calibrating vissim to analyze delay at signalized intersectionsdocs.trb.org/prp/17-03211.pdf ·...

CALIBRATING VISSIM TO ANALYZE DELAY AT SIGNALIZED INTERSECTIONS

H. Sebastian Buck1

Institute for Transport StudiesKarlsruhe Institute of TechnologyKaiserstrasse 12D-76131 KarlsruheGermanyPhone +49 721 608-43465, Fax +49 721 608-46777, email: [email protected]

Nicolai MalligInstitute for Transport StudiesKarlsruhe Institute of TechnologyKaiserstrasse 12D-76131 KarlsruheGermanyPhone +49 721 608-44119, Fax +49 721 608-46777, email: [email protected]

Peter VortischInstitute for Transport StudiesKarlsruhe Institute of TechnologyKaiserstrasse 12D-76131 KarlsruheGermanyPhone +49 721 608-42255, Fax +49 721 608-46777, email: [email protected]

Word Count: 4655 words + 8 figure(s) + 1 table(s) = 6905 words

Submission Date: November 14, 2016

1Corresponding Author

Buck, Mallig, Vortisch 1

ABSTRACT1The Level of Service of an intersection is principally determined by control delay. Accordingly,2control delay must be reproduced correctly when using microscopic traffic simulation to evaluate3intersections. This study demonstrates how Vissim can be calibrated for this purpose. We built Vis-4sim models of four signalized intersections for which data had been collected. From this data, we5extracted information on headways, time to pass the intersection, and arrival distribution and used6it for calibration purposes. The calibration of the headways resulted in car-following parameters7for these intersections that differed substantially from the Vissim default values. An adjustment8in the vehicle arrival distribution to the observed distribution was also necessary to reproduce the9measured delay in the simulation.10


INTRODUCTION1Control delay is the principal performance measure used to evaluate the Level of Service (LOS)2at signalized and unsignalized intersections in the U.S. Highway Capacity Manual (HCM)(1) and3in the German Handbuch für die Bemessung von Straßenverkehrsanlagen (HBS)(2). Although4the procedures outlined in the HCM and HBS have a wide scope of application, there are some5situations not addressed by these methods. Here, one must resort to alternative analysis tools (1,6Ch. 6), the most prominent of which is microscopic traffic flow simulation. When using these7simulations to evaluate LOS, it is important to calculate exactly the same performance measures8used in the HCM or HBS.9

Although there are guidelines for the application, calibration, and validation of microscopic10traffic flow simulations (3–6), these guidelines typically operate on a more abstract and software-11agnostic level. That is, they do not cover specific aspects of individual traffic flow simulation soft-12ware. The calibration and validation of PTV Vissim for freeway traffic is quite well documented.13Fellendorf and Vortisch (7) described a calibration procedure based on speed-flow diagrams. Men-14neni et al. (8) developed this approach further. Gomes et al. (9) performed an extensive simulation15and calibration study for a U. S. freeway using Vissim. For German freeways, Geistefeldt et al.16(10) performed a comprehensive calibration study that evaluated different traffic flow simulations.17For Vissim, Leyn and Vortisch (11) described the calibration process and the resulting parameter18sets of driving behavior.19

For intersections, the literature on Vissim calibration is sparser. Cicu et al. (12) describe20the calibration of Vissim for roundabouts. Park et al. (13), (14) describe a Vissim calibration21procedure for signalized intersections in which they use the travel time for calibration and the22maximum queue length for validation. Cunto and Saccomanno (15) also calibrated Vissim for23traffic at signalized intersections, but focused on safety performance measures and not on delays24or travel times. Manjunatha et al. (16) describe the calibration of Vissim for signalized intersections25in India. Because traffic in India is very different from traffic in the U. S. or Germany, however,26these results are not transferable.27

The goal of this study was to calibrate Vissim so as to reproduce realistic delay. For this28purpose, we collected video measurements at four signalized intersections in Germany and ex-29tracted data on headway, time to pass the intersection, and arrival distributions. A Vissim model30was built for each intersection and the data extracted from the measurements was used to calibrate31the models. We validated the correct calibration of the models using the total delay.32


DATA AND MODELS1This section describes the study sites, the measurement process, and the construction of the simu-2lation models.3

