Transport related Technical & Engineering Advice and Research Lot 2 Roads

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1 Transport related Technical & Engineering Advice and Research Lot 2 Roads Task 263: Re-validation of Speed Flow Curves Project Sponsor: Peter Grant Package Order Ref: 263(4/45/12)ATK Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 1

2 Highways Agency/DfT Framework for Transport Related Technical and Engineering Advice and Research Lot 2 Task Ref: 263 (4/45/12)ATKS Task Title: Re-Validation of Speed Flow Curves Project Sponsor: Peter Grant Final Report Submitted by: AECOM Limited Notice This document has been produced by ATKINS for the Highways Agency solely for the purpose of the task. It may not be used by any person for any other purpose other than that specified without the express written permission of ATKINS. Any liability arising out of use by a third party of this document for purposes not wholly connected with the above shall be the responsibility of that party who shall indemnify ATKINS against all claims costs damages and losses arising Document History Revision Purpose Description Originated Checked Reviewed Authorised Date 1 Final Report Draft Brian Vaughan Nick Woollett George Lunt Nick Woollett 18 th Sep Final Report including client comments Brian Vaughan Nick Woollett George Lunt George Lunt 24 th October 2014 Contents Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 2

3 Section Page Glossary of Terms 4 1. Introduction Objectives and Aims 5 2. Background and Literature Review Introduction Current COBA Curves and Relationship to Modelling TRL Dual Carriageways and Motorways (1990s) TRL Rural Single Carriageways (1990s) Comparison of Speed Flow Relationships Issues to be Addressed in the Study Methodology Overview of Approach Site Selection Data Sources Analysis Methodology Site Selection and Data Processing Introduction Sites Included Data Availability Database Conversion Process Sample of Final Data Preliminary Analysis Introduction Identification of Sites with Suitable Data Site-by-Site Linear Regression Summary of Findings Regression Analysis by Road Type Introduction Identification of Break Points Dual Carriageways and Motorways Multiple Stepwise Regression Rural Single Carriageways Multiple Stepwise Regression Recommended Speed Flow Curves and Parameters Overview Single Rural Carriageways Dual Carriageways and Motorways Speed Flow Curve Comparisons Power Curves Areas for Future Research Summary and Conclusions 96 Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 3

4 Glossary of Terms Terms used in Speed / Flow Curve Formulations V L0 / V H0 V L / V H Q Q B The free flow speed of light and heavy vehicles respectively (kph) The speed of light and heavy vehicles respectively (kph) Traffic flow. Within this report, units include: vehicles per hour, vehicles per hour per lane, pcus per hour and pcus per hour per lane. Breakpoint: the value of Q at which the speed / flow slope of light vehicles changes in existing COBA curves. For the new speed / flow relationships defined within this report, Q B represents the point where lane density is such that drivers begin to be constrained by slower moving vehicles and speeds start to drop more rapidly Q C Q F Slope Capacity flag: defined as the maximum realistic value of Q For the new speed / flow relationships defined within this report: the point at which free flow speeds are no longer maintainable. The gradient of the line indicating the change in speed as over a given flow range for any specified speed / flow curve. Road and Traffic Definitions pcus Passenger car unit, measure assigning car equivalence values to all vehicle types (e.g. a value of 2.5 is applied to heavy vehicles in this report). Heavy vehicles For the purposes of this report a heavy vehicle is considered to be any vehicle over 6.6m in length (as classified by the automatic counters used on the Highways Agency s network) Road type The following Highways Agency link types are included in the report: Class 1 S2 rural single carriageways; Class 2 D2AP rural 2-lane all-purpose dual-carriageway; Class 3 D3AP rural 3-lane all-purpose dual-carriageway; Class 4 D2M rural 2-lane motorway; Class 5 D3M rural 3-lane motorway; Class 6 D4M rural 4-lane motorway. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 4

5 1. Introduction AECOM is pleased to submit this Final Report following work with the Highways Agency to review the current speed / flow relationships on Highways Agency roads and update the current COBA speed / flow curves that are used to forecast average hourly vehicle speeds based on a link s traffic flow and geometric parameters, primarily used in traffic models. For this commission AECOM is taking the technical lead on this project on behalf of Atkins. The existing curves are specified in the Design Manual for Roads and Bridges, Volume 13 Economic Assessment of Road Schemes, Section 1 the COBA Manual, Part 5 Speeds on Links (Highways Agency, May 2002). The inception and technical workshop meeting on the 11/02/2014 included a wide ranging discussion around the project specification, the project data requirements and the required outputs of the task. These requirements were summarised in the Scoping Report submitted to the Agency on 27 th February A second technical workshop took place on the 24 th July and focussed on the initial outcomes of the analysis and the proposed approach to concluding the research and updating the speed / flow relationships. This report summarises the basis of the work undertaken, describes the process undertaken to select sites, collate data and analyse speed / flow relationships by road type for the selected links. The remainder of this report is structured as follows: Section 2: Background and Literature Review; Section 3: Methodology; Section 4: Site Selection and Data Processing; Section 5: Preliminary Analysis; Section 6: Regression Analysis by Road Type; Section 7: Recommended Speed / Flow Curves and Parameters; Section 8: Areas for Future Research; 1.1 Objectives and Aims Section 9: Summary and Conclusions. The project objectives as set out in the Highways Agency s task specification are as follows: 1. To update the speed-flow curves for each road type on the HA network to be based on average link speeds (not spot speeds) and link traffic flows; 2. To identify whether it is statistically significant to include link length within the speed flow relationship; and 3. To provide guidance on the statistical accuracy of the speed flow relationship for each set of discrete flow ranges. The road types on the HA network are specified in Table 1.1 below. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 5

