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ScienceDirect Procedia Engineering 111 (2015) 522 – 529
XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP) (TFoCE 2015)
Traffic flow modeling based on the ISOHDM Study Jan Mikolaja, Lubos Remeka* b
University of Zilina, Univerzitna 8215/1, Zilina 01001, Slovakia
Abstract The article deals with impacts of road capacity on traffic speed and road user costs. Calculation of free speeds and operating speeds in the Highway Design and Management HDM-4 model are explained. In a case study, decrease of traffic speeds and increase of road user costs are observed if free flow capacity, nominal capacity and ultimate capacity is changed. Methodology for Annual Average Daily Traffic recalculation into passenger car space equivalent/lane/hr is explained. The article gives an insight into traffic flow modeling based on the ISOHDM study. © 2015 The Authors. Published by Elsevier B.V. © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil (http://creativecommons.org/licenses/by-nc-nd/4.0/). Engineering (24RSP) under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP) Peer-review Keywords: Traffic flow, HDM-4, ISOHDM, Free speed, Operating speed.
1. Introduction Decision based processes in road management are mostly based on economic analysis. Only rarely a road infrastructure is so viable that it should be constructed to provide a financial gain for its administrator. However, the road infrastructure is administered by a public authority which main aim is to provide civil services for the inhabitants of a given country. From this point of view, the administrator, funded by the public, is obligated to ensure smooth, safe, comfortable and environmental friendly transport in his area of competence. The decision of how to allocate his limited budget is thus based on the social effects the investment entails. The positive difference between state without the investment and with the investment is called socio-economic benefit − provided the difference is positive which should be the point in the first place. These socio-economic benefits may be direct – benefits for road infrastructure
* Corresponding author. Tel.: +421-41-513-5863; fax: +421-41-5135-510. E-mail address:
[email protected]
1877-7058 © 2015 Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license
(http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of organizing committee of the XXIV R-S-P seminar, Theoretical Foundation of Civil Engineering (24RSP)
doi:10.1016/j.proeng.2015.07.126
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users and indirect – environmental benefits, gross domestic product growth, regional development decrease of unemployment, etc. Traffic speed, having direct impact on travel time demands and vehicle operating costs, is a viable indicator of transportation quality and also economic benefits when evaluating acquisition of a new road infrastructure. Many factors influence traffic speed: traffic data – intensity and composition of traffic, road capacity, horizontal and vertical alignment, overtaking possibilities, and pavement quality. Free speed is a theoretical speed of particular vehicles moving on a road section un-influenced by other traffic. Operating speed is the real speed of vehicles in given conditions including other vehicles in the traffic flow. The results of economic analyses are quite sensitive especially to traffic data, and most benefits that justify road improvements arise from savings in road user costs. The representation of traffic needs to be at an appropriate level of detail for any meticulous economic evaluation. This article describes methods for traffic speed calculation based on the ISOHDM study. Calculation of free speed is described, consecutively, method for operating speed calculation is shown. 2. Vehicle free speed Free speed is a theoretical speed of particular vehicles moving on a road section un-influenced by other traffic. [1] The calculation of free speed in HDM-4 is based on mechanistic-behavioral model. The mechanistic model predicts forces opposing motion of the vehicle.
Fg
Fi Fa
Fr Ftr Fig. 1. Forces acting on vehicle. Ftr - tractive force; Fa - aerodynamic drag resistance force; Fg - gradient resistance force; Fr - rolling resistance force; Fi - inertial resistance force.
The premise is that when the tractive force, empirically defined for particular vehicles, is in balance with forces opposing motion the vehicle drives with a constant speed, when those forces are greater the vehicle decelerated, when tractive force is greater the vehicle accelerates. This equilibrium is one of constrains limiting free speed of a vehicles, other being limiting curve speed and road speed limited by pavement roughness. The behavioral model predicts driver’s desired speed – a speed limited by economic and safety consideration of travel. This speed is mostly influenced by gradients, curvature, road width and enforced speed limit. Driver’s desired speed is, together with forces acting on vehicle equilibrium main constraining free speed limit. The whole calculation procedure is too complex to list, but the main formula (1) and graphical example of its use are presented in equation 1 and chart on picture 1. [2]
Vfs
ªV 2 º exp « » ¬ 2 ¼ 1 1 1 1 1 ª º E E E E § · 1 1 1 1 § · § · § · § 1 ·E » « ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ «¨© Vdrive ¸¹ © Vbrake ¹ © Vcurve ¹ © Vdesir ¹ » © Vrough ¹ »¼ ¬«
E
(1)
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Where, Vdrive Vbrake Vcurve V rough Vdesir σ,β
free speed limit by engine force (for uphill drive) [m/s], free speed limit by brake force (for downhill drive) [m/s], free speed limit for curve drive thru [m/s], free speed limit by pavement roughness [m/s], free speed limit by desired free speed [m/s], empiric coefficient (Weibull).
