Question $-5$: Problem Solving

$"10-$Marks"

An average of $10$ cars per hour arrive at a single$-$server drive$-$in teller. Assume that the average service time for each customer is $4$ minutes, and both interarrival times and service times are exponential. The cost of customer waiting time in line is $$70$ per hour and the operating cost of the teller is $$25$ per hour. Answer the following questions.

A$.$ What is the probability that the teller is idle?

So

B$.$ What is the average number of cars waiting in line for the teller? $($A car that is being serve not considered to be waiting in line.$)$

C$.$ What is the average amount of time a drive$-$in customer spends in the bank parki $($including time in service$)?$

D$.$ On average, how many customers per hour will be served by the teller?

E$.$ Compute the total expected cost of the given system.