1.1.1 TAG Unit 2.9 and TAG Unit 3.10 explain why variable demand modelling needs to be considered and provide guidance on how to carry out such modelling for highway schemes. This Unit forms stage 4 of the overall process; TAG Units 3.10.1, 3.10.2 and 3.10.3, detail the previous stages.

1.1.2 Important recommendations are shown in bold. If those actions are not followed, analysts will need to provide rigorous justification for the course of action taken.

1.2 Use of DIADEM

1.2.1 Once the extent of the necessary variable demand modelling has been decided, the next question is how to build the model. Few users will have the resources available to build their own model from scratch, nor is this a sensible approach unless there is a need for a general-purpose model for policy analysis much wider than assessment of an individual scheme. Most users will need to identify available software packages which incorporate the necessary demand mechanisms, and can accept the data and parameters appropriate to the scheme under study. In most cases these mechanisms are provided by way of macros developed for each study, rather than as generic model formulations.

1.2.2 In tandem with the development of this TAG unit, software called DIADEM: Dynamic Integrated Assignment and Demand Modelling has been developed to provide simple multi-stage demand models and an interface with commercially available packages.

1.2.3 The DIADEM procedures provide an adjustable hierarchical structure of trip frequency, mode choice, distribution, and time of day choice, and an interface to assignment. It is also possible to use DIADEM for a simple "own-cost" elasticity calculation where applicable. The DIADEM framework controls iteration within assignment, and between demand and assignment, to ensure that the calculation reaches an acceptable equilibrium.

1.2.4 At present, DIADEM has been developed with an interface to the CONTRAM and SATURN assignment packages. It is expected, however, that the suppliers of other assignment packages will provide equivalent functionality or suitable interfaces with DIADEM; so that it can be used with whatever assignment model is available for the scheme to be assessed. As ever, there is no monopoly on the most convenient way to achieve best practice: as with choice of assignment package, which one to adopt is a matter of individual preferences and priorities. If a decision is made to use DIADEM then Section 1.3 provides a summary of the approach. If other software is to be used then Section 1.4 gives guidance on how alternative software should be used.

1.3 DIADEM Procedures

1.3.1 The DIADEM procedures cover all the demand-side issues that must be considered when applying multi-stage models, as described in VDM Key Processes (TAG Unit 3.10.3), and provides the user with the necessary choice between alternative formulations and full control over each aspect.

1.3.2 Model Type: the model can be incremental at present although an absolute alternative is ultimately envisaged to every response in the overall application.

1.3.3 Demand responses: DIADEM allows the following responses to be included:

elasticity model: the elasticity model has a 2-parameter Tanner form, which is intended to be used in its extremes, setting one of the parameters to 0 to return either a power or an exponential form, as discussed in VDM Key Processes (TAG Unit 3.10.3). The use of both parameters together in the Tanner form is not recommended.
trip frequency model: the trip frequency model is an exponential elasticity function, but unlike general elasticity models (which operate at the OD level), the trip frequency model applies to the zone level, using composite zone (accessibility) costs as discussed in VDM Key Processes (TAG Unit 3.10.3).
modal choice model: the mode choice model is a binomial logit formulation. The model does not automate the hierarchical modelling of public transport modes i.e. sub mode choice. Any lower-level split between different public transport modes would have to be estimated independently or at assignment as discussed in VDM Key Processes (TAG Unit 3.10.3). However, this sub-mode choice will rarely be needed in a road-based scheme appraisal.
distribution model: the trip distribution model can be singly-origin constrained or singly-destination constrained (to approximate to Production /Attraction constraints) or doubly-constrained as discussed in VDM Key Processes (TAG Unit 3.10.3).
time of day choice model: a macro time period choice model in logit form is currently available. Micro time period choice using HADES is planned for future release.

1.3.4 There are still a number of technical issues to be resolved, concerned with incremental formulation of the HADES model, the composite cost formulae, and the use of scheduling costs. For a discussion on alternative model forms of departure-time choice, see VDM Key Processes (TAG Unit 3.10.3) and Batley et al (2001).

1.3.5 Model hierarchy: DIADEM allows a different range of responses, a different model form and a different hierarchy to be applied to each individual purpose and traveller type combination.

1.3.6 Model parameters: Each modelled response is driven by a single user-defined λ parameter, per purpose and traveller type combination, apart from the elasticity models which as Tanner formulations are driven by 2 parameters (though normally one of these should be set to zero, returning the Tanner function to either a power or an exponential function). Calibration areas with potentially different parameters in each area will ultimately be provided.

1.3.7 Generalised costs: Generalised cost coefficients are defined for each purpose and traveller type combination, allowing for time, distance and monetary components. Any weighting of in-vehicle, waiting or walking time must be done within the assignment stage or outside the DIADEM environment, and a similar argument applies to crowding effects. The analyst will be provided with a flexible tool in DIADEM to arrange the sequence of demand responses and warned if the proposed sequence does not reflect demand sensitivities. However, the analyst will still need to ensure that the definitions of generalised cost in the demand and assignment phases include all the necessary terms and are sufficiently compatible.

1.3.8 Model running: Guidance on how to run the DIADEM software is given in the user guide to the software. It should be noted that the solution closest to equilibrium may not necessarily be the one produced by the last iteration of the DIADEM demand/assignment modelling system. The solution from the iteration with the lowest GAP value should be used for appraisal purposes. This may require an additional run of the assignment package using this 'best' trip matrix to obtain a converged solution.

1.4 Other Software

1.4.1 Section 1.3 outlined the use of the DIADEM procedures. However, using DIADEM is not the only approach that could be adopted and the practitioner may wish to develop an approach based on existing software packages that have not developed interfaces with DIADEM. Such software is being developed continually, and only the more widely used packages are mentioned here.

1.4.2 There are a number of different approaches than can be adopted when using non DIADEM procedures:

1.4.3 Combined assignment-demand models. Firstly, one can use other software that can handle demand-supply responses as a combined assignment-demand model. This is the preferred alternative solution to using DIADEM in most cases since the software will be constructed to ensure, as far as possible, that the model is properly integrated, computationally efficient and sufficiently converged to a correct solution. At present the main drawback is that the demand responses that can be modelled may be limited, either in number or in the sequence order. For example, in the case of the SATURN software package, assignment can be combined with elastic demand and one or both of mode-choice and singly constrained trip distribution. The approach, at present, does have the disadvantage that the sequencing allowed is restricted. Similarly, the EMME/2 transportation suite allows a combined model of trip assignment with elastic demand or mode-choice through the use of built-in modules but other combinations need to use individual models of demand and assignment constructed by the user using the suites macro language. With these models, more exact measures of convergence can be defined than the % relative GAP measure recommended in Section 1.5. This arises from the nature of the combined demand-supply formulation (such as that used by the SATURN program). At present, no fixed level to be obtained from such measures has been set but details of the approach to improve convergence should be given in the Validation Report. (The latest version of the SATURN suite can give values from which to calculate the % GAP function.). The TUBA tests outlined in the next section can be done to ensure that convergence is to the level required by the scale of the scheme.

