Question

Huang’s television-repair service receives an average of 8 TV sets per 8-hour day to be repaired. The service manager would like to be able to tell customers that they can expect their TV back in 5 days.

What average repair time per set will the repair shop have to achieve to provide 5-day service on the average? (Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.)

Answer 1

SOLUTION:

Given That Huang’s television-repair service receives an average of 8 TV sets per 8-hour day to be repaired. The service manager would like to be able to tell customers that they can expect their TV back in 5 days.

So

This is M/M/1 queue system with following parameters

Arrival rate, a = 8/8 =1 per hour

Let s be the service rate (TV sets repaired per hour)

Average turnaround time, W = 1/(s-a)

W must be <= 5

1/(s-a) <= 5

s >= a+1/5 = 1+1/5 = 6/5

Average repair time per set = 1/s = 6/5 hour

= (6/5)*60 minutes

= 72 minutes

Average repair time per set = 1/s = 72/60=1.2 hour