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<h1><img src="postfix-logo.jpg" width="203" height="98" ALT="">Postfix
Queue Scheduler</h1>

<hr>

<h2> Disclaimer </h2>

<p> Many of the <i>transport</i>-specific configuration parameters
discussed in this document will not show up in "postconf" command
output before Postfix version 2.9. This limitation applies to many
parameters whose name is a combination of a master.cf service name
such as "relay" and a built-in suffix such as
"_destination_concurrency_limit". </p>

<h2> Overview </h2>

<p> The queue manager is by far the most complex part of the Postfix
mail system. It schedules delivery of new mail, retries failed
deliveries at specific times, and removes mail from the queue after
the last delivery attempt.  There are two major classes of mechanisms
that control the operation of the queue manager. </p>

<p> Topics covered by this document: </p>

<ul>

<li> <a href="#concurrency"> Concurrency scheduling</a>, concerned
with the number of concurrent deliveries to a specific destination,
including decisions on when to suspend deliveries after persistent
failures.

<li> <a href="#jobs"> Preemptive scheduling</a>, concerned with
the selection of email messages and recipients for a given destination.

<li> <a href="#credits"> Credits</a>, something this document would not be
complete without.

</ul>

<!--

<p> Once started, the qmgr(8) process runs until "postfix reload"
or "postfix stop".  As a persistent process, the queue manager has
to meet strict requirements with respect to code correctness and
robustness. Unlike non-persistent daemon processes, the queue manager
cannot benefit from Postfix's process rejuvenation mechanism that
limit the impact from resource leaks and other coding errors
(translation: replacing a process after a short time covers up bugs
before they can become a problem).  </p>

-->

<h2> <a name="concurrency"> Concurrency scheduling </a> </h2>

<p> The following sections document the Postfix 2.5 concurrency
scheduler, after a discussion of the limitations of the earlier
concurrency scheduler. This is followed by results of medium-concurrency
experiments, and a discussion of trade-offs between performance and
robustness.  </p>

<p> The material is organized as follows: </p>

<ul>

<li> <a href="#concurrency_drawbacks"> Drawbacks of the existing
concurrency scheduler </a>

<li> <a href="#concurrency_summary_2_5"> Summary of the Postfix 2.5
concurrency feedback algorithm </a>

<li> <a href="#dead_summary_2_5"> Summary of the Postfix 2.5 "dead
destination" detection algorithm </a>

<li> <a href="#pseudo_code_2_5"> Pseudocode for the Postfix 2.5
concurrency scheduler </a>

<li> <a href="#concurrency_results"> Results for delivery to
concurrency limited servers </a>

<li> <a href="#concurrency_discussion"> Discussion of concurrency
limited server results </a>

<li> <a href="#concurrency_limitations"> Limitations of less-than-1
per delivery feedback </a>

<li> <a href="#concurrency_config"> Concurrency configuration
parameters </a>

</ul>

<h3> <a name="concurrency_drawbacks"> Drawbacks of the existing
concurrency scheduler </a> </h3>

<p> From the start, Postfix has used a simple but robust algorithm
where the per-destination delivery concurrency is decremented by 1
after delivery failed due to connection or handshake failure, and
incremented by 1 otherwise.  Of course the concurrency is never
allowed to exceed the maximum per-destination concurrency limit.
And when a destination's concurrency level drops to zero, the
destination is declared "dead" and delivery is suspended.  </p>

<p> Drawbacks of +/-1 concurrency feedback per delivery are: <p>

<ul>

<li> <p> Overshoot due to exponential delivery concurrency growth
with each pseudo-cohort(*). This can be an issue with high-concurrency
channels. For example, with the default initial concurrency of 5,
concurrency would proceed over time as (5-10-20).  </p>

<li> <p> Throttling down to zero concurrency after a single
pseudo-cohort(*) failure. This was especially an issue with
low-concurrency channels where a single failure could be sufficient
to mark a destination as "dead", causing the suspension of further
deliveries to the affected destination. </p>

</ul>

<p> (*) A pseudo-cohort is a number of delivery requests equal to
a destination's delivery concurrency. </p>

<p> The revised concurrency scheduler has a highly modular structure.
It uses separate mechanisms for per-destination concurrency control
and for "dead destination" detection.  The concurrency control in
turn is built from two separate mechanisms: it supports less-than-1
feedback per delivery to allow for more gradual concurrency
adjustments, and it uses feedback hysteresis to suppress concurrency
oscillations.  And instead of waiting for delivery concurrency to
throttle down to zero, a destination is declared "dead" after a
configurable number of pseudo-cohorts reports connection or handshake
failure.  </p>

<h3> <a name="concurrency_summary_2_5"> Summary of the Postfix 2.5
concurrency feedback algorithm </a> </h3>

<p> We want to increment a destination's delivery concurrency when
some (not necessarily consecutive) number of deliveries complete
without connection or handshake failure.  This is implemented with
positive feedback g(N) where N is the destination's delivery
concurrency.  With g(N)=1 feedback per delivery, concurrency increases
by 1 after each positive feedback event; this gives us the old
scheduler's exponential growth in time. With g(N)=1/N feedback per
delivery, concurrency increases by 1 after an entire pseudo-cohort
N of positive feedback reports; this gives us linear growth in time.
Less-than-1 feedback per delivery and integer truncation naturally
give us hysteresis, so that transitions to larger concurrency happen
every 1/g(N) positive feedback events.  </p>

<p> We want to decrement a destination's delivery concurrency when
some (not necessarily consecutive) number of deliveries complete
after connection or handshake failure.  This is implemented with
negative feedback f(N) where N is the destination's delivery
concurrency.  With f(N)=1 feedback per delivery, concurrency decreases
by 1 after each negative feedback event; this gives us the old
scheduler's behavior where concurrency is throttled down dramatically
after a single pseudo-cohort failure.  With f(N)=1/N feedback per
delivery, concurrency backs off more gently.  Again, less-than-1
feedback per delivery and integer truncation naturally give us
hysteresis, so that transitions to lower concurrency happen every
1/f(N) negative feedback events.  </p>

<p> However, with negative feedback we introduce a subtle twist.
We "reverse" the negative hysteresis cycle so that the transition
to lower concurrency happens at the <b>beginning</b> of a sequence
of 1/f(N) negative feedback events.  Otherwise, a correction for
overload would be made too late.  This makes the choice of f(N)
relatively unimportant, as borne out by measurements later in this
document.  </p>

<p> In summary, the main ingredients for the Postfix 2.5 concurrency
feedback algorithm are a) the option of less-than-1 positive feedback
per delivery to avoid overwhelming servers, b) the option of
less-than-1 negative feedback per delivery to avoid giving up too
fast, c) feedback hysteresis to avoid rapid oscillation, and d) a
"reverse" hysteresis cycle for negative feedback, so that it can
correct for overload quickly.  </p>

<h3> <a name="dead_summary_2_5"> Summary of the Postfix 2.5 "dead destination" detection algorithm </a> </h3>

<p> We want to suspend deliveries to a specific destination after
some number of deliveries suffers connection or handshake failure.
The old scheduler declares a destination "dead" when negative (-1)
feedback throttles the delivery concurrency down to zero. With
less-than-1 feedback per delivery, this throttling down would
obviously take too long.  We therefore have to separate "dead
destination" detection from concurrency feedback.  This is implemented
by introducing the concept of pseudo-cohort failure. The Postfix
2.5 concurrency scheduler declares a destination "dead" after a
configurable number of pseudo-cohorts suffers from connection or
handshake failures. The old scheduler corresponds to the special
case where the pseudo-cohort failure limit is equal to 1.  </p>

