A post office has a counter for customer drive-through to pay the bill. The design of the drivethrough lane allows for unlimited queue length. The arrival and service rate are Poisson distributed with = 40 customers per hour arriving on average and =50 customers per hour can be served on average.

1. Compute the average number of arrivals. (2 Marks)

2. Compute the average time a customer wait. (2 Marks)

3. Compute the average number of arrivals in the system. (2 Marks)

4. Compute the average time a customer is in the system. (2 Marks)

5. Compute the probability that less than or equal to 2 customers are in the system. (3 Marks)

6. Due to the covid-19 pandemic, the unlimited queuing length has been modified to limited queuing length to control the number of cars waiting. The queue length has been limited to 4 cars only with = 40 and =50. Compute (a) and (b). (4 Marks)