No. 64 ' 1981 Statens väg och trafikinstitut (VTI) - 581 01 Linköping National Road & Traffic Research Institute - S-581 01 Linköping - Sweden
Very Minor Road Improvements
Simulation Model
by S Johnsen, Department of Transport, England,
and G Gynnerstedt,
National Road and Traffic Research Institute, Sweden
M
Paper presented at the PTRC Summer Annual Meeting, 13 16 July, 1981,
at the University of Warwick, England.
No. 64 - 1981 Statens väg- och trafikinstitut (VTI) - 581 01 Linköping National Road & Traffic Research Institute - S 581 01 Linköping - Sweden
Very Minor Road Improvements
Simulation Model
by S Johnsen, Department of Transport, England,
and G Gynnerstedt,
National Road and Traffic Research Institute, Sweden
M Paper presented at the PTRC Summer Annual Meeting, 13 16 July, 1981,
MINOR ROAD IMPROVEMENTS SIMULATION MODEL by G Gynnerstedt and S Johnsen
Introduction
1. This paper deals with an individual vehicle Monte
Carlo simlation model which will be incorporated into
a minor road improvements economic evaluation package
for use in the UK. The computer based simulation
considers simultaneously all vehicles present at any one time on the simulated road stretch and produces a detailed account of all occurrences including
over-takings, speeds, platooning, etc. The economic
evaluation tool will be based on observing how this account is altered when the simulated road is altered. The system will generate randomly a traffic stream of chosen composition and intensity for the road in
question.
||
2. The model is the brainchild of Mr Gosta Gynnerstedt,
working at the National Road and Traffic Institute in
Linkoping, Sweden. It has undergone refinement and
development by Mr Gynnerstedt's team for about 10 years. It is now finding application as an evaluation tool not only in Sweden, where it is extensively used, but in
Finland, the UK, and New Zealand. Supported by the
World Bank it is being implemented in India and in &aZilo
3. The paper first indicates how the model functions,
what it is capable of and the way it can be applied in
practice. It then describes the work done to date at
the UK Department of Transport to calibrate and validate the model for use in the UK, by analysis of UK survey data and. with assistance from Mr Gynnerstedt's team and
from Martin and Voorhees Associates. A final section
outlines future work on the model at the Department of Transport, London.
How the Model Works
4. The model is an event based Monte Carlo simulation
program written in the computer language SIMULA using
Jackson Structured Programming techniques. A computer
file contains in chronological order of entry time to the simulated road stretch, descriptions of individual
vehicles making up the simulated traffic stream. Part
of the Monte Carlo element in the simulation may
consist in randomly choosing vehicle type, time headways
and other characteristics. It is also possible, as in
the calibration and validation work to be described, to use observed input vehicle time headways and
sampled decisions on whether to overtake or to abort overtaking in different circumstances of visibility and
oncoming traffic. The novelty and power of the system
lies in its high level of realism, which is achieved by considering as simulation events such occurrences as change of lane, overtaking manoeuvres, etc.
5. The simulation algorithm.functions by dealing with
events involving the traffic in strict chronological
order. At any one instant of time every single vehicle
on the road has associated with it one next event, the details of that event, and its predicted time of
occurrence. The program arranges these events in_a list ordered according to predicted time of occurrence. The next most immediate of the events in this list is
always what is currently being processed. The
process-ing of an event may involve changprocess-ing the status of the vehicles involved.in the event and may involve
scheduling new events for these vehicles. These new
predicted events replace previously predicted events
which are deleted from the events list. After one event
has been processed the next most immediate event in the
list is processed, and.so on.
The first (last) event
for a vehicle is always its entry to (exit from) the
simulated road stretch.
