A fast food restaurant has one drive in window. cars arrive according to a poission distribution at the rate of 2 cars every 5 minutes.

A fast food restaurant has one drive in window. cars arrive according to a poission distribution at the rate of 2 cars every 5 minutes. the space in front of the window can accommodate at most 10 cars including the one being served. other cars can wait outside this space if necessary. the service time per customer is exponential, with a mean of 1.5minutes. determine the following

a) probability that the facility is idle

b) expected number of customers expected to be served

c) expected waiting time until a customer reaches the window to place an order

d) the probability that the waiting line will exceed the 10-space capacity