<h3> <a name="pseudo_code_2_5"> Pseudocode for the Postfix 2.5 concurrency scheduler </a> </h3>

<p> The pseudo code shows how the ideas behind new concurrency
scheduler are implemented as of November 2007.  The actual code can
be found in the module qmgr/qmgr_queue.c.  </p>

<pre>
Types:
        Each destination has one set of the following variables
        int concurrency
        double success
        double failure
        double fail_cohorts

Feedback functions:
        N is concurrency; x, y are arbitrary numbers in [0..1] inclusive
        positive feedback: g(N) = x/N | x/sqrt(N) | x
        negative feedback: f(N) = y/N | y/sqrt(N) | y

Initialization:
        concurrency = initial_concurrency
        success = 0
        failure = 0
        fail_cohorts = 0

After success:
        fail_cohorts = 0
        Be prepared for feedback &gt; hysteresis, or rounding error
        success += g(concurrency)
        while (success >= 1)            Hysteresis 1
            concurrency += 1            Hysteresis 1
            failure = 0
            success -= 1                Hysteresis 1
        Be prepared for overshoot
        if (concurrency &gt; concurrency limit)
            concurrency = concurrency limit

Safety:
        Don't apply positive feedback unless
            concurrency &lt; busy_refcount + init_dest_concurrency
        otherwise negative feedback effect could be delayed

After failure:
        if (concurrency &gt; 0)
            fail_cohorts += 1.0 / concurrency
            if (fail_cohorts &gt; cohort_failure_limit)
                concurrency = 0
        if (concurrency &gt; 0)
            Be prepared for feedback &gt; hysteresis, rounding errors
            failure -= f(concurrency)
            while (failure &lt; 0)
                concurrency -= 1        Hysteresis 1
                failure += 1            Hysteresis 1
                success = 0
            Be prepared for overshoot
            if (concurrency &lt; 1)
                concurrency = 1
</pre>

<h3> <a name="concurrency_results"> Results for delivery to concurrency-limited servers </a> </h3>

<p> Discussions about the concurrency scheduler redesign started
early 2004, when the primary goal was to find alternatives that did
not exhibit exponential growth or rapid concurrency throttling.  No
code was implemented until late 2007, when the primary concern had
shifted towards better handling of server concurrency limits. For
this reason we measure how well the new scheduler does this
job.  The table below compares mail delivery performance of the old
+/-1 feedback per delivery with several less-than-1 feedback
functions, for different limited-concurrency server scenarios.
Measurements were done with a FreeBSD 6.2 client and with FreeBSD
6.2 and various Linux servers.  </p>

<p> Server configuration: </p>

<ul> <li> The mail flow was slowed down with 1 second latency per
recipient ("smtpd_client_restrictions = sleep 1"). The purpose was
to make results less dependent on hardware details, by avoiding
slow-downs by queue file I/O, logging I/O, and network I/O.

<li> Concurrency was limited by the server process limit
("default_process_limit = 5" and "smtpd_client_event_limit_exceptions
= static:all"). Postfix was stopped and started after changing the
process limit, because the same number is also used as the backlog
argument to the listen(2) system call, and "postfix reload" does
not re-issue this call.

<li> Mail was discarded with "local_recipient_maps = static:all" and
"local_transport = discard". The discard action in access maps or
header/body checks
could not be used as it fails to update the in_flow_delay counters.

</ul>

<p> Client configuration: </p>

<ul>

<li> Queue file overhead was minimized by sending one message to a
virtual alias that expanded into 2000 different remote recipients.
All recipients were accounted for according to the maillog file.
The virtual_alias_expansion_limit setting was increased to avoid
complaints from the cleanup(8) server.

<li> The number of deliveries was maximized with
"smtp_destination_recipient_limit = 2". A smaller limit would cause
Postfix to schedule the concurrency per recipient instead of domain,
which is not what we want.

<li> Maximum concurrency was limited with
"smtp_destination_concurrency_limit = 20", and
initial_destination_concurrency was set to the same value.

<li> The positive and negative concurrency feedback hysteresis was
1.  Concurrency was incremented by 1 at the END of 1/feedback steps
of positive feedback, and was decremented by 1 at the START of
1/feedback steps of negative feedback.

<li> The SMTP client used the default 30s SMTP connect timeout and
300s SMTP greeting timeout.

</ul>

<h4> Impact of the 30s SMTP connect timeout </h4>

<p> The first results are for a FreeBSD 6.2 server, where our
artificially low listen(2) backlog results in a very short kernel
queue for established connections. The table shows that all deferred
deliveries failed due to a 30s connection timeout, and none failed
due to a server greeting timeout.  This measurement simulates what
happens when the server's connection queue is completely full under
load, and the TCP engine drops new connections.  </p>

<blockquote>

<table>

<tr> <th>client<br> limit</th> <th>server<br> limit</th> <th>feedback<br>
style</th> <th>connection<br> caching</th> <th>percentage<br>
deferred</th> <th colspan="2">client concurrency<br> average/stddev</th>
<th colspan=2>timed-out in<br> connect/greeting </th> </tr>

<tr> <td align="center" colspan="9"> <hr> </td> </tr>

<tr><td align="center">20</td> <td align="center">5</td> <td
align="center">1/N</td> <td align="center">no</td> <td
align="center">9.9</td> <td align="center">19.4</td> <td
align="center">0.49</td> <td align="center">198</td> <td
align="center">-</td> </tr>

<tr><td align="center">20</td> <td align="center">5</td> <td
align="center">1/N</td> <td align="center">yes</td> <td
align="center">10.3</td> <td align="center">19.4</td> <td
align="center">0.49</td> <td align="center">206</td> <td
align="center">-</td> </tr>

<tr><td align="center">20</td> <td align="center">5</td> <td
align="center">1/sqrt(N)</td> <td align="center">no</td>
<td align="center">10.4</td> <td align="center">19.6</td> <td
align="center">0.59</td> <td align="center">208</td> <td
align="center">-</td> </tr>

<tr><td align="center">20</td> <td align="center">5</td> <td
align="center">1/sqrt(N)</td> <td align="center">yes</td>
<td align="center">10.6</td> <td align="center">19.6</td> <td
align="center">0.61</td> <td align="center">212</td> <td
align="center">-</td> </tr>

<tr><td align="center">20</td> <td align="center">5</td> <td
align="center">1</td> <td align="center">no</td> <td
align="center">10.1</td> <td align="center">19.5</td> <td
align="center">1.29</td> <td align="center">202</td> <td
align="center">-</td> </tr>

<tr><td align="center">20</td> <td align="center">5</td> <td
align="center">1</td> <td align="center">yes</td> <td
align="center">10.8</td> <td align="center">19.3</td> <td
align="center">1.57</td> <td align="center">216</td> <td
align="center">-</td> </tr>

<tr> <td align="center" colspan="9"> <hr> </td> </tr>

</table>

<p> A busy server with a completely full connection queue.  N is
the client delivery concurrency.  Failed deliveries time out after
30s without completing the TCP handshake. See text for a discussion
of results. </p>

</blockquote>

<h4> Impact of the 300s SMTP greeting timeout </h4>

<p> The next table shows results for a Fedora Core 8 server (results
for RedHat 7.3 are identical). In this case, the artificially small
listen(2) backlog argument does not impact our measurement.  The
table shows that practically all deferred deliveries fail after the
300s SMTP greeting timeout. As these timeouts were 10x longer than
with the first measurement, we increased the recipient count (and
thus the running time) by a factor of 10 to keep the results
comparable. The deferred mail percentages are a factor 10 lower
than with the first measurement, because the 1s per-recipient delay
was 1/300th of the greeting timeout instead of 1/30th of the
connection timeout.  </p>

