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 (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $400 per week per data unit 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.
Chapter 5. (M/M/s/K Model). Leia is responsible for 13 data units in the IT offices in a small business called DataWish. Each data unit 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 data unit 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 (ρ) |
|
% |
|
Performance Measures |
|
|
|
P0 (probability that sytem is empty) |
|
% |
|
L (average units in system) |
|
units |
|
Lq (average units waiting in queue) |
|
units |
|
W (average time in the system) |
|
weeks |
|
Wq (average time in the queue) |
|
weeks |
c. If we assign a cost of waiting as $400 per week per data unit 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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