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Transport Modelling Guidelines

Volume 2: Strategic Modelling

Date: 26/4/2012

Version: Draft 3

Document information

|Criteria |Details |

|Document title: |Transport Modelling Guidelines, Volume 2: Strategic Modelling |

|Document owner: |Douglas Harley |

|Document author: |Len Ng |

|Version: |Draft 3 |

|Issue date: |26/4/2012 |

Contents

List of Figures iv

List of Tables v

1 Introduction 1

2 Model Validation 1

2.1 Convergence 1

2.1.1 Assignment Convergence 2

2.1.2 Feedback Convergence 4

2.2 Trip Length Distribution 6

2.3 Screenlines 6

2.4 Scatter Plots 9

2.5 Percent Root Mean Square Errors 9

2.6 Travel Time 10

2.7 Other Validation Measures 13

2.7.1 Volume Bandwidth Plot 13

2.7.2 Difference Plot of Survey and Model Volumes 14

2.7.3 Comparison of Survey and Model Volumes on Key Roads 14

2.7.4 GEH 15

3 Matrix Estimation 16

3.1 K-factors 18

4 Model Output Requirements 18

4.1 Option Assessment Report 18

4.2 Other Modelling Reports 28

5 Induced Traffic 31

5.1 Definitions 31

5.2 Fixed Trip Matrix Method 32

5.3 Variable Trip Matrix Method 33

5.3.1 Matrix-based Computation 34

5.3.2 Link-based Computation 34

5.4 Peaking Spreading/Contraction 35

5.5 Land Use/Transport Interaction 37

5.6 Additional Trips 37

6 Subarea Model 38

Reference 39

List of Figures

Figure 1: Change of max GEH with feedback cycle 5

Figure 2: Comparison of observed and estimated trip length distribution 6

Figure 3: Maximum desirable screenline difference (%) for 2-hr (top) and 24-hr 1-way traffic volumes 7

Figure 4: Plot of percent difference between model and survey traffic volumes against screenline targets 8

Figure 5: Screenline and traffic count locations 8

Figure 6: Scattered plot of model versus survey 1-way 7-9am volumes 9

Figure 7: Time-distance graph of survey and model travel time 11

Figure 8: Routes for measuring travel time 11

Figure 9: 7-9am 1-way volumes (‘000) 13

Figure 10: Difference between model and survey volumes, 7-9am peak direction 14

Figure 11: Model and survey volumes on Princes Freeway West, 7-9am east bound 15

Figure 12: GEH plot of 1-way 1-hr equivalent link volume 16

Figure 13: Trip length distributions before and after matrix estimation 17

Figure 14: Number of trip ends (productions/attractions) before and after matrix estimation. 18

Figure 15: Road network lanes 20

Figure 16: Road network posted speed 21

Figure 17: 1-Way 7-9am volumes 22

Figure 18: 2-Way 24-hr volumes 23

Figure 19: Peak direction volume/capacity ratio 24

Figure 20: Peak direction travel speed 25

Figure 21: Difference in 1-way 7-9am volume between base and option 26

Figure 22: Select link analysis for 1-way 7-9am volumes 27

Figure 23: Proposed projects 2017-2021 29

Figure 24: Model zone population in 2008 30

Figure 25: Model zone population change, 2008-2046 31

List of Tables

Table 1: Percent root mean square error 10

Table 2: Values of the t statistic for calculation of 95% confidence intervals 12

Table 3: GEH percentile reporting 16

Table 4: Level of service (LOS) and volume/capacity (V/C) ratio 19

Table 5: Recommended colour scheme for plotting V/C ratio and travel speed 19

Table 6: Proposed projects 2017-2021 29

Table 7: Methods of dealing with induced traffic 32

Introduction

This manual brings together and updates the two sets of modelling guidelines previously developed by VicRoads (2006, 2010).The output requirements for modelling reports are also specified in this manual to ensure modelling results are presented consistently and adequately in VicRoads’ reports.

To address the issue of induced traffic raised by the Victorian Auditor-General’s Office (2011), this manual includes the guidelines to estimate induced traffic and its benefits. The Department of Transport (2011) has a position paper on induced travel demand but this manual contains more detail in the methods of estimating induced traffic and its benefits.