<blockquote>

<table>

<tr> <th>client<br> limit</th> <th>server<br> limit</th> <th>feedback<br>
style</th> <th>connection<br> caching</th> <th>percentage<br>
deferred</th> <th colspan="2">client concurrency<br> average/stddev</th>
<th colspan=2>timed-out in<br> connect/greeting </th> </tr>

<tr> <td align="center" colspan="9"> <hr> </td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/N</td> <td align="center">no</td> <td
align="center">1.16</td> <td align="center">19.8</td> <td
align="center">0.37</td> <td align="center">-</td> <td
align="center">230</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/N</td> <td align="center">yes</td> <td
align="center">1.36</td> <td align="center">19.8</td> <td
align="center">0.36</td> <td align="center">-</td> <td
align="center">272</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/sqrt(N)</td> <td align="center">no</td>
<td align="center">1.21</td> <td align="center">19.9</td> <td
align="center">0.23</td> <td align="center">4</td> <td
align="center">238</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/sqrt(N)</td> <td align="center">yes</td>
<td align="center">1.36</td> <td align="center">20.0</td> <td
align="center">0.23</td> <td align="center">-</td> <td
align="center">272</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1</td> <td align="center">no</td> <td
align="center">1.18</td> <td align="center">20.0</td> <td
align="center">0.16</td> <td align="center">-</td> <td
align="center">236</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1</td> <td align="center">yes</td> <td
align="center">1.39</td> <td align="center">20.0</td> <td
align="center">0.16</td> <td align="center">-</td> <td
align="center">278</td> </tr>

<tr> <td align="center" colspan="9"> <hr> </td> </tr>

</table>

<p> A busy server with a non-full connection queue.  N is the client
delivery concurrency. Failed deliveries complete at the TCP level,
but time out after 300s while waiting for the SMTP greeting.  See
text for a discussion of results.  </p>

</blockquote>

<h4> Impact of active server concurrency limiter </h4>

<p> The final concurrency-limited result shows what happens when
SMTP connections don't time out, but are rejected immediately with
the Postfix server's smtpd_client_connection_count_limit feature
(the server replies with a 421 status and disconnects immediately).
Similar results can be expected with concurrency limiting features
built into other MTAs or firewalls.  For this measurement we specified
a server concurrency limit and a client initial destination concurrency
of 5, and a server process limit of 10; all other conditions were
the same as with the first measurement. The same result would be
obtained with a FreeBSD or Linux server, because the "pushing back"
is done entirely by the receiving side. </p>

<blockquote>

<table>

<tr> <th>client<br> limit</th> <th>server<br> limit</th> <th>feedback<br>
style</th> <th>connection<br> caching</th> <th>percentage<br>
deferred</th> <th colspan="2">client concurrency<br> average/stddev</th>
<th>theoretical<br>defer rate</th> </tr>

<tr> <td align="center" colspan="9"> <hr> </td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/N</td> <td align="center">no</td> <td
align="center">16.5</td> <td align="center">5.17</td> <td
align="center">0.38</td> <td align="center">1/6</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/N</td> <td align="center">yes</td> <td
align="center">16.5</td> <td align="center">5.17</td> <td
align="center">0.38</td> <td align="center">1/6</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/sqrt(N)</td> <td align="center">no</td>
<td align="center">24.5</td> <td align="center">5.28</td> <td
align="center">0.45</td> <td align="center">1/4</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1/sqrt(N)</td> <td align="center">yes</td>
<td align="center">24.3</td> <td align="center">5.28</td> <td
align="center">0.46</td> <td align="center">1/4</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1</td> <td align="center">no</td> <td
align="center">49.7</td> <td align="center">5.63</td> <td
align="center">0.67</td> <td align="center">1/2</td> </tr>

<tr> <td align="center">20</td> <td align="center">5</td> <td
align="center">1</td> <td align="center">yes</td> <td
align="center">49.7</td> <td align="center">5.68</td> <td
align="center">0.70</td> <td align="center">1/2</td> </tr>

<tr> <td align="center" colspan="9"> <hr> </td> </tr>

</table>

<p> A server with active per-client concurrency limiter that replies
with 421 and disconnects.  N is the client delivery concurrency.
The theoretical defer rate is 1/(1+roundup(1/feedback)).  This is
always 1/2 with the fixed +/-1 feedback per delivery; with the
concurrency-dependent feedback variants, the defer rate decreases
with increasing concurrency. See text for a discussion of results.
</p>

</blockquote>

<h3> <a name="concurrency_discussion"> Discussion of concurrency-limited server results </a> </h3>

<p> All results in the previous sections are based on the first
delivery runs only; they do not include any second etc. delivery
attempts. It's also worth noting that the measurements look at
steady-state behavior only. They don't show what happens when the
client starts sending at a much higher or lower concurrency.
</p>

<p> The first two examples show that the effect of feedback
is negligible when concurrency is limited due to congestion. This
is because the initial concurrency is already at the client's
concurrency maximum, and because there is 10-100 times more positive
than negative feedback.  Under these conditions, it is no surprise
that the contribution from SMTP connection caching is also negligible.
</p>

<p> In the last example, the old +/-1 feedback per delivery will
defer 50% of the mail when confronted with an active (anvil-style)
server concurrency limit, where the server hangs up immediately
with a 421 status (a TCP-level RST would have the same result).
Less aggressive feedback mechanisms fare better than more aggressive
ones.  Concurrency-dependent feedback fares even better at higher
concurrencies than shown here, but has limitations as discussed in
the next section.  </p>

<h3> <a name="concurrency_limitations"> Limitations of less-than-1 per delivery feedback </a> </h3>

<p> Less-than-1 feedback is of interest primarily when sending large
amounts of mail to destinations with active concurrency limiters
(servers that reply with 421, or firewalls that send RST).  When
sending small amounts of mail per destination, less-than-1 per-delivery
feedback won't have a noticeable effect on the per-destination
concurrency, because the number of deliveries to the same destination
is too small. You might just as well use zero per-delivery feedback
and stay with the initial per-destination concurrency. And when
mail deliveries fail due to congestion instead of active concurrency
limiters, the measurements above show that per-delivery feedback
has no effect.  With large amounts of mail you might just as well
use zero per-delivery feedback and start with the maximal per-destination
concurrency.  </p>

<p> The scheduler with less-than-1 concurrency
feedback per delivery solves a problem with servers that have active
concurrency limiters.  This works only because feedback is handled
in a peculiar manner: positive feedback will increment the concurrency
by 1 at the <b>end</b> of a sequence of events of length 1/feedback,
while negative feedback will decrement concurrency by 1 at the
<b>beginning</b> of such a sequence.  This is how Postfix adjusts
quickly for overshoot without causing lots of mail to be deferred.
Without this difference in feedback treatment, less-than-1 feedback
per delivery would defer 50% of the mail, and would be no better
in this respect than the old +/-1 feedback per delivery.  </p>

<p> Unfortunately, the same feature that corrects quickly for
concurrency overshoot also makes the scheduler more sensitive for
noisy negative feedback.  The reason is that one lonely negative
feedback event has the same effect as a complete sequence of length
1/feedback: in both cases delivery concurrency is dropped by 1
immediately.  As a worst-case scenario, consider multiple servers
behind a load balancer on a single IP address, and no backup MX
address.  When 1 out of K servers fails to complete the SMTP handshake
or drops the connection, a scheduler with 1/N (N = concurrency)
feedback stops increasing its concurrency once it reaches a concurrency
level of about K,  even though the good servers behind the load
balancer are perfectly capable of handling more traffic. </p>