6. Each time an event is processed, the program.writes
a record containing an optional amount of information about the conditions during -, and outcome of -, that
event. These records are written to a computer file
known as the "events file". This file is thus a
chronological record containing an optional amount of
detail about the traffic process. By looking at the
"events file" produced by passing a given stream of traffic over a given road using the simulation program, it is possible to obtain a very detailed picture of
traffic characteristics and occurrences. Journey times,
spot speeds, platooning, overtakings can be looked at
and calculated. Computer programs which abstract and
summarise the information.in "events files" are available.
7. The description of the simulated road needed as
input to the system.includes its varying width,
horizontal curvature, vertical alignment, forward and
backward sigh distances, etc. This information is input
to the model which condenses it so that the road is
broken.up into a series of consecutive blocks. Within
each block conditions are regarded.as uniform. The
blocks have, associated with them, a median "basic desired speed", calculated from.consideration of the
block road geometry and speed limits. This quantity is
an estimate of the median speed in the block of a
representative selection.of vehicles. It is based on
results from field studies indicating the influence on speed of road geometry and speed limits.
8.
The description of a vehicle input to the
simul-ation includes its "basic desired speed in ideal
conditions" and its power/mass ratio.
9. In situations where a vehicle is in "free flow" the
vehicle attempts to maintain a speed calculated by
comparing its "basic desired speed in ideal conditions" with the median "basic desired speed" of the road block
the vehicle is in. The power/mass ratio together with
the vertical alignment then.determine, through the equation of motion, the actual speed at any instant of "free flow".
10. Overtaking opportunity acceptance rates in various
conditions have been calibrated. These rates are used
in the model to decide stochastically on acceptance or rejection of overtaking opportunities.
ll. vehicles input to the model have associated with
them numbers (from 1 to 3) representing their vehicle
type. These types are:
type 1: passenger cars
type 2: light goods vehicles and vans type 3: lorries and other heavy vehicles. 12. Junction effects are not modelled in detail. Junction entry and exit of vehicles from.the modelled road stretch is all that the model considers. Network
distribution effects likewise cannot be directly modelled.
How the Model can be Applied in Practice
13. To evaluate economically a proposed minor road
improvement the road is simulated with and without the
improvement. The two "events files", one from.each of
these simulations, are then analysed and compared for differences in journey times, fuel consumption, accident risk.
14.
To carry out these two (with/without) simulations,
one needs a description, with and without the improve-ment, of about 2 km of road, centred on the improveimprove-ment,
suitable for input to the model. Also needed is a
representative traffic stream for the road containing
about one hour of simulated traffic. This traffic
stream is sampled randomly from a pOpulation which
consists of representative flows for the two directions with correct proportions of vehicles in each of the three vehicle classes, and with realistic speeds of entry to the modelled road stretch.
15. "Events files" contain information on the fuel
obtained during the simulation by integrating the
tractive effort (found from the equation of motion) of
each vehicle with respect to the distance travelled
along the road (this part of the model is not yet fully
validated).
16. By examining the "events file" the relative
positions and movements of all vehicles on the road at
any one instant can be inferred. When dangerous
situations occur, such as an overtaking vehicle heading straight for an oncoming vehicle, one speaks of
conflict situations . Work is in hand to calibrate the
relationship between frequency of occurrence of various types of "conflict situation" at a particular point of the road, and the frequency of occurrence of various
types of accident at that point of the road. Thus, it
will be possible, by examining "events files" to infer accident risk.
Adaptation for UK Conditions Introduction
17. The model incorporates a number of calibration constants. One example of this is in the formulae for working out the median "basic desired speed" for a road block given speed limits, curvature, carriageway width. Another example is the acceptance rates for overtaking
opportunities in different situations. The calibration
of these submodels was done in Sweden using extensive
field surveys. Clearly these calibrations need to be
adjusted and the adjusted values need to be validated before one can apply the model with any degree of
confidence to the UK situation. In this section we
describe the way this re calibration was carried out. The Calibration Strategy
18.
It was decided to calibrate the model for UK
conditions by collecting individual vehicle data for the traffic streams on a fairly wide selection of different
types of road in the UK. In this way all aspects of
model behaviour could be examined by comparing the modelling of traffic behaviour at each of the chosen
sites with actual observed field data behaviour.
