In an M/M/1 queueing system, customers arrive at a mean rate of 8 customers per hour and each service can be completed in 5 minutes on average. Using the template, input values for A, and s to answer the following questions. Some questions require the use of the Poisson Table. Round probability answers to 3 decimal places. Otherwise round answers to the nearest tenth, if needed. 1. What is the probability that the server will be idle? 2. What is the probability of having more than 5 customers in the system? 3. What is the probability of having 3 or fewer customers in the system? 4. What percentage of time is the server busy serving customers? 5. What is the expected number of customers in the system? 6. How many minutes can the customer expect to be in the system? 7. What is the expected number of customers in the queue? 8. How many minutes can the customer expect to wait in line before being served? % 9. What is the probability that the customer will have to wait in line more than 5 minutes before getting served? 10. What is the probability that the customer will be in the system longer than 10 minutes? 11. What is the probability that at most ten customers arrive in a one hour period? 12. What is the probability that less than four customers arrive in a one hour period? 13. What is the probability that at least one customer arrives in a minute time period? 14. What is the probability that one customer arrives in a five minute period? 15. What is the probability that more than one customer arrives in a five minute period?
In an M/M/1 queueing system, customers arrive at a mean rate of 8 customers per hour and each service can be completed in 5 minutes on average. Using the template, input values for A, and s to answer the following questions. Some questions require the use of the Poisson Table. Round probability answers to 3 decimal places. Otherwise round answers to the nearest tenth, if needed. 1. What is the probability that the server will be idle? 2. What is the probability of having more than 5 customers in the system? 3. What is the probability of having 3 or fewer customers in the system? 4. What percentage of time is the server busy serving customers? 5. What is the expected number of customers in the system? 6. How many minutes can the customer expect to be in the system? 7. What is the expected number of customers in the queue? 8. How many minutes can the customer expect to wait in line before being served? % 9. What is the probability that the customer will have to wait in line more than 5 minutes before getting served? 10. What is the probability that the customer will be in the system longer than 10 minutes? 11. What is the probability that at most ten customers arrive in a one hour period? 12. What is the probability that less than four customers arrive in a one hour period? 13. What is the probability that at least one customer arrives in a minute time period? 14. What is the probability that one customer arrives in a five minute period? 15. What is the probability that more than one customer arrives in a five minute period?
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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Transcribed Image Text:In an M/M/1 queueing system, customers arrive at a mean rate of 8 customers per hour and each service can be completed in 5 minutes on average. Using the template, input values for A,
and s to answer the following questions. Some questions require the use of the Poisson Table. Round probability answers to 3 decimal places. Otherwise round answers to the nearest tenth, if
needed.
1. What is the probability that the server will be idle?
2. What is the probability of having more than 5 customers in the system?
3. What is the probability of having 3 or fewer customers in the system?
4. What percentage of time is the server busy serving customers?
5. What is the expected number of customers in the system?
6. How many minutes can the customer expect to be in the system?
7. What is the expected number of customers in the queue?
8. How many minutes can the customer expect to wait in line before being served?
%
9. What is the probability that the customer will have to wait in line more than 5 minutes before getting served?
10. What is the probability that the customer will be in the system longer than 10 minutes?
11. What is the probability that at most ten customers arrive in a one hour period?
12. What is the probability that less than four customers arrive in a one hour period?
13. What is the probability that at least one customer arrives in a minute time period?
14. What is the probability that one customer arrives in a five minute period?
15. What is the probability that more than one customer arrives in a five minute period?
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