There are 4 swings in the playground in Evelyn Greer Park. Two of them are for small kids (less

than 2 years old) whereas the other two are for bigger kids. Children come to play the swing

according to a Poisson distribution with the average arrival of 6 per 15-min (i.e., 24 per hour).

Among them, two are small kids and 4 are big kids. Assume all kids come alone so the arrivals

of small and big kids are independent. A small kid will play the swing for 10 min on average, but

a big kid will only play for 5 min and get attracted away by other more exciting activities. The

playing time is exponentially distributed for all kids.

1.What is the utilization of the 4 swings; what is the utilization of the two for the small kids?

2.On average how long must a big kid wait until it's his/her turn to play?

3.How many kids will you see on average either playing the swing or waiting for their turns?

4.What is the probability that a kid comes to the playground and finds 4 empty swings?

5. On average how many small kids are playing swings? How many are waiting for their turns?