Practical Management Science
6th Edition
ISBN: 9781337406659
Author: WINSTON, Wayne L.
Publisher: Cengage,
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Chapter 12.5, Problem 35P
Summary Introduction
To determine: The system that have the smaller W and L.
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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An emergency room (ER) at a Prisma Health Hospital has 10 total
beds it can hold patients, i.e., the capacity of the queueing system of this ER is 10. Patients
arrive to the ER at a rate of 5 per hour. Therefore, we have that λn = 6 for n = 0, 1, . . . , 9
and λ10 = 0 for this queueing system. A patient is seen by an ER doctor as the ‘service’
of this queueing system. The amount of time required for an ER doctor to treat a patient
is exponentially distributed with a mean of .4 hours. We seek the minimum number of ER
doctors so that the expected time of a patient waiting to be seen (so the Wq) is less than
or equal to 15 minutes (.25 hours). You should begin by analyzing s = 1 and show any
calculations that were used to determine Wq for each number of servers that you considered
until you meet the target metric.
Consider a system of two infinite queues in series, where each service facility has a server. All service times are independent and have an exponential distribution with a mean of 3 min at facility 1 and 4 min at facility 2. Facility 1 has Poisson inputs with a mean rate of 10 per hour. Find the total expected number of customers in the system and the total expected waiting time (with service) for a customer.
We are in a M/M/1/3 queueing system in which we
wish to determine the cost of operating the system. Each customer in the queue costs us
$100 per hour and each customer being served costs us $50 an hour. Customers arrive at a
rate of 4 per hour and the server can serve customers at a rate of 5 per hour. The following
table in the picture provides Pn values, W, and Wq:
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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- In queueing theory, λ represents the mean arrival rate; for example, the number of peoplearriving at the service counter per hour. What does 1/λ represent?o Service rateo Interarrival timeo Service time Nonearrow_forwardA manufacturing cell has 4 operators (working independently in parallel) and a shared buffer space that can fit at most 6 incoming jobs. During a production period, jobs arrive to the cell with rate of 10 jobs per hour (Poisson arrival, i.e., exponential inter-arrival time). The average processing time of a job is 30 minutes (exponentially distributed service time). Answer the following questions using the analytical formulas learned in class. (a) Which queueing model should be used to model this problem? (b) What is the long-term average waiting time of a job in the buffer? (c) What is the probability that an arriving job cannot be admitted into the cell due to full occupancy? (d) If the desired the rejection probability is no more than 10% in this case, what would you suggest? Use calculations to justify your answer.arrow_forwardAn M/M/1 queueing system has that customers arrive to it at a rate of 5 per hour, i.e., its interarrival times between two consecutive arrivals follows an exponential distribution with parameter 5 per hour. This question will ask you to evaluate two options for designing the server in the system. Both options for the single server provide the same service for the customers in the queueing system but they cost different amounts to implement. In addition, the total costs of the queuing system are the implementation costs plus the customer costs. Currently, the customer costs are $100 per hour per customer in the queueing system. In comparing these options, it costs us $100 per hour per customer in the queueing system. (a) The first option for the server is one that has a service time that follows an exponential distribution with mean 10 minutes. Determine L, W, Lq, and Wq for this system. (b) The second option for the server is one that has a service time that follows an…arrow_forward
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