<p> This noise problem gets worse as the amount of positive feedback
per delivery gets smaller.  A compromise is to use fixed less-than-1
positive feedback values instead of concurrency-dependent positive
feedback.  For example, to tolerate 1 of 4 bad servers in the above
load balancer scenario, use positive feedback of 1/4 per "good"
delivery (no connect or handshake error), and use an equal or smaller
amount of negative feedback per "bad" delivery.  The downside of
using concurrency-independent feedback is that some of the old +/-1
feedback problems will return at large concurrencies.  Sites that
must deliver mail at non-trivial per-destination concurrencies will
require special configuration.  </p>

<h3> <a name="concurrency_config"> Concurrency configuration parameters </a> </h3>

<p> The Postfix 2.5 concurrency scheduler is controlled with the
following configuration parameters, where "<i>transport</i>_foo"
provides a transport-specific parameter override.  All parameter
default settings are compatible with earlier Postfix versions. </p>

<blockquote>

<table border="0">

<tr> <th> Parameter name </th> <th> Postfix version </th> <th>
Description </th> </tr>

<tr> <td colspan="3"> <hr> </td> </tr>

<tr> <td> initial_destination_concurrency<br>
<i>transport</i>_initial_destination_concurrency </td> <td
align="center"> all<br> 2.5 </td> <td> Initial per-destination
delivery concurrency </td> </tr>

<tr> <td> default_destination_concurrency_limit<br>
<i>transport</i>_destination_concurrency_limit </td> <td align="center">
all<br> all </td> <td> Maximum per-destination delivery concurrency
</td> </tr>

<tr> <td> default_destination_concurrency_positive_feedback<br>
<i>transport</i>_destination_concurrency_positive_feedback </td>
<td align="center"> 2.5<br> 2.5 </td> <td> Per-destination positive
feedback amount, per delivery that does not fail with connection
or handshake failure </td> </tr>

<tr> <td> default_destination_concurrency_negative_feedback<br>
<i>transport</i>_destination_concurrency_negative_feedback </td>
<td align="center"> 2.5<br> 2.5 </td> <td> Per-destination negative
feedback amount, per delivery that fails with connection or handshake
failure </td> </tr>

<tr> <td> default_destination_concurrency_failed_cohort_limit<br>
<i>transport</i>_destination_concurrency_failed_cohort_limit </td>
<td align="center"> 2.5<br> 2.5 </td> <td> Number of failed
pseudo-cohorts after which a destination is declared "dead" and
delivery is suspended </td> </tr>

<tr> <td> destination_concurrency_feedback_debug</td> <td align="center">
2.5 </td> <td> Enable verbose logging of concurrency scheduler
activity </td> </tr>

<tr> <td colspan="3"> <hr> </td> </tr>

</table>

</blockquote>

<h2> <a name="jobs"> Preemptive scheduling </a> </h2>

<p>

The following sections describe the new queue manager and its
preemptive scheduler algorithm. Note that the document was originally
written to describe the changes between the new queue manager (in
this text referred to as <tt>nqmgr</tt>, the name it was known by
before it became the default queue manager) and the old queue manager
(referred to as <tt>oqmgr</tt>). This is why it refers to <tt>oqmgr</tt>
every so often.

</p>

<p>

This document is divided into sections as follows:

</p>

<ul>

<li> <a href="#<tt>nqmgr</tt>_structures"> The structures used by
nqmgr </a>

<li> <a href="#<tt>nqmgr</tt>_pickup"> What happens when nqmgr picks
up the message </a> - how it is assigned to transports, jobs, peers,
entries

<li> <a href="#<tt>nqmgr</tt>_selection"> How the entry selection
works </a>

<li> <a href="#<tt>nqmgr</tt>_preemption"> How the preemption
works </a> - what messages may be preempted and how and what messages
are chosen to preempt them

<li> <a href="#<tt>nqmgr</tt>_concurrency"> How destination concurrency
limits affect the scheduling algorithm </a>

<li> <a href="#<tt>nqmgr</tt>_memory"> Dealing with memory resource
limits </a>

</ul>

<h3> <a name="<tt>nqmgr</tt>_structures"> The structures used by
nqmgr </a> </h3>

<p>

Let's start by recapitulating the structures and terms used when
referring to queue manager and how it operates. Many of these are
partially described elsewhere, but it is nice to have a coherent
overview in one place:

</p>

<ul>

<li> <p> Each message structure represents one mail message which
Postfix is to deliver. The message recipients specify to what
destinations is the message to be delivered and what transports are
going to be used for the delivery. </p>

<li> <p> Each recipient entry groups a batch of recipients of one
message which are all going to be delivered to the same destination
(and over the same transport).
</p>

<li> <p> Each transport structure groups everything what is going
to be delivered by delivery agents dedicated for that transport.
Each transport maintains a set of queues (describing the destinations
it shall talk to) and jobs (referencing the messages it shall
deliver). </p>

<li> <p> Each transport queue (not to be confused with the on-disk
active queue or incoming queue) groups everything what is going be
delivered to given destination (aka nexthop) by its transport.  Each
queue belongs to one transport, so each destination may be referred
to by several queues, one for each transport.  Each queue maintains
a list of all recipient entries (batches of message recipients)
which shall be delivered to given destination (the todo list), and
a list of recipient entries already being delivered by the delivery
agents (the busy list). </p>

<li> <p> Each queue corresponds to multiple peer structures.  Each
peer structure is like the queue structure, belonging to one transport
and referencing one destination. The difference is that it lists
only the recipient entries which all originate from the same message,
unlike the queue structure, whose entries may originate from various
messages. For messages with few recipients, there is usually just
one recipient entry for each destination, resulting in one recipient
entry per peer. But for large mailing list messages the recipients
may need to be split to multiple recipient entries, in which case
the peer structure may list many entries for single destination.
</p>

<li> <p> Each transport job groups everything it takes to deliver
one message via its transport. Each job represents one message
within the context of the transport. The job belongs to one transport
and message, so each message may have multiple jobs, one for each
transport. The job groups all the peer structures, which describe
the destinations the job's message has to be delivered to. </p>

</ul>

<p>

The first four structures are common to both <tt>nqmgr</tt> and
<tt>oqmgr</tt>, the latter two were introduced by <tt>nqmgr</tt>.

</p>

<p>

These terms are used extensively in the text below, feel free to
look up the description above anytime you'll feel you have lost a
sense what is what.

</p>

<h3> <a name="<tt>nqmgr</tt>_pickup"> What happens when nqmgr picks
up the message </a> </h3>

<p>

Whenever <tt>nqmgr</tt> moves a queue file into the active queue,
the following happens: It reads all necessary information from the
queue file as <tt>oqmgr</tt> does, and also reads as many recipients
as possible - more on that later, for now let's just pretend it
always reads all recipients.

</p>

<p>

Then it resolves the recipients as <tt>oqmgr</tt> does, which
means obtaining (address, nexthop, transport) triple for each
recipient. For each triple, it finds the transport; if it does not
exist yet, it instantiates it (unless it's dead). Within the
transport, it finds the destination queue for given nexthop; if it
does not exist yet, it instantiates it (unless it's dead). The
triple is then bound to given destination queue. This happens in
qmgr_resolve() and is basically the same as in <tt>oqmgr</tt>.