6 Table 1.1 The HA s Road Classes in COBA COBA Road Class Road Type Description 1 S2 Rural single carriageway 2 D2AP Rural all-purpose dual 2-lane carriageway 3 D3AP Rural all-purpose dual 3 or more lane carriageway 4 D2M Motorway, dual 2-lanes 5 D3M Motorway, dual 3-lanes 6 D4M Motorway, dual 4 or more lanes In addition to the six road types listed above, data were obtained for a small number of Smart Motorway links (representing sections of the motorway network with one or both of the following features: controlled motorway and hard-shoulder running. The motivation for the review and update to the existing COBA relationships is a desire from the Highways Agency to improve highway models. In particular, to reduce the costs of modelling by improving the speed / flow relationships applied within models so that the calibration and validation of models to observations is a less time intensive task. By identifying the individual factors that dictate how speeds vary as flow changes across a wide range of link types the hope is that less local calibration of the models is required as the relationships defined are more accurate across a wide range of parameters. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 6

7 2. Background and Literature Review 2.1 Introduction This section summarises the background to the research undertaken in this project. section is structured as follows: The Current COBA Curves and Relationship to Modelling a discussion of the existing COBA relationships and how they are applied in UK modelling and economic appraisal; TRL Dual Carriageways and Motorways (1990s) a short literature review of the TRL research on road classes 2-6; TRL Rural Single Carriageways (1990s) - a short literature review of the TRL research on road class 1; Comparison of Speed Flow Relationships a comparison of the existing COBA relationships with other commonly used relationships; Issues to be Addressed in the Study a summary of the issues identified in the preceding sub-sections which need to be considered in this study. 2.2 Current COBA Curves and Relationship to Modelling The current COBA speed flow curves for Classes 1 6 were derived in studies published by TRL in 1992 and Since then these curves have been used extensively in transport modelling and economic appraisal. The existing curves are piecewise linear formulations with a minimum speed cap which applies to flows at a point beyond the calculated capacity of the highway. Two-types of parameter influence the relationship between speed / flow for each road class: The proportion of heavy vehicles in the total traffic flow; and Various geometric parameters (e.g. hilliness and bendiness). Figure 2.1 shows typical curves for single carriageway roads for three design standards (assuming 15% heavy vehicles). There is a reduction in speed as flow increases towards a breakpoint (varying between approximately 900 and 1,200 vehicles per lane) and then a steeper rate of decline as flows further increase. 1 Class 1: Transport Research Laboratory, Department of Transport Contractor Report 319, Speed/Flow/Geometry Relationships for Rural Single Carriageway Roads, 1993 Classes 2-6: Transport and Road Research Laboratory, Department of Transport Contractor Report 279, Speed/Flow/Geometry Relationships for Rural Dual-Carriageways and Motorways, 1992 Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 7

8 Kph Task Ref: Task 263(4/45/12) Figure 2.1 Existing COBA Speed / Flow Relationships for Class ,000 1,200 1,400 1,600 1,800 2,000 Vehicles / hour / lane TD9 10m TD9 7.3m Non TD9 7.3m Note: Curves use bendiness of 75 degrees per km, hilliness of 15 m per km and 15% heavy vehicles. Figure 2.2 shows typical curves for dual two carriageways and motorways. There is a gentle reduction in speed as flow increases towards the breakpoint (of approximately 1,200 vehicles per lane) and then a steeper rate of decline as flows further increase. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 8

9 Kph Task Ref: Task 263(4/45/12) 120 Figure 2.2 Existing COBA Speed / Flow Relationships for Classes ,000 1,500 2,000 2,500 Vehicles / hour / lane D2AP D3AP D2M D3M or D4M Note: Curves use bendiness of between 20 and 30 degrees per km, hilliness of 15 m per km and 15% heavy vehicles. Historically the curves have been applied in UK scheme economic appraisal using the COBA software. In these cases a COBA model is constructed using traffic flow outputs from a traffic model or other source and the speed / flow relationships are defined within the COBA software by measuring the geometric characteristics of each modelled link to ensure that the curves are calibrated to the COBA standard. This approach is now rare, as COBA economic appraisal is limited to fixed-trip matrices and the majority of current appraisal requires a more sophisticated approach where demand varies according to a number of mechanisms including time period choice, mode choice and destination choice. UK appraisal usually now requires TUBA which uses matrix-based outputs from transport models to calculate travel time savings and other user benefits. Many highway assignment models make use of the COBA curves as a reference for the speed / flow curves specified within the modelling software; however, a number of observations should be made: The formulations used within highway assignment software packages differ from the COBA specification requiring a fitting of the functional form within the software to the COBA specification (for example, SATURN 2, the most frequently used highway assignment package in the UK, has a power formulation for speed / flow relationships). To achieve a good degree of convergence in the highway assignment ideally requires a continuous functional form and this is an important driver in adopting power 2 SATURN (Simulation and Assignment of Traffic to Urban Road Networks) is a suite of flexible network analysis programs developed at the Institute for Transport Studies, University of Leeds and distributed by Atkins since Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 9