1.4.4 Combining separate demand and assignment models: The next best alternative is to make use of a transportation suite software's matrix manipulation software to construct the model of demand responses oneself and iterate between the assignment program and the demand model. This will at least ensure that the supply and demand data are in compatible format. However, it is likely to require expertise both in transportation modelling and in knowledge of the workings of the transportation software. Various transportation software packages are available which cover both demand and assignment functions. The most widely-used in the UK are probably the Citilabs' TRIPS transportation suite (now part of the CUBE family of models), which includes public transport and highway assignment and demand functions within the same modelling environment, the EMME/2 suite as noted above and PTV's VISEM (in the form of tours instead of trips) and VISUM suites will also perform similar functions.

1.4.5 The user in these circumstances will need to ensure that that the final solution meets the convergence criteria set out in Section 1.5. To do this, it may necessary to devise a sophisticated approach to cycling between the assignment and demand responses that will ensure a stable converged solution in a reasonable time. The most common solutions are simply to iterate between the converged assignment model and the demand response model, passing travel costs from the assignment model to the demand model and passing trips (or most commonly vehicle trips) from the demand model to the assignment model. However, this approach is not guaranteed to converge, except when using techniques such as the Method of Successive Averages (MSA). Both techniques can, in some circumstances, take a long time to reach a sufficiently converged solution. (This is one of the reasons that algorithms that incorporate both the demand and assignment phases in one procedure have been developed.) It is difficult to provide a single ready-made solution for all software and all schemes, and it may be necessary to seek advice from the software developers. For these models the iteration between supply (assignment) model and demand models should give statistics from which to calculate the % GAP statistic, as recommended in section 1.5. The approach to iterating between the supply and demand models, and the monitoring of the convergence progress should be detailed in the Validation Report. Evidence should be provided that the models meet the convergence requirements set out in Section 1.5 (1.5.7).

1.4.6 Combining models from different transportation suites: In some cases the assignment package and the software used to model the demand responses may not be from the same package, or software used in highway assignment may be different from that used for public transport assignment. Examples of this can be found in many of the Multi-Modal Studies, for example using SATURN for the highway assignment and TRIPS for the demand. This should not, in itself, prove too much of a problem provided that care is taken in transferring data from one package to another. In other Multi-Modal Studies the demand modelling was split between two different software packages, for general road traffic and public transport. However, the difficulties in transferring data from one transportation suite to another should not be underestimated and time and resources should be allowed to ensure that the data is compatible.

1.4.7 Users are responsible with most software for arranging the sequence of demand responses and for ensuring that the proposed sequence reflects demand model sensitivities. Analysts also need to ensure that the definitions of generalised cost in the demand and assignment phases include all the necessary terms and are sufficiently compatible. They also need to ensure that a stable, converged, solution to both the assignment and demand responses is produced in a reasonable time. This is particularly important when assessing small schemes with large models. For these models the iteration between supply (assignment) model and demand models should give statistics from which to calculate the recommended convergence statistic. The approach to iterating between the supply and demand models and the monitoring of the convergence progress should be detailed in the Validation Report.

1.4.8 Whatever approach is adopted the user should ensure that documentation is provided in sufficient detail for a third party to follow all the steps and the convergence properties of the combined model are detailed.

1.4.9 Convergence: This is a key to achieving good modelling practice. High levels of convergence should be achieved in any assignment modelling. This applies to both small networks and, especially, large networks where small percentage changes in convergence may result in large changes in flows and times around a potential scheme. In addition, the demand - supply convergence should be monitored by using the convergence measure (% relative GAP) defined in 1.5.2, with the aim of reaching the convergence level determined by para 1.5.6. If that cannot be reached then a convergence level of at least 0.2% is recommended.

1.4.10 In summary, if an integrated approach similar to DIADEM is not used the main issues are:

That the approach adequately addresses the issues of correct sequencing of demand responses and consistency in the definitions of generalised cost in the demand and assignment phases.
Where a combined assignment/demand model is used, that the convergence statistics output at the end of the modelling meet the requirements set out in Section 1.5 below.
Where a combined model is not used or not applicable, then care needs to be taken over the cycling between assignment and demand modelling modules so that convergence in travel costs and trips is reached in a reasonable time.
Sufficient documentation is provided that the approach adopted can be understood and the convergence properties of the model clearly stated.

1.5 Convergence

1.5.1 The original impetus for DIADEM was in the need to improve convergence of demand-supply models, and DIADEM procedures have internal capabilities to apply a range of convergence improving techniques, guided by a number of convergence measures and desired stop criteria. Preliminary tests indicate that improved demand convergence can reduce the convergence errors to less than 10% of the economic benefit. Demand modelling software, such as DIADEM may provide a number of measures of convergence, both relating to proximity (how close to the true equilibrium), and stability (how much the results are changing each iteration). For our purposes the proximity measures are the more important.

1.5.2 The recommended criterion for measuring convergence between demand and supply models is the demand/supply gap defined by:

Where;

X_ijctm is the current flow vector or matrix from the model
C(X_ijctm) is the generalised cost vector or matrix obtained by assigning that matrix
D(C(X_ijctm)) is the flow vector or matrix output by the demand model, using the costs C(X_ijctm) as input
ijctm represents origin i, destination j, demand segment/user class c, time period t and mode m.

This is a measure of how far the current flow is from the equilibrium point and will be zero in a perfectly converged model. The demand-supply gap is represented, for one flow, by the shaded area in the figure above. As convergence improves, and the difference in trips between successive iterations decreases so the shaded area decreases until the equilibrium point is reached. One of the reasons for the choice of this statistic is that it is easily calculated and is not dependant on the precise form of demand-supply modelling undertaken. It is referred to as the %GAP, reflecting its relative nature.

1.5.3 The demand/supply model used may report other measures of convergence. Some of these may be stability statistics that indicate how much the solution is changing from one iteration to the next. An example of this could be the maximum change in flows. It is often assumed that a stable solution implies convergence. However, it can also be an artefact of the particular algorithm being used so stability statistics are, in general, not a good indicator of how close the solution is to equilibrium.

1.5.4 The demand/supply gap, as defined in 1.5.2 above, is the most appropriate measure for gauging the error in economic benefit calculations caused by imperfect convergence. It can be calculated for any variable demand/supply modelling system and is not dependant on the form of demand/supply modelling approach.

