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Transportation Research Procedía 6 (2015) 158- 171
Transportation
Procedía
www.elsevier.com/locate/procedia
4th International Symposium of Transport Simulation-ISTS'14, 1-4 June 2014, Corsica, France
Calibration and validation of a Swedish space-time analytical model
Per Strömgrena*
aRoyal Institute of Technology (KTH), Department of Transportation and Logistics (ToL), SE-100 44 Stockholm
Abstract
The present capacity models for freeways descended from the early 70th, and were partly using the HCM 1965 Highway Research Board (1965) as background. Not especially valid for the todays freeway network. During the last decade one large project, Traffic Performance on Major Arterials (TPMA) Carlsson et al. (2000a), Carlsson et al. (2000b) and Carlsson et al. (2002) has been implemented. New models for basic freeway segment, merging and weaving segment was developed. A new model for weaving were developed 2010 with new empirical data Stromgren (2011). In addition to the manual calculation method for not oversaturated condition a time-space model that also handled oversaturated conditions has been included. The development of the model started with analysis of video and aerial photo to be able to calculate the jam density, the last point in the oversaturated regime curve. The oversaturated flow-density curve has been developed using the density at capacity for a certain cross section and speed limit based on empirical data of flow and density in oversaturated conditions including jam density.
The development of the Swedish space-time model used FREEVAL Transport research Board (2010). The resulting computer model, called CALMAR, CALculation of performance for Motorway ARterial facilities, was built in VB.NET and VBA. Calibration of the model was done by using the Swedish capacity models for link, merging, diverging and weaving but also flow-density estimations. All other country specific parameters as speed limits etc. was set to Swedish conditions. A traffic environmental factor was implemented describing the environment where the freeway is situated, and divided into rural or urban. Urban conditions has an interchange density higher or equal to 0.5 (interchanges/km), rural conditions has a density lower than 0.5 (interchanges/km).
The model was calibrated for four and six lane freeways with merging or weaving lanes. The speed limit range from 70 kph to 120 kph in step of 10 kph. The model has its limitations. Lane width, shoulder width, distance to obstacles, gradients for ramps and length of merging was not taken into account, since no relationship could be found in the empirical data.
The validation of the model was carried out for three different cases on the A4 freeway south of Stockholm, one
* Corresponding author. Tel.: +46(0)70-6653876; fax: +46(0)8-212899. E-mail address: perstro@kth.se
2352-1465 © 2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).
Selection and/or peer-review under responsibility of the Organizing Committee of ISTS'14 doi:10.1016/j.trpro.2015.03.013
accident, one vehicle break down and one at oversaturated condition due to high demand flow. Recorded flows from the motorway control system (MCS) as well as the automatic incident detection (AID) data from this system were used to identify queue increases and decreases. Reports from the roadside assistance team were also used to identify the degree and duration of bottleneck blockade.
A careful collection of flows including bottleneck throughput and upstream demand were collected in the cases of accidents. The throughput and the upstream flow (demand) on the upstream not affected link before the end of the queue were registered for each time step (60 minutes). The throughput flow was used as the capacity value in CALMAR, and the demand flow upstream as the segment demand. This was repeated for each time step of 60 minutes. In the case with oversaturated condition no explicit change of the capacity in the bottleneck was done. The capacity was indirectly changed by the related interchange, where the number of lanes was changed from 3 to 2 lanes and the speed limit decreased from 100 kph to 80 kph. The demand flow was captured as in the two first cases. To estimate the queue length AID data was collected from the MCS database and converted from binary to decimal format. Data from 12 MCS gantries for each accident in the southbound direction, and 18 gantries in the northbound direction were collected. The average gantry spacing was 200-300 m.
For each time step the end of the queue was registered as a length from the bottleneck where the AID alarm was registered. The AID gives a sign of 30 kph without flashing lamps and has a threshold of 22 kph. This means that the speed is in the range of 0 to 22 kph. A check is also done in the speed flow data from the MCS, if speed less than approximately 10 kph the density is too high for the radar detectors and no data will be recorded. The result from the validation showed a good fit. The CALMAR model gives in case 1, southbound accident, a maximum queue length of 2472 m and the maximum empirical queue length was 2635 m. Case 2, northbound vehicle breakdown gave a CALMAR queue length result of 3608 m compared to a maximum empirical queue length of 3530 m. Case 3, northbound oversaturated condition, gave a CALMAR result of 4149 m queue length and an maximum empirical queue length of 4310 m.
