This exercise works with Situation 1. So choose it from the menu File.
1. Enter phases yourself a) Provide a traffic control with two phases and a round length of 60 seconds.
Remark: New phases can be added with the plus symbol. The length of the phase sets automatically to a default value. Lane A should have once green and once red. You change to color of the traffic light of a lane by clicking on the colored circle below the name of the lane in the traffic control panel. Name at least one situation in everyday life where it occurs, that traffic on a street runs sometimes and sometimes not.
2. Arrival rate and distribution
We now take a closer look at the arrival rate. In the panel Traffic Volume you can change its values and whether it is Poisson or uniform distributed. a) Set the arrival rate to 20 cars per minute, Poisson distributed and run the simulation for some rounds. Observe how the arrival rate changes in the Charts panel. Remark: Choose the Charts tab and there click on arrival rate to show this graph. You can click on this tab while the simulation is running. Draw a sketch of the resulting curve. b) Observe what change if you change the Traffic Volume to be uniform distributed.
Draw again a sketch of the resulting curve. c) How do the two sketched curves from a and b differ? d) What do the tow curves have in common? e) When would you choose Poisson distribution, when uniform? Justify your answer.
3. Throughput and utilization a) What is for these settings the theoretical throughput
 t, the arrival rate

and the utilization

? Remark: There is a sample calculation on the introductory slides. b) Run the simulation for 5 rounds. Note the values of the effective throughput
 e the arrival rate

and the utilization

from the statistics tab.
, c) How do you need to change the traffic control in order to have the effective throughput
 e
closer to the theoretical throughput
 t
?
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4. First experiment a) Start a simulation with the following settings: Situation 1, arrival rate = 35 cars/minute, 2 phases of same length (28 seconds), one phase with red and the other one with green traffic light, round length 60 seconds. Wait until at least 5 rounds are over before reading the values, this leave us with a situation that is settled down. b) What values do you get from the simulation for arrival rate

, effective throughput
 e
and utilization

? c) Take a look at the chart and draw a sketch of how the number of waiting cars changes over time. What happens here?
5. Second experiment a) Decrease the arrival rate to 10 cars/minute. b) What is the utilization now? Calculate it first and then note it from the data tab of the simulation. Is there traffic jam? c) How does the number of waiting cars change over time? Observe the chart and explain the changes.
6. Third experiment a) Run the simulation again with an arrival rate

= 35 cars/minute. Change to the
Data tab and print the values of the effective throughput and the arrival rate.
Explain these two curves, i.e. why these settings lead to traffic jam. b) What needs to hold for arrival rate and throughput so that this traffic setting does not cause congestion? c) The utilization

is the quotient between arrival rate

and throughput
 t
:

=
For which values of the utilization can “traffic jam unlikely” be predicted? For

/
 t
. which values of the utilization can traffic jam be predicted?
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7. Traffic control with two phases
In this exercise you build a traffic control for Situation 2. The uniform distributed arrival rate for lane A is 30 cars/minute and for lane B 5 cars/minute. Create two phases with a round length of 60 seconds. a) Set both phases to 28 seconds, one phase green traffic light for lane A, the other green traffic light for lane B. Run the simulation for 5 rounds. Observe in the charts the changes in the arrival rates of lane A and B. Take as well a look at the values of the utilization. Do we get congestion in this traffic? Justify your answer. b) Does the situation improve if the length of the green phase of lane A is increased to 40 seconds? Justify your answer. c) Change the length of both phases such that the traffic runs as smoothly as possible. How do you do that? Keep the length of one round at 60 seconds.
8. How many phases are needed?
This exercise works with Situation 5 . The Poisson distributed arrival rates are: lane A: 10 cars/minute, lane B: 30 cars/minute, lane C: 5 cars/minute, lane D: 25 cars/minute, lane E: 5 cars/minute, the length of a round as before 60 seconds. a) How many phases are at least needed such that each lane has a green traffic lane in at least one phase? Why? b) Work with three phases of 18 seconds each. Try to get a traffic control where the traffic runs as smoothly as possible by only changing the color of traffic lights of the individual lanes. Hint: Try to maximize the number of lanes that have green traffic lights at a certain time. c) How do the values of the utilization change in your simulation? Observe the utilization in the charts; it might be best to draw the utilization of each lane on the same chart. Where seems there to be a bottleneck? Can you do anything against this (except decreasing the arrival rates)?
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