</p>

<p>

Then for each triple which was bound to some queue (and thus
transport), the program finds the job which represents the message
within that transport's context; if it does not exist yet, it
instantiates it. Within the job, it finds the peer which represents
the bound destination queue within this jobs context; if it does
not exist yet, it instantiates it.  Finally, it stores the address
from the resolved triple to the recipient entry which is appended
to both the queue entry list and the peer entry list. The addresses
for same nexthop are batched in the entries up to recipient_concurrency
limit for that transport. This happens in qmgr_assign() and apart
from that it operates with job and peer structures it is basically the
same as in <tt>oqmgr</tt>.

</p>

<p>

When the job is instantiated, it is enqueued on the transport's job
list based on the time its message was picked up by <tt>nqmgr</tt>.
For first batch of recipients this means it is appended to the end
of the job list, but the ordering of the job list by the enqueue
time is important as we will see shortly.

</p>

<p>

[Now you should have pretty good idea what is the state of the
<tt>nqmgr</tt> after couple of messages was picked up, what is the
relation between all those job, peer, queue and entry structures.]

</p>

<h3> <a name="<tt>nqmgr</tt>_selection"> How the entry selection
works </a> </h3>

<p>

Having prepared all those above mentioned structures, the task of
the <tt>nqmgr</tt>'s scheduler is to choose the recipient entries
one at a time and pass them to the delivery agent for corresponding
transport. Now how does this work?

</p>

<p>

The first approximation of the new scheduling algorithm is like this:

</p>

<blockquote>
<pre>
foreach transport (round-robin-by-transport)
do
    if transport busy continue
    if transport process limit reached continue
    foreach transport's job (in the order of the transport's job list)
    do
	foreach job's peer (round-robin-by-destination)
	     if peer-&gt;queue-&gt;concurrency &lt; peer-&gt;queue-&gt;window
		 return next peer entry.
	done
    done
done
</pre>
</blockquote>

<p>

Now what is the "order of the transport's job list"? As we know
already, the job list is by default kept in the order the message
was picked up by the <tt>nqmgr</tt>. So by default we get the
top-level round-robin transport, and within each transport we get
the FIFO message delivery. The round-robin of the peers by the
destination is perhaps of little importance in most real-life cases
(unless the recipient_concurrency limit is reached, in one job there
is only one peer structure for each destination), but theoretically
it makes sure that even within single jobs, destinations are treated
fairly.

</p>

<p>

[By now you should have a feeling you really know how the scheduler
works, except for the preemption, under ideal conditions - that is,
no recipient resource limits and no destination concurrency problems.]

</p>

<h3> <a name="<tt>nqmgr</tt>_preemption"> How the preemption
works </a> </h3>

<p>

As you might perhaps expect by now, the transport's job list does
not remain sorted by the job's message enqueue time all the time.
The most cool thing about <tt>nqmgr</tt> is not the simple FIFO
delivery, but that it is able to slip mail with little recipients
past the mailing-list bulk mail.  This is what the job preemption
is about - shuffling the jobs on the transport's job list to get
the best message delivery rates. Now how is it achieved?

</p>

<p>

First I have to tell you that there are in fact two job lists in
each transport. One is the scheduler's job list, which the scheduler
is free to play with, while the other one keeps the jobs always
listed in the order of the enqueue time and is used for recipient
pool management we will discuss later. For now, we will deal with
the scheduler's job list only.

</p>

<p>

So, we have the job list, which is first ordered by the time the
jobs' messages were enqueued, oldest messages first, the most recently
picked one at the end. For now, let's assume that there are no
destination concurrency problems. Without preemption, we pick some
entry of the first (oldest) job on the queue, assign it to delivery
agent, pick another one from the same job, assign it again, and so
on, until all the entries are used and the job is delivered. We
would then move onto the next job and so on and on. Now how do we
manage to sneak in some entries from the recently added jobs when
the first job on the job list belongs to a message going to the
mailing-list and has thousands of recipient entries?

</p>

<p>

The <tt>nqmgr</tt>'s answer is that we can artificially "inflate"
the delivery time of that first job by some constant for free - it
is basically the same trick you might remember as "accumulation of
potential" from the amortized complexity lessons. For example,
instead of delivering the entries of the first job on the job list
every time a delivery agent becomes available, we can do it only
every second time. If you view the moments the delivery agent becomes
available on a timeline as "delivery slots", then instead of using
every delivery slot for the first job, we can use only every other
slot, and still the overall delivery efficiency of the first job
remains the same. So the delivery <tt>11112222</tt> becomes
<tt>1.1.1.1.2.2.2.2</tt> (1 and 2 are the imaginary job numbers, .
denotes the free slot). Now what do we do with free slots?

</p>

<p>

As you might have guessed, we will use them for sneaking the mail
with little recipients in. For example, if we have one four-recipient
mail followed by four one recipients mail, the delivery sequence
(that is, the sequence in which the jobs are assigned to the
delivery slots) might look like this: <tt>12131415</tt>. Hmm, fine
for sneaking in the single recipient mail, but how do we sneak in
the mail with more than one recipient? Say if we have one four-recipient
mail followed by two two-recipient mails?

</p>

<p>

The simple answer would be to use delivery sequence <tt>12121313</tt>.
But the problem is that this does not scale well. Imagine you have
mail with thousand recipients followed by mail with hundred recipients.
It is tempting to suggest the  delivery sequence like <tt>121212....</tt>,
but alas! Imagine there arrives another mail with say ten recipients.
But there are no free slots anymore, so it can't slip by, not even
if it had just only one recipients.  It will be stuck until the
hundred-recipient mail is delivered, which really sucks.

</p>

<p>

So, it becomes obvious that while inflating the message to get
free slots is great idea, one has to be really careful of how the
free slots are assigned, otherwise one might corner himself. So,
how does <tt>nqmgr</tt> really use the free slots?

</p>

<p>

The key idea is that one does not have to generate the free slots
in a uniform way. The delivery sequence <tt>111...1</tt> is no
worse than <tt>1.1.1.1</tt>, in fact, it is even better as some
entries are in the first case selected earlier than in the second
case, and none is selected later! So it is possible to first
"accumulate" the free delivery slots and then use them all at once.
It is even possible to accumulate some, then use them, then accumulate
some more and use them again, as in <tt>11..1.1</tt> .

</p>

<p>

Let's get back to the one hundred recipient example. We now know
that we could first accumulate one hundred free slots, and only
after then to preempt the first job and sneak the one hundred
recipient mail in. Applying the algorithm recursively, we see the
hundred recipient job can accumulate ten free delivery slots, and
then we could preempt it and sneak in the ten-recipient mail...
Wait wait wait! Could we? Aren't we overinflating the original one
thousand recipient mail?

</p>

<p>

Well, despite it looks so at the first glance, another trick will
allow us to answer "no, we are not!". If we had said that we will
inflate the delivery time twice at maximum, and then we consider
every other slot as a free slot, then we would overinflate in case
of the recursive preemption. BUT! The trick is that if we use only
every n-th slot as a free slot for n&gt;2, there is always some worst
inflation factor which we can guarantee not to be breached, even
if we apply the algorithm recursively. To be precise, if for every
k&gt;1 normally used slots we accumulate one free delivery slot, than
the inflation factor is not worse than k/(k-1) no matter how many
recursive preemptions happen. And it's not worse than (k+1)/k if
only non-recursive preemption happens. Now, having got through the
theory and the related math, let's see how <tt>nqmgr</tt> implements
this.

