the scheme, the change in reliability can be estimated and valued.

6.3.4 Estimating the value road users place on reliability is difficult and there have been few studies into this. However, the Department is able to offer advice on values of the 'reliability ratio' that may be used to incorporate reliability into generalised cost. The reliability ratio is the ratio of the value of one unit of the standard deviation of travel time to one unit of travel time itself.

6.4 Modelling packages of measures

6.4.1 It will often be necessary to model road pricing in conjunction with other measures. Where this is the case, the modelling must be fit for purpose for modelling road pricing and fit for purpose for modelling whatever other measures are to be examined. This guidance focuses on the requirements for modelling road pricing. Guidance on modelling for other measures is given in other guidance documents in WebTAG or in the Design Manual for Roads and Bridges (DMRB).

7. Validation

7.1.1 The usual requirements for model validation are as important for modelling road pricing as any other transport scheme. Models for road pricing are expected to meet the same validation standards as any other model. General guidance on validation is given in Chapter 11 of the Traffic Appraisal Manual (DMRB Volume 12), while Traffic Appraisal in Urban Areas (DMRB 12.2.1) provides guidance on assignment validation for congested networks. Guidance on fitness for purpose tests for variable demand modelling is given in Variable Demand Modelling - Convergence, Realism and Sensitivity (TAG Unit 3.10.4).

7.1.2 It is important that the network model correctly reflects not only the absolute values of delays on links and at junctions in the base year, but also has the correct gradient for delays. This can be difficult to validate as it requires observations of delays for different flow levels, preferably over a wide range. Peak and off-peak journey time data and flows can help in this respect.

7.1.3 In addition, comparisons of peak and off-peak flow differences between observed and forecast flows can reveal anomalous results, such as opposite signs in those differences or large changes, that may provide an indication of a gradient problem.

7.1.4 In any event, where significant changes in routes are forecast, the realism of the model's capacities and junction modelling should be examined under a range of different price levels. Correspondingly, where forecast re-routeing of through trips is low, the realism of the model's representation of minor roads should be examined.

7.1.5 Some curious routeings are implied by some models. This suggests that great care should be taken to ensure that routeings between origins and destinations are sensible, even in the no-price case. In all cases a check should be made on vehicle routeings to ensure that the routes chosen are behaviourally realistic. However, it should be recognised that circuitous routeing may be a logical and rational response in some circumstances. The imposition of road pricing may result in routes that would otherwise be unattractive becoming realistic unpriced alternatives to priced routes.

8. Further information

The following documents provide information that follows on directly from the key topics covered in this Unit.

9. References

DfT (June, 2006) Transport, Wider Economic Benefits and Impacts on GDP.

Black, I., J. Fearon., C. Gilliam., A. Kerr and S.Porter (2004) The Variability of Urban Travel Times.

Highways Agency (1996) ,em>Traffic Appraisal in Urban Areas (Design Manual for Roads and Bridges (DMRB) 12.2.1).

Highways Agency (1996) Traffic Appraisal Manual (Design Manual for Roads and Bridges (DMRB) 12.1.1).

Mackie, P, Wardman I, Fowkes, A, Whelan, G, Nellthorp, J, & Bates, J (2003) Values of Travel Time Savings in the UK.

10. Document provenance

This Transport Analysis Guidance (TAG) Unit revises guidance published for consultation in July, 2006.

Technical queries and comments on this Unit should be referred to:

11. Annex A: Segmentation and values of time for road pricing models

11.1.1 This Annex presents the segmentations by income and journey purpose, together with the values of time for each segment for use in the modelling of road pricing schemes. The segments and values of time have been derived using national studies conducted on behalf of the Department for Transport. Segmentation by income is a core requirement for the modelling of road pricing schemes unless more localised approaches are considered appropriate.

11.1.2 If information is available on the distribution by income and distance of trips in the study area, then this may be used to establish local segmentations and local values of time may be estimated. More information on estimating local values of time is provided in this Annex.

11.2 Segmentation

11.2.1 For non-work trips, segmentation is provided for journey purpose (commuting, other, and total non-work trips) and income. For trips made in the course of business, segmentation is by income and mode. Based on national research, income has been segmented in to three bands representing household income per annum in 2002 prices.

Segmentation for non-work trips

11.2.2 If data on income has not been collected, the table below provides the relative proportions, at the national level, of trips in each income segment for commuting and 'other' trips. Matrices may be multiplied by the factors given in the table to create separate matrices for each income segment. If commuting and other trips are combined (for assignment, for example), the proportions in the 'all non-work' column of the table should be used.