Study Sites4Measurements were taken at four fixed-time signalized intersections of different sizes in German5urban environments (Berlin and Karlsruhe). Figure 1 shows sketches of those intersections with6numbered lanes. All intersections had a speed limit of 50 km/h and the traffic volume of the7lanes ranged from about 100 to 640 vehicles per hour. Lanes with permitted left-turn, i. e., lanes8where the progress could only be made after yielding the right-of-way, were excluded from further9analysis (gray numbers in Fig. 1).10

Measurement11The traffic was observed by video cameras for several hours to determine the input variables for12the simulation model (volume, vehicle fleet), the measures to calibrate the model, and the delay13of all vehicles. From the videos, the following information and time stamps were extracted over a14period of 90 minutes, comprising the peak hour and the 15-minute intervals before and after:15

• vehicle type16• lane and movement17• time of arriving at end of queue taQ18• time of arriving at stop line taSL19• time of passing stop line tpSL20• time of leaving the intersection area tpIS21To extract time stamps, the videos were preprocessed using standard video-processing soft-22

ware. Colored markers were inserted in the videos to clearly visualize the locations at the stop line23and at the end of the intersection area where time stamps were to be taken. Recordings from24different cameras were integrated into one video to cover the whole pathway for each movement.25

We evaluated the videos manually with the aid of a software tool based on Microsoft Excel,26Visual Basic for Applications and ActiveX. The software tool displays the videos frame-accurately27and allows one to record the current video time stamp by pressing buttons. The precision of the28time stamps is 1/25 seconds. In total, we collected data from 10260 vehicles in 38 different lanes.29

Simulation Models30The Vissim simulation models of the intersections are based on the geometry of the intersections,31as derived from the videos and aerial images. The lengths of the modeled access links to the32intersections are around 300 meters. Based on the arrival time stamps taQ, a Poisson-distributed33vehicle input with a resolution of 5-min intervals was generated. For the same intervals, static34vehicle routes were used to model turning relations. In Vissim, road geometry has no direct impact35on speed; rather, the influence on speed must be modeled explicitly. For each lane, we added a36reduced speed area, which can be used to calibrate the speed. In Vissim, each vehicle chooses37a new desired speed within the reduced speed areas. The required deceleration is assumed to be38completed at the beginning of the reduced speed area. The reduced speed areas were placed in39the middle of the intersection and had a length of two meters each. We chose Wiedemann 99 as40car-following model, and accepted the default lane-change behavior. The fixed-time signal timings41of the intersection were reproduced exactly in Vissim.42


20m

1 2 3 4 5

678

912

13

15

(a) Intersection 1 (Berlin)

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20m

(b) Intersection 2 (Berlin)

20m

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3

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5

(c) Intersection 3 (Karlsruhe)

20m

1 2

34

56

(d) Intersection 4 (Karlsruhe)

FIGURE 1 : Site plans of analyzed intersections


Vissim’s vehicle record evaluation was used for the analysis. The record was configured to1include the following data for each vehicle in each simulation step:2

• simulation second3• vehicle number4• link and lane number5• speed6• vehicle type7Using MATLAB, we developed an automated process to extract the same time stamps from8

the vehicle records as were extracted from the videos. This process emulates the video evaluation9process for the simulation. Thus, the data specified above in the Measurement section was available10for both the measurement and the simulation.11

CALIBRATION12Delay at intersections operating in undersaturated conditions results from geometric delay and13control delay. Geometric delay is the delay due to vehicles passing the intersection with reduced14speed, especially in turn movements. Control delay is the delay due to traffic control at the in-15tersection. One important aspect of control delay is the share of cycle time that the vehicles are16stopped by a red signal. Another is the queue of waiting vehicles. Due to the induced queue, the17vehicles are delayed even after the beginning of green time. These sources of delay are taken into18account during the calibration and are described below.19

The calibration of geometric delay is based on the time to pass the intersection. This time20was calibrated by adjusting the desired speed of the reduced speed areas inside the intersections.21

The time a vehicle spends in the queue depends on the length of the queue ahead of the22vehicle and the dissipation rate of the queue, as described by the base saturation flow rate. The23inverse of the saturation flow rate is the time difference between two vehicles passing the stop line,24the saturation headway. In the simulation, the headway can be adjusted by the parameters of the25car-following model.26

