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imes that differ by Δt, t2 = t1 + Δt. Using similar triangles,
it could be shown that the critical gap, tc, is
( ) ( )
( )
1 n p r m
t t t r m c − + −
= + Δ − [1]
where
m = number of accepted gaps less than t1
r = number of rejected gaps greater than t1
n = number of accepted gaps less than t2
p = number of rejected gaps greater than t2.
This calculation of critical gaps was done for all the sites and was used for the simulation
program input. The results of these sites from the program were compared with the field values.
Measures of Effectiveness Data
The measures of effectiveness (MOEs) data that were reduced from the tapes of the data
collection sites were used to validate the event-based simulation program. The MOEs examined
included “number of stopped left-turning vehicles” at unsignalized sites and “green times on the
subject link,” “average left-turn vehicle stopped delay,” and the “maximum queue length on the
subject link” at signalized sites. Since the traffic signal controller at these sites was actuated, the
green times were not constant for all cycles. The main MOE data that were extracted from the
videotapes for signalized and unsignalized intersection are described as follows:
• MOEs for signalized intersections. The queues that were present (on the subject link)
at the beginning of green times were counted from the videotapes. These were used
in validating the simulation program. In other words, the queue length counter was
incorporated in the program and the queue lengths generated by the program was
compared with the ones seen in the field. In addition to the queue length, left-turn
vehicle delay was also reduced from the videotapes. The times of left-turn vehicle
arrivals and departures were recorded from the videotapes, and each left-turn vehicle
delay was calculated by subtracting arrival time from departure time. An average leftturn
vehicle delay from the field was compared with the distribution of average leftturn
delays from the simulation output.
• MOEs for unsignalized intersections. The MOE used for validation of the
unsignalized model was “number of left-turning vehicles that were stopped” on the
subject link. These data were reduced at every site by examining the subject link and
manually counting the number of left-turning vehicles that had to stop at the
intersection.
9
Development of Event-Based Simulation Model
Event-based simulation programs were developed in this study because existing
commercial programs do not directly provide various MOEs needed for developing left-turn lane
guidelines. In addition, an event-based simulation tends to be easier to code and execute faster
than microscopic simulations, given that the analyst cannot use a commercial package and thus
will have to develop the original software.
The event-based simulation programs developed in the project are part of a complete
package named the Left Turn Guidelines Analysis Package (LTGAP). In an event-based
simulation, the program has a list of events and jumps (in time) from one event to another. For
example, the arrival of the vehicles on a particular approach is an event, as are the departures and
signal phase changes. The system time moves in steps from one event to another rather than
moving in a fixed time s