4. There are two tennis courts in a park. Pairs of players arrive at rate 3 per hour and play for a random time which ha
Posted: Wed May 11, 2022 8:28 pm
4. There are two tennis courts in a park. Pairs of players arrive at rate 3 per hour and play for a random time which has exponential distribution with mean 1 hour. If there are already two pairs of players waiting then the new arrivals will immediately leave. (a) Find the stationary distribution of the process. Hint: find a reversible measure. (b) What is the long run average number of pairs at the tennis courts? (We only keep track of the pairs that are playing or waiting for a court.)