© 2015The Authors.PublishedbyElsevierB.V. Thisis an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Selection and/or peer-review under responsibility of the Organizing Committee of ISTS'14 Keywords: analytic; freeway; queue estimation; over-saturated; time-space
1. Introduction
The former Swedish capacity model for motorways was developed 15 years ago and was not published in the form of a capacity manual. During the last 4 years a new Swedish capacity manual has been produced, replacing the 1977 version, in a project called METKAP. For motorway environments a computer model with the basic structure from FREEVAL Transport Research Board (2010) was developed. CALMAR is designed as a macroscopic flow simulation model. The time-space model is similar to FREEVAL Transport Research Board (2010). The model is mandatory to use for calculation and control of new construction, improvement and control of the existing road, within government road administration.
The focus of this paper is calibration and validation of basic motorway segments, calibration of on and off ramps and weaving segments, in the new time-space model for Sweden, CALMAR.
The model covers motorway, in both rural and urban environmental. Component parts are basic segment, on-ramp, off-ramp and weaving segments. The method includes the calculation of capacity, degree of saturation, and travel speed. The vehicles that are incorporated in the model are private car, truck without trailer and truck with trailer. Travel speed refers to both conditions with or without over saturation.
2. Calibration
The calibration has been done according to new speed-flow relationship for different motorway environments. The geometric configuration and speed-flow relationship of basic motorway segments is based upon empirical values collected 2009-2011 and analyzed 2012 Olstam et al. (2013). The on-ramp model is from the TPMA project
Carlsson et al. (2000b) and the model for weaving segment was developed 2010 Stromgren (2011) by using data from the Motorway Control System (MCS) in Stockholm and Gothenburg.
CALMAR has been calibrated for 15 different motorway configurations. The parameters the possible setting are, number of lanes (2 or 3 lanes in each direction), mandatory speed limits (70, 80, 90, 100, 110 and 120 kph) and environment (urban or rural), see tab. 1. The model has its limitations, lane width, shoulder width, distance to obstacles, gradients and length of merging for on-ramps is not taken into account, since no relationship could be found in the empirical data.
Tab.1 The 15 different motorways configurations.
Mandatory speed
(kph) Rural Urban
6 lanes 4 lanes 6 lanes 4 lanes
120 X
110 X X
100 X X X X
90 X X X X
80 X X
70 X X
The new developed regime curve for oversaturated conditions in combination with the models for under saturated condition that is defined by the "The effects of roadwork: New construction and improvements" Vagverket (2009) is the base for the model. The new weaving model is used for weaving sections. In fig. 1 the process for the time and space analysis is shown.
Fig. 1 Methodology for time & space analysis.
The model uses the oversaturated regime curve to describe a shockwave within a traffic system. Three most important parameters in the regime curve are the capacity level, density at capacity and jam density.
The fundamental part of FREEVAL is the calculation of oversaturated segments. The first step is to calculate the demand for segments, on-ramps and off-ramps and also the minimum number of vehicle that can be on the segment at any time.
The demand is corrected for truck share and gradient, according to Equation 1 Stromgren (2011). Current vehicle composition gives a factor, Fpe, for conversion to passenger car units (pcu).
Nomenclature
Fpe Factor for transformation of traffic flow to pcu
pLBn Share of trucks without trailer and also bus
pLps Share of trucks with trailer
Pekv LBn Passenger car equivalent for trucks without trailer and also bus according to tab. 2
Pekv Lps Passenger car equivalent for trucks with trailer according to tab. 2
a 0.975 for sight class 1 and 0.94 for sight class 2
Tab. 2 Values for Pekv LBn och Pekv Lps dependent on gradient
Gradient (%)_Pekv LBn_Pekv Lps
< 3 1.3 1.7
3-4 2.0 2.6
> 4 2.6 3.4
Next step is to calculate the main line flow (MI). There is six different constraints, Main line input (MI) is the maximum number of vehicles that will enter a node, Main line output 1 (MO1) is the constraint caused by the on-ramp flow, Main line output 2 (MO2) is the constraint that depends on segment storage of queues on a downstream segment, Main line output 3 (MO3) is the constraint caused by front clearing queues, Upstream segment capacity and Downstream segment capacity, see fig. 2.
