Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 12.5, Problem 24P
a)
Summary Introduction
To determine: The average number of potential customers enter the system each hour.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
b)
Summary Introduction
To determine: The probability that the server is busy at a point of time.
Introduction: In order to predict the waiting time and length of the queue, queueing model will be framed. Queueing theory is the mathematical model that can be used for the decision-making process regarding the resources required to provide a service.
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A service facility consists of one server who can serve an average of two customers per hour (service times are exponential). An average of three customersper hour arrive at the facility (interarrival times are assumed to be exponential). The system capacity isthree customers: two waiting and one being served.a. On average, how many potential customers enter the system each hour?b. What is the probability that the server is busy at atypical point in time?
Customers arrive at Best-Bank-in-Town’s (BBT) sole ATM location at a rate of 21 customers per hour. It is assumed that the arrival process is random. BBT recently hired an intern who estimated that the average service time is 2 minutes per customer with a standard deviation of 1.2 minutes. [Assume that the arrival rate is the same throughout the day without peak and off-peak considerations and that there is only one ATM machine at that location]
1. Calculate average waiting time for ATM user at the BBT location
2. Calculate average length of queue at the ATM location (i.e. average numbers of customers waiting for service)?
3. What is the probability that an arriving customer has no waiting time to use the ATM?
4. BBT wants to cut the average waiting time in half without necessarily adding another ATM machine. They are in discussions with their ATM software provider who has told them that their new software is very consistent with information retrieval and can greatly minimize the…
In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour.
What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.)
What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimal places.)
What is the expected number of customers in the queue(Lq)? (Round your answer to 3 decimal places.)
What is the expected waiting time in the queue(Wq)? (Express the waiting time in hours, round your answer to 3 decimal places.)
Chapter 12 Solutions
Practical Management Science
Ch. 12.3 - Prob. 1PCh. 12.3 - Explain the basic relationship between the...Ch. 12.3 - Prob. 3PCh. 12.3 - Prob. 4PCh. 12.4 - Prob. 5PCh. 12.4 - Prob. 6PCh. 12.4 - Prob. 7PCh. 12.4 - Prob. 8PCh. 12.5 - Prob. 9PCh. 12.5 - Prob. 10P
Ch. 12.5 - Prob. 11PCh. 12.5 - Prob. 12PCh. 12.5 - Prob. 13PCh. 12.5 - Prob. 14PCh. 12.5 - Prob. 15PCh. 12.5 - Prob. 16PCh. 12.5 - Prob. 17PCh. 12.5 - Prob. 18PCh. 12.5 - Prob. 19PCh. 12.5 - Prob. 20PCh. 12.5 - Prob. 21PCh. 12.5 - Prob. 22PCh. 12.5 - On average, 100 customers arrive per hour at the...Ch. 12.5 - Prob. 24PCh. 12.5 - Prob. 25PCh. 12.5 - Prob. 26PCh. 12.5 - Prob. 27PCh. 12.5 - Prob. 28PCh. 12.5 - Prob. 29PCh. 12.5 - Prob. 30PCh. 12.5 - Prob. 31PCh. 12.5 - Prob. 32PCh. 12.5 - Prob. 33PCh. 12.5 - Prob. 34PCh. 12.5 - Prob. 35PCh. 12.5 - Two one-barber shops sit side by side in Dunkirk...Ch. 12.5 - Prob. 37PCh. 12 - Prob. 46PCh. 12 - Prob. 47PCh. 12 - Prob. 48PCh. 12 - Prob. 49PCh. 12 - Prob. 50PCh. 12 - Prob. 51PCh. 12 - Prob. 52PCh. 12 - Prob. 54PCh. 12 - Prob. 56PCh. 12 - Prob. 57PCh. 12 - Prob. 58PCh. 12 - Prob. 59PCh. 12 - Prob. 60PCh. 12 - Prob. 61P
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