The owner of an exclusive restaurant has two tables but only one waiter. If the second table is occupied, the owner waits on that table himself. Service times are exponentially distributed with mean 1 hour, and the time between arrivals is exponentially distributed with mean 1.5 hours. When the restaurant is full, people must wait outside in line.
a) What percentage of the time is the owner waiting on a table?
b) If the owner wants to spend at most 10% of his time waiting on tables, what is the maximum arrival rate that can be tolerated?