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 300 per hour. It will take exactly 5.0 seconds to verify the debit card.
A. In how much time would you expect the customer to wait in line, pay with the debit card, and leave?


B. How many cars would you expect to see in the system?

Answer 1

Answer:

expect the customer to wait = 6.74  sec

1 car would expect to see in the system.

Explanation:

given data

arrive rate λ = 300 per hour

verify the debit card u = 1 card per 5 second = 720 card per hour

solution

L(q) = 300² ÷ ( 2 × 720 (730-300) )  

L(q) = 0.1453

L(q) = 2.0833

and

L(s) = 0.1453 + 300/720

L(s) = 0.5619   W(s)

so

expect the customer to wait = 0.5619 ÷ 300

expect the customer to wait =0.001873  

expect the customer to wait = 6.74  sec

and

L(s) 0.5619 = 1 cars

so 1 car would expect to see in the system.