Depending on the scope of the modelling work, the appropriate guidelines in this manual should be followed in all modelling work and reports done for VicRoads.

The guidelines in this volume are meant for strategic modelling. The guidelines for mesoscopic modelling and microsimulation would be in Volumes 3 and 4 of the guidelines respectively.

Model Validation

The approach recommended by VicRoads for the validation of strategic transport models involves the careful checking of each component in the modelling process. A detailed discussion of such an approach is presented in a report prepared for the USA’s Federal Highway Administration (1997).

Although the approach by the Federal Highway Administration should generally be followed in developing the model, only the guidelines and criteria set in the following sections need to be addressed in the consultant report.

A model that does not meet all the guidelines documented in this manual may still be acceptable if the larger discrepancies are concentrated away from the area of greatest importance to the appraisal or in the contra-peak direction. Conversely, a model that passes the guidelines but has significant discrepancies on the most crucial links or in the peak direction may not be acceptable.

If for any reason, such as lack of data, any of the following validation steps cannot be carried out, the consultant should get agreement with VicRoads or explain this in the model calibration and validation report.

Care should also be taken to ensure that the units of model volume used in the validation - either vehicles or passenger car units (PCUs) - are the same as those used in the survey. The PCU weighting factors used (if any) should be clearly stated in the model validation report.

Convergence

In general, iterative methods for reaching equilibrium in mathematical models will not converge absolutely, and user-defined stopping criteria are required to describe the point at which satisfactory convergence is considered to have been achieved.

The term ‘model convergence’ may relate either to only the assignment step in four-step models, or include feedback between the assignment step and trip distribution (or even trip generation). Section 2.1.1 considers convergence of the assignment step only. Section 2.1.2 considers convergence of the feedback loop of a four-step model.

The importance of achieving convergence is related to the need to provide stable, consistent and robust model results. When the model outputs are being used to compare the base and option scenario, and to estimate the economic benefits of an option, it is important to be able to distinguish real differences from those associated with different degrees of convergence and spurious mathematical effects. Similar considerations apply when the benefits of different options are being compared. Model convergence is therefore a key to robust economic appraisal.

It should also be noted that because convergence is greatly affected by the level of congestion in the network, greater computational demands tend to be required when modelling future years. Thus in general, longer run times and more iterations will be required to achieve a similar level of convergence in forecast years relative to the base year.

1 Assignment Convergence

The guidelines documented below relate to the use of equilibrium or incremental assignment algorithms. In cases where stochastic assignments are warranted, other guidelines may apply.

Convergence of congested assignment models can be monitored using a variety of indicators. These can be classified as follows:

0. global stability indicators, based on comparisons between successive iterations of network-wide values of total travel time, total travel distance, total or average travel costs or average speed.

0. disaggregate stability indicators, based on absolute changes in values of individual link flows, costs or times, origin-destination (OD) costs or a combination of these,

0. proximity indicators, reflecting how close the current flow and cost pattern is to the assignment objective.

Stability at global level (e.g. total travel time, costs or distance) is not sufficient for ensuring model convergence. Such measures may hide substantial uncertainty at a lower level, such as in individual link flows or OD-costs. Even though global stability may provide useful information during the iterative process, it should always be accompanied by disaggregate analyses at link or OD-level.

Of a large number of disaggregate stability indicators, the following three have been identified as being straightforward to compute, easy to interpret and explain, and robust in their explanation of assignment stability.

0. average absolute difference in link flows between successive iterations:

[pic] (1)

where: N = number of links

Van = flow on link a in iteration n

0. relative average absolute difference in link flows between successive iterations:

[pic] (2)

0. Pdiff: Percent of links whose change in volumes between iterations is less than a set value.

Most transport assignment packages that are suitable for the appraisal of urban road projects provide one or more proximity indicators for convergence. On the Cube/Voyager platform, the most appropriate one to use is:

[pic] (3)

where Can-1 = cost of link a in iteration n

Fan = all or nothing flow in iteration n based on Can-1

Although proximity and stability usually accompany each other, they both should be assessed separately, as each relates to different aspects of the iterative process. The following criteria, adapted from UK’s Department for Transport (1996), should lead to stable and robust assignment results.