Segmentation for work purposes

11.2.3 Table A2 provides the relative proportions, at the national level, of trips made for business purposes by income band and mode. Information on other modes is available on request from the Department.

11.3 Values of time

Values for time for non-work trips

11.3.1 Table A3 below presents the values of time for commuting, other and all non-work purposes segmented by income. The values presented are perceived costs and as consumers perceive costs in the market price unit of account, these values are also the market prices. The resource cost values can be calculated by dividing the perceived cost by the indirect tax correction factor, (1+t), where t is the average rate of indirect taxation in the economy. For further information on unit of account and indirect taxation see Values of Time and Operating Costs (TAG Unit 3.5.6).

11.3.2 Note that the average values of time, £4.85 for commuting trips and £4.33 for other non-work trips, differ from those presented in Values of Time and Operating Costs (TAG Unit 3.5.6). This is due to differences in uprating the values in line with GDP. To ensure consistency, the values given here should be used when comparing appraisal results based on segmented values with those based on aggregate values. See Appraisal of Road Pricing Schemes (TAG Unit 3.12.3) for further details.

11.3.3 Growth in income may be assumed to be the same across all income bands. This implies that the boundaries of the income bands (£17,500 and £35,000) will increase, but the proportion of trips in each income band will be unaffected. The growth in the values of time for each band should be estimated by applying the forecast growth in the real value of non-working time, given in Table 3 of Values of Time and Operating Costs (TAG Unit 3.5.6).

Values of time for working trips

11.3.4 Table A4 below provides values of time for work trips segmented by income and mode. Values for other modes are available from the Department on request. The table presents the perceived costs and as businesses perceive costs in the factor cost unit of account these values are also the resource costs. Market price values can be derived by multiplying the perceived cost values by the indirect tax correction factor as discussed above.

11.3.5 As for the non-work purposes (see above), the average values of time, displayed in the bottom row, differ from those presented in Values of Time and Operating Costs (TAG Unit 3.5.6). Again, to ensure consistency, the values given here should be used when comparing appraisal results based on segmented values with those based on aggregate values.

11.3.6 As growth in income may be assumed to be the same across all income bands, the annual growth rates for work values of time as given in Table 3 of Values of Time and Operating Costs (TAG Unit 3.5.6) should be applied to the values in the table above.

11.4 Local values of time

Locla values of time for non-work trips

11.4.1 If information is available on the distribution by income and distance of trips in the study area, then local values of time can be estimated using the model below. This is taken from Values of Travel Time Savings in the UK, a research study commissioned by the Department for Transport and undertaken by the Institute of Transport Studies, University of Leeds in association with John Bates Services.

11.4.2 Data on household income and mileage travelled is required. This data should be collected in the segments that are to be adopted (these need not be the same as those discussed above). An average household income and an average mileage must be calculated for each of the chosen income segments as well as for the overall sample. (Note that it is important to calculate the average mileage for each segment, as well as the average income. Average mileage is likely to increase with income, so assuming the same average mileage for all segments will result in a biased result. The values derived using national studies and presented above take account of the national distribution of average mileage with income.)

11.4.3 The term K is a correction for inflation between the year 1994 and the year in which local data is collected. It is given by the Retail Prices Index (RPI) in the relevant year divided by the same quantity for 1994. Table A5 below provides the RPI and K values for years between 2002 and 2005 compared with 1994.

11.4.4 The parameter values for each non-work purpose are presented in Table A6 below. Inc represents the average household income in £'000 p.a. based on local data. Inc₀ is set equal to K multiplied by 35. D is the average distance travelled in miles from the local data and D₀ is 7.58 miles.

11.4.5 The model and the parameters given in the table above will calculate the values of time for non-work purposes in the year you specify. The values will be expressed as market prices and in pence per minute. To convert to pounds per hour simply multiply the values by 60 and divide by 100.

11.4.6 Growth in the values should be treated in the same way as the nationally based values (see above). Table 3 in Values of Time and Operating Costs (TAG Unit 3.5.6) provides the required growth figures.

11.4.7 Further guidance on the use of the ITS model is available from the Department on request.

A worked example

11.4.8 Assume that data has been collected in 2003 for three income bands. It has been found that the average income in each of these bands is £9,000, £26,000 and £55,000 respectively. Mileage data for each income band was also collected and the average mileage in each band was calculated to be 10miles, 10miles and 19miles respectively. For the overall sample the average income was calculated as £22,500 and the average mileage is 11miles.