Fig. 2.
HDM speed model prediction [2].
The chat shows an example of free speed calculation of a heavy truck. We can see that for the steep gradients less than -6% and more than 4%, forces oppressing motion equilibrium is the main constraint. Within this interval the desired speed was constraining frees peed. Obviously neither pavement roughness nor curvature influenced free speed in this case. 3. Vehicle operating speed Traffic interactions result in speed fluctuations and decrease free speed. These interactions lead to additional fuel and tyre costs while decrease in speed leads to an increase in travel time. Consequently, it is important to consider traffic interactions in any analysis with moderate to high traffic levels. Traffic interactions may arise in several different ways: Overtaking delays – occur on single or two lane roads when a vehicle catches up with a slower moving vehicle and cannot overtake immediately. It is forced to travel at, or near to, speed of the slower vehicle (often called a platoon or bunch leader) until an overtaking opportunity presents itself. Demand delays – arise on multi-lane highways and are similar to overtaking delays. Multi-lane highways have greatly improved overtaking capabilities compared to two-lane roads, but as the demand increases, the headways between vehicles decrease, thereby decreasing the overtaking opportunities. Vehicles are forced to travel at more uniform speeds, and, as the demand increases, to increase the speeds decline and may eventually cause the facility to become jammed. Crossing delays – are caused by interactions between vehicles travelling in opposite directions. While negligible on wide two-lane roads or multi-lane roads, they can be substantial on narrow roads where vehicles may be forced to move off the carriageway onto shoulders. [1]
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The concept of road capacity is integral to the understanding and modelling of speed volume effects. TRB Highway capacity manual [3] states that capacity is: „The maximum rate of flow that can be accommodated by a given traffic facility under prevailing conditions. “ It is useful to conceive of the capacity by considering density of the traffic. While capacity is a flow, expressed in veh/h, density is the number of vehicles occupying a given length of roadway, averaged over time and expressed in vehicles/km. It describes the proximity of vehicles to one another and reflects the freedom to manoeuvre. 3.1. Traffic density expressed in passenger car space equivalency Traffic streams are comprised of a range of vehicles, from passenger cars to heavy trucks. For the purposes of defining the capacity it is necessary to convert these into a homogenous traffic stream. The passenger car space equivalency (PCSE) is based on the area occupied by the vehicle relative to a passenger car. The preposition is that each vehicle has a typical length as well as typical leading and following headways. PCSE factors vary by road type, and narrow roads have higher PCSE values than wide roads. Table 1 gives the values of PCSE by vehicle class and road type estimated by Hoban, 1994 [4]. Table 1. HDM-4 default PCSE values by vehicle class. Average Length
Space Headway
Total Space
(m)
(m)
(m)
4.0
32.0
36.0
Utilities
4.5
36.0
Heavy Bus
14.0
44.0
Light Truck
5.0
Medium Truck Heavy Truck Trailer
Vehicle Car
Recommended values Basic PCSE 2-4 lane
Narrow 2lane
1-lane
1.0
1.0
1.0
1.0
40.5
1.0
1.0
1.0
1.0
58.0
1.6
1.8
2.0
2.2
40.0
45.0
1.3
1.3
1.4
1.5
7.0
44.0
51.0
1.4
1.5
1.6
1.8
9.0
48.0
57.0
1.6
1.8
2.0
2.4
11.0
50.0
65.0
1.8
2.2
2.6
3.0
The PCSE values in Table 1 were calculated by firstly establishing the total space occupied by passenger cars (default 36m). The values for other vehicle classes were then determined from the ratio of their total space to the passenger car space. The basic value was then subjectively adjusted for width effects to obtain the recommended values in the final three columns. 3.2. Speed-flow model The, capability to model the effects of traffic volume on speeds is provided to enable the economic consequences of road capacity improvements to be determined. The, factors that determine speed-flow relationships are described below: Capacity - The maximum number of vehicles that can pass a point, or traverse' a road section, in one hour (total both directions). Capacity values determine the shape of speed-flow-curves by establishing the ultimate capacity value. Free speed - The speed of each vehicle at zero (or very low) flow. It is unaffected by other traffic but is affected by the physical characteristics of the road and other non-traffic factors. The average speed is calculated for each vehicletype Speed at capacity - As traffic flow increases, average speeds for all vehic1es converge towards the speeds of the slowest vehicles in the stream, as passing becomes more and more restricted. As flow approaches the ultimate capacity, average speeds may fall even lower than slow vehicle free speeds, and any small disturbances in the traffic stream causes a stop-and-go situation. An estimate of average speed at ultimate capacity, also known as jam speed, is needed to describe the speed-flow-capacity relationship.