0. RGAP < 1% (proximity)

and one of the following (stability)

0. RAAD in flows < 1% or

0. AAD in flows < l veh/h or

0. Pdiff (changing less than 5%) > 95%

These criteria should be satisfied for two consecutive iterations. At least one of the stability criteria should be satisfied, the values of the other two measures should also be reported. If examination of the statistics in more detail shows that (rather than oscillating about a constant value) all these indicators still move in the same direction, it is necessary to continue the iterative process further.

In multiple user class assignment stability should be monitored for each class separately; proximity should be assessed for total flow.

In addition to satisfying the above criteria, VicRoads further requires that the base and option scenario both be evaluated for the same number of iterations. This is expected to provide a more reliable basis for assessing link by link travel time savings in project evaluation.

In order to satisfy the latter requirement, the maximum number of iterations to achieve the convergence criteria for any model run, will first need to be established for the most congested future-year option. Other options and model years may then need to be run for the same number of iterations. The consultant will need to check and report on the convergence statistics for each model run.

If it appears that the desired convergence criteria cannot be met, the model network coding must be reassessed. Convergence problems can often be traced back to local or global over-capacity problems. Poorly or non-converged assignment models produce unreliable flow and cost estimates - no reliance should be placed on any apparent validation or set of results from a model run in the absence of convergence.

2 Feedback Convergence

The guidelines documented below relate to the use of convergence of a feedback loop between the assignment and distribution steps of a four-step model. In cases where different looping arrangements are applied, other guidelines may apply.

Attention should be given to what type of feedback process is used. The process should be chosen based on whether (1) it has been reported in the literature that this process is convergent with similar types of model; and (2) that the process converges sufficiently quickly. The first of these criteria is particularly important as some simple feedback schemes such as ‘naïve feedback’ where time skims from the assignment process are fed directly back to the distribution step at each cycle often result in divergent rather than convergent model behaviour. Usually some sort of averaging is required between cycles. VicRoads has found applying the ‘method of successive averages’ (Boyce et al. 1994) to link volumes from successive cycles, then reskimming the network costs and feeding these back to the distribution step to be a reliable, but rather slowly converging, method.

VicRoads recommends either of the following two statistics be used to test for feedback convergence (Rogerson & Carnovale 2007).

0. The percent root mean square error for travel time or link flow:

[pic] (4)

where N = total number of OD pairs or links

Van = travel time of OD pair or flow of link a in feedback cycle n

0. The maximum GEH for link flows. The GEH statistic is defined as:

[pic] (5)

with the maximum GEH statistic over all links defined as:

Max(GEHa) where a = 1 to N (6)

Rogerson and Carnovale (2007) recommended the following stopping criteria:

0. %RMSE statistics for travel time and link flows < 1%

or

0. Max GEH for link flows < 2

Previous work has shown that convergence is very slow to achieve using these stopping criteria. Therefore VicRoads, at present, requires no stopping criteria to be adhered to. However, a convergent feedback process between assignment and distribution is required, and reporting on one of the above convergence measures for each feedback cycle is required. Figure 1 shows an example of such a report.

[pic]

Figure 1: Change of max GEH with feedback cycle

Trip Length Distribution

Compare average trip lengths and their frequency distribution by purpose in the study area. The most standard validation checks of trip distribution models used as part of the calibration process are comparisons of observed and estimated trip lengths. If a generalised cost is used as the measure of impedance, average trip lengths and trip length frequency distributions should be checked using the individual components of generalised cost (e.g. time and distance). The trip length frequency distribution shows how well the model can replicate observed trip lengths over the range of times. Visual comparison of distributions is an effective method for validation (see Figure 2).

[pic]

Figure 2: Comparison of observed and estimated trip length distribution

Screenlines

Compare surveyed and modelled traffic volumes across screenlines in the study area. The comparison is required for each direction (peak and contra-peak) and modelled period.

0. Target: Percent difference for all screenlines (by direction) within the bounds of the functions presented in Figure 3.

The power function used in Figure 3 is based on curve fitting to Figure 7-2, Page 91, of the manual published by USA’s Federal Highway Administration (1997) and includes an arbitrary 25% reduction in the maximum percent difference for 24-hrs. For 2-hr peak traffic volumes, the maximum desirable difference between survey and modelled traffic volumes is selected to be slightly higher (i.e. less stringent) than for the 24-hr case in order to account for the greater variation found in traffic volume data.