Beside the headway, the number of vehicles in the queue in front of a subject vehicle27is important. The queue length, measured in vehicles, depends on the total number of vehicles28arriving during the cycle time and the proportion of vehicles arriving either during red time or29during the time when there is an existing queue. The proportion of green to red time is defined by30emulating the real signal timings in the simulation. Especially in urban environments, the arrival31of vehicles at an intersection is unevenly distributed. Signalized intersections upstream create32platoons, and these platoons may arrive during green time or during red time. Thus, to correctly33replicate the delay, one must correctly replicate the arrival distribution.34

The calibration was performed in three sequential steps, which considered the time to pass35the intersection, the headway at the intersection, and the arrival time distribution, respectively. The36three steps are independent, except that the time to pass the intersection slightly influences the37headway at the stop line. In each calibration step, we performed enough simulation runs to ensure38stable results.39

Time to pass the intersection40The time to pass the intersection is the difference of time stamps tpSL and tpIS, and is the product of41length of the link and the vehicle speed. Because the geometry is specifically modeled, the desired42speed distribution is the only factor remaining to adjust the time to pass the intersection. Therefore,43


0 2 4 6 8 10 12time to pass intersection [sec]

0

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0.8re

lativ

e sh

are

of v

eh.

5.64

2.88

OL: 0.05D: 0.49

measurementsimulationmean

(a) before calibration

0 2 4 6 8 10 12time to pass intersection [sec]

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veh

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OL: 0.83D: 0.03


(b) after calibration

FIGURE 2 : Time to pass intersection for Intersection 1 Lane 8

we modeled reduced speed areas for each lane inside the intersection. Since, in reality, the driven1speed depends on the movement and the movement corresponds to a lane, each lane was calibrated2separately.3

To analyze the time to pass the intersection, we considered the arithmetic mean and distri-4bution. The distribution was analyzed based on histograms using relative shares. The width of the5bins was set to 0.25 seconds or 0.5 seconds, depending on the number of observations. Figure 2a6shows the distribution of the time to pass the intersection for one specific lane. The displayed7simulation results are based on Vissim default parameters. The mean is shown along with the8histogram. To quantify the quality for calibration, an adequate error measure is required.9

The similarity between the distributions of time to pass the intersection was evaluated by10the overlap between measured and simulated data according to following equation:11

OL =N

∑c=1

min(xc,sim,xc,obs)

OL overlap12xc,sim share of vehicles in class c (simulation)13xc,obs share of vehicles in class c (measurement)14N number of classes15

The sum of minima of each class is considered for the overlap. If both distributions match16exactly, the overlap will be one, since xc,sim and xc,obs are equal. If the distributions do not overlap17at all, the overlap OL will be zero. In this case, either xc,sim or xc,obs is zero, and therefore the18minimum of each class is also zero.19


0 2 4 6 8sim. time to pass intersection [sec]

0

2

4

6

8ob

s. ti

me

to p

ass

inte

rsec

tion

[sec

]RMSPE: 0.38R: 0.36

mean per laney=0.56 x+3.05


0 2 4 6 8sim. time to pass intersection [sec]

0

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8

obs.

tim

e to

pas

s in

ters

ectio

n [s

ec]

RMSPE: 0.08R: 0.96

mean per laney=1.10 x+-0.15


FIGURE 3 : Time to pass intersection in simulation and measurement

To evaluate the average time to pass the intersection, the relative distance between the1means is used:2

D =|x̄obs− x̄sim|

x̄obs

D relative distance of means3x̄sim mean of simulated data4x̄obs mean of observed data5

Hence, an optimal calibration should lead to an overlap OL of 1 and a distance D of 0.6The speed distributions for each reduced speed area were adjusted iteratively, aiming to reduce the7distance of means as much as possible, while at the same time achieving a good overlap of the8distributions. The desired speed distributions are specified by choosing rectangular distributions9as the default in Vissim.10

For the lane displayed in Figure 2, the default distribution from 48 km/h to 58 km/h before11calibration (Fig. 2a) was replaced by a distribution from 15 km/h to 40 km/h (Fig. 2b). After12calibration, an overlap of 0.83 and a distance of means of 0.03 was achieved.13

Before calibration, the average total time to pass the intersection was too low and the distri-14bution on most lanes was too narrow. The measured and simulated values are compared in Figure 3.15For a quantitative assessment of all lanes of simulated and measured data, a linear regression was16computed.17


The deviation between the simulated and measured data is measured by the root mean1squared percentage error (RMSPE):2

RMSPE =

√1N

N

∑i=1

(xi,sim− xi,obs

xi,obs

)2

RMSPE root mean squared percentage error3xi,sim simulated data4xi,obs observed data5