10 formulations in SATURN. Similar functional forms have been developed such as the Bureau of Public Roads (BPR) 3 and Akcelik 4 curves; The complexity and detail of traffic models means that speed / flow curves are not usually calibrated by measurement of the detailed geometric characteristics of links as defined in COBA, but by some other classification system, usually based upon a broader definition of link type using the road standard and an indicator of design standard/condition; Although the existing COBA formulations define light and heavy vehicles separately at the input stage, the resulting COBA curve is an all vehicle average relationship. Consequently, traffic models tend to apply a curve for all vehicles with a simplistic reduced maximum speed applied to heavy vehicles. Separately specified speed / flow relationships for light and heavy vehicles would be an enhanced approach in terms of the realism of traffic models. 2.3 TRL Dual Carriageways and Motorways (1990s) The 1990 study into speed flow relationships on rural single carriageways was designed to update the COBA relationships that had been developed back in 1977/78. The 1990 work was approached as a periodic update rather than a fundamental review and as such it drew heavily on existing knowledge. Thirteen separate links were identified for inclusion in the study comprised of: One D4M site; Five D3M sites; Two D2M sites; and Five D2AP sites. The travel times on the links were obtained by moving observer techniques and covered 16 hours of observations at each site. The links were selected to avoid any junction effects, and the travel time data was filtered to eliminate any incidents and blocking back effects. Aggregating the data into 10 minute bands resulted in around 30 speed/flow observations per link and a relatively small sample of 755 observations in total across all the links. Due to the small sample size and limited number of links by road type a number of issues were identified with the data including: An absence of observations at low flow: the majority of speed data was collected for flow levels of 500 2,000 vehicles per lane. This was a particular problem for the motorway sites, as shown in Figure 2.2, in that there were almost no observations in the expected free flow part of the curve; Significant scatter in the data due to the small sample sizes; and Potential for correlations due to the small number of sites in relation to the number of variables to be estimated. This meant that the data was pooled across the sites as within-road type analyses could not really be supported by the data. 3 The BPR equation was originally fitted to the 1965 Highway Capacity Manual freeway speed data; 4 The Akcelik equation was derived by Akcelik from the steady state delay equation for a single channel queuing system. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 10

11 At the outset the study determined that there was no evidence to support a move away from the existing two part COBA relationships, and as such adopted the existing COBA Q B (Q B is the flow at which the gradient of the existing COBA speed / flow curves increase) values of 1,080 vehicles per hour per lane and 1,200 vehicles per hour per lane for D2AP and motorway sites respectively. All subsequent analyses were undertaken based on this assumption. The absence of low flow data observations would have meant it would have been very difficult to examine whether more complex relationships actually existed. The absence of low flow data also caused problems in defining the intercept points and this resulted in the existing COBA slope values to Q B of for light vehicles and zero for heavy vehicles being imposed on the analysis. The main findings from the study were: That light and heavy vehicle speeds had increased significantly since the 1977/78 study; A significant change had taken place in the effect of hilliness on light vehicle speeds: this now had a much reduced impact; That the extent of scatter led to wide variance in the estimation of the slope from Q B to Q C by site of to which made definitive conclusions difficult; and Bendiness and rises were shown to be the most significant contributors to explaining variation in light vehicle speeds. The recommended light vehicle speed flow relationship was: V L = C 0.12 * Bendiness * Rises * Q L * Q L with C defined as follows: D4M = 124kph D3M = 118kph D2M = 111kph D2AP = 108kph where V L = light vehicle speed; and Q L = total vehicle flow per lane. The recommended heavy vehicle speed flow relationship was: V H = * Bendiness * Rises * Q L 7 * D2AP where V H = heavy vehicle speed; and Q L = total vehicle flow per lane The study outputs were such that it was concluded that there was minimal empirical evidence to make significant changes to the COBA curves. The following scatter plots of the data observations available in the study show the limitations with which the study was presented. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 11

12 Figure 2.2 Scatter Plots of TRL 1990 Data for D2M/D3M/D2AP Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 12

13 2.4 TRL Rural Single Carriageways (1990s) Work was undertaken in 1991/2 to review and update, as necessary, the COBA curves on rural single carriageways that had been derived from a study in The study used registration number plate matching to obtain a large sample of vehicle speeds, as opposed to all earlier work that used moving observer methods which restricted sample sizes. This resulted in almost 146,000 speed measurements across the 42 sites chosen for use in defining the speed flow relationships. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 13

14 The vehicle speeds were aggregated to ten minute intervals, as in previous studies, and this led to the development of a database of speed/flow observations of 3,649 light vehicles and 3,624 heavy vehicles. With the higher sample size, more robust estimates of speeds in each ten minute slot (due to an average of 40 observations in each period) and wider coverage of sites, the study was able to explore a wide range of variables including: BENDS Bendiness; HS - Continuous metre hardstrip; CONSTRIP - Continuous 0.3 metre hardstrip; CONEDGE - Continuous edge lining; SWIDTH - Hardstrip width; SFLOWL - Same direction light veh. Flow; JCNS Intersections; NEW - Modern, designed road; SFLOWH - Same direction heavy veh. Flow; CWIDTH - Carriageway width; REGION - Regional variable; NETGRAD - Net gradient; FIELDS - Field entrances; OFLOWA - Opposite direction total flow; PEAK - AM or PM peak period; VISI Visibility; VERGE - Verge width; RAIN Rainfall; RISES - Upgrade metres; FALLS - Downgrade metre; LAYBYS - Lay-bys; TOTHILL - Total upgrade and downgrade metres; v1 - Light vehicle speed; Vh - Heavy vehicle speed; P - Proportion of heavy vehicles; and F - Total vehicle flow. Not all the variables in the above list were considered appropriate for application in the appraisal of road schemes (e.g. rainfall, region, day of week, time of day etc.) and these were excluded from the final recommended relationships. This led to the following recommendations for the variables and the coefficients that were most appropriate for application. After the recommended set of coefficients had been determined the constant term was recalculated so as to provide the closest replication of the speeds observed for each class of vehicle. The final recommended formula for light vehicle speeds was: V L = (( (0.075 x NEW)) x BENDS) - ( x ((RISES+FALLS) x BENDS) ) - (0.11 x NETGRAD) [one-way links only] - (( (0.027 x P)) x F) + (2.0 x CWIDTH) + (1.6 x CONEDGE) + (1.1 x SWIDTH) + (0.3 x VERGE) - (1.9 x JCNS) + (0.005 x VISI) Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 14