; Segment, ; Segmenti+1 ; Segmenti2 ; Segment^, ; Segmenti4 ,
■ ■ ' M t< MF ( ■ M„v III III
Node, Nodei+1 Nodei+2 Nodei+3 Nodei+4 Nodei+5
Parameter Explanation
Segmenti Homogenous segment number i
Nodei Node number i
Mi Main line incoming flow that arrives to noden
Mf Main line through flow that can pass segmentn
Mo(i) Maximum output flow that can pass out from segmentn with respect to on-ramp flow (ONRf)
Mo(2) Maximum output flow that can pass out from segmentn with respect to queue in downstream segmentn+1
Mo(3) Maximum output flow that can pass out from segmentn with respect to discharge in queue front and limitations in up- and downstream capacity
ONRf On-ramp flow
OFRf Off-ramp flow
Fig. 2. The different incoming and output flows within a segment.
The wave speed is estimated by the slope of the dotted line from the bottleneck throughput to the point where it reaches the capacity. The jam density estimated with empirical data to 135 (pcu/km/lane) was used to set the jam density for each motorway type (Stromgren 2011). Individually the density at capacity was set and calculated from the speed-flow relationship from the new empirical values collected 2009-2001 (Olstam et al. 2013). In combination with empirical values from oversaturated conditions the oversaturated regime curve was done by a regression (Stromgren 2011), as an example see fig. 3.
Flow (pc/h)
Qc 5 Density (pc/km/lane)
Qc 3
/ V
/ \
/ \
/ \
! \
/ \
/ \
/ N
kBo ttle nec k th rou ghp ut
/ j
1 0 1 5 2 02 5 3 0 3 5 4 04 55 05 5 6 0 6 5 7 0 7 5 8 0 8 5 9 0 9 51 0 10 51 10 1 15 1 01 51 30 1 51 01
Fig. 3. Example of flow-density relationship with oversaturation regime curve. (Qc=Capacity (pc/h), KQc=Density at capacity(pc/km/ln), WS=Wave speed (m/s) and Kj=Jam density (pc/km/ln)).
For the 15 different types of motorways a speed-flow relationship has been developed from the regression of flow-density relationship at oversaturated conditions, see tab. 3.
Tab. 3. Speed-flow relationships at oversaturated conditions.
Type of Motorway Density at capacity (pcu/km/lane) Equation
MV urban 6 ln 70 kph 35,4 Vö = 0,000016-Qö 2-0,0016Qö
MV urban 6 ln 80 kph 33,9 Vö = 0,000016-Qö 2-0,0014Qö
MV urban 6 ln 90 kph 32,8 Vö = 0,000016-Qö 2-0,00094 Qö
MV urban 6 ln 100 kph 30,6 Vö = 0,00001636-Qö 2-0,0001 Qö
MV rural 6 ln 90 kph 31,6 Vö = 0,000017-Qö 2-0,0012-Qö
MV rural 6 ln 100 kph 29,1 Vö = 0,0000187-Qö 2-0,0017Qö
MV rural 6 ln 110 kph 27,8 Vö = 0,0000187-Qö 2-0,00017 Qö
MV urban 4 ln 70 kph 38,4 Vö = 0,0000088-Qö 2+0,0082-Qö
MV urban 4 ln 80 kph 37,3 Vö = 0,0000099-Qö 2+0,0061 Qö
MV urban 4 ln 90 kph 36,3 Vö = 0,0000089-Qö 2+0,008 Qö
MV urban 4 ln 100 kph 34,2 Vö = 0,000096-Qö 2+0,0078 Qö
MV rural 4 ln 90 kph 35,3 Vö = 0,000012-Qö 2+0,0024-Qö
MV rural 4 ln 100 kph 32,5 Vö = 0,0000147-Qö 2-0,0006 Qö
MV rural 4 ln 110 kph 31,1 Vö = 0,0000152-Qö 2-0,00089 Qö
MV rural 4 ln 120 kph 29,6 Vö = 0,0000157-Qö 2-0,00042-Qö
The non-linear relationship between flow and density in CALMAR is used to calculate the wave speed (WS) for the queue. The equation (1) gives the wave speed dependent on the density.
H^ = j4B5(0.2442 ■ K - 39.37)
The wave speed in turn is used to calculate the time it takes for the queue front condition to reach the upstream end of the segment. To put a restriction at a node the downstream conditions at a time in the past that are equal with wave travel time.
3. Validation
Validation of the CALMAR model was carried out using traffic data from the Motorway Control System (MCS) in Stockholm. The output from the system is flow, speed and Automatic Incident Detection (AID). The AID gives the recommended speed on the Variable Message Sign (VMS) over the roadway, which also gives a good estimation of the queue end, see fig 4.