The results of the regression and the RMSPE are also displayed in Figure 3. In addition,6Pearson’s correlation coefficient R was calculated. This measure defines the intensity of the linear7relation of two measurement series.8

R =covsim,obs

ssim · sobs

R Pearson product-moment correlation coefficient9covsim,obs covariance10ssim standard deviation (simulated)11sobs standard deviation (observed)12

With a RMSPE of nearly 40 %, the simulation data differs significantly from the measured13data before calibration (Fig. 3a). The low correlation coefficient R of 0.38 also is a result of14the deviation on various lanes between simulation and measurement. The improvement of the15first calibration step can be seen in Figure 3b. The low RMSPE of 8 % and the high correlation16coefficient (R=0.96) prove that the desired speed distribution inside the intersection was calibrated17successfully for each lane.18

Headways19The headway for each vehicle was calculated as follows. The time a vehicle passed the stop line20was recorded, along with its position in the queue. The headway was then calculated from the21difference between the time stamps tpSL of the vehicle and its leading vehicle. Only vehicles22already arrived at end of queue before the start of green time or before the leading vehicle passed23the stop line were considered.24

In Vissim, the headway at the intersection depends essentially on two factors: the desired25speed behind the stop line and the parameters of the car-following model. Lower desired speeds26mean a smaller difference between current speed and desired speed and hence result in lower ac-27celeration and higher headways. In the modeled networks, the speed behind the stop line is limited28by the reduced speed areas within the intersection, which were configured in the first calibration29step.30

The Wiedemann 99 driving behavior model contains 10 configurable parameters (CC0 to31CC9). Of these parameters, two have the most influence on the headway at the intersection: stand-32still distance (CC0) and minimum headway (CC1). Parameters CC2 to CC7 are related to oscil-33lation behavior. While accelerating at the stop line, vehicles will not enter the interaction state34Follow and therefore will not oscillate. With CC8 and CC9 and with the Maximum and Desired35Acceleration Functions, the actual acceleration is chosen. Hence, these parameters could have an36


1 2 3 4 5 6position in queue

0

0.5

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4he

adw

ay [

sec]

2.251.99

D: 0.11RMSPE: 0.13



1 2 3 4 5 6position in queue

0

0.5

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way

[se

c]

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D: 0.03RMSPE: 0.05



FIGURE 4 : Headway at Intersection 3

impact on the dissipation of the queue. Granted, vehicle accelerations are not accounted for in the1measurement and, for this reason, we accepted the Vissim default settings.2

CC0 is the average desired distance between two vehicles in meters at standstill while3queuing in front of the traffic signal. The headway CC1 describes the speed-dependent part of the4safety distance the driver desires. In Vissim the safety distance dxsafe at a given vehicle speed is5calculated as follows (17):6

dxsafe = CC0+CC1 · v

dxsafe safety distance [m]7CC0 standstill distance [m]8CC1 headway [sec]9v speed [m/sec]10

The influence of CC0 and CC1 on vehicles in the queue is different: CC0 has more impact11on vehicles in positions close to the stop line, while CC1 has more impact on vehicles more distant12from the stop line. The increasing influence of CC1 for vehicles starting at positions far from the13stop line is the result of these vehicles crossing the stop line at higher speeds.14

The average headway for each queue position at Intersection 3 is shown in Figure 4a. The15results look similar for the other intersections. Obviously, the headway depends on the position in16the queue. The average headway for all vehicles regardless of position is also shown (dotted line).17The deviation between the simulated and measured data is measured by RMSPE. To evaluate the18average headway for the entire intersection, the difference of the means D was used.19

The calibration of the headway was performed in two steps. First, the headway was cali-20brated for vehicles in the first position in the queue. Second, an optimal parameter combination of21CC0 and CC1 was determined for the following vehicles.22

The vehicles in the first position are treated separately, since they react directly to the23changed signal and not to a leading vehicle. Vissim allows one to set a value for the distance to the24