1.5.5 Tests indicate that gap values of less than 0.1% can be achieved in many cases, although in more problematic systems this may be nearer to 0.2%. Where the convergence level, as measured by the %GAP, is over 0.2% remedial steps should be taken to improve the convergence, by increasing the assignment accuracy.

1.5.6 Convergence and scheme benefits. The required level of convergence needs to be linked to the scale of the benefits of the scheme being appraised, relative to the network size. For instance the calculation of benefits from small schemes in large networks will be much more sensitive to convergence than large schemes in small networks. On the basis of testing it has been discovered that ideally the user benefits, as a percentage of network costs, should be at least 10 times the % Gap achieved in the Do-Minimum and Do-Something scenarios. The estimation of user benefits can be estimated either by using matrix manipulation of the with and without scheme trip and skimmed generalised cost matrices to produce an estimate of the consumer surplus by the rule of a half, or by using the DfT's TUBA program. In either case the worst case convergence of the with and without scheme runs should be taken as the one to compare with the size of the benefits.

Example:

Suppose we have the following outputs from TUBA:

DM&DS_USER_COSTS
Total value of user costs, DM and DS. £000s.
Mode	Year	DMtot_time	DMtot_charge	DMtot_fuel	DMtot_nonfuel
Road	2007	34897	0	2022	966

(TUBA output table modified to show DM costs only)

MODE
User benefits and changes in revenues by mode, all years. £000s.
Mode	Year	User Time	User_Charges PT_fares	Vehicle_Operating_Cost		Operator_Rev PT_fares	Indirect Taxes
				Fuel	Non_fuel
Road	2007	2236	0	-211	-36	0	165

From the MODE table we can obtain the total user benefits. This is done by ignoring the change in operator and indirect tax revenues and summing the user time, charge and VOC benefits. In this case this is equal to 2236+0-211-36=1989.

From the DM&DS_USER_COSTS table we can obtain the total DM network costs. In this case this is equal to 34897+0+2022+966=37885.

Dividing the former by the latter and expressing as a % we obtain 1989/37885=5.3%.

Suppose now that in our model runs we obtained demand/supply gaps of 0.3% and 0.5% for the DM and DS respectively. Taking the worse of the these (0.5%) we can see that it is very much smaller than the benefits expressed as a proportion of network costs (5.3%) and can conclude that in this case we have a robust estimate of economic benefits.

This example shows one modelled year and mode only. In practice this calculation will need to be done for each modelled year.

Note that these calculations can be carried out with TUBA.

1.6 Realism Testing

1.6.1 Once a variable demand model has been constructed, it is essential to ensure that it behaves 'realistically', by changing the various components of travel costs and times and checking that the overall demand response accords with general experience. If it does not, then the values of the parameters controlling the response of demand to costs should be adjusted until an acceptable response is achieved. There will be more scope for adjustments to model parameters where they have been imported and where the model form is incremental, and less scope where the model parameters have been estimated from local data and/or where the model form is absolute. Ways of adjusting models to improve the outcome of the realism tests are discussed in Section 1.7.

1.6.2 In this section, the calculations required for the realism tests are defined. Advice is also provided on how the acceptability of the test results may be judged.

1.6.3 It will be apparent from the preceding units on Variable Demand Modelling that many of the parameters controlling the behaviour of a model ought to reflect local circumstances. However, even if there are adequate local data for an acceptable estimation or calibration of a model, the fact that a model replicates the travel patterns in base year cross-sectional data satisfactorily does not guarantee that the model is a good predictor of the demand responses to changes in travel costs over time and in response to changes in travel costs brought about by schemes in the forecast year. Also, in cases where a local estimation or calibration is not possible and parameter values are imported from other models or from the illustrative values provided in Variable Demand Modelling - Key Processes (TAG Unit 3.10.3), it will be important to check that the behaviour resulting from these parameter values is plausible in their new context.

1.6.4 If the model does not behave in accordance with general experience, it should not be used to appraise a transport scheme, unless a convincing case can be made to explain the differences in terms of special local circumstances. Instead, the model parameters should be modified until its responses are plausible (as advised in Section 1.7).

Demand Elasticities

1.6.5 The acceptability of the model's responses is determined by its demand elasticities. These demand elasticities are calculated by changing a cost or time component by a small global proportionate amount and calculating the proportionate change in trips made. These changes may be implemented on either a link basis and skimmed to yield the interzonal changes or applied directly at the matrix cell level. The elasticity recommended which is the arc elasticity formulation is:

e = (log(T¹)-log(T⁰))/(log( C¹)-log(C⁰))

where the superscripts 0 and 1 indicate values of demand, T, and cost, C, before and after the change in cost, respectively. For example, if car fuel costs increase by 10% and trips by car fall by 2%, then the elasticity of car trips with respect to fuel cost would be log(0.98)/log(1.10)=-0.212. For the purposes of these realism tests, demand would be in terms of car-kms (for private modes) or person trips (for public transport). Elasticities would normally represent long-term responses unless indicated otherwise.

The Tests Required

1.6.6 Any component of cost or travel time can be used to calculate demand elasticities; however, they are not all independent so that there may be little point in checking all of them separately. The different components of generalised cost for any particular journey are interlinked by the weights applied in calculating the generalised cost (see Variable Demand Modelling - Key Processes (TAG Unit 3.10.3)). Thus, if one weighted component always accounts for twice as much as another in the total cost, the elasticity of demand relative to it will always be twice as much. Nevertheless, it is desirable to test the more important components in this way to ensure that the formulation of generalized cost in the model is correct.

1.6.7 The primary realism tests require that car fuel cost and public transport fare elasticities lie within specified bands (as set out below). Car fuel cost elasticity tests are required in all cases. Public transport fare elasticity tests are required in all cases where changes in public transport generalised costs, including changes in fares, are modelled. Car journey time elasticity tests are also required (as a potentially useful diagnostic). Other realism tests - for example, of a model's ability to reproduce elasticities of demand with respect to other charges, such as parking charges and tolls - may be appropriate where empirical elasticities are available.

1.6.8 The elasticities should be calculated using the base year model.

1.6.9 In order to achieve acceptable results from these realism tests, it may be necessary to modify or 'dampen' the generalised cost changes used in the demand model for longer trips. The mechanisms by which cost damping may be implemented are specified in Variable Demand Modelling - Scope of the Model (TAG Unit 3.10.2). In models where the parameter values are estimated or calibrated from local data, cost damping, if it is to be employed, should be built in to the model at the estimation or calibration stage; in these cases, the realism tests should always include the cost damping. In models where parameter values are imported, the need for cost damping should be proven by means of the realism tests; in these cases, therefore, the initial realism tests should be undertaken without cost damping (as discussed in Section 1.7). Advice on the introduction of cost damping, should the realism tests not be met, is provided in the next section in this Unit.

