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 a rate of 750 per hour. It will take exactly four seconds to verify the debit card. (Answers in Appendix D)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?

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 a rate of 750 per hour. It will take exactly four seconds to verify the debit card. (Answers in Appendix D)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?

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Description: 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 a rate of 750 per hour. It will take exactly four secon

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 9P

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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 atthe rate of 750 per hour. It will take exactly four seconds to verify the debit card.a. In how much time would you expect the customer to wait in line, pay with the debitcard, and leave?b. How many cars would you expect to see in the system?
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. How much time would you expect a customer to wait in line, pay with a debit card, and leave? Note: Do not round intermediate calculations. How many cars would you expect to see in the system? Note: Round your answer to 2 decimal places.
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 3.0 seconds to verify the debit card.a. How much time would you expect a customer to wait in line, pay with a debit card, and leave? (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.) b. How many cars would you expect to see in the system? (Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places.)
An average of 90 patrons per hour arrive at a hotel lobby(interarrival times are exponential), waiting to check in. At present, there are 5 clerks, and patrons are waiting in a singleline for the first available clerk. The average time for a clerkto service a patron is 3 minutes (exponentially distributed).Clerks earn $10 per hour, and the hotel assesses a waitingtime cost of $20 for each hour that a patron waits in line.a Compute the expected cost per hour of the currentsystem.b The hotel is considering replacing one clerk with an Automatic Clerk Machine (ACM). Management esti-mates that 20% of all patrons will use an ACM. An ACM takes an average of 1 minute to service a patron.It costs $48 per day (1 day 8 hours) to operate anACM. Should the hotel install the ACM? Assume thatall customers who are willing to use the ACM wait in asingle queue.
Circle Electric Supply is considering opening a second service counter to better serve their electrical contractor customers. The arrival rate is 11 per hour. The service rate is 16 per hour. If the cost of waiting is $31 and the cost of each service counter is $23 per hour, should the second counter be opened? (Give your numerical values in dollars per hour. Round your answers to two decimal places.) With one counter, the cost per hour is $ . With two counters, the cost per hour is $ . The second counter ---Select--- should should not be opened.
Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 45 an hour between 7:00 pm and 9:00 pm. Currently, three inspectors are on duty during those hours, each of whom can inspect 25 trucks an hour. Please show work. Question: How many trucks would you expect to see at the weighing station, including those being inspected?
An average of 17 cars per hour arrive at a single-server drive-in teller. Assume the average service time for each customer is 4 minutes, and both interarrival times and service times are exponential. Answer the following questions:a. What is the mean arrival time? b. What is the mean service time? c. What is the probability that the teller is busy?d. What is the average number of cars waiting in line for the teller? e. What is the average amount of time a drive-in customer spends waiting in the parking lot? f. What is the average number of cars in the system? g. Describe the possible behavior of customer arrivals. Justify your answer.
A university cafeteria line in the student center is a self-serve facility in which students select the food items they want, then form a single line to pay the cashier. Students arrive at a rate of about four per minute according to a Poisson distribution. The single cashier ringing up sales takes about 12 seconds per customer, following an exponential distribution. a. What is the probability that there are more than two students in the system? More than three students? More than four? b. What is the probability that the system is empty? c. How long will the average student have to wait before reaching the cashier? d. What is the expected number of students in the queue? e. What is the average number in the system? f. If a second cashier is added (who works at the same pace), how will the operating chareristics computed in parts (b), (c), (d), and (e) change? Assume that customers wait in a single line and go to the first available cashier.
Students arrive randomly at the counter of the CIT Library. There is only one library assistant, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem?
A student arrive in a photocopy service. There is only one photocopy operator, and the time required for inquiry varies from student to student. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem? Select one: a. 2.28 minutes b. 4.35 minutes c. 3 minutes d. 1 minute
Trucks are required to pass through a weighing station so that they can be checked for weight violations. Trucks arrive at the station at the rate of 40 an hour between 7:00 p.m. and 9:00 p.m. Currently two inspectors are on duty during those hours, each of whom can inspect 25 trucks an hour.a. How many trucks would you expect to see at the weighing station, including those being inspected?
Drivers who come to get their licenses at the department ofmotor vehicles have their photograph taken by an automatedmachine that develops the photograph onto the license cardand laminates the complete license. The machine requires aconstant time of 4.5 minutes to develop a completed license.If drivers arrive at the machine at the mean rate of 11 perhour (Poisson distributed), determine the average length ofthe waiting line and the average waiting time.