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juga
sbws
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5a44410a
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5a44410a
authored
May 20, 2020
by
juga
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fix: doc: Update/clarify Torflow aggregation
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3edf2fe2
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docs/source/torflow_aggr.rst
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...
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@@ -3,27 +3,34 @@
Torflow measurements aggregation
==================================
From Torflow's README.spec.txt (section 2.2)::
Torflow aggregation or scaling goal is:
From Torflow's `README.spec.txt`_ (section 2.2)::
In this way, the resulting network status consensus bandwidth values
are effectively re-weighted proportional to how much faster the node
was as compared to the rest of the network.
The variables and steps used in Torflow:
With and without PID control
----------------------------
Per relay measurements' bandwidth
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
**strm_bw**::
They are calculated in the same way whether or not `PID controller`_ feedback
is used.
From Torflow's `README.spec.txt`_ (section 1.6)::
The strm_bw field is the average (mean) of all the streams for the relay
identified by the fingerprint field.
strm_bw = sum(bw stream x)/|n stream|
**filt_bw**::
The filt_bw field is computed similarly, but only the streams equal to
or greater than the strm_bw are counted in order to filter very slow
streams due to slow node pairings.
**filt_sbw and strm_sbw**::
In the code, `SQLSupport.py`_, ``strm_bw`` is ``sbw`` and
``filt_bw`` is ``filt_sbws``::
for rs in RouterStats.query.filter(stats_clause).\
options(eagerload_all('router.streams.circuit.routers')).all():
...
...
@@ -46,36 +53,73 @@ The variables and steps used in Torflow:
if sbw_cnt: rs.filt_sbw = tot_sbw/sbw_cnt
else: rs.filt_sbw = None
**filt_avg, and strm_avg**::
This is also expressed in pseudocode in the `bandwidth file spec`_, section B.4
step 1.
Calling ``bw_i`` to ``strm_bw`` and ``bwfilt_i`` to ``filt_bw``,
if ``bw_j`` is a measurement for a relay ``i`` and ``m`` is the number of
measurements for that relay, then:
.. math::
bw_i = \mu(bw_j) = \frac{\sum_{j=1}^{m}bw_j}{m}
.. math::
bwfilt_i &= \mu(max(\mu(bw_j), bw_j))
= \frac{\sum_{j=1}^{m} max\left(\frac{\sum_{j=1}^{m}bw_j}{m}, bw_j\right)}{m}
Network measurements' bandwidth average
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From `README.spec.txt`_ (section 2.1)::
Once we have determined the most recent measurements for each node, we
compute an average of the filt_bw fields over all nodes we have measured.
::
In Torflow's `aggregate.py`_ code
::
filt_avg = sum(map(lambda n: n.filt_bw, nodes.itervalues()))/float(len(nodes))
strm_avg = sum(map(lambda n: n.strm_bw, nodes.itervalues()))/float(len(nodes))
**true_filt_avg and true_strm_avg**::
Both in the code with PID and without, all types of nodes get the same
average.
for cl in ["Guard+Exit", "Guard", "Exit", "Middle"]:
true_filt_avg[cl] = filt_avg
true_strm_avg[cl] = strm_avg
This is also expressed in pseudocode in the `bandwidth file spec`_, section B.4
step 2.
In the non-pid case, all types of nodes get the same avg
Calling ``bwstrm`` to ``strm_avg`` and ``bwfilt`` to ``fitl_avg``, if ``n`` is
the number of relays in the network, then:
**n.fbw_ratio and n.fsw_ratio**::
.. math::
bwstrm &= \mu(bw_i)
= \frac{\sum_{i=1}^{n}bw_i}{n}
= \frac{\sum_{i=1}^{n} \frac{\sum_{j=1}^{m}bw_j}{m} }{n}
.. math::
bwfilt &= \mu(bwfilt_i)
= \frac{\sum_{i=1}^{n}bwfilt_i}{n}
= \frac{\sum_{i=1}^{n}\frac{\sum_{j=1}^{m}max(\mu(bw_j), bw_j)}{m}}{n}
= \frac{\sum_{i=1}^{n}\frac{\sum_{j=1}^{m}max\left(\frac{\sum_{j=1}^{m}bw_j}{m}, bw_j\right)}{m}}{n}
for n in nodes.itervalues():
n.fbw_ratio = n.filt_bw/true_filt_avg[n.node_class()]
n.sbw_ratio = n.strm_bw/true_strm_avg[n.node_class()]
**n.ratio**::
Per relay bandwidth ratio
~~~~~~~~~~~~~~~~~~~~~~~~~
From `README.spec.txt`_ (section 2.2)::
These averages are used to produce ratios for each node by dividing the
measured value for that node by the network average.