Car Fuel Cost Elasticity

1.6.10 The car fuel cost elasticity required is the percentage change in car vehicle-kms with respect to the percentage change in fuel cost. The calculations should be carried out for a 10% or a 20% fuel cost increase. (A 10% increase is preferred but, in some cases, a larger increase, such as 20% has proved necessary for plausible results to be obtained.) Care should be taken not to increase non-fuel operating costs in this process.

1.6.11 These fuel cost elasticities should be calculated from a converged run of the demand/supply loop. This requirement arises from the fact that these observed elasticities, against which the modelled elasticities are to be compared, are the result of the real world interaction of demand responses, congestion and crowding.

1.6.12 Car fuel cost elasticities should be calculated in both of the following ways.

Matrix-based
- The change in car vehicle-kms should be calculated from the car trip matrices and skimmed distance matrices which relate to the before and after fuel cost change model runs. The movements included in this calculation should relate only to the movements to which the full range of demand responses apply in the demand model.
- For example, if external to external trips are treated as fixed, then it could be argued that the responses of external to internal trips would not be fully responsive as the model would not allow change of destination so that external to internal trips became external to external and vice versa. In this case, the matrix-based calculations should use only the internal to external and internal to internal trips.
- Even if external to external trips are not fixed, they will very often be modelled in a very approximate manner using very simplified networks and speed/flow relationships and approximate estimates of demand. In all such cases, external to external movements should be excluded from the elasticity calculations.
- Complete trips, from real origin to real destination, should be used for these elasticity calculations. This can often require a zoning system and network which covers a large area. These calculations should be carried out by time period and car trip purpose, and also aggregated over time periods and trip purposes to produce an overall average elasticity.
- The calculations can be carried out on either an OD or PA basis, although the former is likely to be the more convenient.

Network-based

Car vehicle-kms should be accumulated over a specified network from the before and after fuel cost change runs and the difference taken. The network used for this calculation should extend to cover the area over which the highway assignment model has been validated but should exclude external areas where the model is more approximate. Centroid connector vehicle-kms should be excluded.
This calculation is likely to underestimate the fuel cost elasticity if the change in car-kms includes fixed elements, such as external to external trips (unless the external to external car-kms can be excluded from the calculations). These calculations should be carried out by time period and car user class, and also aggregated over time periods and trip purposes to produce an overall average elasticity.

1.6.13 A demand weighted average of these elasticities by time period and demand segment or user class should be taken so that the result ideally represents the average elasticity for the whole year, including weekends and holidays. This is because the target elasticity specified below relates to all periods of the year. The annualisation factors used for the Transport Economic Efficiency appraisal may be used for this purpose - see Transport User Benefit Calculation (TAG Unit 3.5.3). Where the annualisation factors do not account for all periods of the year, the available factors should be used but their limitations should be noted in the realism test reporting.

1.6.14 A number of studies in this country using time-series data on car travel and fuel prices and costs have shown an elasticity of car use with respect to fuel cost of about -0.3 (see Bradburn and Hyman (2002), Graham and Glaister (2002), Hanly, Dargay and Goodwin (2002)) and this value equates well with a review of European research on this topic (TRACE, 1999). Taking account of this research, unless analysts can provide a good reason otherwise, the Department's view is that:

the annual average fuel cost elasticity should lie within the range -0.25 to -0.35; and
the annual average fuel cost elasticity should lie on the right side of -0.3, taking account of the levels of income and average trip lengths prevailing in the modelled area - see below for advice on what is the 'right' side of -0.3.

1.6.15 Fuel cost elasticities would be expected to be weaker than -0.30 (ie closer to zero) where trip lengths are shorter than average, car driver mode shares are higher than average, and where proportions of low elasticity demand segments, such as employers' business, are higher than average, and stronger (ie further from zero) where the opposite applies. Higher than average income levels may also be consistent with a weaker elasticity. However, it is generally difficult to estimate the magnitude of the effects of these factors and therefore the extent to which the true elasticity for the area being modelled may vary from the figure of -0.30. It is for this reason that an acceptable range, from -0.25 to -0.35, is specified and analysts should not use models for scheme appraisal which have elasticities outside this range without providing a reasoned case for doing so and without the Department's approval.

1.6.16 Note that, if local variations in values of time are used to argue for a particular target fuel cost elasticity, local values of time should be used in the model. In this case, as explained in Variable Demand Modelling - Convergence Realism and Sensivity (TAG Unit 3.10.4), evidence for the local values of time will be required.

1.6.17 Elasticities may also be regarded as more plausible if:

the pattern of annual average elasticities shows values for employers' business trips near to -0.1, for discretionary trips near to -0.4, and for commuting and education somewhere near the average; and
the pattern of all-purpose elasticities shows peak period elasticities which are lower than inter-peak elasticities which are lower than off-peak elasticities.

1.6.18 While there is little or no empirical evidence to support the variation in elasticities by purpose and time period, most models show the pattern suggested above, although a few models which are otherwise acceptable have been created which show morning peak elasticities which are higher than inter-peak elasticities which are higher than evening peak elasticities. In the case of models which show different variations in elasticities by purpose and time period, an explanation for the differences will need to be provided.

Public Transport Fare Elasticities

Public Transport Main mode

1.6.19 The public transport fare elasticity required is the percentage change in public transport trips by all public transport modes with respect to the percentage change in public transport fares. The calculations should be carried out for a 10% or a 20% public transport fare increase. (A 10% increase is preferred but, in some cases, a larger increase, such as 20% has proved necessary for plausible results to be obtained.) The percentage fare increase should be applied to all public transport modes equally.

1.6.20 These public transport fare elasticities should be calculated from a converged run of the demand/supply loop. This requirement arises from the fact that these observed elasticities, against which the modelled elasticities are to be compared, are the result of the real world interaction of demand responses, congestion and crowding. However, running a model to full equilibrium may be time-consuming and it may be more practical to explore the sensitivity of the demand elasticities to changes in the model parameter values using either fewer iterations (that is, accepting a lower level of convergence than normal) or even a single iteration of the demand/ supply loop. If this approach is adopted, the extent to which the elasticities resulting from the smaller number of iterations are changed by further iteration to convergence should be established at the outset.

1.6.21 Public transport fare elasticities should be calculated on a matrix-basis, by time period and trip purpose. The movements included in this calculation should relate only to the movements to which the full range of demand responses apply in the demand model and should generally exclude external to external movements in any event. Complete trips, from real origin to real destination, should be used for these elasticity calculations.

