Queuing systems, Little, Pasta - compulsory test

Hint: these questions can be answered using the basic definitions and rules we covered on the lecture. You do not need to define and solve Markov chains!

1. A dangerous new virus is spreading in Wonderland. There are on average 10 new infected elves every day, and they recover, on average, after 14 days.  On average, how many elves are sick at the same time? 

2. There is a full day consultation in the queuing theory course. Students arrive  according to a Poisson process, with an intensity of 2 students per hour.  The teacher answers the students one by one. Students wait if the teacher is busy and then they ask questions for a random amount of time, on average for 20 minutes. What is the probability that the teacher is busy at a random point of time? What is the probability that an arriving student finds the teacher busy? Motivate your answer. Give the queuing model of the consultation with Kendall notation.

3. Students are scheduled for an oral exam, one student for every 30 minutes. The exam takes exactly 20 minutes. What is the probability that the teacher is busy at a random point of time? What is the probability that an arriving student finds the teacher busy? Motivate your answer. Give the queuing model of the exam with Kendall notation.