11.4.9 Using this data, we can apply the ITS model to calculate the values of time for the commuting journey purpose for each segment, as follows.

1.4.10 The values are in market prices at 2003 prices. and in. To convert pence per minute to pounds per hour simply multiply the values by 60 and divide by 100. So for the example, the values of time would equal £2.32, £3.39, £5.81 and £3.35 for the first, second, third segments and for the overall sample respectively.

Local values of time for work trips

11.4.11 Estimating values of time for working trips requires data on mileage and individual gross income, (note this is different to the income required for non-work trips), and the calculation of a mileage weighted income. Income should be collected for a large number of income bands and total mileage should be collected for each of those bands. A mileage-weighted income is then calculated by multiplying the average income of each band by the total mileage for that band. To then segment income in to three segments as above involves summing the mileage-weighted income over a segment and dividing by the total mileage for that segment.

11.4.12 Added to this is an estimate for the non-wage labour costs such as national insurance and pensions. The Department uses a 21.2% mark-up for this, based on the 2000 Labour Cost Survey. This figure is then divided by the annual hours worked; at a national level this is 1804 hours. This gives the perceived cost for the year used and as businesses perceive costs in the factor cost unit of account these values are also the resource costs. The market price can be derived by multiplying the perceived cost by the indirect tax correction factor, see Values of Time and Operating Costs (TAG Unit 3.5.6).

11.4.13 Growth in the values should be treated in the same way as the nationally based values (see 11.3.6). Table 3 in Values of Time and Operating Costs (TAG Unit 3.5.6) provides the required growth figures.

11.4.14 Further advice and guidance on calculating local values of time for work purposes is available from the Department on request.

11.5 Freight

11.5.1 Segmentation by income for freight has been investigated by the Department. In the context of urban areas, given the low proportion of heavy goods vehicles (HGVs), income segmentation is not considered an issue but vehicle type segmentation could still be appropriate.

11.5.2 The Department is still investigating the impact on inter-urban flows and will shortly be commissioning research leading to the release of new guidance on freight modelling and freight values of time.

11.5.3 Currently the Department has a single value of time of £10.18 (2002 market prices and values) for freight business time savings for use in appraisal. This value applies to all vehicle classes and drivers as well as passengers. The values only represent the value of driver's time and it is considered that this might be overlooking other important aspects of freight time savings benefits. For instance there could be a value applicable to the load being carried, no adjustment is currently made for unloaded vehicles compared with loaded, and some consider there to be a value for the just in time delivery. All of these aspects are to be examined in the research to be commissioned in the summer.

12. Annex B: Modelling marginal social cost based prices

12.1 Introduction

12.1.1 This annex provides advice on the modelling of marginal social cost (MSC) based prices in highway assignment models. The advice given is based on modelling work carried out in the Department to modify the assignment model within the National Transport Model suite to estimate marginal social cost based prices at the national level. It may be necessary to make changes to the methods suggested here when implementing them in other assignment models. Analysts are encouraged to discuss implementation with the Department.

12.1.2 The annex is presented in two parts. The first provides a detailed specification of some of the calculations required. The second section outlines techniques that can be employed for the iterative calculation of MSC-based prices with highway assignment models.

12.1.3 In some cases, particularly for local pricing schemes, it may only be necessary to use the congestion element of marginal external costs in determining prices. This is discussed further in Designing Efficient Road Pricing Schemes (TAG Unit 3.12.1).

12.2 Section 1 - calculation of marginal social costs and prices

12.2.1 In order to determine the correct price for a link, the 'marginal social cost' associated with using the link needs to be calculated. The marginal social cost is defined as the sum of two components:

• the time and vehicle operating resource costs directly associated with driving the length of the link in prevailing traffic conditions (the marginal private resource cost, U), and
• the resource costs imposed on society, i.e. the change in the total delay caused to all others on the link, and total change in vehicle operating resource costs faced by others on the link (the marginal external resource cost, X) by a marginal vehicle.

12.2.2 The marginal private resource cost is not the same as the perceived cost used in transport modelling. It represents those costs borne directly by the user, measured in terms of the resources consumed. As such, it does not include taxes or other charges that are transfer payments. Thus, vehicle operating costs (fuel and non-fuel) should exclude fuel duty and VAT for all traveller types.

12.2.3 Where different traveller types (user classes) are distinguished to represent different trip purposes or income groups and/or where information on varying vehicle occupancies is available, Equation 2 can be rewritten as:

12.2.4 The marginal external resource costs can be broken down into three parts - the rise in the time spent travelling by other link users (X(T)); the change in the vehicle operating costs of other link users (X(F)); and other changes in external costs such as environmental externalities (X(O)).