::
In Torflow's `aggregate.py`_ code::
for n in nodes.itervalues():
n.fbw_ratio = n.filt_bw/true_filt_avg[n.node_class()]
n.sbw_ratio = n.strm_bw/true_strm_avg[n.node_class()]
[snip]
# Choose the larger between sbw and fbw
if n.sbw_ratio > n.fbw_ratio:
...
...
@@ -83,68 +127,267 @@ In the non-pid case, all types of nodes get the same avg
else:
n.ratio = n.fbw_ratio
**desc_bw**:
This is also expressed in pseudocode in the `bandwidth file spec`_, section B.4
step 2 and 3.
It is the minimum of all the descriptor bandwidth values::
Calling ``rf_i`` to ``fbw_ratio`` and ``rs_i`` to ``sbw_ration`` and ``r_i``
to ``ratio``:
.. math::
rf_i = \frac{bwfilt_i}{bwfilt}
rs_i = \frac{bw_i}{bwstrm}
.. math::
r_i = max(rf_i, rs_i)
= max\left(\frac{bwfilt_i}{bwfilt}, \frac{bw_i}{bwstrm}\right)
= max\left(\frac{bwfilt_i}{\mu(bwfilt_i)}, \frac{bw_i}{\mu(bwfilt_i)}\right)
Per relay descriptors bandwidth
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
From `TorCtl.py`_ code, it is the minimum of all the descriptor bandwidth
values::
bws = map(int, g)
bw_observed = min(bws)
[snip]
return Router(ns.idhex, ns.nickname, bw_observed, dead, exitpolicy,
ns.flags, ip, version, os, uptime, published, contact, rate_limited,
ns.orhash, ns.bandwidth, extra_info_digest, ns.unmeasured)
Because of the matched regular expression, ``bws`` is **not** all the descriptor
bandwidth values, but the observed bandwidth and the burst bandwidth, ie., it
does not take the average bandwidth, what seems to be a bug in Torflow.
This is passed to ``Router``, in which the consensus bandwidth is assigned to the
descriptor bandwidth when there is no consensus bandwidth::
(idhex, name, bw, down, exitpolicy, flags, ip, version, os, uptime,
published, contact, rate_limited, orhash,
ns_bandwidth,extra_info_digest,unmeasured) = args
[snip]
if ns_bandwidth != None:
self.bw = max(ns_bandwidth,1) # Avoid div by 0
else:
self.bw = max(bw,1) # Avoid div by 0
[snip]
self.desc_bw = max(bw,1) # Avoid div by 0
**new_bw**::
And written by `SQLSupport.py`_ as descriptor and conensus bandwidth::
f.write(" desc_bw="+str(int(cvt(s.avg_desc_bw,0))))
f.write(" ns_bw="+str(int(cvt(s.avg_bw,0)))+"\n")
Without PID control
-------------------
Per relay scaled bandwidth
~~~~~~~~~~~~~~~~~~~~~~~~~~
From `README.spec.txt`_ (section 2.2)::
These ratios are then multiplied by the most recent observed descriptor
bandwidth we have available for each node, to produce a new value for
the network status consensus process.
::
In `aggregate.py`_ code
::
n.new_bw = n.desc_bw*n.ratio
The descriptor observed bandwidth is multiplied by the ratio.
This is also expressed in pseudocode in the `bandwidth file spec`_, section B.4
step 5.