1.6.22 A demand weighted average of these elasticities by time period and demand segment or user class should be taken so that the result ideally represents the average elasticity for the whole year, including weekends. This is because the target elasticity specified below relates to all periods of the year. The annualisation factors used for the Transport Economic Efficiency appraisal may be used for this purpose - see Transport User Benefit Calculation (TAG Unit 3.5.3). Where the annualisation factors do not account for all periods of the year, the available factors should be used but their limitations should be noted in the realism test reporting.

1.6.23 Elasticities of public transport trips with respect to public transport fares have been found to lie typically in the range -0.2 to -0.9 for changes over a period longer than a year (TRL, 2004). Values close to -0.2 are unlikely for the whole public transport market unless this includes a high proportion of concessionary fare trips with a significant number made free of charge. Unless analysts can provide a good reason otherwise, the Department's view is that the annual average public transport fare elasticity should lie within this range.

1.6.24 The elasticities may also be regarded as more plausible if:

the pattern of annual average public transport fare elasticities shows values for non-discretionary purposes which are lower than those for discretionary trips; and
the pattern of all-purpose public transport fare elasticities shows peak period elasticities which are lower than inter-peak elasticities which are lower than off-peak elasticities;
the elasticities for car-available segments are greater than the non-car-available segments since the former have greater choice than the latter, although there are arguments to suggest that non-car-available fare elasticities may be higher where incomes are lower.

However, there is little or no empirical evidence available to support these patterns and other patterns may be acceptable.

Public Transport Sub-modes

1.6.25 In addition to calculating elasticities for all public transport trips, separate elasticities should be calculated for all public transport sub-modes which carry significant shares, where the model structure allows such calculations to be undertaken in an appropriate manner. In order for valid fare elasticities for individual public transport sub-modes to be calculated, the fares applicable to the sub-mode would need to be explicitly included in the generalised costs used in the model. In the case of models which forecast the choice between the main modes of car/park-and-ride, public transport, and walk and cycle in the demand model, with the split between the public transport sub-models being handled in the public transport assignment model, fares for each sub-mode would need to be included in both the demand model and the public transport assignment model. In models which split demand between public transport sub-modes in the demand model, fares by each sub-mode would need to be included in the costs used in that choice process (but would not be needed in the assignments which would be restricted in each case to a single sub-mode).

1.6.26 Elasticities of bus trips with respect to bus fares for full fare paying passengers have been found to lie typically in the range -0.7 to -0.9 for changes over a period longer than 5 years (Dargay and Hanley). Unless analysts can provide a good reason otherwise, the Department's view is that the annual average bus fare elasticity should lie within this range. It should be noted that up to a third of bus trips made in the off-peak and some in the morning peak are made by concessionary passengers free of charge. Their demand will be unaffected by changes in fares. If possible, it would be useful to estimate the fare elasticity for full fare paying passengers separately noting that there are several half-fare or similar schemes for children and students. Including concessionary passengers would tend to reduce the elasticities given above to around -0.4 with a lower elasticity in the off-peak. There is no available evidence of the long-run fare elasticities for heavy and light rail.

Car Journey Time Elasticity

1.6.27 The car journey time elasticity required is the change in car trips with respect to the change in journey time (calculated using the arc formulation given in 1.6.5).

1.6.28 These journey time elasticities should be calculated using a single run of the demand model because the target elasticities in this case were derived from stated preference data, where the costs of each option and attribute were exogenous.

1.6.29 Modelled journey time elasticities can be derived from modelled fuel cost elasticities and the values of time. However, in order to provide a more independent test, journey time elasticities should be calculated from both a model run and on a matrix-basis using times from the networks, for each trip purpose in each time period. Complete trips, from real origin to real destination, should be used for these elasticity calculations.

1.6.30 Journey time elasticities will vary much more than the fuel cost elasticities. The output elasticities should be checked to ensure that the model does not produce very high output elasticities (say stronger than -2.0).

1.7 Model Adjustment

1.7.1 The previous section has explained how the realism tests should be conducted. This section now explains what should be done if a model fails to yield elasticities in the specified ranges.

1.7.2 There are five model features that the analyst should consider, as follows:

the fuel cost, journey time and public transport fare elasticities;
the model sensitivity parameters;
the values of time;
the cost damping function; and
the trip lengths.

1.7.3 The first and the last items in the above list are conditions that the model should satisfy, whereas the middle three are the mechanisms for adjusting the model so that it does satisfy the required conditions.

1.7.4 These features are considered in turn, for each of two kinds of model:

first, models which have been developed by importing sensitivity parameter values from either an existing model whose parameters have been estimated* statistically reliably or from Variable Demand Modelling - Key Processes (TAG Unit 3.10.3); and
secondly, models for which parameter values, and possibly values of time also, have been estimated statistically from local data.

* In this context, 'estimation' is a statistical process and 'calibration' is a process of adjustment, often by trial and error. Thus, demand model parameters are often 'estimated' while assignment models are often 'calibrated'.

Models Developed by Importing Initial Parameter Values

1.7.5 Elasticities. As explained in the previous section, the Department expects that:

fuel cost elasticities should lie in the range from either -025 to -0.3 or -0.3 to -0.35 depending on the characteristics of the area;
public transport fare elasticities should lie in the range from -0.2 to -0.9*; and
car journey time elasticities should be no stronger than -2.0.

* The comment in paragraph 1.6.23 should be noted.

1.7.6 The previous section also indicated the expected patterns of:

fuel cost elasticities by trip purpose and time period; and
public transport fare elasticities by trip purpose, time period and car availability.

1.7.7 As noted in the previous section, for models with imported parameters, the realism tests should be conducted initially without cost damping.

1.7.8 If a model fails to meet expectations, attempts should be made to adjust the model parameters so that more compliant elasticities result. It is unlikely that the Department will be persuaded by arguments that the target elasticity ranges are inappropriate.

1.7.9 Sensitivity Parameters. The data base used to derive the WebTAG illustrative lambda and theta demand parameter values was limited to seven models. These parameters are described in Variable Demand Modelling - Key Processes (TAG Unit 3.10.3). The following points should be noted about these illustrative values.

The seven models were the only ones of a generally WebTAG-compliant form which were available at the time for which parameters had been estimated, in some cases rigorously but in other cases not so rigorously. All the models were trip-based, all based on linear generalized cost (time) formulations, and none used cost damping in any form.
All the illustrative parameter values relate to generalised costs in minutes (generalised times), derived using the WebTAG linear formulations and the standard values of time, which were probably taken from TEN or even HEN2 (as opposed to using the current values in Values of Time and Vehicle Operating Costs (TAG Unit 3.5.6)). It is thought that standard values are likely to have been used in most cases, the only exception being the LTS Model where London values could have been used.