19. Each of the sites used in these surveys was such
that it consisted of two consecutive stretches each
about 2 km.in length. On the first stretch the road
geometry exhibited to a marked degree a characteristic
whose modelling was to be looked at. The second stretch
was to be of such favourable geometry that traffic on it would be travelling very nearly at its "basic desired
speed". The intention in choosing the second stretch
in this way was to enable the "basic desired speed" of each observed vehicle to be obtained as effectively as
required as a simulation input for each vehicle simulated.
20. The field data obtained at each of the sites
surveyed included a sufficient description of the road geometry to enable simulation of the road.
21. Special cameras were placed at the beginning and
end of the entire road stretch and where the first and second stretch joined. Adjacent to each camera two pressure sensitive cables separated by one metre were
stretched across the road. When a vehicle passed a
camera, the camera was triggered by the cables to take a photograph of the vehicle so that its type, direction
and number plate could be identified. Included on.each
photograph was the time of travel between the cables
thus giving the vehicle spot speed. Also included in
the photographs was the time of day. Battery powered
electronic equipment was interposed between the cables and the camera to trigger the camera and to supply the data included in the photographs.
22. The traffic data for each surveyed site thus
comprised reels of photographs from each of three cameras. For each site it was planned to collect
traffic data at the three cameras for about two or three hours.
23. Once the films had been developed, the individual
photographs were displayed in time order on,a screen. The time speed, license number, and vehicle type were then coded by hand to computer files.
24. Matching of the license numbers for individual
vehicles at the three cameras then enabled the calculation of spot speeds at the cameras, journey speeds over the stretches, time or arrival at each
camera, basic desired speed", and time headway.
25. For each site the stream of vehicles observed was
fed.into the simulation model and the resulting "events
files analysed. In these simulations the "basic
desired speed" of each vehicle was derived by combining
the spot speeds with the road geometry at the three
cameras. The other input required for each vehicle was
the power/mass ratio.
This quantity was sampled
stochastically from a calibrated distribution governed
by the vehicle basic desired speed" and the vehicle
type. The exception.to this was where the second road
stretch had a steep upward gradient. Then.the actual
power/mass ratio could be directly estimated from the
equation of motion, the road geometry, and spot speeds at beginning and end of the stretch.
26. The method used to judge the goodness of fit of a
trial set of values of model constants was to compare simulation values with field data values for the
following:
(l)
Journey speeds for three classes of vehicle.
(2) Time headways
"
"
n
n
n
(3) Net overtakings " " " n ||
27. Spot speeds were not compared.in assessing
goodness of fit because they were an indirect input to the simulation.
The Actual Calibration
28.
The program.which assigns power/mass ratios to
individual vehicles by sampling from a power/mass
distribution dependent on.the "basic desired speed" and vehicle type caused a lot of problems at first by
assigning very low power/mass ratio to one or two
vehicles. For the survey sites of Duncton and Midhurst
which have steep gradients and poor overtaking
opportunities this problem.was particularly acute. The
effect was that the simulated traffic was slowed down to a ridiculous extent by platooning behind vehicles
of low power/mass ratios.
At this early stage the
problem.was circumwented by raising the power/mass
ratios of the few vehicles in question.and repeating the simulatian.
29. It was then found that the overtaking rates by
vehicles of class 2 (light vans) and class 3 (lorries)
were consistently too low in the model, causing
excessive platooning. The difficulty with using
Swedish calibrated values of overtaking rates for vehicles of classes 2 and 3, in the model, with UK road and traffic data, appeared to be that Swedish vehicles of classes 2 and.3 tended to be heavier than
the corresponding classes of vehicles in the UK. The
overtaking rates parameters used in the model for
vehicles of classes 2 and 3 were altered. The modelled
overtaking rates were now comparing substantially better, although not yet acceptably close.
