Queueing: In a railway marshalling yard, goods train arrive at a rate of 30 trains per day.

Assume that inter-arrival time and the service time distribution follows an exponential distribution with an average of 36 minutes.

Using M/M/I Calculate and Explain the following:

1. Service Rate
2. Mean queue size
3. Service Utilization
4. Expected No of units Waiting in system
5. Expected Waiting Time in system
6. Expected Waiting Time in the Queue
7. The probability that queue size exceeds 11
8. If the input of the train increases to an average of 35 per day, what will be the changes in queue size?

M/M/I probability formula: P n = (lambda / mean)^2 * (1 - lambda / mean)

Please Explain the steps in details.