Counting Cars: @RISK Models Traffic Congestion

In their article titled “Estimation of Mixed Traffic Densities in Congested Roads Using Monte Carlo Analysis” in Air & Waste Management Association’s April 2015 EM Magazine, authors Brian Freeman, Bahram Gharabaghi, and Jesse Thé use @RISK to create a novel method to estimate the number and type of vehicles on a 1-km stretch congested roadway.

When researchers need to model traffic patterns, they go out and count cars, multiple times a day at multiple locations, explains researcher Brian Freeman. Thus, he wanted to devise a more efficient method for evaluating traffic congestion.


Freeman and his colleagues first assumed that each vehicle occupies road space based on its length (L) and inter-vehicle gap (IVG) during congested traffic. Both IVG and L are independent variables subject to a wide range of values. A vehicle’s length may average from 1.8 m for a sedan, and up to 9.7 m for a large bus. IVGs are independent of the vehicle due to driver behavior and changes in speed due to the vehicle traveling ahead. The authors accounted for four classes of vehicle types, including sedans, SUVs, midsized buses, and large buses, and considered speeds from 5 to 40 KPH.

Each vehicle length was assigned its own PERT distribution from vehicle manufacturer data. Using @RISK, the authors ran their stochastic model using 5,000 iterations on each variable at 5, 10, 15, 20, and 40 KPH at the same time, for 1-KM stretch of road. During each iteration, a vehicle class was randomly selected from the four classes for each space.

The resulting graphs of the @RISK model yielded a power curve that approximates the expected number of cars at each speed, thus giving researchers a fast, convenient tool for better understanding and estimating vehicle numbers in traffic. For Freeman, the benefit of using @RISK for this research was its efficiency. “You can quickly create a model in Excel that would otherwise require a very complicated statistical tool package to set up,” he says. “You can easily create your model without having to become an expert in statistics.”

Read the EM Magazine article here, and see the Palisade case study here.


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