1.7.10 Notwithstanding these caveats, the Department considers that analysts should start with the median lambdas and thetas (given in Variable Demand Modelling - Key Processes (TAG Unit 3.10.3)) and adopt a cautious, simple and systematic process for modifying these. In general, care should be taken to avoid over-complicating the adjustments to the median lambdas and thetas.

1.7.11 A record of all the changes made and their results should be kept (and made available if requested). The aim should be to reduce the chances of peculiar combinations being selected for no good reason. Consistency in matters like this helps the Department interpret appraisals and check results for plausibility. Typically, revised lambdas and thetas which were within ±25% of the median illustrative values, given in TAG Unit 3.10.3, would be regarded as acceptable and values outside this range would merit investigation.

1.7.12 The illustrative parameter values given in given in Variable Demand Modelling - Key Processes (TAG Unit 3.10.3) relate to trip-based models. If home-based tours are modelled, that is, the outbound-from-home and return-to-home legs combined are modelled in the choice processes, the total costs for both legs of the tour taken together need to be used (rather than the costs of each leg separately as in a trip-based model). In these instances, the lambda values which govern the destination choice process given in TAG Unit 3.10.3 should be halved. The theta values which govern the mode choice process are scaling parameters and do not need to be halved.

1.7.13 Values of Time. Varying the value of non-working time is one of the recommended forms of cost damping (although the use of cost damping is optional) and is considered below under cost damping. The advice here is concerned with the notion of changes to the average values of time, irrespective of distance.

1.7.14 The advice in the Design Manual for Roads and Bridges, Volume 12, allows the analyst to adjust the value of time in an assignment model but then advises that the resulting distance coefficient should be held constant in forecasting. This approach causes inconsistencies with the demand model where vehicle operating costs and values of time are normally changed over time in forecasting. The Department's current preference is for the generalised costs used in both assignment and demand models to be compatible* and that values of time and vehicle operating costs given in Values of Time and Vehicle Operating Costs (TAG Unit 3.5.6) should be used. This is the basis for the advice in Forecasting Using Transport Models (TAG Unit 3.15.1).

* Except to the extent that certain elements of generalized cost may be relevant to only one of the models and that the costs should relate to vehicles in the assignment model and persons in the demand model.

1.7.15 If an analyst were to change the values of time in order to achieve better elasticities, a revalidation, and possibly a recalibration also, of the assignment model would also be required or, if the values in the assignment model were left unchanged and were only changed in the demand model, an inconsistency would arise between the values used in the demand and assignment models.

1.7.16 Given these considerations, analysts should:

start with WebTAG values of time unless they can put forward good reasons for doing otherwise; and
start with compatible generalised cost coefficients (vehicle operating costs and values of time) in the assignment and demand models.

1.7.17 That said, it is allowable to estimate values of time which differ from the WebTAG values (see Forecasting Using Transport Models (TAG Unit 3.15.1), for example). Thus, analysts may adjust the starting WebTAG values of time to achieve better elasticities, but only if they have good evidence from estimation using either revealed or stated preference data which show local values of time which are different from the values in Values of Time and Operating Costs (TAG Unit 3.5.6).

1.7.18 If analysts do choose to change the value of time, analysts should not restrict such changes to the demand model but should also revisit the validation, and possibly the calibration, of the assignment model as well. (Note that if variation in the value of time is introduced, as a cost damping mechanism, that would itself introduce inconsistencies between the resulting values of time used in the demand model and the values of time used in the assignment model. Nevertheless, the proposition is that the underlying average values of time should remain consistent between the demand and assignment models.)

1.7.19 The Department would require a strong justification for changes to the WebTAG average values of time in excess of ±20%.

1.7.20 Cost Damping Function. Recommended forms of cost damping mechanisms are set out in Variable Demand Modelling - Scope of the Model (TAG Unit 3.10.2). While the application of cost damping is optional (to be introduced at the analyst's discretion), if cost damping is to be employed, the following forms or functions are recommended:

variation in the value of non-working time with distance;
damping of generalised cost by either a function of distance or a power function; and
use of a log cost term along with the conventional linear cost term in the generalised cost function.

1.7.21 In the two damping functions in the middle point in the above list, there are parameters that can be adjusted by the analyst and the cost damping guidance specifies the limits within which these parameters must lie. Other forms would be permitted only where they can be shown to be superior to the recommended forms and only with the agreement of the Department.

1.7.22 The cost damping functions given in Unit 3.10.2 effectively scale the generalised costs. In principle, therefore, the functions and suggested parameter values apply equally to trip-based and tour-based models, although, in practice, parameter values may need to vary according to local characteristics.

1.7.23 Trip Lengths. If the model is a true incremental model (that is, the model predicts changes in demand when fed by changes in costs), and if the model has been set up by initially importing parameter values, checks on how well the final parameter values reproduce observed trip lengths are not required. However, if the model is an absolute model, whether used in absolute form (that is, when the synthesised trip matrices are assigned directly) or applied incrementally (that is, when the difference between two absolute model forecasts are applied to base assignment matrices), then checks should be made to assess how well the model parameters reproduce observed trip lengths.

1.7.24 It is quite possible that the task of finding, by heuristic means, a set of model parameters which both satisfy the requirements of the realism tests and replicate observed trip lengths adequately will prove too demanding. A true incremental model, however, need only satisfy the requirements of the realism tests, which is why this model form is to be preferred.

1.7.25 In summary: in the case of models which have been developed by importing sensitivity parameter values, there is scope to achieve more acceptable elasticities by:

adjusting the sensitivity parameters within a defined range; and
using a form of cost damping and adjusting the parameters which define that function.

Models for Which Parameter Values, and Possibly Values of Time, Have Been Calibrated

1.7.26 Elasticities. The target elasticities and their ranges are not affected by how the model has been developed and therefore apply to this category of models too.

1.7.27 Sensitivity Parameters. In this category of models, sensitivity parameters and alternative-specific constants (ASCs) will have been estimated to reproduce observed trip lengths for each demand segment (as well as observed trip patterns and volumes). In some cases, it may be possible to adjust the sensitivity parameters to yield more appropriate elasticities while maintaining the fit to the observed trip length distributions by means of adjustments to the ASCs. However, in most cases, this could be a complicated and arguably impractical process. Therefore, the scope for adjusting estimated sensitivity parameters is probably quite limited (although revised parameters may arise from some of the other adjustments below).

