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Huang’s television-repair service receives an average of 9 TV sets per 6-hour day to be repaired....

Huang’s television-repair service receives an average of 9 TV sets per 6-hour day to be repaired. The service manager would like to be able to tell customers that they can expect their TV back in 4 days. What average repair time per set will the repair shop have to achieve to provide 4-day service on the average?

(Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.) (Round answer to 2 decimal places, e.g. 2.75.)

Average repair time per set ___ hour

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Answer #1

Arrival Rate = 9 units/6 hours = 9 units/day

Expected Wait Time = 4 days

We know, Expected wait time = 1/(Service Rate - Arrival Rate)

Therefore, Service Rate = (1+Expected Wait Time*Arrival Rate)/(Expected Wait Time) = (1+4*9)/(4) = 9.25 units/day

Thus, Average repair time per set = 1/Service Rate = 1/9.25 days = 6/9.25 hours = 0.6486 hours ~ 0.65 hours or 38.9189 minutes ~ 38.92 minutes

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