Salem Tid 32110 32540 32330 33350 33665 34020 34310 34620 34335 35175 35415 Aspen 35615 36025
16:18 O O 0 0 0 0 0 0 0 0 0 0 0
16:19 O O o o o o o o o o o o o
16:20 O o o o o o o o o o o o o
16:21 • 5 o o o o o o o o o o
16:22 • O # o o o o o o o o o o
16:23 O o o o o o o o o o o o o
16:24 • • 9 o o o o o o o o o o
16:25 • Q 9 o o o o o o o o o o
16:26 • O o o o o o o o o o o o
16:27 • O G o o o o o o o o o o
16:28 • O a o o o o o o o o o
16:28 O o Q o o o o o o o o o
16:30 O Q Q o o o o o o o o
16:31 O O Q o o o o o o o o
16:32 O O O o o o o o o o o
16:33 O O o o o o o o o o o
16:34 O O o o o o o o o o o
16:35 O o o o o o o o o o
16:36 O Q o o o o o o o o
16:37 O • o • o o o o o o
16:38 O o Q o o o o o o o
16:38 O Q o o o o o o o o
16:40 O O o o o o o o o o
16:41 O O o o o o o o o o
16:42 O o o o o o o o o
16:43 O Q o o o o o o o
16:44 O o o o o o o o o
16:45 o 9 o o o o o o
16:46 o o o o o o o o
16:47 O o o o o o o o o
16:48 O o o o o o o o o
16:43 O 9 9 o o o o o
16:50 O o o o o o o o
16:51 O o o o o o o o
16:52 O o 9 o o o o o
16:53 O 9 o o o o o
16:54 O o o o o o o
16:55 O o o o o o
16:56 O o |a o o o
16:57 O o 9~ o o o
16:58 O o ■T o o o
16:53 O |o o o
17:00 O o a o o
17:01 O 9 <T o o
17:02 0 ■T |o o o
17:03 0 ■T |o o o
17:04 0 o 9 o o
17:05 0 o a o o
17:06 0 • 9" 9~ o
17:07 0 • |o |o o
17:08 0 • |o |o o
17:03 0 • 9 9 o
17:10 O o |a o o o
17:11 O o 9~ o o o
17 12 O O o o o o o o
17 13 O o o o o o o o o
17 14 O o o o o o o o o o o
17 15 O o o o 9 o o o o o o
17 16 O o o O o o o o o o o o o
17 17 O o o o o o o o o o o o o
17 18 O o o o o o o o o o o o o
17 18 O o o o o o o o o o o o o
17:20 O o o o o o o o o o o o o
Fig. 4. Recommended speed due to queue warning algorithm. o=turned off,
=70 kph ^=50 kph.
The AID gives a sign of 50 kph without flashing lamps and has a threshold of 35 kph. This means that the speed is in the range of 0 to 35 kph. A check is also done in the speed flow data from the MCS, is the speed less than approximately 10 kph the density is too high for the radar detectors, no data will be recorded. To estimate the queue length the AID was collected from the database of the MCS, data is binary and a translation was necessary to be done.
Three different occasions has been studied during the validation phase, an accident, a capacity breakdown and a vehicle breakdown, for details see tab. 3. To identify the three different incidents, information from the report system at the traffic management centre in Stockholm has been used. This has been done with information from the system called NTS (National Traffic management System), where all incidents in the traffic network is logged. The data gives primary information of type of incident, location and duration.
NTS has been used to find useful situations for analysis, as well as control in terms of scope and duration. Incident detection has been used to locate end of queue ends for every minute during the queue duration. The assumption of the queue end is that it is in the middle between the last detected AID and the first without AID.
To provide CALMAR with the input values, the throughput flow at the bottleneck was taken from the empiric value from the MCS database and used as capacity flow. The upstream flow, not affected of the incident, was used as the demand flow. For each hour that was influenced of the incident, the number off passed vehicle through the bottleneck was compiled.
Three incidents of different type were chosen from the NTS-database, see tab. 4.
Tab. 4. Specification of bottlenecks, situation and number of lanes.
Bottleneck Situation Duration Capacity loss (vph) Number of lanes
Interchange Salem Accident 21 maj 55 min 50 % 3
Interchange Hallunda Vehicle breakdown 27 maj 20 min 35 % 2
Interchange Hallunda Capacity break down 20 maj 400 min 40 % 2
Data from each MCS gantry, approximately with a space of 200-300 m, gave 12 gantries for the accident in southbound direction, 18 gantries for the accident in northbound direction and in the case with oversaturated condition.