12.2.5 The marginal external resource cost associated with the additional congestion and time delays on a link, X(T) is calculated from:

• the rate of change of link transit time from a unit increase in traffic volume (these derivatives can be based on the model's speed-flow function or may be derived from model outputs);
• the volume and type of trips affected.

12.2.6 Note that X(T) is the marginal external congestion cost, MECC, discussed in the Annex to Designing Effective Road Pricing Schemes (TAG Unit 3.12.1). The equation given there can be shown to be an approximation to Equation 3 given in the box above.

12.2.7 The marginal external resource cost associated with changed vehicle operating costs due to changed link speeds, X(F), is calculated from:

• rate of change of vehicle operating resource cost from a unit increase in traffic volume (these derivatives may be based on the vehicle operating cost functions used in the model, on the vehicle operating cost models in Values of Time and Operating Costs (TAG Unit 3.5.6), or they may be derived from model outputs);
• volume of vehicles by vehicle type affected.

12.2.8 In this case fuel consumption is related to flow through the impact of flow on link transit time.

12.2.9 The marginal external costs associated with environmental / other externalities can be complex to calculate. For the purposes of modelling they could be approximated as an external cost per vehicle kilometre.

12.2.10 The terms in equations 2, 3, 4 and 5 can be drawn together to give the full marginal social cost of a vehicle using a link. In circumstances where X(T), the marginal external congestion cost, is large, it may be satisfactory to omit the marginal external resource costs associated with changed vehicle operating costs (X(F)) and environmental and other externalities (X(O)). However, where marginal external congestion costs are not large, it is important to include these terms.

12.2.11 The ultimate aim of the price setting process should be to determine a set of link prices that, when added to the average perceived private cost in the absence of road pricing for a vehicle of a given type, is equal to the marginal social cost of it using the link. The average perceived private cost in the absence of road pricing, Y, is a demand-weighted average of the costs (including any existing tolls) faced by the users of a given vehicle type on the link. The average perceived private costs should include indirect taxation.

12.2.12 The perceived vehicle operating costs should vary by vehicle type depending on whether non-fuel costs and VAT are perceived - see Values of Time and Operating Costs (TAG Unit 3.5.6).

12.2.13 The additional price required on a link is the difference between the marginal social cost and the average perceived private costs in the absence of road pricing.

12.2.14 Note that, if private costs are correctly perceived, then the marginal social cost based price is equal to the marginal external costs minus the existing tax element of vehicle operating costs and any existing tolls.

12.2.15 Once a price has been levied, the demand for use of the link will change, as will the private and social costs. Consequently the price calculation problem needs to be solved iteratively. Section 2 (below) presents modelling techniques that may be used to determine equilibrium prices.

12.2.16 This analysis assumes that fuel duty and VAT will continue to be levied as now and thus the resultant equilibrium prices may be positive or negative. In congested conditions, where the marginal external costs are large, prices will be positive. In un-congested conditions, where the marginal external costs are minimal, the prices will be negative. This phenomenon reflects the fact that fuel duty and VAT are taxes levied on a per litre basis, and are not intended to capture congestion externalities. Consequently in some instances average perceived private costs in the absence of pricing may exceed marginal external resource costs.

12.2.17 A discussion of the merits of fuel duty and EU tax regulations is clearly beyond the scope of this guidance note. However, in order to model an efficient distribution of traffic across the road network, it may be necessary to include negative prices. It should be remembered when analysing and presenting results that the resultant system of marginal social cost prices are a theoretical construct for use as a sensitivity test, rather than an explicit representation of the prices that would be imposed under a possible future national road pricing regime.

12.3 Section 2 - methods for achieving equilibrium prices

12.3.1 An iterative process is required to calculate equilibrium marginal social cost prices for a transport model, because application of prices within the model will cause the flows on links and, therefore, marginal social costs, to change. This section presents techniques that have been applied with the Department's National Transport Model to address this iterative problem.

12.3.2 The processes discussed below focus on establishing an equilibrium, given a fixed level of demand. This can be achieved using an assignment model in isolation. However, it is expected that road pricing will have an impact on demand, so the iterative processes below must be embedded within a demand/supply structure that is itself iterated to an acceptable level of convergence.

12.3.3 Two distinct approaches to solving the problem have been used. The first, faster technique requires the modification of traffic assignment software to calculate prices as part of the assignment process. The second technique can be applied without such software modifications but requires the repeated running of assignment software to achieve equilibrium prices.

