# [ntp:questions] Asymmetric Delay and NTP

Joe Gwinn joegwinn at comcast.net
Tue Mar 18 00:36:36 UTC 2014

```In article <5327757E.5040504 at rubidium.dyndns.org>, Magnus Danielson
<magnus at rubidium.dyndns.org> wrote:

> Joe,
>
> On 16/03/14 23:16, Joe Gwinn wrote:
> > I recall seeing something from Dr. Mills saying that a formal proof had
> > been found showing that no packet-exchange protocol (like NTP) could
> > tell delay asymmetry from clock offset.  Can anyone provide a reference
> > to this proof?
>
> It's relative simple.
>
> You have two nodes (A and B) and a link in each direction (A->B and B->A).
>
> You have three unknowns, the time-difference between the nodes (T_B -
> T_A), the delay from node A to B (d_AB) and the delay from node B to A
> (d_BA).
>
> You make two observations of the pseudo-range from node A to node B
> (t_AB) and from node B to node A (t_BA). These are made by the source
> announcing it's time and the receiver time-stamping in it's own time
> when it occurs.
>
> t_AB = T_B - T_A + d_AB
> t_BA = T_A - T_B + d_BA
>
> We thus have three unknowns and two equations. You can't solve that.
> You can't win this game.
>
> There are things you can do. Let's take out observations and add them,
> then we get
>
> RTT = t_AB + t_BA = (T_B - T_A) + d_AB + (T_A - T_B) + d_BA
>      = d_AB + d_BA
>
> Now, that is useful. If we diff them we get
>
> /|T = t_AB - t_BA = (T_B - T_A) + d_AB - (T_A - T_B) - d_BA
>      = 2(T_B - T_A) + d_AB - d_BA
>
> TE = /|T / 2 = T_B - T_A + (d_AB - d_BA)/2
>
> So, diffing them gives the time-difference, plus half the asymmetric delay.
> If we assume that the delay is symmetric, then we can use these measures
> to compute the time-difference between the clocks, and if there is an
> asymmetry, it *will* show up as a bias in the slave clock.
>
> The way to come around this is to either avoid asymmetries like the
> plague, find a means estimate them (PTPv2) or calibrate them away.
>
> Is that formal enough for you?

It may be.  This I did know, and would seem to suffice, but I recall a
triumphant comment from Dr. Mills in one of his documentation pieces.
Which I cannot recall well enough to find.  It may be the above
analysis that was being referred to, or something else.

I also took the next step, which is to treat d_AB and d_BA as random
variables with differing means and variances (due to interference from
asymmetrical background traffic), and trace this to the effect on clock
sync.  It isn't pretty on anything like a nanosecond scale.  The
required level of isolation between PTP traffic and background traffic
is quite stringent.

Joe Gwinn

```