Answer to Question #283309 in Finance for abc

Question

At one Starbucks café in Swansea, cars arrive at the Drive-Thru at a rate of 25

per hour and only one drive-thru till is open. The average time it takes for an

order and collection is 5 minutes. Assuming that the interarrival time and the

service time are both exponentially distributed. Calculate the average number

of customers arriving at the till and the average time they must wait before

exiting Starbucks Drive-Thru.

Answer 1

The average time required for ordering and receiving is 5 minutes, that is, 12 cars are served per hour.

Then the average number of customers arriving at the checkout:

$25/12=2$

mean arrival rate of customers:

$\lambda=25$ per hour

mean service rate:

$\mu=60/5$ min = $12$ per hour

average time they must wait:

$W_Q=\frac{\lambda}{\mu(\mu-\lambda)}$

The service rate must be greater than the arrival rate

if $\mu\le \lambda$ , the waiting line would eventually grow infinitely large