a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) % Performance Measures PO (probability that sytem is empty) % L (average units in system) units Lq (average units waiting units lin queue)

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Chapter 5. (M/M/s/K Model). Leia is responsible for 12 dataunits in the IT offices in a small business called DataWish. Each dataunit runs on an average for 3 weeks and
requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each dataunit for service and
an exponential distribution to the actual service provided, answer the following questions:
a. The arrival rate would be
units per week and the service rate would be
units per week.
b. Calculate the following operating characteristics for the M/M/S/K system:
Utilization Factor (p)
%
Performance Measures
PO (probability that sytem
is empty)
%
L (average units in system)
units
Lq (average units waiting
in queue)
units
W (average time in the
weeks
system)
Wq (average time in the
queue)
weeks
c. If we assign a cost of waiting as $400 per week per dataunit and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines?
dollars
d. If DataWish decides to hire another individual to help Leia, what would the new Total Time Cost per week be?
dollars.
Transcribed Image Text:Chapter 5. (M/M/s/K Model). Leia is responsible for 12 dataunits in the IT offices in a small business called DataWish. Each dataunit runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each dataunit for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/S/K system: Utilization Factor (p) % Performance Measures PO (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the weeks system) Wq (average time in the queue) weeks c. If we assign a cost of waiting as $400 per week per dataunit and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines? dollars d. If DataWish decides to hire another individual to help Leia, what would the new Total Time Cost per week be? dollars.
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