Calling ``bwnew_i`` to ``new_bw`` and ``descbw_i`` to ``use_bw``:
.. math::
descbw_i = min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right)
bwnew_i =& descbw_i \times r_i \
&= min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times max(rf_i, rs_i) \
**Limit the bandwidth to a maximum**::
&= min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times max\left(\frac{bwfilt_i}{bwfilt}, \frac{bw_i}{bwstrm}\right) \
&= min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times max\left(\frac{bwfilt_i}{\mu(bwfilt_i)}, \frac{bw_i}{\mu(bw_i)}\right)
With PID control
----------------
Per relay descriptors bandwidth
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Even though `README.spec.txt`_ talks about the consensus bandwidth, in
`aggregate.py`_ code, the consensus bandwidth is never used, since
``use_desc_bw`` is initialized to True and never changed::
self.use_desc_bw = True
[snip]
if cs_junk.bwauth_pid_control:
if cs_junk.use_desc_bw:
n.use_bw = n.desc_bw
else:
n.use_bw = n.ns_bw
Per relay scaled bandwidth
~~~~~~~~~~~~~~~~~~~~~~~~~~
From `README.spec.txt`_ section 3.1::
The bandwidth authorities measure F_node: the filtered stream
capacity through a given node (filtering is described in Section 1.6).
[snip]
pid_error = e(t) = (F_node - F_avg)/F_avg.
[snip]
new_consensus_bw = old_consensus_bw +
old_consensus_bw * K_p * e(t) +
old_consensus_bw * K_i * \integral{e(t)} +
old_consensus_bw * K_d * \derivative{e(t)}
[snip]
For the case where K_p = 1, K_i=0, and K_d=0, it can be seen that this
system is equivalent to the one defined in 2.2, except using consensus
bandwidth instead of descriptor bandwidth:
new_bw = old_bw + old_bw*e(t)
new_bw = old_bw + old_bw*(F_node/F_avg - 1)
new_bw = old_bw*F_node/F_avg
new_bw = old_bw*ratio
In Torflow's code, this is actually the case and most of the code is not
executed because the default ``K`` values.
It seems then that ``F_node`` is ``filt_bw`` in Torflow's code or ``bwfilt_i``
here, and ``F_avg`` is ``filt_avg`` in Torflow's code or ``bwfilt`` here.
In `aggregate.py`_ code, pid error also depends on which of the ratios is
greater::
if cs_junk.use_best_ratio and n.sbw_ratio > n.fbw_ratio:
n.pid_error = (n.strm_bw - true_strm_avg[n.node_class()]) \
/ true_strm_avg[n.node_class()]
else:
n.pid_error = (n.filt_bw - true_filt_avg[n.node_class()]) \
/ true_filt_avg[n.node_class()]
[snip]
n.new_bw = n.use_bw + cs_junk.K_p*n.use_bw*n.pid_error
Calling ``e_i`` to ``pid_error``, in the case that ``rs_i`` > ``rf_i``:
.. math::
e_i = \frac{bw_i - bwstrm}{bwstrm} = \frac{bw_i}{bwstrm} - 1
bwn_i = descbw_i + descbw_i \times e_i = descbw_i \times (1 + e_i)
= descbw_i \times (1 + \frac{bw_i}{bwstrm} - 1)
= descbw_i \times \frac{bw_i}{bwstrm} = descbw_i \times rs_i
And in the case that ``rs_i`` < ``rf_i``:
.. math::
e_i = \frac{bwfilt_i - bwfilt}{bwfilt} = \frac{bwfilt_i}{bwfilt} - 1
bwn_i = descbw_i + descbw_i \times e_i = descbw_i \times (1 + e_i)
= descbw_i \times (1 + \frac{bwfilt_i}{bwfilt} - 1)
= descbw_i \times \frac{bwfilt_i}{bwfilt} = descbw_i \times rf_i
So, it is the same as the scaled bandwidth in the case without PID controller,
ie.:
.. math::
bwn_i = descbw_i \times max(rf_i, rs_i)
With and without PID control
----------------------------
Per relay scaled bandwidth limit
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Once each relay bandwidth is scaled, it is limited to a maximum, that is
calculated as the sum of all the relays in the current consensus scaled
bandwidth per 0.05.
