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?

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?

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 26P

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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…
Angkut Deras Hauling Company has two long-trip cars rental servicesinclusive with a driver at Kota Kinabalu International Airport. The companyhas determine during the late-evening hours on weekend, customersrequest driver for cars rental at a rate that follows the Poisson distributionwith a mean of 0.8 per hour. Travel and assistance time is exponential witha mean of 1 request per hour. Find each of the performance measures ofthis waiting line system. a) What is the system utilization rate for Angkut Deras Hauling Company?b) Probability that both drivers will be busy when a customer request.c) The average number of customer waiting in line.d) The average time customers wait for a driver.e) What is the customers average waiting time on arrival?
When designing a waiting line system, what "qualitative" concems need to be considered?
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92 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 2.5 per hour. It will take Benny an average of 20 minutes to give a haircut. Based on these figures, find the following: a. The average number of customers waiting Note: Round your intermediate calculations to 3 decimal places and final answer to 2 decimal places. b. The average time a customer waits. Note: Round your answer to 2 decimal places. c. The average time a customer is in the shop. Note: Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.
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Describe what is meant by the waiting-line terms balk and renege. Provide an example of each.
40) Burger Cart April has a popular burger cart where an average of 12 customers per hour arrive to buy a burger. April can serve an average of 20 customers per hour. What is the average time a person spends waiting in line? Group of answer choices a) 16.0 minutes b) 2.25 minutes c) 3.0 minutes d) 12.0 minutes e) 7.0 minutes f) 4.5 minutes g) 9.0 minutes h) 1.2 minutes
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Describe the behavior of a waiting line where lambda > mu . Use both analysis and intuition.
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.