12.3.4 The problem of finding equilibrium prices lends itself to solution with the algorithms used by assignment software. Assignment software packages already employ iterative techniques to find equilibrium flows and speeds for the links within a network. With software modification the same algorithms can be employed to determine equilibrium flows, speeds and prices. The Department employed consultants to modify the assignment software used as part of the National Transport Model to internally calculate and apply marginal social cost based prices.

12.3.5 It should be noted from the algebraic exposition above that the aim is to provide a price for each vehicle class. The analysis recognises that each vehicle class will include user segments with different values of time. Thus, in equation 6, the equation giving the average private costs for a given vehicle type, link transit time is multiplied by a weighted average of the values of time for each user segment. Similarly, in equation 3, the equation giving the marginal external congestion cost, traffic flows for a given vehicle class are subdivided by user segment and each segment is multiplied by the value of time for that segment. It is important to ensure that this analysis is correctly implemented in modified assignment software. This can be ensured by calculating prices in units of money.

12.3.6 Once the price for a vehicle type has been calculated, its use in the assignment is straightforward. If the assignment is in generalised time terms, the price has to be divided by the value of time for the specific user segment. If generalised cost is being used, link transit times must be multiplied by the value of time for the specific user segment.

12.3.7 Note that a segmented 'system optimal' assignment routine that represents externalities in units of time will return a price for each user segment, reflecting the value of time for that user segment. While such prices may be considered to be 'more optimal' than those resulting from the approach set out above, they are (even more) impractical.

12.3.8 The second technique does not require the modification of modelling software but is considerably slower. For this second technique the assignment software needs to be run repeatedly within an iterative price setting structure.

12.3.9 To aid the description of the second technique a new concept is introduced - marginal residual cost. The marginal residual cost (MRC) is the difference between the marginal social cost and the average perceived private cost for a given vehicle type for a given iteration.

12.3.10 In effect, the MRC is the amount by which the price needs to be adjusted to internalise the externalities at a given flow rate. The aim of the price setting algorithm should be to reach an equilibrium where the MRCs for all of the links in the network are equal to or close to zero.

12.3.11 Equation 9 may be used for calculating the price for the first price setting iteration. In effect, a price of two-thirds (or alternative dampening factor) of the marginal residual costs is applied as a first estimate of the equilibrium price.

12.3.12 Once this model run is complete and the marginal residual costs for iteration 1 have been calculated, one of two approaches may be adopted to reach price equilibrium.

• Continue with the method expressed in Equation 9, where two thirds of the marginal residual costs from the last iteration are added to the price from the last iteration to calculate the price for the next, or
• Use Equation 10 to interpolate/extrapolate, from the previous two price setting iterations, the price at which marginal residual costs would be zero.

13. Annex C: Core requirements for modelling road pricing

13.1 Introduction

13.1.1 This annex summarises the core requirements for modelling. Analysts may adopt simpler or more complex approaches. Where this is the case, clear justifications for departure from these core requirements must be provided, based on the requirements of the study in hand. The guiding principle is that the model should be fit for purpose.

13.2 General

13.3 Segmentation

13.3.1 The guidance on segmentation given in Variable Demand Modelling - Scope of the Model (TAG Unit 3.10.2) is a core requirement for modelling road pricing.

13.3.2 Use of the segmentation by income and associated values of time presented in Annex A is a core requirement for modelling unless more localised approaches are considered to be appropriate.

13.3.3 The core requirement for assignment segmentation is to ensure that the number of user classes is sufficient to represent the heterogeneity of values of time.

13.3.4 Segmentation of the demand model to reflect the variation in value of time with income is a core requirement for modelling for road pricing.

13.4 Assignment

13.5 Demand modelling

13.5.1 Detailed guidance on variable demand modelling is given in Variable Demand Modelling (TAG Unit 3.10). This represents the core requirement for modelling for road pricing.

13.5.2 Variable Demand Modelling - Convergence, Realism and Sensitivity (TAG Unit 3.10.4) recommends the use of the 'demand-supply gap' statistic as a measure of convergence and provides guidance on what is an acceptable level of convergence. Convergence in line with this guidance is a core requirement.

13.5.3 If a tiered modelling approach is being considered, it is a core requirement that the demand estimated by the higher tier model and supply estimated by the detailed model meets the Department's published guidelines for acceptable demand-supply convergence (see Variable Demand Modelling - Convergence, Realism and Sensitivity (TAG Unit 3.10.4)).