The first incident, an accident, shows that CALMAR gives a queue length of 2472 m and the AID-system gives a queue length of 2635 m, see fig. 5.
Fig. 5. Queue length as function of time during the increase and the discharge of the queue for an accident.
As one can see the time-period is not the same in fig. 4 and fig. 5, the reason for this is that the discharge of the Queue in the AID-system is when the speed reach 55 (kph), when the queue move more synchronic. CALMAR could on the other hand only handle full hours, which mean that the queue could discharge during the first 15 min, but the result is for a full hour. The MCS-data shows on the other hand that it takes approximately 1.5 hours before the speed is normal again.
To verify the results above also a calculation with data from the MCS-system has been performed in this case. The output during the period shows that the demand upstream is 2900 vehicles and the throughput at the bottleneck is 2554 vehicles, this means that 346 vehicles are allocated in the queue. If the MCS data for speed and flow are used this gives a queue length of 2562 m, which correlates with the queue estimate from the AID and the CALMAR results.
The second incident of type vehicle break down shows a queue length for CALMAR of 3608 m and the empirical data from the AID-system 3530 m, see fig 6. The peek is not correlated, CALMAR results shows a little too slow queue increase in the initial phase and also too slow discharge of the queue.
Fig. 6. Queue length as function of time during the increase and the discharge of the queue for a vehicle breakdown.
The third incident of type capacity break down shows a queue length for CALMAR of 4149 m and the empirical data from the AID-system 4310 m, see fig. 7. The peek is correlated, but CALMAR result shows a little too slow queue increase in the initial phase.
Fig. 7. Queue length as function of time during the increase and the discharge of the queue.
In the case with oversaturated condition the capacity was indirectly changed by the related interchange, where the number of lanes was changed from 3 to 2 lanes and the speed limit decreases from 100 kph to 80 kph.
4. Conclusions and Future Research
Calibration of the CALMAR was done by using the Swedish capacity models for link, merging, diverging and weaving. All other country specific parameters as speed limits etc. was set to Swedish conditions. A traffic environmental factor was implemented describing the environment where the motorway is situated, and divided into rural or urban. Urban conditions has an interchange density higher or equal to 0.5 (interchanges/km), rural conditions has a density lower to 0.5 (interchanges/km).
The model was calibrated for four and six lane freeways with merging or weaving lanes. The speed limit range goes from 70 kph to 120 kph in step of 10 kph, totally 15 different types of motorways. The model has its limitations. Lane width, shoulder width, distance to obstacles, gradients for ramps and length of merging was not taken into account, since no relationship could be found in the empirical data.
The validation of the model was carried out for three different cases on the A4 freeway south of Stockholm, one accident, one vehicle break down and one at oversaturated condition due to high demand flow. Recorded flows from the motorway control system (MCS) as well as automatic incident detection (AID) data from this system were used to identify queue increases and decreases.
A careful collection of flows including bottleneck throughput and upstream demand were collected in the cases of an incident. The throughput and the upstream flow (demand) on the upstream not affected link before the end of the queue were registered for each time step (60 minutes). The throughput flow was used as the capacity value in CALMAR, and the demand flow upstream as the segment demand. This was repeated for each time step of 60 minutes.
For each time step the end of the queue was registered as a length from the bottleneck where the AID alarm was registered. The AID gives a sign of 50 kph without flashing lamps and has a threshold of 35 kph. This means that the speed is in the range of 0 to 35 kph. A check is also done in the speed flow data from the MCS, if speeds less than approximately 10 kph the density is too high for the radar detectors and no data will be recorded.
The result from the validation showed a good fit. The CALMAR model gives in case 1, southbound accident, a maximum queue length of 2472 m and the maximum empirical queue length was 2635 m. Case 2, northbound vehicle breakdown gave a CALMAR queue length result of 3608 m compared to a maximum empirical queue length of 3530 m. Case 3, northbound oversaturated condition, gave a CALMAR result of 4149 m queue length and an maximum empirical queue length of 4310 m.
Future research includes calibration and validation of queue distribution between main line through flow and the on-ramp flow and studies of the capacity drop at oversaturated conditions. Variations in capacity occur and the present Swedish capacity values are set to approximately the 50-percentile. The research aims to calculate a distribution buy using recorded flows and speeds.
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