1.7.28 Values of Time. If values of time have been taken from WebTAG initially, they may be adjusted only if an estimation using local revealed or stated preference data supports the change. If changes to the initial values of time are made on these grounds, the sensitivity parameters and ASCs would need to be re-estimated.

1.7.29 In some cases, values of time are estimated as part of the model estimation process. Once these have been accepted as plausible, it would be very hard to find good reason to adjust them in order to achieve more acceptable elasticities.

1.7.30 Cost Damping. In principle, the same range of cost damping forms is available for use in this category of models as in the models which started with imported parameters. However, in this case, these functions must be employed at the stage where sensitivity parameters and ASCs, and values of time, are estimated. Cost damping cannot be retro-fitted without re-estimation.

1.7.31 It is open to the analyst to adjust the parameters which define the cost damping function, with the same scope for adjustment being available as for the models which start with imported sensitivity parameters. These adjustments may be carried out initially without re-estimating the model but, once a favoured set of cost damping parameters has emerged, the sensitivity parameters, ASCs and values of time, must be re-estimated.

1.7.32 It is possible that there will be a number of combinations of cost damping parameters, choice model sensitivity parameters, and ASCs that would yield an acceptable model. The safest course would be to minimise the role of cost damping.

1.7.33 Trip Lengths. The statistical estimation processes are designed to identify sensitivity parameters, ASCs and values of time which mean that the model should replicate observed trip lengths. It may be necessary to allow some flexibility in the estimation in order that the requirements of the realism tests may be met. It may be that some relaxation of the fit of the model to the data is required, perhaps by altering the explanatory power of the sensitivity parameters and the ASCs, for the realism test requirements to be satisfied.

1.7.34 In summary: in the case of models for which parameter values, and possibly values of time also, have been estimated from local data, there should be scope to achieve more acceptable elasticities by:

adjusting the sensitivity parameters and ASCs; and
using a form of cost damping and adjusting the parameters which define that function.

1.7.35 The practicality of adjusting the sensitivity parameters and ASCs may be restricted, as may be the scale of any changes which could be made by these means. If is decided that cost damping should be introduced (not having been included in the initial estimation), the model would have to be re-estimated with the chosen cost damping function and parameters.

1.8 Sensitivity Testing

1.8.1 Sensitivity testing, as distinct from realism testing, is aimed at identifying the relative effects of the various parameters on the outcome of a scheme appraisal, rather than in checking the model responses against experience. Especially where the model parameter values are uncertain it is important to know how sensitive the appraisal results are to these uncertainties, so that confidence can be invested in the conclusions.

1.8.2 The realism testing of Section 1.6 was aimed at ensuring that the model's responses were consistent with previous experience of travel demand and the way it responds to changes in travel costs. Even if the model is satisfactory in these respects, there may still be considerable uncertainty attached to some of its forecasts because of uncertainty in its parameter values. It is important to quantify the effects of this on scheme appraisal, as far as possible, so that the final conclusions on a scheme's value can be robust against these uncertainties. This can be investigated by sensitivity testing of the model's behaviour against variation in those parameters which are judged to:

have a substantial effect on the model's prediction of changes, and
be uncertain in their calibration.

1.8.3 The most obvious values are the sensitivity parameters that govern the individual demand mechanisms (i.e. the lambda values). If they have been calibrated on local data, the extent of possible error in their calibration should be examined from the statistics calculated during the fitting, which is usually substantial. If they have been imported, the uncertainty will be even greater since they are being used in a context different from their original application. The illustrative values given in VDM Key Processes (TAG Unit 3.10.3) were obtained from a review of current models, and typically the range of values was twice the mean value. This indicates the degree of uncertainty in values imported from other studies.

1.8.4 If the lambda values have been calibrated on local data, whether for the variable demand model itself or for an existing local model, then check the overall result of the scheme appraisal against runs of the model with the lambdas set at plus the standard deviation of the mean value, or at least +25% of the mean if the actual standard deviation is smaller. Behaviour of the model will not necessarily be symmetrical against increases and decreases in the parameter, but the increase will indicate the strength of the response, and if it is an important factor the result can also be tested against a decrease. If the values have been imported then test the result against +50% of the mean. This range is to reflect the greater uncertainty that occurs with imported values. Unless there are convincing reasons for not doing so, the changes are to be made to all parameters in the same direction at the same time so that the gradation of parameter values is still consistent with the hierarchy.

1.8.5 Given the acknowledged uncertainty of distribution parameters obtained from cross-sectional fitting, this larger margin could be applied even to locally calibrated distribution lambdas. It is the stronger variable demand mechanisms which will have most effect on the assessment, so there may be no point in testing the result against a small trip frequency response, for example, when distribution or mode choice are dominant. Generally, in a scheme aimed at congestion relief, the net benefit will be reduced by increases in the demand for car travel, so that it is the increased lambda values that will test the robustness of the result. If the scheme remains well justified against these higher values then a conclusion that the scheme is beneficial will be robust against the effects of induced traffic. Where the model includes time of day choice it will be essential to test variation of the assumed sensitivity. Evidence for these values is more uncertain and wide sensitivity factors say: +50% and -50% are suggested. The range will be limited by the need to ensure that any changes in the values are still consistent with the hierarchy.

1.8.6 Sensitivity testing should not be limited to the response parameters, however. Any parameter that seems likely to have a substantial effect on the net benefit, and where appreciable uncertainty is likely to affect the assessment substantially, should also be tested. An example of this may be the assumed distribution of willingness-to-pay bands in road-tolling exercises.

1.8.7 There are other sensitivity tests that should be undertaken for forecast years to test the sensitivity of the appraisal to variations in other inputs such as changes in the build-up of demand, values of time, or differing economic forecasts. These tests are described in more detail in the advice on Major Scheme Appraisal in Local transport plans: part 3. Annex F (DfT, 2003).

1.8.8 Although sensitivity testing is important, there is a danger in using it to obtain such a wide range of values that any prediction is mistrusted. In interpreting the results it is important to understand (and to emphasise in presentation) that the central values are still the best available prediction of the likely outcome, and additional forecasts obtained by sensitivity testing are purely to establish the effects of uncertainty around this central forecast. The aim is for the modeller to make clear the extent of the possible uncertainty, while providing clear central predictions to support policy making and assessment.

1.9 Reporting

1.9.1 The results of the realism tests, along with the sensitivity tests discussed in Section 1.7 should be documented in a validation report, either as an addition to the Validation Report required of all road scheme appraisals with regards to model calibration and fit, or as a separate document validating the variable demand aspects of the model. The items that should be included in a Validation Report are set out in significant detail in DMRB Volume 12 Section 2 Part 1.

