Discrete Mathematics: Introduction to Mathematical Reasoning
Discrete Mathematics: Introduction to Mathematical Reasoning
1st Edition
ISBN: 9780495826170
Author: Susanna S. Epp
Publisher: Cengage Learning
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Chapter 1.1, Problem 13ES

a.

To determine

To calculate: The solutions of the blank using the variable.

b.

To determine

To calculate: The solutions of the blank using the variable.

c.

To determine

To calculate: The solutions of the blank using the variable.

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Please use the infinite series formula and specify how you did each step. Thank you.
In a small office, there are m = 5 typists who need to use a single typewriter to complete their reports. Assume the time each typist takes to prepare a report follows an exponential distribution with an average of 20 minutes per preparation (A = 3 reports/hour), and the service time for the typewriter to type out a report also follows an exponential distribution, averaging 30 minutes to complete a report (μ 2 reports/hour). Given that the number of typists is finite and all typists = share one typewriter, they will form a waiting queue. (1). Describe this queuing system and explain how it fits the characteristics of the M/M/1/∞0/m model. (2). Calculate the probability that any typist is using the typewriter at steady-state. (3). Calculate the average number of typists waiting in the queue at steady-state. (4). Considering the need to reduce waiting time, if an additional typewriter is introduced (turning into a two-server system, or M/M/2/∞0/m model), analyze the expected impact,…
Use Laplace transform to solve the initial value problem y' + y = tsin(t), y(0) = 0
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