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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?

Respuesta :

letmeanswer

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.

Parrain

Based on the rate the cars arrive and the time taken to verify the debit card, the following are true:

  • Time customer waits in line, pays, and leaves is = 14 seconds.
  • Number of cars in system = 2.1967 cars.

What is the number of cars in the system?

This can be found as:

= Average number of cars in line + (Rate / service rate)

Service rate:

= 1/4 x 3,600 seconds in hour

= 900 cars per hour

Number of cars in system:

= 2.0833 + (750 / 900)

= 2.9167 cars

What is the time the customer waits in line?

= Number of cars in system / Rate x 3,600 seconds in hour

= 2.9167/ 750 x 3,600

= 14 seconds

Find out more on rate of service at https://brainly.com/question/24746230.

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