Unformatted text preview: al distributions for representing speed
profile are the normal, lognormal, and composite distributions [24]. The normal
distribution was used in the ARENA simulation model to simulate the traffic. The
cumulative frequency graphs of the actual data and the normal distribution using actual
data parameters are given in Figure 16 for driving lane and in Figure 17 for passing lane. 60
1.2
N= 11870
Average= 60 MPH
Standard Deviation= 4.73 MPH Cumulative Percentage (%) 1 Minimum= 44 MPH
Maximum= 67 MPH 0.8 0.6 0.4 0.2 0
35 45 55 65 75 85 95 Speed (MPH)
Normal Distribution Actual Data Figure 16: Comparison of Actual Speed Data for Driving Lane Collected on
08/20/2004 Friday with the Normal Distribution
1.2
N= 6987
Average= 66 MPH
Standard Deviation= 4.97 MPH
Minimum= 51 MPH
Maximum= 73 MPH Cumulative Percentage (%) 1 0.8
0.6
0.4
0.2
0
35 45 55 65 75 85 95 Speed (MPH)
Normal Distribution Actual Data Figure 17: Comparison of Actual Speed Data for Passing Lane Collected on
08/20/2004 Friday with the Normal Distribution 61
The mean and the standard deviation for the speeds at the beginning of the work
zone were calculated using the field data and they were entered into the model. In
addition to assigning speeds to the vehicles at the beginning of the simulation for free
flow conditions, speeds were also assigned to the vehicles at the beginning of the taper
according to the average and standard deviations calculated using the field data. In Table
15, the assigned speeds for the vehicles before the construction zone and at the
construction zone are given for both driving and passing lane. As mentioned earlier the
microwave radar trailers provide the moving average speed of last 16 vehicles recorded
in the output. The averages and standard deviations given below are the moving average
speed of 16 vehicles. The same distributions were used for the 24 hour simulation time
period. Table 15: Vehicle Speeds used for the Transporters in the ARENA Simulation
Model Driving Lane
Passing Lane At the Beginning of Simulation
Standard
Average
Deviation
(feet/second)
(feet/second)
88
3.47
97
3.67 At First Merging Sign
Standard
Average
Deviation
(feet/second)
(feet/second)
75
10.27
84
8.80 62
3.2.2.1.5 Car Following Behavior
The car following behavior of the vehicles is dependent on the gap acceptance of
the following vehicles. The distance between two consecutive vehicles provides safe
following distance for the vehicles. The safe distance is dependent on the speed of the
vehicles, length of the vehicles, deceleration and acceleration rates of the vehicles, and
response time of the drivers.
In ARENA simulation program, the guided vehicle property of the transporters
module automatically adjusts the distance between the transporters according to their
acceleration and deceleration rates and speeds. The model prevents the collision between
the transporters. However, in the simulation model minimum following distance is also
specified for the vehicles. The car following distance between the vehicles is not less than
50 ft when the vehicles are in free flow conditions. The car following distance is not less
than 25 ft for the jam density conditions, and when there are vehicles waiting in the
queue for merging the minimum distance between the vehicles is not less than 4 feet for
passenger cars and not less than 5 feet for trucks. The safe distances between two
vehicles when they are stopping are integrated into the model using additional lengths for
the vehicle length attribute of the transporters as it was mentioned earlier. The distance
between two vehicles was not less than these minimum distances.
3.2.2.1.6 Gap Acceptance for Merging and Lane Changing Behavior
Gap acceptance is the main factor affecting the lane changing behavior. When a
termination of a lane occurs, the vehicles on that lane have to stop until they can find 63
sufficient gap on the traveling lane. The acceptable gap for changing lanes is dependent
on the speed of the vehicle which will change lane, and the speed of the vehicles on the
other lane. The distance (gap) between two vehicles is calculated using the link and zone
properties of ARENA simulation program. Lengths are assigned to the links and each
link is composed of zones which have different lengths. According to the speeds of the
vehicles, the model checks the occupancy of the links and zones for the needed gap and if
there is an available distance for changing lanes, the vehicles change their lanes. The
required gap is also dependent on the type of the vehicles. There are two types of vehicles
simulated in the model; passenger cars and trucks. Their length is added to the required
gap for lane changing. Figure 18 shows the placement of the vehicles in the gap
acceptance calculations. Required
Gap
Vehicle
Length Lag
Gap Lead
Gap Figure 18: Gap Acceptance Kanaris et al. [32] defined a minimum safety spacing during lane changing
(MSSLC) between the leading vehicle and following vehicle on the desired travel lane 64
for the lane changing vehicle. He stated that the distance between two vehicles should not
be...
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 Spring '13
 Mr.Kau
 Normal Distribution, ........., Cumulative distribution function, Driving Lane

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