Answered: a. The arrival rate would be units per… | bartleby

Practical Management Science

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 21P

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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.

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