</p>

<p>

Each job has so called "available delivery slot" counter. Each
transport has a <i>transport</i>_delivery_slot_cost parameter, which
defaults to default_delivery_slot_cost parameter which is set to 5
by default. This is the k from the paragraph above. Each time k
entries of the job are selected for delivery, this counter is
incremented by one. Once there are some slots accumulated, job which
requires no more than that number of slots to be fully delivered
can preempt this job.

</p>

<p>

[Well, the truth is, the counter is incremented every time an entry
is selected and it is divided by k when it is used.
But for the understanding it's good enough to use
the above approximation of the truth.]

</p>

<p>

OK, so now we know the conditions which must be satisfied so one
job can preempt another one. But what job gets preempted, how do
we choose what job preempts it if there are several valid candidates,
and when does all this exactly happen?

</p>

<p>

The answer for the first part is simple. The job whose entry was
selected the last time is so called current job. Normally, it is
the first job on the scheduler's job list, but destination concurrency
limits may change this as we will see later. It is always only the
current job which may get preempted.

</p>

<p>

Now for the second part. The current job has certain amount of
recipient entries, and as such may accumulate at maximum some amount
of available delivery slots. It might have already accumulated some,
and perhaps even already used some when it was preempted before
(remember a job can be preempted several times). In either case,
we know how many are accumulated and how many are left to deliver,
so we know how many it may yet accumulate at maximum. Every other
job which may be delivered by less than that number of slots is a
valid candidate for preemption. How do we choose among them?

</p>

<p>

The answer is - the one with maximum enqueue_time/recipient_entry_count.
That is, the older the job is, the more we should try to deliver
it in order to get best message delivery rates. These rates are of
course subject to how many recipients the message has, therefore
the division by the recipient (entry) count. No one shall be surprised
that message with n recipients takes n times longer to deliver than
message with one recipient.

</p>

<p>

Now let's recap the previous two paragraphs. Isn't it too complicated?
Why don't the candidates come only among the jobs which can be
delivered within the number of slots the current job already
accumulated? Why do we need to estimate how much it has yet to
accumulate? If you found out the answer, congratulate yourself. If
we did it this simple way, we would always choose the candidate
with least recipient entries. If there were enough single recipient
mails coming in, they would always slip by the bulk mail as soon
as possible, and the two and more recipients mail would never get
a chance, no matter how long they have been sitting around in the
job list.

</p>

<p>

This candidate selection has interesting implication - that when
we choose the best candidate for preemption (this is done in
qmgr_choose_candidate()), it may happen that we may not use it for
preemption immediately. This leads to an answer to the last part
of the original question - when does the preemption happen?

</p>

<p>

The preemption attempt happens every time next transport's recipient
entry is to be chosen for delivery. To avoid needless overhead, the
preemption is not attempted if the current job could never accumulate
more than <i>transport</i>_minimum_delivery_slots (defaults to
default_minimum_delivery_slots which defaults to 3). If there is
already enough accumulated slots to preempt the current job by the
chosen best candidate, it is done immediately. This basically means
that the candidate is moved in front of the current job on the
scheduler's job list and decreasing the accumulated slot counter
by the amount used by the candidate. If there is not enough slots...
well, I could say that nothing happens and the another preemption
is attempted the next time. But that's not the complete truth.

</p>

<p>

The truth is that it turns out that it is not really necessary to
wait until the jobs counter accumulates all the delivery slots in
advance. Say we have ten-recipient mail followed by two two-recipient
mails. If the preemption happened when enough delivery slot accumulate
(assuming slot cost 2), the delivery sequence becomes
<tt>11112211113311</tt>. Now what would we get if we would wait
only for 50% of the necessary slots to accumulate and we promise
we would wait for the remaining 50% later, after we get back
to the preempted job? If we use such slot loan, the delivery sequence
becomes <tt>11221111331111</tt>. As we can see, it makes it no
considerably worse for the delivery of the ten-recipient mail, but
it allows the small messages to be delivered sooner.

</p>

<p>

The concept of these slot loans is where the
<i>transport</i>_delivery_slot_discount and
<i>transport</i>_delivery_slot_loan come from (they default to
default_delivery_slot_discount and default_delivery_slot_loan, whose
values are by default 50 and 3, respectively). The discount (resp.
loan) specifies how many percent (resp. how many slots) one "gets
in advance", when the number of slots required to deliver the best
candidate is compared with the number of slots the current slot had
accumulated so far.

</p>

<p>

And it pretty much concludes this chapter.

</p>

<p>

[Now you should have a feeling that you pretty much understand the
scheduler and the preemption, or at least that you will have it
after you read the last chapter couple more times. You shall clearly
see the job list and the preemption happening at its head, in ideal
delivery conditions. The feeling of understanding shall last until
you start wondering what happens if some of the jobs are blocked,
which you might eventually figure out correctly from what had been
said already. But I would be surprised if your mental image of the
scheduler's functionality is not completely shattered once you
start wondering how it works when not all recipients may be read
in-core.  More on that later.]

</p>

<h3> <a name="<tt>nqmgr</tt>_concurrency"> How destination concurrency
limits affect the scheduling algorithm </a> </h3>

<p>

The <tt>nqmgr</tt> uses the same algorithm for destination concurrency
control as <tt>oqmgr</tt>. Now what happens when the destination
limits are reached and no more entries for that destination may be
selected by the scheduler?

</p>

<p>

From user's point of view it is all simple. If some of the peers
of a job can't be selected, those peers are simply skipped by the
entry selection algorithm (the pseudo-code described before) and
only the selectable ones are used. If none of the peers may be
selected, the job is declared a "blocker job". Blocker jobs are
skipped by the entry selection algorithm and they are also excluded
from the candidates for preemption of current job. Thus the scheduler
effectively behaves as if the blocker jobs didn't exist on the job
list at all. As soon as at least one of the peers of a blocker job
becomes unblocked (that is, the delivery agent handling the delivery
of the recipient entry for given destination successfully finishes),
the job's blocker status is removed and the job again participates
in all further scheduler actions normally.

</p>

<p>

So the summary is that the users don't really have to be concerned
about the interaction of the destination limits and scheduling
algorithm. It works well on its own and there are no knobs they
would need to control it.

</p>

<p>

From a programmer's point of view, the blocker jobs complicate the
scheduler quite a lot. Without them, the jobs on the job list would
be normally delivered in strict FIFO order. If the current job is
preempted, the job preempting it is completely delivered unless it
is preempted itself. Without blockers, the current job is thus
always either the first job on the job list, or the top of the stack
of jobs preempting the first job on the job list.

</p>

<p>

The visualization of the job list and the preemption stack without
blockers would be like this:

</p>

<blockquote>
<pre>
first job-&gt;    1--2--3--5--6--8--...    &lt;- job list
on job list    |
               4    &lt;- preemption stack
               |
current job-&gt;  7
</pre>
</blockquote>

<p>

In the example above we see that job 1 was preempted by job 4 and
then job 4 was preempted by job 7. After job 7 is completed, remaining
entries of job 4 are selected, and once they are all selected, job
1 continues.

</p>

<p>

As we see, it's all very clean and straightforward. Now how does
this change because of blockers?

</p>

<p>

The answer is: a lot. Any job may become blocker job at any time,
and also become normal job again at any time. This has several
important implications:

</p>

<ol>

<li> <p>

The jobs may be completed in arbitrary order. For example, in the
example above, if the current job 7 becomes blocked, the next job
4 may complete before the job 7 becomes unblocked again. Or if both
7 and 4 are blocked, then 1 is completed, then 7 becomes unblocked
and is completed, then 2 is completed and only after that 4 becomes
unblocked and is completed... You get the idea.

