5 There is an insert for use in parts (iii) and (iv) of this question.
This question concerns the simulation of cars passing through two sets of pedestrian controlled traffic lights. The time intervals between cars arriving at the first set of lights are distributed according to Table 5.1.
\begin{table}[h]
| Time interval (seconds) | 2 | 5 | 15 | 25 |
| Probability | \(\frac { 3 } { 7 }\) | \(\frac { 2 } { 7 }\) | \(\frac { 1 } { 7 }\) | \(\frac { 1 } { 7 }\) |
\captionsetup{labelformat=empty}
\caption{Table 5.1}
\end{table}
- Give an efficient rule for using two-digit random numbers to simulate arrival intervals.
- Use two-digit random numbers from the list below to simulate the arrival times of five cars at the first lights. The first car arrives at the time given by the first arrival interval.
Random numbers: \(24,01,99,89,77,19,58,42\)
The two sets of traffic lights are 23 seconds driving time apart. Moving cars are always at least 2 seconds apart. If there is a queue at a set of lights, then when the red light ends the first car in the queue moves off immediately, the second car 2 seconds later, the third 2 seconds after that, etc.
In this simple model there is to be no consideration of accelerations or decelerations, and the lights are either red or green.
Table 5.2 shows the times when the lights are red.
\begin{table}[h]
| \multirow{2}{*}{} | red start time | 14 | 50 | 105 | 155 |
| \cline { 2 - 6 } | red end time | 29 | 65 | 120 | 170 |
| \multirow{2}{*}{} | red start time | 10 | 55 | 105 | 150 |
| \cline { 2 - 6 } | red end time | 25 | 70 | 120 | 165 |
\captionsetup{labelformat=empty}
\caption{Table 5.2}
- Complete the table in the insert to simulate the passage of 10 cars through both sets of traffic lights. Use the arrival times given there.
- Find the mean delay experienced by these cars in passing through each set of lights.
- How could the output from this simulation model be made more reliable?