15 The recommended formula for heavy vehicles was: V H = (( (0.10 x NEW)) x BENDS) - (0.07 x (RISES+FALLS)) - (0.13 x NETGRAD) [one-way links only] - ( x F) + (0.3 x VERGE) - (1.1 x JCNS) + (0.007 x VISI) These formulae revealed that light vehicles are more influenced by flow and geometric effects than heavy vehicles which are more constrained by vehicle performance. Bendiness is the most important determinant of speed for both light and heavy vehicles although its impact is substantially reduced on modern, designed links (no bendiness effect was discerned for heavy vehicles on such links). Hilliness and net gradient are important speed determinants for heavy vehicles. Carriageway width has an impact on light, but not on heavy, vehicles. The provision of continuous edge lining, if in both directions, adds 1.6 km/h to light vehicles speeds. Continuous hardstrips, an element not currently incorporated within formulae, appear to increase light vehicle speeds by some 1.1 km/h for each metre of width (averaged over both directions). Verge width and intersections both influence speed although other forms of accesses do not have a significant effect. Visibility also affects speed. The above formulae form the basis for the current COBA curves for rural single carriageways with minor modifications having been made, resulting in the following formulations. The current COBA formula for light vehicle speeds is: V L = x BENDS x (RISES+FALLS) x BENDS x NETGRAD [one-way links only] - (( (0.027 x P)) x F) x CWIDTH x VERGE -(1.9 x JCNS x VISI The current COBA formula for heavy vehicle speeds is: V H = x BENDS x (RISES+FALLS) x NETGRAD [one-way links only] x F x VERGE x JCNS x VISI Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 15

16 2.5 Comparison of Speed Flow Relationships Prior to commencing the study it is informative to compare the current COBA curves with other commonly used speed flow relationships to identify any significant differences that exist. Three alternative speed flow curves have been used for this comparison: The relationships used in FORGE 5 ; Highway Capacity Manual (HCM) 6 relationships for freeways; and The Akcelik curves which are used extensively in Australia and other countries and which are referred to in WebTAG as being a suitable form for determining speeds beyond Q C. Figure 2.3 shows the form of these curves for a typical D3M in comparison to the current COBA curve. In the diagram all of the curves have used a common intercept point for free flow speed so that the profiles can be compared from a common base. The diagram indicates that the COBA curve is steeper up to Q B and that the implied Q B in the other curves is at a higher flow than COBA, around 1,400 veh/hour/lane compared to the COBA value of 1,200 veh/hour/lane. After the Q B point the other curves have a steeper slope and a wider variance on what the speed at Q C is, although the HCM curve is close to the COBA curve speeds at Q C. The diagram also indicates that the non-coba curves represent a period where the free flow speed is almost level, up to about 600 vehs/hour/lane, and that the speed flow curves for motorways may have three sections as follows: A very shallow section where free flow speeds are essentially achievable and which terminates around 600 vehs/hour/lane; A section with gradually decreasing speeds as flow increases up to a breakdown point Q B, and that this Q B may be occurring at a higher flow level than COBA predicts, around 1,400 veh/hour/lane; and A steep decline in speeds beyond Q B to Q C which may be steeper than implied by the COBA slope beyond Q B simply as a result of the later point at which Q B occurs in non- COBA curves. The FORGE, HCM and Akcelik 7 curves have all been updated more recently than the COBA curves and may better reflect the current situation on motorways due to the continuing improvements in the vehicle fleet and its performance. 5 FORGE stands for Fitting On of Regional Growth and Elasticities, it is the highway supply module of the National Transport Model. 6 The HCM is a publication of the Transportation Research Board of the National Academies of Science in the United States. It contains concepts, guidelines, and computational procedures for computing the capacity and quality of service of various highway facilities. 7 The Akcelik equation was derived by Akcelik from the steady state delay equation for a single channel queuing system. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 16

17 Speed (kph) Task Ref: Task 263(4/45/12) Figure 2.3 Comparison of Light Vehicle Speed Flow Formulations (D3M Example) ,000 1,200 1,400 1,600 1,800 Vehicles / hour / lane HCM FORGE COBA Akcelik 2.6 Issues to be Addressed in the Study The preceding sections have identified a number of issues that the current study should be aware of and address directly in order to undertake a thorough review of speed/flow relationships for use in transport models. These are: The need to have a database of speed/flow observations that covers the full flow ranges encountered on each type of road. The TRL studies of the 1990s were unable to collect data at low flows and this presented significant limitations, particularly for dual carriageways and motorways; The need to have an extensive coverage of sites by each road category in order to enable variables to be examined both within road type and across road types to establish whether there are significant differences. Again the TRL work on dual carriageways and motorways had a limited number of sites and had to pool data across road types to undertake any meaningful analyses; That the TRL work in 1991/2 on rural single carriageways was a more robust study due to the significantly higher speed/flow sample base and coverage of sites, 42 in total. The main limitation in this work would again be the absence of low flow data and what the implications of that are for the derivation of the slope to Q B ; and Evidence from other speed/flow relationships, that have been updated more recently than COBA, is that there is a different functional form in that there may be three distinct Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 17

