For office use only
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Team Control Number
69427
Problem Chosen
B
For office use only
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2017
MCM/ICM
Summary Sheet
Optimal Design of Toll Plaza Based on Minimum Risk Maximum Flow
The design of highway toll plaza is crucial to the traffic flow and tollbooths operation efficiency.
We study the optimal design program of toll plaza from three aspects：accident rate, traffic flow
and construction cost. At the same time, we give the design figures and merging pattern of toll plaza.
The first stage, we determine the number of tollbooths by assuming that the traffic condition is
normal. The number of toll lanes is decided by traffic capacity, traffic flow and service level. We
establish a function model of tollbooths through the above three indexes. When the number of lanes is
3, we know that the number of single-way toll lanes should be 7 by calculating the traffic data from
the highway tollbooths of 417 highway in Florida. We find in the sensitivity analysis that the traffic
flow is positively related to the number of toll lanes.
The second stage, the optimal model of the merging pattern based on minimum risk and
maximum throughput is established. This model is on account of the analysis of the performance of
the existing toll plaza to optimize its design program, and we regard the deceleration shunt and
acceleration merging of the whole toll plaza as a directed and weighted network flow. Similarly, by
using the data of the highway tollbooths of 417 road in Florida, we obtain the program of merging
pattern (Shown in Fig.5). The maximum traffic flow of this program can reach 1375 vehicles per hour,
the accident rate can be reduced to 0.9%.
The third stage, taking into account the vehicle's variable motion in the toll plaza, we employ the
driving distance between the front and rear vehicles and the braking distance of the rear vehicle to
determine the size of the toll plaza, and establish a optimization model to minimize the construction
cost. Likewise, using the data from the highway tollbooths of 417 road in Florida, we obtain the
smallest toll plaza (Shown in Fig.6) whose area about 4650.1875 square meters.
Remarkably, we test the model in detail. The traffic flow and the accident rate are lower in light
traffic flow. When the traffic flow is larger, the accident rate is increased by 0.05% compared with the
slight traffic flow, that is, the size of traffic flow on the toll plaza design is not significant. After
examining the impact of adding autonomous vehicles into mixed traffic, we add 500 autonomous
vehicles into the traffic flow based on unit traffic flow on Highway 95 in New Jersey. And the accident
rate was reduced by 0.83%. In view of the proportion of the three tollbooths, the greater the proportion
of automatic tollbooths, the smaller the entire toll area, the smaller the number of tollbooths, the
stronger the capacity of the tollbooths.
Finally, we apply the model to study the optimal design of the highway toll plaza in New Jersey.
We select the New Jersey Highway No.95 as the research object, and we get its shape about toll plaza
and the figure of merge pattern (See Fig.12). The number of toll lanes is 10, and the proportions of the
three tollbooths is 5:3:2, the area of the toll plaza is 9614.56
2
m
. Last but not least, writing a letter to
the New Jersey Turnpike Authority about the design scheme．
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