# Study Group 2nd BEES Group – ESGI 134. Modelling Departure Traffic

#### Here we would like to present the second problem proposed by city of Koblenz and called “Modelling Departure Traffic”.

Loreley Open-Air Theatre is located on the Lorelei rock in St. Goarshausen in Germany. It is a popular location for concerts and music festivals with a capacity of about 15,000 people.

It is possible to get to the place only by car or by local bus. The car park provides up to 5,250 parking places. Thus, huge traffic jams happen because all the cars usually try to leave simultaneously after the end of the show and there is the only one road leading from the car park. Leaving the car park can take up to 4 hours even with police regulation and additional traffic, at worst.

The main problem occurs at the crossroad where the two lanes are merged into the one at the turn. The average velocity of the car flow decreases dramatically and this results traffic jams.

Therefore, the task was to find a way to reduce the time of departure.

The group started their work with rough time estimation of leaving for all cars. The average velocity was defined from the video provided by the problem supervisor.

The next step was to create a graph model of roads and parking lots. Ten parking lots were considered sources and crossroads were presented as nodes. Roads were assigned different traffic capacity. This graph model was implemented in Matlab and two different variants of regulation were tested.

The first one had principal main road with three independent lanes and the second one contained partly merged main road with only two independent lanes. This allowed to decrease leaving time.

The first basic idea was to take consequently all cars from one parking lot and then to move them to another one. Indeed it can give quite good result but only if the feelings of drivers are ignored. It is obviously unfair to keep one lot waiting much longer than the other. Another idea was exactly the opposite and it was to take a car at a time from each parking lot. But in this case another problem arises as every car needs to accelerate, average velocity decreases and time increases. Thus, a regulation on the main crossroad as shown on the picture below was decided to be set.

Three different cases were considered. Allow the traffic during

1. Equal time (one minute) for each road, main road has three lanes;
2. Equal time (one minute) for each road, main road has two lanes;
3. 7 minutes for the yellow road, 1 minute for the blue road, 0.5 minute for the green road.

The departure took  4 hours in the first case and 3 hours in the second one. The third case was the most successful one as the departure took 2 hours and 45 minutes.

Hence, our recommendations for traffic improvement were

• to relocate the flow merging place on junction

• to regulate the crossroads via policemen or traffic lights,

• to create special regulation for cars turning right and to prioritize the parking lots.

Finaly, we would like to take the presented opportunity and to thank all the facilitators, hosts and participants of the Study Group 2nd BEES Group – ESGI 134. It was a great pleasure to participate in this event and we are looking forward to the next one.