18 parts to the curve to Q C, and that speeds are maintained at a higher level for longer before experiencing a more rapid decline as traffic conditions deteriorate. This also tallies with the work carried out by the HA, which prompted this study, using HATRIS data on D3M links that indicated differences to COBA in the low and high flow ranges. With the availability of extensive real time speed/flow data it is an opportune time to undertake a fundamental review of the speed/flow relationships for use in traffic models. The work should not take current COBA curves as the benchmark but derive appropriate functional forms that are supported by the data. It is also important to bear in mind that the emphasis is on speed/flow curves for use in transport modelling and as such the variables contained in the relationships should be practical ones for the user to collate the necessary information. The research should not produce overly complicated formulations that would place an undue burden on the modelling process as this would be counter to the primary aim of the study. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 18

19 3. Methodology 3.1 Overview of Approach This section sets out the methodology adopted to develop a database and undertake the analysis of speed and flow data for a broad selection of sites across the Highways Agency s network as follows: Site Selection the approach adopted to generate a list of Highways Agency links which are representative of the road types and characteristics required for the study; Data Sources a summary of the key sources of data for establishing the database for the purpose of analysis; and Analysis Methodology the framework adopted to review the data, apply filtering to remove outliers, preliminary regression analysis on each individual site and finally stepwise regression analysis of each road type to produce updated speed / flow relationships. 3.2 Site Selection The purpose of the site selection phase was to identify a set of highway links providing reasonable coverage of all the road types and characteristics which form part of the analysis for this project. The approach adopted is illustrated in Figure 3.1. Figure 3.1 Site Selection Process Bottom-up Analysis Manually select around 300 sites on the Highways Agency networks aiming to: Get an even spread across English Regions; and An even spread across road types. Selection undertaken with an awareness of other analysis parameters such as length and link geometry in order to increase likelihood of good coverage across these parameters. Top-down Review Tabulation of selected sites according to analysis parameters in order to demonstrate sufficient coverage. Revised List of Sites Review sites against available data and produce updated list of sites. Table 3.1 sets out the parameters which were agreed to be included in the analysis during the project scoping stage. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 19

20 Table 3.1 Categories for Site Selection Category English Region Land-Use Road Type Link Length Hilliness and Bendiness Other Class 1 Parameters Heavy vehicle Percentages Category Description Which of the nine English Regions the site lies in Although all of the roads selected are officially rural trunk roads, a categorisation of urban is reported for a number of these indicating that they serve a large conurbation. COBA classes 1-6 and additionally sections of Smart Motorway. Length of the studied link. Hilliness in terms of rises and falls per km and bendiness in terms of degrees per km for all of the selected links. For single carriageways a further assessment of the characteristic of the nature of the road, i.e. categorisation of carriageway width, hard strip and verge. The heavy vehicle percentage of each link at every observation point (could also be described in terms of absolute numbers of heavy vehicles). 3.3 Data Sources The project Scoping Report set out four types of data required to construct a database for the analysis of speed / flow relationships. These are summarised in Table 3.1 Table 3.1 Required Data Types Data Type 1 - Traffic Flow 2 - Journey Time 3 - Category 4 - Exclusion Purpose / Definition To provide information on the flow in the middle of a link. These data need to represent average values across an hour, with the ability to disaggregate by vehicle type and by time of year, day of week and time of day. In selecting links there is a need to ensure that the flow is essentially homogenous along the link within specified tolerances. To provide an average journey time along the length of a link. These data need to represent average values across an hour, with the ability to disaggregate by vehicle type and by time of year, day of week and time of day. It is also desirable that the data has sufficient spatial detail to exclude the sections of a link around a merge / diverge, or on the approach to a junction where the link loses priority. Data sources which enable the selection of sites which provide a representative sample of all of the categories to be included in the study. The categories are discussed in detail below, but for example, this will include link length, geometric parameters, road type and landuse. These data will highlight specific conditions which would require data records to be excluded from the analysis; for example, records of incidents. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 20

21 An investigation into the best available sources of each data type was undertaken at the beginning of the project. Table 3.2 indicates the data sources chosen to cover the four categories listed in Table 3.1. Table 3.2 Data Sources for Analysis Data Source Data Type TRADS (HATRIS) 1 Function for Analysis Source of all traffic flow data for the task. Records are at least hourly, generally categorised into light and heavy vehicles and also often include mid-link spot speeds which are useful for checking / calibration against average speeds. Access Direct access through HATRIS database. TrafficMaster GPS data by ITN link from DfT 2 Source of light / heavy vehicle flows along links mapped to ITN GIS layer. The ITN network is spatially more detailed than the HATRIS network providing a means of removing merge / diverge effects for a majority of links. Access from DfT Congestion team. HAPMS Data 3 Geometric highway data from the HAPMS team. Estimates of radius and change in height approximately every 10m directly mapped to HATRIS links. Access through Highways Agency HAPMS team OpenOS 3 GIS data source used to look at landuse around selected links. Online. GoogleMaps 3 & 4 HATO records 4 Satellite mapping and StreetView for confirmation of number of lanes, confirming consistency of characteristics along selected links. Database of incidents affecting live carriageways and hard shoulders which can be provided by HATRIS link. Online. Access through the Highways Agency Traffic Management Directorate. 3.4 Analysis Methodology The project specification requires an analysis of available data in order to update the following COBA speed / flow parameters for road classes 1-6: V L0, V H0 the initial speed of light and heavy vehicles (kph); Q B the vehicle flow per hour per lane at which the speed / flow slope changes; and V B the speed of vehicles at flow Q B. These parameters (and additionally the capacity (Q C ) and speed at capacity (V C )) are illustrated in Figure 3. (the dashed portion of the line represents the current COBA for flows beyond Q C. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 21

