Example: Single-Lane Traffic Analysis

It is described in different sources [1, 2]. So, this is chapter 15 of [2] and section 6.18 of [1].

The system to be modeled in this example consists of the traffic flow from
two directions along a two-lane road, one lane of which has been closed for
500 meters for repairs. Traffic lights have been placed at each end of
the closed lane to control the flow of traffic through the repair section.
The lights allow traffic to flow for a specified time interval from only
one direction. When a light turns green, the waiting cars start and pass
the light every two seconds. If a car arrives at a green light when there
are no waiting cars, the car passes through the light without delay. The car
arrival pattern is exponentially distributed, with an average of 9 seconds
between cars from direction 1 and 12 seconds between cars from direction 2.
A light cycle consists of green in direction 1, both red, green in direction 2,
both red, and then the cycle is repeated. Both lights remain red for 55 seconds
to allow the cars in transit to leave the repair section before traffic from
the other direction can be initiated.

The objective is to simulate the above system to determine values for
the green time for direction 1 and the green time for direction 2 which
yield a low average waiting time for all cars.

[1] A. Alan B. Pritsker, Simulation with Visual SLAM and AweSim, 2nd ed.
[2] Труб И.И., Объектно-ориентированное моделирование на C++: Учебный курс. - СПб.: Питер, 2006