1. A service line consists of a single-machine station. The jobs are arriving with an average inter-arrival time of 25 sec., with the standard deviation of inter-arrival time being 10 sec. The machine, when it is up-and-running, can process a job in 18 sec., with the standard deviation of process time being 9 sec.

(a) The machine is old and its software is not up-to-date. Thus, it is subjected to frequent random failure. On the average, the machine can run for 54 minutes before it crashes, and it takes exactly 6 minutes to reactivate the machine after it crashes. Furthermore, the machine needs to be rebooted every time after it has processed 100 jobs. The rebooting takes exactly 10 minutes. Compute the resultant effective process time and the coefficient of variation of the effective process time of the machine.

(b) Finally, the IT staff has upgraded the software of the machine. It is still subjected to frequent random failure: Still, on the average, the machine can run for 54 minutes before it crashes, and it takes exactly 6 minutes to reactivate the machine after it crashes. But now, the machine does not need periodic maintenance (i.e. no longer need to reboot the machine after it has processed 100 jobs). Compute the resultant effective process time and the coefficient of variation of the effective process time of the machine.

For Q1, the line consists of a single station with a single machine in it.

In part (a), we have the combined effect of (i) natural variability, (ii) variability due to random failure (i.e. pre-emptive outgage) and (iii) variability due to scheduled maintenance (i.e. non-pre-emptive outage). We discussed about how to deal with this type of situation in one of the zoom lectures.

In part (b), we only have the combined effect of (i) and (ii). Thus, if you know how to do (a), (b) will be very easy.

ID