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HDM-4 uses the speed volume model proposed by Hoban, 1987 [5] and shown in figure 2. It is built around the predicted free speed and five key parameters which vary by road class: Qult the ultimate capacity of the road in PCSE/h, Qnom the nominal capacity in PCSE /h where all vehicles are travelling at the same speed, Qo the flow in PCSE /h where interactions commence, Snom the speed in km/h at nominal capacity, and, Sult the speed in km/h at ultimate capacity.
Fig. 3. Speed flow model [5].
The actual S1 to S3 are free flow speeds of different vehicle types in (km/h). 3.3. Capacity and speed thresholds The key parameters for use in the speed-flow model vary depending upon the road type and width. Table 2 lists the recommended values for these parameters. The values for Qo and Qnom are expressed relative to Quil. Note that in HDM-4 the ultimate capacity for the road section Qult is obtained from the product of the ultimate capacity per lane (QLult) and the number of lanes for the road section. [1] The ratio of Qo to Qult is designated by XQ1, and is expressed as follows: XQ1
Qo Qult
(2)
The ratio of Qnom to Qult is designated by XQ2, and is expressed as follows: XQ 2
Qnom Qult
(3)
Table 2 Capacity and speed flow parameters thresholds for different road types [1]. Road type Single lane road Intermediate road Two lane road Wide two lane road Four lane road
Width (m) 12.0
XQ1
XQ2
0.0 0.0 0.1 0.2 0.4
0.70 0.70 0.90 0.90 0.95
Qlult
Sult
σmaxr
(PCSE/lane/hr)
(hm/h)
(m/s2)
600 1200 1400 1600 2000
1 20 25 30 40
0.75 0.70 0.65 0.60 0.60
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Since these data apply to individual road, it is important to ensure that the data relates to a single and not dual carriageway. This ensures consistency with the definition of a road section as used in HDM-4. The data in table 2 describing the capacity of road sections are specified for each road type: x Ultimate capacity per lane (QLult) (PCSE/lane/hr). The ultimate capacity for the road section Qult
QLult number of lanes
(4)
x Free flow capacity as a proportion of the ultimate capacity (XQ1) x Nominal capacity as a proportion of the ultimate capacity (XQ2) x Speed at ultimate capacity (Sult) (km/h) Free speed value for each vehicle type is determined initially using the mechanistic-behavioral free speed model. The speed at nominal capacity is estimated to be 85% of the free speed of the slowest vehicle in the traffic stream. The maximum acceleration noise (σmaxr) represents the maximum standard deviation of acceleration for each road type. This is required for modeling the effect of speed change cycles (that is, speed variations along the road) on vehicle operating costs. In addition to driver behavior, speed fluctuations are sensitive to road geometry, road condition, the presence of non motorized traffic, roadside friction, intersections, etc. This is however out of the scope of this article. [2] 4. Applying the ISOHDM model in SR conditions Theory, data and procedures described in previous chapters were applied in a computational experiment performed in HDM-4. Road network of three 10 km long trunk road sections were modeled in the program, these had the typical road parameters of SR Ist IInd and IIIrd class road network. STN EN 73 6101 [6] labels them as C 7.5, C 9.5 and C 11.5. Their width composition is shown in Figure 3 and Table 4.