1.9.2 The items in the Validation Report should include:

a description of the model used and its development (including evidence of the fit achieved to the calibration data, and a description of any sensitivity tests undertaken, and their results);
a description of the data used in building and validating the model;
evidence of the validity of the network employed;
a validation of the trip matrices employed;
a validation of the trip assignment;
a validation of any other special features (e.g. higher tier model inputs, trip end models, modal choice models, etc) employed; and
a present year validation, if appropriate.

1.9.3 The validation of special features including details of the variable demand model chosen and should include at least the following items:

The background to the decision on the particular demand responses included in the model. This will include a statement on any demand tests.
A description of the reasoning behind the choice of lambda parameter values, including any local calibration should be given. The parameter values should be explicitly shown together with details of the elements of generalised cost, and the route-choice factors.
Where public transport schemes are being considered then the public transport assignment model will need to be validated.
Details should be given of any realism tests, which should, at least, include the estimation of the elasticity of car travel (trips or kilometres) to changes in car fuel cost and, if possible, to car journey time. Where a mode-choice has been included the realism checks should also include the sensitivity to changing bus/rail fares. The Report should also include details of any changes to the model parameters arising from these tests.

1.9.4 Details should be given of any base year sensitivity tests undertaken.

1.10 Main Changes from Existing Advice

1.10.1 This Section describes those aspects of the Advice where the Department for Transport's expectations of good practice have changed and where departures from existing guidance have been recommended.

1.10.2 The intention of this Advice is to describe the basis of variable demand modelling as clearly and simply as possible, and to recommend simple versions of best current practice. It suggests a minimum set of requirements for testing transport scheme appraisal against the likely response of demand, and is intended to represent generally-accepted practice at this relatively basic level. Consequently, it is not aimed at suggesting fundamental changes to existing practice in demand modelling. However, because it is intended for application in the wider area of scheme assessment where, until recently, the response of travel demand to a scheme was often considered rather cursorily, if at all, it does represent a significant step forward in general appraisal practice, and a change in the Department for Transport's expectations of good practice.

1.10.3 The main points to note are the following.

Overall, there should now be a presumption that the effects of variable demand and induced traffic on scheme benefits WILL be estimated quantitatively unless there is a compelling reason for not doing so.
Throughout the Advice there are a number of important recommendations shown highlighted and in bold: if these actions are not followed, analysts will need to provide rigorous justification for the course of action taken.
Even if induced traffic does not weaken the case for the scheme appreciably, the assessment may be criticised if it cannot demonstrate that the case is robust against possible changes in demand.
In modelling demand, some segmentation by trip and traveller type is essential: at minimum there should be categorisation by trip purpose (at least home-based work/education, employer's business, and 'other' purposes; some form of distinction between travellers with and without a car available is also very desirable, especially where mode-choice is to be considered. In many cases, modelling multi-car ownership is desirable, and should be practical, if household survey data is available.
The amount of detail required in demand modelling will depend upon the particular application, since the effort and cost involved should be commensurate with the investment being assessed and the scale of its effects. Where a multi-level variable demand model is appropriate, it should include a distribution mechanism, and it will generally be desirable to include other mechanisms which can generate or suppress car trips as congestion reduces or grows.
The Department's long-established preferred approach to use an incremental rather than an absolute model, unless there are strong reasons for not doing so is reinforced by the above changes.
Where variable demand modelling is justified, compatibility (convergence) between the assignment and the demand model(s) is very important. To optimise processing time and ensure true converged solutions the travel cost formulations used in both should contain the same ratio of weights of journey time relative to journey distance.
The sensitivity parameters in the demand mechanisms should use robust calibrated local parameters wherever possible (from existing local models, for example). Failing this the Advice provides illustrative values in obtained from a review of current multi-stage demand models.
The sequence of the distribution and mode split stages in the calculation hierarchy should depend upon the relative strengths of the sensitivity parameters, but trip frequency should always be calculated first and micro time period choice (peak-spreading), if it is to be included, will generally be lowest in the hierarchy. However, the sensitivity parameters should always increase along this sequence from highest to lowest, and this may require different sequences for different categories of travel.
It is essential to apply "realism testing" to ensure that the model responds rationally and with acceptable elasticities. As a minimum, it is necessary to check the elasticity of demand with respect to car journey time and car fuel costs.
It is also desirable to apply sensitivity testing to the results of the assessment against variation in those parameters that are uncertain. Generally, in a scheme aimed at congestion relief the net benefit will be reduced by increases in the demand for car travel, so that increasing the sensitivity parameters in the demand mechanisms will test the robustness of the result. If the scheme remains well justified against these higher values then a conclusion that the scheme is beneficial will be robust against the effects of induced traffic.

2. Further Information

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

For information on:	See:	TAG Unit number:
Individual demand responses	Variable Demand Modelling - Key Processes	Unit 3.10.3
Background information on elasticity values	Variable Demand Modelling - Appendices	Unit 3.10.5

3. References

Batley R, T Fowkes,, G Whelan and A Daly.(2001) Models for choice of departure time. European Transport Conference, Seminar on methodological innovations Homerton College, Cambridge September 2001.

Bradburn, P and Hyman, G (2002). An econometric investigation of car use in the National Transport Model for Greet Britain. European Transport Conference, September 2002, Seminar on Applied Transport Methods, Homerton College Cambridge 2002.

Dargay J.M. & Hanley M. (1999) Bus Fare Elasticities.

Department for Transport (2003) Major Scheme Appraisal in Local Transport Plans, October 2003.

DMRB 12.2.2 HMSO February 1997 - withdrawn Summer 2004.

Graham D & S Glaister (2002) Review of Income and Price Elasticites of Demand for Road Traffic. Final report to the DTLR. July 2002.

Hanly M, J Dargay & P Goodwin (2002) Review of Income and Price Elasticities in the Demand for Road traffic. Final Report to DTLR. March 2002.

TRACE (1999). TRACE Final Report, www.transport-research.info/web/projects/project_details.cfm?id=766.

TRL (2004) The Demand for Public Transport: A Practical Guide. TRL Report TRL593. Crowthorne UK.

4. Document Provenance

This Transport Analysis Guidance (TAG) Unit reflects the consultation comments received on the Convergence, Realism & Sensitivity Testing Stage of the draft Variable Demand Modelling Advice produced by TRL in June 2003.

Section 1.6 on realism testing was revised in May 2009 and Section 1.7 on model adjustment was added at the same time.

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

Integrated Transport Economics and Appraisal (ITEA) Division
Department for Transport
Zone 3/06, Great Minster House
33 Horseferry Road
London SW1P 4DR

Email: itea@dft.gsi.gov.uk
Tel: 020 7944 6176
Fax: 020 7944 2198

Updated: April 2011