</p>

<p>

[Interesting side note: even when jobs are delivered out of order,
from single destination's point of view the jobs are still delivered
in the expected order (that is, FIFO unless there was some preemption
involved). This is because whenever a destination queue becomes
unblocked (the destination limit allows selection of more recipient
entries for that destination), all jobs which have peers for that
destination are unblocked at once.]

</p>

<li> <p>

The idea of the preemption stack at the head of the job list is
gone.  That is, it must be possible to preempt any job on the job
list. For example, if the jobs 7, 4, 1 and 2 in the example above
become all blocked, job 3 becomes the current job. And of course
we do not want the preemption to be affected by the fact that there
are some blocked jobs or not. Therefore, if it turns out that job
3 might be preempted by job 6, the implementation shall make it
possible.

</p>

<li> <p>

The idea of the linear preemption stack itself is gone. It's no
longer true that one job is always preempted by only one job at one
time (that is directly preempted, not counting the recursively
nested jobs). For example, in the example above, job 1 is directly
preempted by only job 4, and job 4 by job 7. Now assume job 7 becomes
blocked, and job 4 is being delivered. If it accumulates enough
delivery slots, it is natural that it might be preempted for example
by job 8. Now job 4 is preempted by both job 7 AND job 8 at the
same time.

</p>

</ol>

<p>

Now combine the points 2) and 3) with point 1) again and you realize
that the relations on the once linear job list became pretty
complicated. If we extend the point 3) example: jobs 7 and 8 preempt
job 4, now job 8 becomes blocked too, then job 4 completes. Tricky,
huh?

</p>

<p>

If I illustrate the relations after the above mentioned examples
(but those in point 1)), the situation would look like this:

</p>

<blockquote>
<pre>
                            v- parent

adoptive parent -&gt;    1--2--3--5--...      &lt;- "stack" level 0
                      |     |
parent gone -&gt;        ?     6              &lt;- "stack" level 1
                     / \
children -&gt;         7   8   ^- child       &lt;- "stack" level 2

                      ^- siblings
</pre>
</blockquote>

<p>

Now how does <tt>nqmgr</tt> deal with all these complicated relations?

</p>

<p>

Well, it maintains them all as described, but fortunately, all these
relations are necessary only for purposes of proper counting of
available delivery slots. For purposes of ordering the jobs for
entry selection, the original rule still applies: "the job preempting
the current job is moved in front of the current job on the job
list". So for entry selection purposes, the job relations remain
as simple as this:

</p>

<blockquote>
<pre>
7--8--1--2--6--3--5--..   &lt;- scheduler's job list order
</pre>
</blockquote>

<p>

The job list order and the preemption parent/child/siblings relations
are maintained separately. And because the selection works only
with the job list, you can happily forget about those complicated
relations unless you want to study the <tt>nqmgr</tt> sources. In
that case the text above might provide some helpful introduction
to the problem domain. Otherwise I suggest you just forget about
all this and stick with the user's point of view: the blocker jobs
are simply ignored.

</p>

<p>

[By now, you should have a feeling that there is more things going
under the hood than you ever wanted to know. You decide that
forgetting about this chapter is the best you can do for the sake
of your mind's health and you basically stick with the idea how the
scheduler works in ideal conditions, when there are no blockers,
which is good enough.]

</p>

<h3> <a name="<tt>nqmgr</tt>_memory"> Dealing with memory resource
limits </a> </h3>

<p>

When discussing the <tt>nqmgr</tt> scheduler, we have so far assumed
that all recipients of all messages in the active queue are completely
read into the memory. This is simply not true. There is an upper
bound on the amount of memory the <tt>nqmgr</tt> may use, and
therefore it must impose some limits on the information it may store
in the memory at any given time.

</p>

<p>

First of all, not all messages may be read in-core at once. At any
time, only qmgr_message_active_limit messages may be read in-core
at maximum. When read into memory, the messages are picked from the
incoming and deferred message queues and moved to the active queue
(incoming having priority), so if there is more than
qmgr_message_active_limit messages queued in the active queue, the
rest will have to wait until (some of) the messages in the active
queue are completely delivered (or deferred).

</p>

<p>

Even with the limited amount of in-core messages, there is another
limit which must be imposed in order to avoid memory exhaustion.
Each message may contain huge amount of recipients (tens or hundreds
of thousands are not uncommon), so if <tt>nqmgr</tt> read all
recipients of all messages in the active queue, it may easily run
out of memory. Therefore there must be some upper bound on the
amount of message recipients which are read into the memory at the
same time.

</p>

<p>

Before discussing how exactly <tt>nqmgr</tt> implements the recipient
limits, let's see how the sole existence of the limits themselves
affects the <tt>nqmgr</tt> and its scheduler.

</p>

<p>

The message limit is straightforward - it just limits the size of
the
lookahead the <tt>nqmgr</tt>'s scheduler has when choosing which
message can preempt the current one. Messages not in the active
queue simply are not considered at all.

</p>

<p>

The recipient limit complicates more things. First of all, the
message reading code must support reading the recipients in batches,
which among other things means accessing the queue file several
times and continuing where the last recipient batch ended. This is
invoked by the scheduler whenever the current job has space for more
recipients, subject to transport's refill_limit and refill_delay parameters.
It is also done any time when all
in-core recipients of the message are dealt with (which may also
mean they were deferred) but there are still more in the queue file.

</p>

<p>

The second complication is that with some recipients left unread
in the queue file, the scheduler can't operate with exact counts
of recipient entries. With unread recipients, it is not clear how
many recipient entries there will be, as they are subject to
per-destination grouping. It is not even clear to what transports
(and thus jobs) the recipients will be assigned. And with messages
coming from the deferred queue, it is not even clear how many unread
recipients are still to be delivered. This all means that the
scheduler must use only estimates of how many recipients entries
there will be.  Fortunately, it is possible to estimate the minimum
and maximum correctly, so the scheduler can always err on the safe
side.  Obviously, the better the estimates, the better results, so
it is best when we are able to read all recipients in-core and turn
the estimates into exact counts, or at least try to read as many
as possible to make the estimates as accurate as possible.

</p>

<p>

The third complication is that it is no longer true that the scheduler
is done with a job once all of its in-core recipients are delivered.
It is possible that the job will be revived later, when another
batch of recipients is read in core. It is also possible that some
jobs will be created for the first time long after the first batch
of recipients was read in core. The <tt>nqmgr</tt> code must be
ready to handle all such situations.

</p>

<p>

And finally, the fourth complication is that the <tt>nqmgr</tt>
code must somehow impose the recipient limit itself. Now how does
it achieve it?

</p>

<p>

Perhaps the easiest solution would be to say that each message may
have at maximum X recipients stored in-core, but such solution would
be poor for several reasons. With reasonable qmgr_message_active_limit
values, the X would have to be quite low to maintain reasonable
memory footprint. And with low X lots of things would not work well.
The <tt>nqmgr</tt> would have problems to use the
<i>transport</i>_destination_recipient_limit efficiently. The
scheduler's preemption would be suboptimal as the recipient count
estimates would be inaccurate. The message queue file would have
to be accessed many times to read in more recipients again and
again.

</p>

<p>

Therefore it seems reasonable to have a solution which does not use
a limit imposed on per-message basis, but which maintains a pool
of available recipient slots, which can be shared among all messages
in the most efficient manner. And as we do not want separate
transports to compete for resources whenever possible, it seems
appropriate to maintain such recipient pool for each transport
separately. This is the general idea, now how does it work in
practice?