0.9 1 1.1 1.2 1.3 1.4 1.5CC1

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C0

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ean

(a) distance mean

0.9 1 1.1 1.2 1.3 1.4 1.5CC1

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SPE

(b) RMSPE

FIGURE 5 : Error measures for headways for CC0/CC1-combinations for Intersection 3

stop line for the first vehicle, the so-called standstill distance for static obstacles. This parameter1influences all vehicles that are not stopping due to other vehicles, but due to a red signal. Another2special feature deals with the reaction time at signals. The regular sequence in Germany is red, red-3amber, green, amber. Passing the stop line is allowed only during green. In Vissim, a red-amber4signal can be interpreted as green or red. The default settings in Vissim assume that vehicles start5accelerating when the signal shows red-amber. The analysis of the measured data shows that this6setting results in a too low headway for the first vehicle. Therefore, the behavior option wait (red)7was set for red-amber signals. Finally, the headway of the first vehicle can be calibrated by setting8the standstill distance for static obstacles.9

In a second step, the parameters CC0 and CC1 were calibrated simultaneously. During this10process, the space of all reasonable combinations of CC0 and CC1 was systematically sampled in11intervals of 0.1. Several Vissim simulation runs were performed for each parameter combination.12As a result of this process, the parameter combination of CC0 and CC1 is determined, that simul-13taneously minimizes D and RMSPE. Figure 5 shows the error measures for one intersection for all14simulated combinations. Based on this information, a set of parameters was manually chosen for15which both error measures were acceptable. Vissim’s default parameter and the calibrated param-16eter sets for the four modeled intersections are shown in Table 1. The headway per position and17the average for Intersection 3 after this calibration step are shown in Figure 4b.18


1 1.5 2 2.5 3 3.5 4sim. headway [sec]

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s. h

eadw

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sec]

RMSPE: 0.14R: 0.47



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hea

dway

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FIGURE 6 : Headways in simulation and measurement

The average headway for all lanes before and after calibration is shown in Figure 6. The1regression parameters and the correlation coefficient show that the default parameters of Vissim do2not replicate the average headway very well. After calibrating CC0 and CC1 for each intersection,3the simulated data matches the measured data much better. Since the parameters were set for the4entire intersection and not separately for each lane, the correlation coefficient is still relatively low5(R = 0.80) but better than with the default values (R = 0.59). The RMSPE decreased from 12 % to68 %. A lane specific calibration could improve the match even further.7

TABLE 1 : Calibrated car-following parameter for different intersections

Parameter default Intersection1 2 3 4

StandDist 1.5 0.3 2.1 1.2 2.9CC0 (W99) 1.5 2.1 2.5 2.0 2.1CC1 (W99) 0.9 1.3 1.3 1.4 1.8

The default settings in Vissim for CC0 and CC1 are rather low, resulting in optimistically8high capacities. To achieve realistic headways, CC1 needs to be about 1.3 or 1.4 seconds. The9default value of 1.5 meters for CC0 is also quite low. Values between 2.0 and 2.5 meters were10determined for the observed intersections.11


0 0.2 0.4 0.6 0.8 1sim. share of veh. w/o stop

0

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s. s

hare

of

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sto

pRMSPE: 0.70R: 0.41


(a) with Poisson distributed vehicle input

0 0.2 0.4 0.6 0.8 1sim. share of veh. w/o stop

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(b) exact input times replicated from measurement

FIGURE 7 : Share of vehicles passing without stopping in simulation and measurement.

Arrival time distribution1The calibration described above was based on a Poisson-distributed vehicle input with only the total2volume defined according to the measurements. Since in an urban environment the vehicle flows3are often influenced by surrounding junctions, the exact arrival distribution should be taken into4account when comparing simulation results with measurement data for calibration. A distribution5diverging from a Poisson-distributed vehicle input can result in a different share of vehicles passing6without stopping due to different levels of coordination between the signalized intersections.7

The standard vehicle input in Vissim is based on a Poisson process. To reproduce the exact8arrival times from the measurements in Vissim, the vehicle generation was controlled through9Vissim ’s API, the COM-interface. This interface allows one to manage objects and their specific10attributes during runtime. The first time stamp recorded for each vehicle in the measurement was11the arrival time at the end of queue. Since the distance between the end of the queue and the stop12line is variable, the exact distance from the stop line is unknown for a vehicle arriving at the end of13the queue. Thus, all vehicles were created at the beginning of the link leading to the intersection,14resulting in a distance to the stop line of about 300 meters.15

To evaluate whether the modeled arrival distribution matches the measured arrival time16distribution, we analyzed the share of vehicles passing without stopping. Figure 7a shows the17situation after calibrating the time to pass the intersection and the headways based on Poisson-18distributed vehicle input. Obviously, the share of simulated vehicles passing without stopping19does not match the share observed. For some lanes, the share is too low and for others, it is too20high. Using the COM-interface to replicate the arrival times from the measurement resulted in21a significant improvement in the share of vehicles passing without stopping (Fig. 7b). However,22since the exact time stamp for the vehicle input 300 meters in front of the intersection was not23recorded in the measurements, this calibration step is still only an approximation.24


