Pop Quiz 2

Oops

The recent shutdown of LAX due to an FAA radio outage was apparently caused by a Windows 2000 integration flaw, possibility related to an old Windows 95 bug. An article at the LA Times claims that the outage was caused by human error, as the system will automatically shut down after 49.7 days (related to this Windows 95 flaw?), and a technician didn't reboot the system monthly as he should have. This happened after an upgrade from Unix to Windows.

--- Windows Upgrade, FAA Error Cause LAX Shutdown
Slashdot, 21 September 2004

An Explanation

The servers are timed to shut down after 49.7 days of use in order to prevent a data overload, a union official told the LA Times. To avoid this automatic shutdown, technicians are required to restart the system manually every 30 days. An improperly trained employee failed to reset the system, leading it to shut down without warning, the official said. Backup systems failed because of a software failure, according to a report in The New York Times.

--- Matthew Broersma, Microsoft crash nearly causes 800-plane pile up
Tech World, 21 September 2004

A Question

The servers are timed to shut down after 49.7 days of use in order to prevent a data overload. To avoid this automatic shutdown, technicians are required to restart the system manually every 30 days.

Assuming typical integral types, what is the most likely size in bytes of the variable that caused the problem?

Some Assumptions

The system's counting time, rather than airplanes or something else.
- This is a dicey assumption but a common source of problems.
The problem's a result of arithmetic overflow ("data overload").
Fifty days is closer to the problem than is thirty days, which seems closer to the solution.
- Nothing happens after thirty days, but after fifty days the system shuts down.

An Estimation

Find a representation of fifty days that's near the overflow value of common variable sizes.

Variable size Overflow value

bytes

1 256 50 days * 24 hours/day = 1200 hours

2 65k 1200 hours * 60 minutes/hour = 72,000 minutes

4 4.2*10⁹ 72,000 minutes * 60 seconds/minute = 4,300,000 seconds

8 18*10¹⁸ 4,300,000 seconds * 1000 msec/second = 4.3*10⁹ msec

72,000 is close to 65k, but 4.3*10⁹ is closer to 4.2*10⁹.
- 72,000 is around 10% larger than 65k, but 4.3*10⁹ is less than 1% larger than 4.2*10⁹.
It seems a four-byte millisecond counter is causing the problem.

Variable size	Overflow value
bytes
1	256	50 days	*	24 hours/day	=	1200 hours
2	65k	1200 hours	*	60 minutes/hour	=	72,000 minutes
4	4.2*10⁹	72,000 minutes	*	60 seconds/minute	=	4,300,000 seconds
8	18*10¹⁸	4,300,000 seconds	*	1000 msec/second	=	4.3*10⁹ msec

This page last modified on 15 November 2004.