The computer lab at King Saud University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a first-come, first-served priority rule. On average, 15 students per hour arrive at the help desk. Student arrivals are best described using a Poisson distribution. The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system. (1) The average utilization of the help desk server. (2) Probability of no students in the system. (3) The average number of students in the system.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Topic Video
Question
100%
The computer lab at King Saud University has a help desk to assist students
working on computer spreadsheet assignments. The students patiently form a
single line in front of the desk to wait for help. Students are served based on a
hour arrive at
first-come, first-served priority rule. On average, 15 students
the help desk. Student arrivals are best described using a Poisson distribution.
per
The help desk server can help an average of 20 students per hour, with the
service rate being described by an exponential distribution. Calculate the
following operating characteristics of the service system.
(1) The average utilization of the help desk server.
(2) Probability of no students in the system.
(3) The average number of students in the system.
(4) The average number of students waiting in queue.
(5) The average time a student spends in the system.
(6) The average time a student spends waiting in queue.
(7) The probability of having 2 students in the system.
(8) The probability of having more than 4 students in the system.
(9) The probability of having less than 4 students arrive at time 0.5 hr.
(10)
Probability of no student arrive at time 0.5 hr.
Transcribed Image Text:The computer lab at King Saud University has a help desk to assist students working on computer spreadsheet assignments. The students patiently form a single line in front of the desk to wait for help. Students are served based on a hour arrive at first-come, first-served priority rule. On average, 15 students the help desk. Student arrivals are best described using a Poisson distribution. per The help desk server can help an average of 20 students per hour, with the service rate being described by an exponential distribution. Calculate the following operating characteristics of the service system. (1) The average utilization of the help desk server. (2) Probability of no students in the system. (3) The average number of students in the system. (4) The average number of students waiting in queue. (5) The average time a student spends in the system. (6) The average time a student spends waiting in queue. (7) The probability of having 2 students in the system. (8) The probability of having more than 4 students in the system. (9) The probability of having less than 4 students arrive at time 0.5 hr. (10) Probability of no student arrive at time 0.5 hr.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman