# [ntp:questions] Asymmetric Delay and NTP

Magnus Danielson magnus at rubidium.dyndns.org
Tue Mar 18 20:20:54 UTC 2014

```On 18/03/14 01:36, Joe Gwinn wrote:
> 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 can't recall. The above I came up with myself some 10 years ago or so.

Will see if I can find Dave's reference.

> 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.

It's even worse when you get into packet networks, as the delays contain
noise sources of variable mean and variable deviation, besides being
asymmetrical. NTP combats some of that, but doesn't get deep enough due
to too low packet rate. PTP may do it, but it's not in the standard so
it will be propritary algorithms. The PTP standard is a protocol
framework. ITU have spent time to fill in more of the empty spots.

Cheers,
Magnus

```