Customers in LineWestern National Bank is considering opening a drive-thru window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of one every three minutes.Part 1 Assuming Poisson arrivals and exponential service, find1. Utilization of the teller.2. The average number in the waiting line.3. The average number in the system.4. The average waiting time in line.5. The average waiting time in the system, including service.

Customers in LineWestern National Bank is considering opening a drive-thru window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of one every three minutes.Part 1 Assuming Poisson arrivals and exponential service, find1. Utilization of the teller.2. The average number in the waiting line.3. The average number in the system.4. The average waiting time in line.5. The average waiting time in the system, including service.

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

See similar textbooks

Similar questions

13. Suppose AirOM passengers arrive to the check-in desk every 100 seconds (on average). The desk is staffed by a single ticketing agent, who takes 1.4 minutes (on average) to process a passenger. The arrivals follow a Poisson process and the service time is distributed exponentially. What is a passenger’s average waiting time (in seconds)? Enter a single number as your answer. If your final number is not integer, keep two decimal places in your answer.
13. Movie Tonight is a typical video and DVD movie rental outlet for home viewing customers. During the weeknight evening, customers arrive at Movies Tonight at the average rate of 1.25 customers per minute. The checkout clerk can serve an average of two customers per minute. Assume Poisson arrivals and exponential service times.What is the probability that no customers are in the system?What is the average number of customers waiting services?What is the average time a customer waits for service to begin?Do the operating characteristics indicate that the one-clerk check out system provides an acceptable level of service?
A vending machine dispenses hot chocolate or coffee. Service time is 35 seconds per cup and is constant. Customers arrive at a mean rate of 66 per hour, and this rate is Poisson-distributed. a. Determine the average number of customers waiting in line. (Round your answer to 2 decimal places.) Average number of customers ?? b. Determine the average time customers spend in the system. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Average time minutes ??
Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business if 4 minutes. It is assumed that service times may be described by the negative exponential distribution. If a single teller is used, find: 1. The average time in line 2. The average number in the line 3. The average time in the system 4. The average number in the system 5. The probability that the bank is empty 6. CEO Benjamin Neve is considering a second teller (who would work at the same rate as the first) to reduce waiting time for customers. A single line would be used, and the customer at the front of the line would go to the first available bank teller. He assumes that this will cut the waiting line in half. If the second teller is added, find the new answers to #1 through 6.
[Queuing Theory - Operations Research] Customers arrive according to the Poisson distribution with mean 20 per hour. Service time is exponential with mean 30 minutes. (a) Determine the minimum number of servers the Salon should have to achieve a steady-state. Explain why. (b) Because of a significant number of customers who balked, the owner wants to determine the number of servers so that the average waiting time before having the service is not more 10 minutes. How many servers should the salon have?
Lanang Cafe has a barista vending machine that takes a constant 48 seconds serving per cup of coffee. The cafe has determined during the weekend, customers expected to arrive for coffees every 10 minutes on average. Find each of the performance measures of this waiting line system for Lanang Café. (Answer for d and e) a) What is the system utilization rate for the cafe? b) Probability that café will be busy when a customer request. c) The average number of customers waiting in line. d) The average time customers wait for a coffee. e) What are the customers average waiting time on arrival?
Benny the Barber owns a one-chair shop. At barber college, they told Benny that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Arrival Time, λ =2 customers per hour Service Time, μ = 20 minute, or 60/20= 3 customer per hour Lq = (2)2 / 3*(3-2) = 1.333 customers Part (b): The average time a customer waits. Wq= 1.333/2=0,665 \~ 0,67 or 40 minutes Part (c): The average time a customer is in the shop. LS = 2/ 3-2 =2 customers. WS = 2/2 = 1 hour Part (d): The average utilization of Benny’s time. P= λ/ μ = 2/3=0,666 percent ~ 0,67 % Benny the Barber (see Question 1) is considering the addition of a second chair. Customers would be selected for a haircut on a FCFS basis from…
5. Eat well is a small drive through fast food restaurant, staffed by an efficient employee John, is located in a super mall area. Customers arrive at the counter at an average of one every 15 minutes, and the customer arrival follows a Poisson distribution. John takes at most 10 minutes to process each food order. a) What is average number of customer being served at any time? b) The expected number of customers waiting to be served. c) Compute the average time customer wait in the system. d) What percentage of time is John Idle?
Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 11 calls per hour. The arrival rate is 22 calls per hour. How many extension lines should be used if the company wants to handle 90% of the calls immediately?fill in the blank 1 lines should be used What is the average number of extension lines that will be busy if your recommendation in part (a) is used? Round your answer to four decimal places.L = fill in the blank 2 What percentage of calls receive a busy signal for the current telephone system with two extension lines? Round your answer to two decimal…
5) A vending machine dispenses hot chocolate or coffee. Service time is 30 seconds per cup and is constant. Customers arrive at a mean rate of 80 per hour, and this rate is Poisson-distributed.Determine:a. The average number of customers waiting in line. b. The average time customers spend in the system. c. The average number in the system.
1. The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What is the service rate? (please include units) b.) What is the arrival rate? (please include units)
Describe two examples of unethical behavior related to waiting line management, and state whichethical principles they violate.CRITICAL THINKINGEXERCISES1. a. λ = 3 customers/hourμ = 5 customers/hourM = 1(1) What is the system utilization?(2) What is the average number of customers waiting for service?(3) What is the average time customers wait in line for service? b. Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copier repairscome in at a mean rate of three per eight-hour day (assume Poisson). Determine:(1) The average number of customers awaiting repairs.(2) System utilization.(3) The amount of time during an eight-hour day that the repairman is not out on a call.(4) The probability of two or more customers in the system.c. An average of 18 customers arrive at a service center each hour. There are two servers on duty,and each server can process 12…