Fig. 4. Width alignment of two-lane road [6]. Table 3 Tested road categories [6] Category C 7.5 C 9.5 C 11.5
a (m)
v (m)
c (m)
e (m)
3 3.5 3.5
0.25 0.25 0.25
0.25 0.5 1.5
0.25 0.5 0.5
The horizontal and vertical alignment of modeled roads was straight and level, thing to note is that vertical alignment has significant impact on road capacity, thus on the whole experiment. For the overall comparison of these three road categories, additional tests with different alignments would have to bee tested. The capacity and speed flow model was based on the default HDM values listed in Table 2. Exact values for tested categories were interpolated and extrapolated by their width. The results are shown in Table 4.
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Jan Mikolaj and Lubos Remek / Procedia Engineering 111 (2015) 522 – 529 Table 4 Capacity and speed flow parameters thresholds for Slovakia road categories. Road type C 7.5 C 9.5 C 11.5
Width (m) 7 8.5 10.5
XQ1
XQ2
0.1 0.1 0.2
0.83 0.90 0.90
Qlult (PCSE/lane/hr) 1385 1477 1600
Sult (hm/h) 24.62 26.92 30
σmaxr (m/s2) 0.65 0.63 0.60
The results are represented in chart on figure 5. Thirty five iterations of the calculation was performed with traffic intensity set as variable. AADT ranged from 1000 to 35000 – shown on the horizontal axis. The resulting lines show the speed of traffic flow on particular road category section. Relation to the chart shown in figure 3 is apparent.
Fig. 5. Traffic flow operation speed in relation to road category and traffic intensity.
The process of traffic flow speed doesn’t stop at this point however. There is a need to take account of the differing levels of traffic congestion at different hours of the day, and on different days of the week and year. Therefore the number of hours of the year for which different ranges of hourly flows are applicable needs to be considered. HDM4 uses traffic flow patterns to account for this issue. By defining the distribution of hourly flows over the 8760 (365 days x 24 hours per day) hours of the year, the AADT data can be converted to hourly flows. Congestion analysis can then be undertaken for a number of hourly traffic flow levels, and the results combined to represent the full year. Because congestion delays and costs are greatest during the highest-flow hours, particular attention should be paid to these hours. These highest-flow hours should be divided into periods of shorter duration. Each specified flow frequency distribution is referred to as traffic flow pattern. For the purpose of this experiment a new traffic flow pattern was created (figure 6).
Fig. 6. Traffic flow pattern. Left- real measured; right – transformed to HDM-4.
The results after the introduction of flow pattern in to the calculation are shown on chart in figure 7. Obviously the hourly capacity of given roads comes into consideration altering the final curves. The more prominent the peek intensities in the traffic flow pattern, the earlier the traffic reaches the saturated flow speeds.
Jan Mikolaj and Lubos Remek / Procedia Engineering 111 (2015) 522 – 529
Fig. 7. Traffic flow operation speed in relation to road category and traffic intensity – with specific traffic flow patterns.
Pavement quality plays also a significant part in the estimation of operating speeds [7], in this experiment all road sections were in perfect working condition. 5. Conclusion The case study, with the theoretical part of the article hopefully provided insight in to the obscured process of vehicle operating speed calculation of HDM-4. The economical aspects of speed changes in traffic flow were omitted due to the length of the article. These of course would be a function of calculated operating speeds, traffic intensity, and length of particular road sections and unit costs of travel time. Acknowledgements The research is supported by the European Regional Development Fund and the Slovak state budget for the project “Research Centre of University of Žilina”, ITMS 26220220183. References [1] World Road Association PIARC,The Highway Develompent and Management Series, ISBN2-84060-058-7, PARIS 2006. [2] Ch. R. Bennett, I. D. Greenwood, Modeling Road User and Environmental Effects in HDM-4, ISBN2-84060-103-6, Paris 2006. [3] Transportation Research Board, Highway Capacity manual, TRB, Washington DC, 2010. [4] C. J. Hoban, W. Reilly and R. Archondo-Callo, Economic Analysis of Road Projects with Congested Traffic, World Bank Publication, Washington DC, 1994. [5] C. J. Hoban, Evaluating Traffic Capacity and Improvements to Road Geometrz, World Banka Technical Paper 74, The World Bank, Washington DC, 1987 [6] Slovak Office of Standards metrology and Testing, STN EN 73 6101 Design of Roads and Motorways, 2008. [7] J. Celko, M. Kovac, M. Decky, Analysis of Selected Pavement Serviceability Parameters, Komunikacie, Volume 13, Issue 3, 2011
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