Resulting Delay1The project’s goal was to calibrate Vissim in a way that allows one to produce realistic delay.2Figure 8 shows how this goal has been reached by comparing simulation results and measurement3data before calibration and after each step of the calibration procedure:4

• before calibration (a)5• calibrated time to pass the intersection (b)6• calibrated headway (c)7• calibrated arrival time distribution (d)8Each displayed point represents the arithmetic mean of the delays of all vehicles on one lane9

within the considered hour. Each diagram includes the previous calibration steps. The calibrated10measures are independent. Only the reduced speed areas have a slight influence on headways at11the intersection. Thus the time to pass the intersection is calibrated before the headways.12

A comparison of Figures 8a and 8b reveals that the time to pass the intersection has a neg-13ligible influence on delay. This is reasonable, since the time spent driving through the intersection14(without waiting times) is only a few seconds, i.e., much less than the time spent waiting.15

The observed average headway at the intersection was higher than in the simulation based16on Vissim default parameters. After adjusting the headway, the delay increased on most lanes17(Figure 8c). This again is reasonable, since higher headways mean lower lane capacities.18

Figure 8d shows that the arrival distribution influences delay significantly. The arrival19distribution is important when the saturation of the intersection is low enough so that a significant20portion of the vehicles arrive during green time and do not have to queue at all. As soon as a21queue has built up, the impact of the arrival distribution decreases, since the queue acts as a buffer22between the stop line and the arrival flow.23


0 10 20 30 40 50 60sim. delay [sec]

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RMSPE: 0.19R: 0.90


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(b) time to pass the intersection calibrated

0 10 20 30 40 50 60sim. delay [sec]

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(c) headway calibrated

0 10 20 30 40 50 60sim. delay [sec]

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ay [

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(d) arrival time calibrated

FIGURE 8 : Measured and simulated delay after each step of the calibration procedure


CONCLUSION1The aim of the present study is to calibrate Vissim for signalized intersections, so that the delay2is correctly reproduced. For this purpose, video measurements were taken at four signalized in-3tersections in urban Germany. The resulting data was used to calibrate Vissim models of these4intersections. Three measures that are relevant for realistic behavior at intersections were iden-5tified: the time to pass the intersection, the average headway, and the arrival distribution of the6vehicles. Calibrating the time to pass the intersection is equivalent to calibrating the geometric7delay. The average headway influences how fast a queue at the intersection dissolves and hence8influences control delay. Another factor influencing control delay is the queue length, measured in9number of vehicles. Besides the rate at which the queue dissolves, the queue length depends prin-10cipally on the arrival distribution of the vehicles, i.e., whether the vehicles arrive at green without11an existing queue or at the end of an existing queue.12

The calibration of time to pass the intersection had only a minor effect on total delay,13since geometric delay is secondary to control delay. The effect of the average headway on total14delay was much greater. Because the default arrival time distribution in the simulation differed15substantially from the observed arrival time distribution, adjustment of the arrival time distribution16had the greatest influence on delay.17

When simulating traffic flow at intersections, it is important to ensure correctly reproduced18control delay, since control delay is the principal performance measure used to evaluate LOS.19Correctly calibrated average headway is one important factor for reproducing measured control20delay. For Vissim, using the Wiedemann 99 model and parameter values in the range from 2.0 m21to 2.5 m for CC0 and 1.3 s to 1.4 s for CC1 produced good results for the average headway at22the signalized intersections used in this study. For comparability of the delay in the simulation23with measured data, it is important to reproduce the measured arrival distribution of the vehicles24in the simulation model. Using the procedure presented here, we showed that delay at signalized25intersections can be realistically modeled, provided the microscopic traffic flow simulation Vissim26has been calibrated correctly.27

ACKNOWLEDGMENT28This paper is based on research sponsored by the German Federal Ministry for Transport and29Digital Infrastructure, represented by the Federal Highway Research Institute, under project no.30FE 03.0424/2007/DGB. The contents of this paper solely reflect the views of the authors. Some of31the video measurements were performed by the Technical University of Dresden, Chair of Traffic32Engineering.33

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