In a railway marshalling yard, goods trains arrive at a rate of 36 trains per day. Assuming that the inter-arrival and service time distributions both follow exponential distribution with an average of 30 minutes, calculate the following:

(i) Traffic intensity

(ii) The mean queue length

(iii) Probability that the queue size exceeds

(i) Traffic Intensity (ρ):

Traffic intensity (ρ) can be calculated using the formula:

\[
\rho = \frac{\lambda}{\mu}
\]

Where:
- \(\lambda\) is the arrival rate, and
- \(\mu\) is the service rate.

Given:
- Trains arrive at a rate of 36 trains per day, so the arrival rate \(\lambda = 36 \text{ trains/day}\).
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