Jim's Coffee has a single drive-in service window. On Friday mornings, customers arrive at the drive-in window according to a Poisson process, at an average rate of 10 customers per hour. Service at the drive-in window is provided at an average rate of 15 customers per hour and follows an Exponential distribution. (For all your answers, you must show your workings)

1. What is the probability that no vehicles are at the drive-up window?
2. What is the probability that a customer must wait for service?
3. On average, what is the total length of time a customer spends in the system?
4. On average, what is the total length of time a customer spends in the queue?
5. Briefly describe the long-term behaviour of the queueing system.