MadMax Burgers has a single drive-up window. On Sunday afternoons, customers arrive at the drive-up window according to a Poisson process, at an average rate of 25 customers per hour. Service at the drive-up window is provided at an average rate of 35 customers per hour and follows an Exponential distribution. (For all your answers, you must show your workings)

1. What is the probability that an arriving customer must wait for service at a given point in time?
2. On average, what is the total length of time a customer spends in the system?
3. On average, what is the total length of time a customer spends in the queue?
4. On average, how many customers are in the system at a given point in time?
5. Briefly describe the long-term behaviour of the queueing system.