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Given the Figure below, represents a single server queue. That is a G/G/1/N/K queuing system with (N23, K23) Answer the next three questions: 400 + 4) The average number of customers in the system. A. 10.0 B. 5.0 C. 0.5 D. 1.4 E. 2.0 5) The average number of customers in the Queue A 3.0 B. 5.0 C. 1.4 D. 0.5 E. 1.0

Given the Figure below, represents a single server queue. That is a G/G/1/N/K queuing system with (N23, K23) Answer the next three questions: 400 + 4) The average number of customers in the system. A. 10.0 B. 5.0 C. 0.5 D. 1.4 E. 2.0 5) The average number of customers in the Queue A 3.0 B. 5.0 C. 1.4 D. 0.5 E. 1.0

College Algebra
College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Systems Of Equations And Inequalities
Section6.6: Linear Programming
Problem 40E: Optimal Labor A manufacturer has two different factories that produce three grades of steel:...
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### Understanding Single Server Queue Systems #### Queue System Overview The diagram shown illustrates a single server queue system, specifically a G/G/1/N/K queuing system where \(N>3\) and \(K>3\). This type of system consists of: - **G/G/1**: General arrival and service time distribution with a single server. - **N**: Represents the maximum number of customers that can be in the system. - **K**: Represents the capacity of the system. #### Graph Analysis The graph depicts the number of customers in the system over a period of time: - **X-axis (t)**: Time intervals from 0 to 10. - **Y-axis (N(t))**: Number of customers in the system. The graph exhibits a step-like pattern, indicating periods where the number of customers remains constant, followed by sudden changes (either increases or decreases) at specific intervals. Key Observations: - At \(t = 0\), the system starts with 1 customer. - The number of customers varies between 1 and 3 throughout the time intervals. - There are notable time points where the number of customers increases to 3, then decreases back to 1, showing patterns typical of queue dynamics (e.g., arrivals and departures). #### Problem Statements and Multiple-Choice Questions 1. **Average Number of Customers in the System** What is the average number of customers in the system? Options: - A. 10.0 - B. 5.0 - C. 0.5 - D. 1.4 - E. 2.0 2. **Average Number of Customers in the Queue** What is the average number of customers in the queue? Options: - A. 3.0 - B. 5.0 - C. 1.4 - D. 0.5 - E. 1.0 #### Explanation: - **Average Number of Customers in the System**: To find the average, consider the values indicated in the graph and the amount of time the system spends at each level of occupancy. Calculate the mean of these values. - **Average Number of Customers in the Queue**: Similarly, review the periods the system spends with different numbers of customers waiting in the queue and compute the average.
Transcribed Image Text:### Understanding Single Server Queue Systems #### Queue System Overview The diagram shown illustrates a single server queue system, specifically a G/G/1/N/K queuing system where \(N>3\) and \(K>3\). This type of system consists of: - **G/G/1**: General arrival and service time distribution with a single server. - **N**: Represents the maximum number of customers that can be in the system. - **K**: Represents the capacity of the system. #### Graph Analysis The graph depicts the number of customers in the system over a period of time: - **X-axis (t)**: Time intervals from 0 to 10. - **Y-axis (N(t))**: Number of customers in the system. The graph exhibits a step-like pattern, indicating periods where the number of customers remains constant, followed by sudden changes (either increases or decreases) at specific intervals. Key Observations: - At \(t = 0\), the system starts with 1 customer. - The number of customers varies between 1 and 3 throughout the time intervals. - There are notable time points where the number of customers increases to 3, then decreases back to 1, showing patterns typical of queue dynamics (e.g., arrivals and departures). #### Problem Statements and Multiple-Choice Questions 1. **Average Number of Customers in the System** What is the average number of customers in the system? Options: - A. 10.0 - B. 5.0 - C. 0.5 - D. 1.4 - E. 2.0 2. **Average Number of Customers in the Queue** What is the average number of customers in the queue? Options: - A. 3.0 - B. 5.0 - C. 1.4 - D. 0.5 - E. 1.0 #### Explanation: - **Average Number of Customers in the System**: To find the average, consider the values indicated in the graph and the amount of time the system spends at each level of occupancy. Calculate the mean of these values. - **Average Number of Customers in the Queue**: Similarly, review the periods the system spends with different numbers of customers waiting in the queue and compute the average.
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