On Tue, Sep 18, 2007 at 02:19:36PM +0200, Jan Hoevers wrote:
> Jan Hoevers wrote on 18-9-2007 1:22:
> > Someone answered me off list that the systematic offset of a stratum 2
> > (or higher) server on an adsl is cancelled out when another host gets
> > time from that server.
> > I think that was a smart and interesting remark too.
>
> If this is true, it would mean that a stratum 1 server on an adsl line
> shows a systematic offset, and a stratum 2 server does not.
>
> I'm stunned.
Example network:
MACHINE A --- ADSL router --- Internet router --- MACHINE B
\
\
---- MACHINE C
A->{B,C} actual latency: 6
{B,C}->A actual latency: 4
Assume B is an atomic clock and has the correct time.
Machine A gets time from machine B by sending a packet a T=0. It
timestamps it 1 (its clock is wrong). At T=6, Machine B receives the
packet, sends back a response with a timestamp of 6. At T=10, Machine A
receives the response. Machine A timestamps the response as 11
(remember, machine A's clock is wrong).
Somehow, machine A must now determine how wrong its clock is. In order
to do so, we must make an assumption: we assume that the path TO machine
B and the path FROM machine B take the same amount of time.
A -> B -> A (RTT): ΔT = receive response timestamp - send request timestamp
= 11-1
= 10
Assumption: A->B = B->A = ½(RTT) = 5
Now, we can compute that our local time when B timestamped the packet
was A->B (5) + transmit time (1) = 6. B told us reality is 6. So we now
conclude our clock is running accurately — even though it is really 1
time-unit fast! We now see why Machine A's clock is wrong.
Now, when Machine C queries us, at T=10, it sends a timestamp of 0 (it's
just starting up, it has no clue of the time). At T=14, we stamp with 15
and send it back. C receives our response at T=20 and stamps it 10.
C now computes:
RTT: 10-0 = 10
½(RTT) = 5
So, when C thought it was T=5, A said reality is T=15. C thus realizes
it is 10 time-units slow — which is absolutely correct.
(Actual NTP setups do, of course, have multiple servers, more
complicated algorithms, etc.)
On the other question, to what extent does this apply to an idle DSL
line? As others have answered: completely. ADSL modems modulate digital
data across the phone line at a defined rate, which differs upstream and
downstream. If you have 1.5mbps down/384kbps up, the rates are:
down: 1.5mbps = ~0.6µs / bit
up: 384kbps = ~2.6µs / bit
Those are simple a straightforward calculations; just take the
reciprocal and do some unit conversions.
[All math in this post 90% unchecked and 150% wrong.]
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