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Nicely draw the rate diagram for this queueing system; clearly indicate all the states of the system and the num alues of the arrival and service rates for each state. Compute: 1) The probability that there are 4 functioning robots on the manufacturing floor. 2) The expected downtime time (in days) of a robot that requires repair. 3) The average utilization of the repairmen.

Nicely draw the rate diagram for this queueing system; clearly indicate all the states of the system and the num alues of the arrival and service rates for each state. Compute: 1) The probability that there are 4 functioning robots on the manufacturing floor. 2) The expected downtime time (in days) of a robot that requires repair. 3) The average utilization of the repairmen.

Practical Management Science
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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A semiconductor company uses four robots in the manufacture of circuit boards. The robots break down periodically, and the company has two additional spare robots to immediately replace a damaged robot. Moreover, there are two repairmen to service a broken robot. When a robot is repaired, if less than four robots are working, it is returned to the manufacturing floor; otherwise it is sent to the spare room. The time between breakdowns is exponentially distributed with a mean of 14 days. The repair time is also exponentially distributed with a mean of 3.6 days. Nicely draw the rate diagram for this queueing system; clearly indicate all the states of the system and the numerical values of the arrival and service rates for each state. Compute: 1) The probability that there are 4 functioning robots on the manufacturing floor. 2) The expected downtime time (in days) of a robot that requires repair. 3) The average utilization of the repairmen.
Transcribed Image Text:A semiconductor company uses four robots in the manufacture of circuit boards. The robots break down periodically, and the company has two additional spare robots to immediately replace a damaged robot. Moreover, there are two repairmen to service a broken robot. When a robot is repaired, if less than four robots are working, it is returned to the manufacturing floor; otherwise it is sent to the spare room. The time between breakdowns is exponentially distributed with a mean of 14 days. The repair time is also exponentially distributed with a mean of 3.6 days. Nicely draw the rate diagram for this queueing system; clearly indicate all the states of the system and the numerical values of the arrival and service rates for each state. Compute: 1) The probability that there are 4 functioning robots on the manufacturing floor. 2) The expected downtime time (in days) of a robot that requires repair. 3) The average utilization of the repairmen.
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