30. It was becoming clear from.comparisons of field and simulation data, for the uphill stretches of the
sites Duncton.and.Midhurst in particular, that power/
mass ratios for class 2 and 3 vehicles were too low for British data. This was another manifestation of the difference between classifications in Sweden and Britain
already encountered with overtaking rates. The problem
did not appear to apply to class 1 vehicles.
Bl.. Accordingly it was decided to calibrate new power/
mass ratio distributions for UK conditions for vehicle
classes 2 and 3. These distributions were calibrated
using the equation of motion, the time pass from.the bottom to the top of the steep stretches at Duncton and Midhurst and the spot speed at the bottom and top of
these stretches.
With these new power/mass ratios the
simulations were repeated and were much improved
particularly for Duncton and.Midhurst. This was to be
expected as the steep gradients at Duncton and Midhurst make these two sites particularly sensitive to
variations in power/mass ratios.
The comparisons at
Luncton and Midhurst were further improved by inserting, for each vehicle in the uphill direction, the actual
power/mass ratio calculated for that vehicle, instead of
a stochastically sampled value.
32. The goodness of fit of the model at the survey
site of Kings Lynn now received attention. The
simulation.gave much too high a journey speed on the bendy first stretch and too low a journey speed.on the
straight second stretch. This situation was never
entirely resolved and Kings Lynn remains a site at which the simulation does not quite achieve the
extremes of journey speeds present in the field data. However, it was decided to alter the way the basic
desired speeds at the central camera at Kings Lynn were
calculated. This was justified on the gounds of the
very changeable nature of the road geometry at the
central camera. This had the effect of raising the
overall level of simulated speeds thus improving the
fit on the straight second stretch. At the same time
simulated journey speeds on the first stretch at Kings Iynn.were lowered by altering the effect of bands in the
road on median basic desired speed. This latter
alter-ation was also called for by the goodness of fit of journey speeds an the bendy second stretch at Downham where simulated journey speeds were also too high.
33. At this stage journey simulated speeds agreed
sufficiently well with field data speeds to allow a detailed examination of the goodness of fit of
overtakings and time headways.
34. The model for Sweden included calibrated separate
overtaking decision probabilities for speeds above -, and for speeds belOW' , 90 kph. It was evident that this division.was not sufficient to cover overtaking rates at speeds much lower than 90 kph, which were
occurring in the UK data. Arne Carlsson of
mr Gynnerstedt's team in Linkoping, suggested.intro-ducing a new category of overtaking rates for below 70 kph.
35. When this suggestion has been implemented it was
considered that the calibration for UK conditions was
satisfactory. The final results are shown in the
appended tables. It can be seen that the model
under-predicts the extremes of effects at Kings Lynn and fails to model the "cautious descent" effect of the downhill stretches at Duncton.and.Midhurst.
Further Developments
There appears to be a clear need, if the model is to be used widely in Britain.in its present form.for scheme evaluation, to simplify its mode of Operation to reduce substantially the level of expertise and
experience needed to use it. Attention is being devoted
to this problem.
Work will shortly commence at the Department of Transport to incorporate the model into a full economic evaluation tool, capable of considering time savings,
vehicle operating costs, and accident costs. This tool
would be appropriate to the evaluation.of schemes smaller than those normally handled using COBA.
The accident risk estimation.potential of the model
requires further development and calibration. Survey
data for several road sites, including information.on road geometry and traffic, as well as accident records,
is available. Traffic on the surveyed road stretches
will be simulated and the rates of occurrence of
various types of accident will be related to rates of occurrence of various conflict situations in the
Simulation.
There is the possibility, using the model, of investigating -, and deriving relationships for , the effect on fuel consumption of a variety of driving
conditions, such as traffic levels and composition, and for different road geometries.
There is the potential to use the model for the economic evaluation of schemes involving the introduct ion of climbing lanes on single carriageway roads. Disclaimer
The views in this paper are those of the authors and do not necessarily represent the views of the Department of Transport.
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