A computing facility has a large computer server dedicated to service on-line applications from users who are scattered about the country. The facility uses an M/M/1 queueing system where the arrival pattern of requests for online applications are random (Poisson distribution with 2 = 4/sec), and the service time provided is random (exponential distribution with u = 6/sec). %3D Question: 1. What is the probability that the system is idle? 2. Based on grading scale below, what is the [approximate] grade that depicts the utilization of this system? F B A 10 20 30 40 50 60 70 80 90 100 3. There are talks of upgrading the queueing system to M/M/C such that the workload be equally divided between 2 smaller computer servers each with half the service rate of the original machine. Use the Report or summary R-functions to verify the following claims: a. The mean number of [clients] in the queue will not change. Is this claim justified? b. The mean time spend in the system will not change. Is this claim justified?

Practical Management Science
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Author:WINSTON, Wayne L.
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A computing facility has a large computer server dedicated to service on-line applications from
users who are scattered about the country. The facility uses an M/M/1 queueing system where
the arrival pattern of requests for online applications are random (Poisson distribution with
1 = 4/sec), and the service time provided is random (exponential distribution with µ = 6/sec).
Question:
1. What is the probability that the system is idle?
2. Based on grading scale below, what is the [approximate] grade that depicts the
utilization of this system?
F
D
A
10
20
30
40
50
60
70
80
90
100
3. There are talks of upgrading the queueing system to M/M/C such that the workload be
equally divided between 2 smaller computer servers each with half the service rate of the
original machine.
Use the Report or summary R-functions to verify the following claims:
a. The mean number of [clients] in the queue will not change. Is this claim justified?
b. The mean time spend in the system will not change. Is this claim justified?
Transcribed Image Text:A computing facility has a large computer server dedicated to service on-line applications from users who are scattered about the country. The facility uses an M/M/1 queueing system where the arrival pattern of requests for online applications are random (Poisson distribution with 1 = 4/sec), and the service time provided is random (exponential distribution with µ = 6/sec). Question: 1. What is the probability that the system is idle? 2. Based on grading scale below, what is the [approximate] grade that depicts the utilization of this system? F D A 10 20 30 40 50 60 70 80 90 100 3. There are talks of upgrading the queueing system to M/M/C such that the workload be equally divided between 2 smaller computer servers each with half the service rate of the original machine. Use the Report or summary R-functions to verify the following claims: a. The mean number of [clients] in the queue will not change. Is this claim justified? b. The mean time spend in the system will not change. Is this claim justified?
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