</p>

<p>

First we have to solve little chicken-and-egg problem. If we want
to use the per-transport recipient pools, we first need to know to
what transport(s) is the message assigned. But we will find that
out only after we read in the recipients first. So it is obvious
that we first have to read in some recipients, use them to find out
to what transports is the message to be assigned, and only after
that we can use the per-transport recipient pools.

</p>

<p>

Now how many recipients shall we read for the first time? This is
what qmgr_message_recipient_minimum and qmgr_message_recipient_limit
values control. The qmgr_message_recipient_minimum value specifies
how many recipients of each message we will read for the first time,
no matter what.  It is necessary to read at least one recipient
before we can assign the message to a transport and create the first
job. However, reading only qmgr_message_recipient_minimum recipients
even if there are only few messages with few recipients in-core would
be wasteful. Therefore if there is less than qmgr_message_recipient_limit
recipients in-core so far, the first batch of recipients may be
larger than qmgr_message_recipient_minimum - as large as is required
to reach the qmgr_message_recipient_limit limit.

</p>

<p>

Once the first batch of recipients was read in core and the message
jobs were created, the size of the subsequent recipient batches (if
any - of course it's best when all recipients are read in one batch)
is based solely on the position of the message jobs on their
corresponding transports' job lists. Each transport has a pool of
<i>transport</i>_recipient_limit recipient slots which it can
distribute among its jobs (how this is done is described later).
The subsequent recipient batch may be as large as the sum of all
recipient slots of all jobs of the message permits (plus the
qmgr_message_recipient_minimum amount which always applies).

</p>

<p>

For example, if a message has three jobs, first with 1 recipient
still in-core and 4 recipient slots, second with 5 recipient in-core
and 5 recipient slots, and third with 2 recipients in-core and 0
recipient slots, it has 1+5+2=7 recipients in-core and 4+5+0=9 jobs'
recipients slots in total. This means that we could immediately
read 2+qmgr_message_recipient_minimum more recipients of that message
in core.

</p>

<p>

The above example illustrates several things which might be worth
mentioning explicitly: first, note that although the per-transport
slots are assigned to particular jobs, we can't guarantee that once
the next batch of recipients is read in core, that the corresponding
amounts of recipients will be assigned to those jobs. The jobs lend
its slots to the message as a whole, so it is possible that some
jobs end up sponsoring other jobs of their message. For example,
if in the example above the 2 newly read recipients were assigned
to the second job, the first job sponsored the second job with 2
slots. The second notable thing is the third job, which has more
recipients in-core than it has slots. Apart from sponsoring by other
job we just saw it can be result of the first recipient batch, which
is sponsored from global recipient pool of qmgr_message_recipient_limit
recipients. It can be also sponsored from the message recipient
pool of qmgr_message_recipient_minimum recipients.

</p>

<p>

Now how does each transport distribute the recipient slots among
its jobs?  The strategy is quite simple. As most scheduler activity
happens on the head of the job list, it is our intention to make
sure that the scheduler has the best estimates of the recipient
counts for those jobs. As we mentioned above, this means that we
want to try to make sure that the messages of those jobs have all
recipients read in-core. Therefore the transport distributes the
slots "along" the job list from start to end. In this case the job
list sorted by message enqueue time is used, because it doesn't
change over time as the scheduler's job list does.

</p>

<p>

More specifically, each time a job is created and appended to the
job list, it gets all unused recipient slots from its transport's
pool. It keeps them until all recipients of its message are read.
When this happens, all unused recipient slots are transferred to
the next job (which is now in fact now first such job) on the job
list which still has some recipients unread, or eventually back to
the transport pool if there is no such job. Such transfer then also
happens whenever a recipient entry of that job is delivered.

</p>

<p>

There is also a scenario when a job is not appended to the end of
the job list (for example it was created as a result of second or
later recipient batch). Then it works exactly as above, except that
if it was put in front of the first unread job (that is, the job
of a message which still has some unread recipients in queue file),
that job is first forced to return all of its unused recipient slots
to the transport pool.

</p>

<p>

The algorithm just described leads to the following state: The first
unread job on the job list always gets all the remaining recipient
slots of that transport (if there are any). The jobs queued before
this job are completely read (that is, all recipients of their
message were already read in core) and have at maximum as many slots
as they still have recipients in-core (the maximum is there because
of the sponsoring mentioned before) and the jobs after this job get
nothing from the transport recipient pool (unless they got something
before and then the first unread job was created and enqueued in
front of them later - in such case the also get at maximum as many
slots as they have recipients in-core).

</p>

<p>

Things work fine in such state for most of the time, because the
current job is either completely read in-core or has as much recipient
slots as there are, but there is one situation which we still have
to take care of specially.  Imagine if the current job is preempted
by some unread job from the job list and there are no more recipient
slots available, so this new current job could read only batches
of qmgr_message_recipient_minimum recipients at a time. This would
really degrade performance. For this reason, each transport has
extra pool of <i>transport</i>_extra_recipient_limit recipient
slots, dedicated exactly for this situation. Each time an unread
job preempts the current job, it gets half of the remaining recipient
slots from the normal pool and this extra pool.

</p>

<p>

And that's it. It sure does sound pretty complicated, but fortunately
most people don't really have to care how exactly it works as long
as it works.  Perhaps the only important things to know for most
people are the following upper bound formulas:

</p>

<p>

Each transport has at maximum

</p>

<blockquote>
<pre>
max(
qmgr_message_recipient_minimum * qmgr_message_active_limit
+ *_recipient_limit + *_extra_recipient_limit,
qmgr_message_recipient_limit
)
</pre>
</blockquote>

<p>

recipients in core.

</p>

<p>

The total amount of recipients in core is

</p>

<blockquote>
<pre>
max(
qmgr_message_recipient_minimum * qmgr_message_active_limit
+ sum( *_recipient_limit + *_extra_recipient_limit ),
qmgr_message_recipient_limit
)
</pre>
</blockquote>

<p>

where the sum is over all used transports.

</p>

<p>

And this terribly complicated chapter concludes the documentation
of <tt>nqmgr</tt> scheduler.

</p>

<p>

[By now you should theoretically know the <tt>nqmgr</tt> scheduler
inside out. In practice, you still hope that you will never have
to really understand the last or last two chapters completely, and
fortunately most people really won't. Understanding how the scheduler
works in ideal conditions is more than good enough for vast majority
of users.]

</p>

<h2> <a name="credits"> Credits </a> </h2>

<ul>

<li> Wietse Venema designed and implemented the initial queue manager
with per-domain FIFO scheduling, and per-delivery +/-1 concurrency
feedback.

<li> Patrik Rak designed and implemented preemption where mail with
fewer recipients can slip past mail with more recipients in a
controlled manner, and wrote up its documentation.

<li> Wietse Venema initiated a discussion with Patrik Rak and Victor
Duchovni on alternatives for the +/-1 feedback scheduler's aggressive
behavior. This is when K/N feedback was reviewed (N = concurrency).
The discussion ended without a good solution for both negative
feedback and dead site detection.

<li> Victor Duchovni resumed work on concurrency feedback in the
context of concurrency-limited servers.

<li> Wietse Venema then re-designed the concurrency scheduler in
terms of the simplest possible concepts: less-than-1 concurrency
feedback per delivery, forward and reverse concurrency feedback
hysteresis, and pseudo-cohort failure. At this same time, concurrency
feedback was separated from dead site detection.

<li> These simplifications, and their modular implementation, helped
to develop further insights into the different roles that positive
and negative concurrency feedback play, and helped to identify some
worst-case scenarios.

</ul>

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