From `aggregate.py`_ code::
NODE_CAP = 0.05
::
[snip]
if n.idhex in prev_consensus:
if prev_consensus[n.idhex].bandwidth != None:
prev_consensus[n.idhex].measured = True
tot_net_bw += n.new_bw
[snip]
if n.new_bw > tot_net_bw*NODE_CAP:
plog("INFO", "Clipping extremely fast "+n.node_class()+" node "+n.idhex+"="+n.nick+
" at "+str(100*NODE_CAP)+"% of network capacity ("+
str(n.new_bw)+"->"+str(int(tot_net_bw*NODE_CAP))+") "+
" pid_error="+str(n.pid_error)+
" pid_error_sum="+str(n.pid_error_sum))
[snip]
n.new_bw = int(tot_net_bw*NODE_CAP)
However, tot_net_bw does not seems to be updated when not using pid.
This clipping would make faster relays to all have the same value.
All of that can be expressed as:
.. math::
bwn_i =& min\left(bwnew_i,
\sum_{i=1}^{n}bwnew_i \times 0.05\right) \
&= min\left(
\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times r_i\right),
\sum_{i=1}^{n}\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times r_i\right)
\times 0.05\right)\
&= min\left(
\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times max\left(rf_i, rs_i\right)\right),
\sum_{i=1}^{n}\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times
max\left(rf_i, rs_i\right)\right) \times 0.05\right)\
&= min\left(
\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times max\left(\frac{bwfilt_i}{bwfilt},
\frac{bw_i}{bwstrm}\right)\right),
\sum_{i=1}^{n}\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times
max\left(\frac{bwfilt_i}{bwfilt},
\frac{bw_i}{bwstrm}\right)\right) \times 0.05\right)
.. math::
bwn_i =& min\\left(bwnew_i,
\\sum_{i=1}^{n}bwnew_i \\times 0.05\\right) \\
&= min\\left(
\\left(min\\left(bwobs_i, bwavg_i, bwbur_i \\right) \\times r_i\\right),
\\sum_{i=1}^{n}\\left(min\\left(bwobs_i, bwavg_i, bwbur_i \\right) \\times r_i\\right)
\\times 0.05\\right)\\
&= min\\left(
\\left(min\\left(bwobs_i, bwavg_i, bwbur_i \\right) \\times max\\left(rf_i, rs_i\\right)\\right),
\\sum_{i=1}^{n}\\left(min\\left(bwobs_i, bwavg_i, bwbur_i \\right) \\times
max\\left(rf_i, rs_i\\right)\\right) \\times 0.05\\right)\\
&= min\\left(
\\left(min\\left(bwobs_i, bwavg_i, bwbur_i \\right) \\times max\\left(\\frac{bwfilt_i}{bwfilt},
\\frac{bw_i}{bwstrm}\\right)\\right),
\\sum_{i=1}^{n}\\left(min\\left(bwobs_i, bwavg_i, bwbur_i \\right) \\times
max\\left(\\frac{bwfilt_i}{bwfilt},
\\frac{bw_i}{bwstrm}\\right)\\right) \\times 0.05\\right)
bwn_i = min\left(
\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times max\left(\frac{bwfilt_i}{bwfilt},
\frac{bw_i}{bwstrm}\right)\right),
\sum_{i=1}^{n}\left(min\left(bwobs_i, bwavg_i, bwburst_i, measuredconsensusbw_i \right) \times
max\left(\frac{bwfilt_i}{bwfilt},
\frac{bw_i}{bwstrm}\right)\right) \times 0.05\right)
Per relay scaled bandwidth rounding
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Finally, the new scaled bandwidth is expressed in kilobytes and rounded a number
of digits.
.. _README.spec.txt: https://gitweb.torproject.org/torflow.git/tree/NetworkScanners/BwAuthority/README.spec.txt
.. _PID Controller: https://en.wikipedia.org/wiki/PID_controller
.. _SQLSupport.py: https://gitweb.torproject.org/pytorctl.git/tree/SQLSupport.py#n493
.. _bandwidth file spec: https://gitweb.torproject.org/torspec.git/tree/bandwidth-file-spec.txt
.. _aggregate.py: https://gitweb.torproject.org/torflow.git/tree/NetworkScanners/BwAuthority/aggregate.py
.. _TorCtly.py: https://gitweb.torproject.org/pytorctl.git/tree/TorCtl.py
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