Module 3 : Microscopic Traffic Flow Modeling

Lecture 16 : Microscopic Traffic Simulation

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Model calibration

The activity of specifying data to the model that describes traffic operations and other features which are site specific is called calibration of the model. In other words, calibration is the process of quantifying model parameters using real-world data. This data may take the form of scalar elements and of statistical distributions. Calibration is a major challenge during the implementation stage of any model. The commonly used methods of calibration are regression, optimization, error determination, trajectory analysis etc. A brief description about various errors and their significance is presented in this section. The optimization method of calibration is also explained using the following example problem.

Numerical example

The parameters obtained in GM car-following model simulation are given in Table below. Field observed values of acceleration of follower is also given. Calibrate the model by finding the value of $\alpha$. Assume l=1 and m=0. Use optimization method to solve the problem.

Table 1: Parameters of GM Model

Observed Acceleration ($a^{obs}$)	Velocity difference, dv	Distance headway, dx
0.23	1.5	29.13
0.46	1.88	29.97
0.67	1.16	30.73
0.82	0.32	31.10

Solution

Step 1: Formulate the objective function (z).

$$\mathrm{Minimize}~z = \sum_{i=1}^4\left(a_i^{obs} - a_i^{cal}\right)^2.$$

Step 2: Express $a_i^{cal}$ in terms of $\alpha$. As per GM model (since l=1 and m=0),

$$a_i^{cal}= \frac{\alpha \times dv}{dx}$$

Step 3: Therefore the objective function can be expressed as:

$$z=(0.23- 0.05 \alpha)^2+ (0.46- 0.06 \alpha)^2+ (0.67- 0.04 \alpha)^2+ (0.82- 0.01 \alpha)^2$$

Step 4: Since the above function is convex, differentiating and then equating to zero will give the solution (as stationary point is the global minimum). Differentiating with respect to and equating to zero,

$$\frac{dz}{d\alpha} = 0$$

Then, value of $\alpha$ is obtained as 9.74.