22 Vehicle Speed (kph) Task Ref: Task 263(4/45/12) Figure 3.2 Key Parameters of Existing COBA Speed / Flow Relationships 120 V L V H0 V C ,000 1,500 2,000 2,500 3,000 3,500 4,000 Q B Q C Vehicles / hour / lane / direction Light Vehicles Heavy Vehicles All Vehicles The approach to analysis has been divided into three distinct sections: Identification & Filtering reviewing the data for each selected site in order to establish the availability and suitability of the data for analysis. Application of filtering to remove elements of the data not suitable for analysis; Preliminary Analysis applying linear regression to the data on a site-by-site basis and producing tabulations of the emerging free flow speeds, flow breakpoints etc by road type; and Regression Analysis by Road Type undertaking stepwise linear regression on all the filtered data for each road type using the outputs from the preliminary analysis to assist with the establishment of models. The stepwise regression is applied to establish which independent variables are significant and thereby produce the final statistical models to evaluate speed / flow relationships. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 22

23 4. Site Selection and Data Processing 4.1 Introduction In this section we have set out the approach used to select a representative set of highway links for analysis and how these data were processed and compiled to form the study database under the following headings: Sites Included summarises the sites included in the database which have been directly used in the analysis; Data Availability summarises the results of compiling data sources in terms of the number of sites where sufficient data were available to undertake analysis; Database Conversion Process describes the processes used to collate and process the data sources to form the project database; and Sample of Final Data summarises the categorisation of the sites used in analysis in order to demonstrate the suitability of the dataset for calculating speed / flow relationships. 4.2 Sites Included The application of the methodology described in Section 3 resulted in a final set of 127 links for analysis (initially 292 sites were selected. Of these 189 had overlapping average speed and flow data, and once a full review of all sites had been undertaken 127 suitable sites remained). Figure 4.1 illustrates the location and road type of the final 127 links (Appendix A contains a larger version of this map). Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 23

24 Figure 4.1 Map of HATRIS Sites used in Study Analysis Figure 4.1 illustrates that good geographical and road type coverage has been achieved. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 24

25 4.3 Data Availability The initial list of 292 sites only included sites where the TRADS counter providing flow information was active. Theoretically, the DfT journey time data were available on all HATRIS links for the 2011/12 and 2012/13 school (September August) years (and so in principal each of these sites should contain the basic data necessary to produce a local plot of average speeds against vehicle flows. However, in reality there were a number of sites where this was not possible, because: The available date ranges where speed and flow data were available did not overlap; or The TRADS data did not provide classified count information (disaggregation between light and heavy vehicles). The sites mapped in Figure 4.1 include filtering to remove sites where there was no successful match of speed and flow data. The most common reason for this is a lack of overlapping time periods when both speed and flow data were available. 4.4 Database Conversion Process The project methodology requires that a database is developed to hold all of the project data in such a way that queries can be run to extract data for an individual site or a sample of sites according to certain criteria in terms of the road type, geometric parameters etc. The following steps were applied to the raw data in order to develop this database: Processing of raw data into the required format; Linking of all data to a common field, the HATRIS link reference; Establishing a summary data table containing each site and all of its characteristics; Developing a query tool to extract data for sites based upon a filtering of the summary table. Table 4.1 outlines how each of the four principal datasets were processed and indexed with a HATRIS link reference to allow the data to be linked within the database. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 25

26 Table 4.1 Data Processing and Indexing Data Source Data Processing Undertaken Indexing Data to HATRIS TRADS DfT Journey Time Data HAPMS Converting all data to hourly intervals, compiling single data file for each site from the individual day reports downloaded Aggregating vehicle categories into light and heavy vehicles. Filtering of data by HATRIS link to remove sections of the link where the road characteristic or flow level changed compared to the location of the applicable TRADS site. Further segmentation of remaining link to identify sections close to merges / diverges and junctions. Filtering of link sections to match the sections resulting from the processing of the DfT journey time data. TRADS site locations mapped against HATRIS links in GIS and matching undertaken. Manual check of matching using site descriptions. Matching of ITN link data to HATRIS network using a Dijkstra 8 algorithm based upon the closest start and end node and manually checked against link descriptions, direction and overall length. HAPMS data provided by HATRIS link. Calculation of bendiness and rises & falls from the raw data to derive values for each site. HATO No processing required. HATO data provided by HATRIS link. The summary data table produced for the front-end of the database outlines all of the key characteristics of each selected site, both in terms of the parameters for analysis, and in terms of describing the link and referencing the various components of data which are required to produce the analysis. Figure 4.2 contains a small portion of the summary table as an indication of the structure. 8 Dijkstra s algorithm is a graph search algorithm which solves the single-source shortest path problem for a graph producing a shortest path tree. It is therefore a useful tool in establishing the shortest path through transport networks. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 26

