# the example problem

**Question description**

In this project, you are to solve the example problem (as shown in Fig. 9 and Table 1) presented in *Optimization of Traffic Signal Settings Mixed-Integer Linear Programming *by Garnter, N.H., Little, J.D.C., and Gabbay, H. using the procedure and methodology discussed in the same paper 1-

Prepare the model input data. Notice that the background cycle length of the example network is set as 80 seconds. Therefore this task mainly includes the *green splits *of each signal. As there is no sufficient information on this in the paper, you can assume 1) all signals are two phases (i.e. all left turns are permissive); and 2) green splits are proportional to the critical lane volume (i.e. the so-called Webster equation), you can assume the lost time per phase is 4.5 seconds. You can also design more sophisticated phases by making appropriate assumptions on the left or right turn volumes.

2-

Present the actual formulation of the optimization model, including the objective and constraints. This means that for each link, report the actual linear approximation formulation of the delay function (in terms of delay) based on the cycle length, green splits, and traffic flow.

3-

Code/solve the optimization model. You can use any software/optimization package for this, including but not limited to, Excel LP Solver, Matlab, Maple, GAMS, C/C++, Java.

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