Erratic slow speeds beyond the telephone exchange.

[#1]

My neighbour, who is with Waitrose/John Lewis broadband, tells me her internet has been very slow for the past few weeks.  I went to help and could see no problems so I installed Router Stats Lite to monitor the router.  The sync rate was solid at 6600kbps and I measured about 5000kbps in a speed test.  I was about to leave when the connection speed ground to near zero, too slow to reload the speed test page in fact.  But the router didn't lose sync or change the SNR which was about 10dB.  So all the indicators are that the connection between the router and the exchange was fine.  But I got the same poor result with a second computer wired to the router.
Since I'm told that the problem keeps recurring I can only think it must be something in or beyond the telephone exchange that affects the practical internet connection speed but not the sync rate or noise level.  What tests can I run that might help to prove (or disprove) this?     

[#2]

10db presumably downstream noise margin is a little high, suggesting the ADSL hasn't been performing well, causing the DLM to increase the target noise margin.
I would start be monitoring all available ADSL stats, particularly CRC, FEC, HEC counts if possible - a local or line issue might show up in those. In the past I have experienced no connection drops and no significant drop in noise margin, but Internet throughput so slow to the point of being unable to load a webpage - entirely due to local REIN and/or rubbish internal wiring.
Alternatively it could be a faulty router.

[#3]

Could be a faulty router but it would have to be two faulty routers because we were already trying a second one to cover that possibility.  And I have never seen a local problem that flips from being absolutely fine to very slow in seconds without that showing up at least as a significant loss of noise margin.  Both I and this neighbour had a REIN problem last year and it was very very obvious just looking at the SNRM.  Yes 10dB indicates that the DLM sees a problem but that could well just be frequent restarts of the router made in an attempt to clear the issue.  And it also indicates there is a lot of noise 'headroom'.
However you are probably right that there must be major packet loss which must surely show up on one of the error counts so I will try to monitor those (for which I would need the full version of Routerstats and a compatible router).  Does the equipment in the telephone exchange check the inbound packets or merely retransmit them? 

[#4]

Or dslstats or it may be sufficient just to look at the numbers every minute (or some routers show counts for 15-second intervals), see the typical rate of increase in the error counts, and manually check the error counts before and after.

Quote from: ReedRichards

Does the equipment in the telephone exchange check the inbound packets or merely retransmit them?

There isn't any automatic retransmission of data over ADSL. The technology / protocol exists in the G.INP ITU recommendation, but it won't be in use now nor anytime soon, not on BT-based ADSL at least. Data received at each end of the ADSL link that doesn't pass the checksum verification will be detected as corrupted and discarded. Anything being retransmitted will be from a higher level, either automatically by a computer's TCP stack, or for something like DNS sent as UDP packets, the DNS query would just have to be re-sent by the DNS software.