27 Road Name Location Figure 4.2 Illustrative Sample of the Summary Data Table Direction HA Region Road Type Road Type Description Lanes Total Length (km) Selected Length (km) Finally, a query tool has been developed which allows the extraction of data dependent upon the categorisation of any of the data analysis parameters or for an individual site. This tool provides the flexibility to extract data for any required combination of sites. A screenshot from this tool is shown in Figure 4.3 overleaf. Length of Merges (km) Length of Diverges (km) Speed Limit (kph) Carriageway Width Category Day Time HGV% Category Night Time HGV% Category Average Weekday Hourly Flow (PCUs) per lane A1(M) Junction Southbound 8 D3M Motorway, du m Low (0-10%Low (0-10% A1(M) Junction Northbound 8 D3M Motorway, du m Low (0-10%Low (0-10% 1, M11 Junction 7-8 Northbound 8 D3M Motorway, du m High (> 20%High (> 20% 1, M11 Junction 7-8 Southbound 8 D3M Motorway, du m High (> 20%High (> 20% 1, M180 Junction 2-3 Westbound 12 D3M Motorway, du m High (> 20%High (> 20% M18 Junction 2-1 Eastbound 12 D3M Motorway, du m Average (1High (> 20% 1, M18 Junction 1-2 Westbound 12 D3M Motorway, du m Average (1High (> 20% 1, M1 Junction Northbound 8 D3M Motorway, du m Average (1High (> 20% 1, M20 Junction Westbound 4 D3M Motorway, du m Average (1Average ( M20 Junction Eastbound 4 D3M Motorway, du m Average (1Average ( M23 Junction 8-9 Southbound 4 D3M Motorway, du m Low (0-10%Low (0-10% 1, M25 Junction Anticlockwise 5 D3M Motorway, du m Average (1High (> 20% 1, M25 Junction Clockwise 5 D3M Motorway, du m Average (1High (> 20% 1, M3 Junction 4a-5 Southbound 3 D3M Motorway, du m Low (0-10%High (> 20% 1, M3 Junction 5-4a Northbound 3 D3M Motorway, du m Low (0-10%High (> 20% 1, M40 J11-J12 Southbound 8 D3M Motorway, du m Low (0-10%Low (0-10% 1, M40 J11-J12 Northbound 8 D3M Motorway, du m Low (0-10%Low (0-10% 1, M40 J6-J7 Southbound 8 D3M Motorway, du m Low (0-10%Low (0-10% 1, Bendiness (degrees per km) Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 27

28 Figure 4.3 Database Query Tool 4.5 Sample of Final Data This section presents a summary of the coverage of the analysis variables across all of the final 127 sites selected for analysis. The summary indicates that good coverage has been obtained across each category; commentary is provided for each table. Table 4.2 summarises the distribution of sites by road type and English Region. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 28

29 Table 4.2 Number of Sites by Road Type and English Region Road Yor & E of NE NW EM WM Class Hum Eng Lon SE SW Total S D2AP D3AP D2M D3M D4M Total Table 4.2 indicates that in general good coverage has been achieved by road type with the following observations: The number of D3AP and D4M sites is lower than the target, particularly for the D3AP category: o o This reflects the fact that the D3AP category is relatively rare and also that although a larger number of D3AP sites were included in the initial list of sites, initial analysis indicated that a number were not suitable for analysis (for example, one site had a 50 mph speed limit applied); The small number of sample D4M sites also reflects the small number of possible sites available. Additionally, many of these have been or are in the process of being converted into some form of smart motorway. Furthermore, a number of D4M sites were ruled out as they operate in congested conditions for large periods of a typical weekday and would therefore yield a limited amount of suitable data for our analysis. A number of smart motorway sites were included in the initial list of sites; however, of these only two sites presented useable data (one was controlled motorway and the other hard-shoulder running) and this was not considered sufficient to undertake any meaningful regression analysis. It is worth noting that a review of these two sites indicated that the speed / flow relationships reflected those of a D4M category road. Table 4.3 summarises the distribution of sites by road type, urban / rural classification and the length of the analysis section. Table 4.3 Number of Sites by Road Type and English Region Road Length (km) Urban Rural Class Total S D2AP D3AP D2M D3M D4M Total Table 4.3 indicates that in general good coverage has been achieved by urban / rural classification and across a range of link lengths: The urban / rural classification was designed to identify sites as urban when they were located in proximity to a large urban area (with population > 250,000) and provided direct access to this urban area (note this definition of urban / rural is bespoke to the study and is a different definition than the urban / rural roads definition outlined in Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 29

