### Understanding Single Server Queue Systems#### Queue System OverviewThe 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 AnalysisThe 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 Questions1. **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. 2.02. **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.

The given problem pertains to a single server queueing system denoted as [G/G/1/N/K], where N…

Answered: Given the Figure below, represents a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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