Figure 4 shows an example of the percent difference plot between model and survey volumes against screenline targets. Individual points are labelled with screenline numbers as defined in Figure 5. As consultants also need to produce a map of traffic count locations used in scatter plots (see Section 2.4), the screenline and traffic count locations can be combined in a single map as shown in Figure 5.

[pic]

[pic]

Figure 3: Maximum desirable screenline difference (%) for 2-hr (top) and 24-hr 1-way traffic volumes

[pic]

Figure 4: Plot of percent difference between model and survey traffic volumes against screenline targets

[pic]

Figure 5: Screenline and traffic count locations

Scatter Plots

Plot surveyed and modelled traffic volumes for roads within the study area. Plots are required for each time period modelled and include 1-way rather than 2-way volumes (see Figure 6). In addition, a map of the survey locations is required to show the coverage of sites (see Figure 5).

Each plot is to be accompanied by the calculation of the best-fit regression line (constrained to pass through the origin) and the coefficient of determination (R²). R² provides a statistical measure of the goodness of fit between the surveyed and modelled traffic volumes whilst the slope of the best-fit regression line through the origin indicates the extent to which modelled values are systematically over or under estimated.

0. Targets: Slope of best-fit regression line between 0.9 and 1.1; and

R² greater than or equal to 0.90

[pic]

Figure 6: Scattered plot of model versus survey 1-way 7-9am volumes

Percent Root Mean Square Errors

The %RMSE statistic provides a good indication of the percent difference between surveyed and modelled volumes. %RMSE is defined as follows:

[pic] (7)

where N = number of count/modelled link pairs

Ma = modelled 1-way volume on link a

Ca = surveyed average 1-way volume on link a

Note the %RMSE is between surveyed and modelled volumes and different from the %RMSE defined in Section 2.1.2 for feedback convergence.

It should be noted however, that the %RMSE tends to be considerably higher for relatively low volume roads and lower for high volume roads (see Table 1).

%RMSE is to be reported for 1-way links for each time period modelled within five volume bins (see Table 1 for recommended format). For urban areas, it was found that the following volume bins are suitable:

0. 2-hr peak period models: 0-1000, 1000-2000, 2000-5000, 5000-10000 and 10000+

0. 24-hr models: 0-5000, 5000-10000, 10000-25000, 25000-50000 and 50000+

For regional towns, other volume bins can be used. For small regional towns or study areas, there may not be enough data to report the %RMSE in volume bins. In this case, it is suffice to report a single overall %RMSE.

0. Target: %RMSE < 30%

Table 1: Percent root mean square error

|7-9am 1-way volume |Number of sites |Sum of survey volumes (103) |Sum of (model-survey)² (106) |%RMSE |

|0-1000 |42 |17 |4 |78 |

|1000-2000 |48 |71 |12 |34 |

|2000-5000 |21 |57 |8 |23 |

|5000-10000 |3 |21 |1 |9 |

|10000+ |4 |50 |11 |15 |

|All |118 |216 |35 |30 |

Travel Time

Compare surveyed and modelled travel times for each modelled period and direction. Travel times should be validated by comparing surveyed travel times over the modelled peak time interval (as measured over a minimum of three days), with those calculated by the model. For peak-period surveys, it is recommended that a number of travel time measurements be repeated for each route on any given day, rather than a single drive-through at the same commencement time each day. In cases where modelling applies to a 24-hr period, travel time comparisons may not be practical.

Modelled and observed journey times along the survey routes should be plotted using cumulative time-distance graphs as shown in Figure 7. This can help in model calibration and validation as it provides a convenient way of identifying the location of any anomalies in the calculation of link delays.

In addition, the routes should be identified on a map (see Figure 8). If the travel time is measured only for one direction, the direction should be indicated in the map or described in the text or a table.

[pic]

Figure 7: Time-distance graph of survey and model travel time

[pic]

Figure 8: Routes for measuring travel time

The following target, adapted from UK’s Department for Transport (1996), is used for travel time validation:

0. Target: Modelled time within 95% confidence limit of the mean surveyed time > 85% of routes.

The 95% confidence interval for the mean journey time is calculated using the equation:

[pic] (8)

where 1-( = desired confidence interval for the population mean

[pic] = sample mean

[pic] = tabulated t statistic for the desired confidence interval and number

of degrees of freedom (N-1)

s = sample standard deviation

N = number of observations

Values of the t statistic for the calculation of 95% confidence intervals are listed in Table 2.