30 COBA. All of the sites included in the study are considered rural roads under the COBA definitions); In general links with length less than 2km were avoided in the initial site selection, in line with the methodology TRL applied in the 1990s studies. One D2AP link has a length of less than 2km. Table 4.4 summarises the distribution of sites by road type and bendiness and hilliness. Table 4.4 Number of Sites by Road Type and Bendiness and Hilliness Bendiness Hilliness Road Class Straight (0-30 deg/km) Moderate (30-60 deg/km) Bendy (>60 deg/km) Flat ( m/km) Rolling ( m/km) Hilly (>45 m/km) S D2AP D3AP D2M D3M D4M Total Table 4.4 indicates that in general good coverage has been achieved across the categories of bendiness and hilliness, except for a lack of sites categorised as bendy: The category bandings reflect the range of expected values reported for Classes 2-6 (dual-carriageways and motorways) in the COBA manual, with the Bendy and Hilly categories representing values above the maximum expected value for these road types. On the basis of the above it is therefore not unexpected that there are no bendy sites in the Class 2-6 roads. A number of sites categorised as Bendy were selected initially amongst the S2 and D2AP categories, but none proved appropriate to be included in the analysis. In general there are a limited number of hilly trunk road sites in England to study. A number of additional sites with higher gradients were included in the initial site list; however, a lack of data in some of these locations has further limited the pool of available sites. Table 4.5 summarises the distribution of sites by road type and daytime (weekday ) HGV percentages. Table 4.5 Number of Sites by Road Type and Daytime HGV Percentage Road Class 0-10% 10-15% 15-20% > 20% Total S D2AP D3AP D2M D3M D4M Total Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 30

31 Table 4.6 summarises the distribution of sites by road type and night-time (weekday ) HGV percentages. Table 4.6 Number of Sites by Road Type and Night-time HGV Percentage Road Class 0-10% 10-20% 20-30% 30-50% > 50% Total S D2AP D3AP D2M D3M D4M Total Tables 4.5 and 4.6 indicate a good coverage across a range of HGV percentages for both daytime and night-time. The range of percentages encountered can be considered typical for the majority of UK highway links. In summary, the review of site selection in terms of coverage across the various analysis parameters indicates that a good range of sites has been achieved in order to undertake stepwise linear regression with these data, having a sufficient number of observations and range of variance in the analysis parameters. However, there is a need to consider the particular nature of each road type; for example, it does not make sense to consider the significance of large ranges of bendiness and hilliness on D4M roads given the limited values included within the study dataset for this road type. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 31

32 5. Preliminary Analysis 5.1 Introduction This section describes the preliminary analysis undertaken using the project database under the following headings: Identification of Sites with Suitable Data describes the review of each site s data in order to ensure its suitability for inclusion in the analysis; Site-by-Site Linear Regression outlines the approach to preliminary analysis which consisted of applying linear regression to the data for each individual site selected for analysis; and Summary of Findings presents the results of the individual site regression analysis in terms of the emerging key parameters (free flow speed, gradient to Q B, Q B, gradient to Q C, and a review of Q C ). 5.2 Identification of Sites with Suitable Data The analysis has been structured in order to ensure that the speed / flow data at each individual site has been reviewed by an analyst and a regression applied prior to these data being compiled with other sites for the stepwise regression. This approach ensures: Any anomalies in the individual site data can be identified; and A comparison of individual site regressions across each road category can be made for the purposes of estimating initial free flow speeds and flow break points. An analysis tool was developed specifically for this purpose. The tool allowed plotting of any sites data and included various tools to identify where any data were not suitable for analysis: Where available the spot speeds from the TRADS data were plotted against the average speed data to highlight any periods where substantial differences occur; An average weekly speed plot is produced to highlight any periods where changes to long-term average speeds occur representing events such as road works, flooding or other major incidents; Separate scatter plots of light and heavy are available to highlight observations which have occurred beyond the capacity of the link, and also as a check that the link in question operates at the national speed limit for the road type. Once an analysis of a site s data has been undertaken using these tools filters are provided to remove, where possible, observations which are not appropriate for the required outputs of this study, that is: Observations occurring beyond the capacity of the link in question; Observations from a period when an incident occurred (using the HATO reference data); Observations where roadworks or another event resulted in the road operating at a reduced speed limit; In some cases the review of a site s data resulted in a decision to remove the site from the analysis because the permanent speed limit of the site was not the national speed limit, the flow data are only available categorised as all vehicles (it is not possible to identify light and heavy vehicles separately). Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 32

33 The completion of the filtering exercise across all sites reduced the number available for analysis from 189 to 127. Figure 5.1 Screenshot of Part of the Site Analysis Tool 5.3 Site-by-Site Linear Regression The site analysis tool provides a facility to undertake linear regression on each site s data, splitting the flow into 50 pcu 9 flow bands per lane and producing separate linear relationships for light and heavy vehicles. In each case the linear regression assumes a piecewise relationship with two parts as defined in the existing COBA relationships. The point Q B at which the fit transitions between the first and second parts of the speed / flow relationship is iterated separately for light and heavy vehicles across a wide range of flows in order to identify the best fit location. The regression tool is flexible and allows application of least absolute error or least squares to either the median or mean speed value in each flow band. A cut-off for the minimum number of observations in any flow band is used to ensure that the results are not skewed by a small number of outliers. For the purposes of this study least absolute error was applied to the median values (which are considered to be less skewed by outliers in the data than the mean). Figure 5.2 Example Linear Regression of Data for a D2M Site Note: horizontal axis: flow in pcus per hour per lane, vertical axis: speed in kph. The results of each site s regression have been compiled by road type in order to provide an indication of the range of values of the free flow speed, flow breakpoint and the gradient of both parts of the fitted speed / flow relationship. This summary has been used for two purposes: To gain an appreciation for the range of values within each road type; and To develop an initial set of parameters for use in the stepwise linear regression to identify the final speed / flow relationships. 9 For the purposes of this study heavy vehicles have been assigned a pcu factor of 2.5. This value is in line with the guidance for the application of speed / flow curves in models as set out in WebTAG Unit M3.1 and D.7. Re-Validation_of_Speed_Flow_Curves_Final_Report Final.docx Page 33