Question

A toll tunnel has decided to experiment with the use of a debit card for the collection of tolls. Initially, only one lane will be used. Cars are estimated to arrive at this experimental lane at the rate of 750 per hour. It will take exactly four seconds to verify the debit card.
In how much time would you expect the customer to wait in line, pay with the debit card, and leave?
How many cars would you expect to see in the system?

Answer 1

Solution:

a. λ = 750

   u = 1 card/4sec = 900 cards / hour

  L(q) = 750^2 / 2*900(900-750) = 2.0833

  L(s) = 2.0833+750/900 = 2.9166 W(s)

         = 2.9166 /750 =0.003889

          = 14.00 sec

In 14.00 sec would you expect the customer to wait in line, pay with the debit card, and leave

b. L(s) 2.9166 =3 cars (from the answer of question a)

3 cars would expect to see in the system.