For degrees of freedom greater than 30, standard statistical tables (available from the Internet or text books) that are consistent with Table 2 can be used.

A model that does not meet the travel time target may still be acceptable if the time-distance graph shows good agreement between the survey and model travel time for most part of the route.

Table 2: Values of the t statistic for calculation of 95% confidence intervals

|Degrees of freedom (N-1) |t0.025,N-1 |Degrees of freedom (N-1) |t0.025,N-1 |Degrees of freedom (N-1) |t0.025,N-1 |

|1 |12.706 |11 |2.201 |21 |2.080 |

|2 |4.303 |12 |2.179 |22 |2.074 |

|3 |3.182 |13 |2.160 |23 |2.069 |

|4 |2.776 |14 |2.145 |24 |2.064 |

|5 |2.571 |15 |2.131 |25 |2.060 |

|6 |2.447 |16 |2.120 |26 |2.056 |

|7 |2.365 |17 |2.110 |27 |2.052 |

|8 |2.306 |18 |2.101 |28 |2.048 |

|9 |2.262 |19 |2.093 |29 |2.045 |

|10 |2.228 |20 |2.086 |30 |2.042 |

Other Validation Measures

The following sections discuss other measures that can be used for model validation. However, no targets need to be met for these measures.

3 Volume Bandwidth Plot

A volume bandwidth plot should be presented for each modelled period. Volumes in peak and contra-peak directions can be presented in the same plot. Figure 7 shows an example of a volume bandwidth plot; the thicker the bandwidth, the higher the volume. Although not a validation criterion, a volume bandwidth plot shows where the highest traffic volumes are in the network and is a quick reality check on the model.

[pic]

Figure 9: 7-9am 1-way volumes (‘000)

4 Difference Plot of Survey and Model Volumes

A difference plot of survey and model volumes should be presented for each modelled period and direction (peak and contra-peak). Figure 10 shows an example of the difference plot of survey and model volumes. This can help in model calibration and validation as it provides a convenient way of identifying locations where modelled volumes are over or underestimated.

[pic]

Figure 10: Difference between model and survey volumes, 7-9am peak direction

5 Comparison of Survey and Model Volumes on Key Roads

A comparison of survey and model volumes should be presented for the key roads in the study area for each modelled period and direction. Figure 11 shows an example of the comparison. The plot can be used for checking not only the difference between the survey and model volumes but also their trends.

[pic]

Figure 11: Model and survey volumes on Princes Freeway West, 7-9am east bound

6 GEH

The GEH statistic, named after Geoff E. Havers, is an alternative measure to scattered plot to compare survey and model volumes. It is widely used in Australia and overseas. The GEH statistic is defined as:

[pic] (9)

where Ma = modelled 1-way volume on link a

Ca = surveyed 1-way volume on link a

Note the GEH is between surveyed and modelled volumes and different from the GEH defined in Section 2.1.2 for feedback convergence.

Results of scattered plots should always be presented for model validation. Only if the validation criteria for scattered plots are marginally not met, the GEH should be used for model validation.

A good GEH statistic indicates that the model is producing volumes with:

0. low absolute errors on roads with small volume counts (percentage error is not a good indicator of performance against small counts).

0. low percentage errors on roads with large volume counts (absolute error is not a good indicator of performance against large counts).

VicRoads (2008) targets for applying the GEH statistic are that:

0. Targets: 50% of cases have a GEH < 5, and

80% of cases have a GEH < 10

The GEH should be calculated for each modelled period and include 1-way rather than 2-way volumes. Reporting should be in the form of a plot of GEH versus 1-hr volume equivalent (see Figure 12) and percentile data as presented in Table 3. If not being modelled, the 1-hr peak volume may be assumed to equal one half the 2-hr peak volume or one tenth the 24-hr volume.

[pic]

Figure 12: GEH plot of 1-way 1-hr equivalent link volume

Table 3: GEH percentile reporting

|GEH |No. Links |% of Links |

| ................
................

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