Another example gets documented (+cosmetics)

[simgrid.git] / docs / source / Models.rst

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.. _models:

The SimGrid Models
##################

This page focuses on the **performance models** that compute the duration of :ref:`every activities <S4U_main_concepts>`
in the simulator depending on the platform characteristics and on the other activities that are currently sharing the
resources. If you look for other kind of models (such as routing models or compute model), please refer to :ref:`the
bottom of this page <models_other>`.

Modeled resources
*****************

The main objective of SimGrid is to provide timing information for three following kind of resources: network, CPU,
and disk.

The **network models** have been improved and regularly assessed for almost 20 years. It should be possible to get
accurate predictions once you properly :ref:`calibrate the models for your settings<models_calibration>`. As detailed
in the next sections, SimGrid provides several network models. Two plugins can also be used to compute the network
energy consumption: One for the :ref:`wired networks<plugin_link_energy>`, and another one for the :ref:`Wi-Fi networks
<plugin_link_energy>`. Some users find :ref:`TCP simulated performance counter-intuitive<understanding_lv08>` at first
in SimGrid, sometimes because of a misunderstanding of the TCP behavior in real networks.

The **computing models** are less developed in SimGrid. Through the S4U interface, the user specifies the amount of
computational work (expressed in FLOPs, for floating point operations) that each computation "consumes", and the model
simply divides this amount by the host's FLOP rate to compute the duration of this execution. In SMPI, the user code
is automatically timed, and the :ref:`computing speed<cfg=smpi/host-speed>` of the host machine is used to evaluate
the corresponding amount of FLOPs. This model should be sufficient for most users, even though assuming a constant FLOP
rate for each machine remains a crude simplification. In reality, the flops rate varies because of I/O, memory, and
cache effects. It is somehow possible to :ref:`overcome this simplification<cfg=smpi/comp-adjustment-file>`, but the
required calibration process is rather intricate and not documented yet (feel free to
:ref:`contact the community<community>` on need).
In the future, more advanced models may be added but the existing model proved good enough for all experiments done on
distributed applications during the last two decades. The CPU energy consumption can be computed with the
:ref:`relevant plugin<plugin_host_energy>`.

The **disk models** of SimGrid are more recent than those for the network and computing resources, but they should
still be correct for most users. `Studies have shown <https://hal.inria.fr/hal-01197128>`_ that they are sensitive
under some conditions, and a :ref:`calibration process<howto_disk>` is provided. As usual, you probably want to
double-check their predictions through an appropriate validation campaign.

LMM-based Models
****************

SimGrid aims at the sweet spot between accuracy and simulation speed. About accuracy, our goal is to report correct
performance trends when comparing competing designs with a minimal burden on the user, while allowing power users to
fine tune the simulation models for predictions that are within 5% or less of the results on real machines. For
example, we determined the `speedup achieved by the Tibidabo ARM-based cluster <http://hal.inria.fr/hal-00919507>`_
before it was even built. About simulation speed, the tool must be fast and scalable enough to study modern IT systems
at scale. SimGrid was for example used to simulate `a Chord ring involving millions of actors
<https://hal.inria.fr/inria-00602216>`_ (even though that has not really been more instructive than smaller scale
simulations for this protocol), or `a qualification run at full-scale of the Stampede supercomputer
<https://hal.inria.fr/hal-02096571>`_.

Most of our models are based on a linear max-min solver (LMM), as depicted below. The actors' activities are
represented by actions in the simulation kernel, accounting for both the initial amount of work of the corresponding
activity (in FLOPs for computing activities or bytes for networking and disk activities), and the currently remaining
amount of work to process.

At each simulation step, the instantaneous computing and communicating capacity of each action is computed according
to the model. A set of constraints is used to express for example that the accumulated instantaneous consumption of a
given resource by a set actions must remain smaller than the nominal capacity speed of that resource. In the example
below, it is stated that the speed :math:`\varrho_1` of activity 1 plus the speed :math:`\varrho_n`
of activity :math:`n` must remain smaller than the capacity :math:`C_A` of the corresponding host A.

.. image:: img/lmm-overview.svg

There are obviously many valuations of :math:`\varrho_1, \ldots{}, \varrho_n` that respect such as set of constraints.
SimGrid usually computes the instantaneous speeds according to a Max-Min objective function, that is maximizing the
minimum over all :math:`\varrho_i`. The coefficients associated to each variable in the inequalities are used to model
some performance effects, such as the fact that TCP tends to favor communications with small RTTs. These coefficients
are computed from both hard-coded values and :ref:`latency and bandwidth factors<cfg=network/latency-factor>` (more
details on network performance modeling is given in the next section).

Once the instantaneous speeds are computed, the simulation kernel determines what is the earliest terminating action
from their respective speeds and remaining amounts of work. The simulated time is then updated along with the values
in the LMM. As some actions have nothing left to do, the corresponding activities thus terminate, which in turn
unblocks the corresponding actors that can further execute.

Most of the SimGrid models build upon the LMM solver, that they adapt and configure for their respective usage. For CPU
and disk activities, the LMM-based models are respectively named **Cas01** and **S19**. The existing network models are
described in the next section.

The TCP models
**************

SimGrid provides several network performance models which compute the time taken by each communication in isolation.
**CM02** is the simplest one. It captures TCP windowing effects, but does not introduce any correction factors. This
model should be used if you prefer understandable results over realistic ones. **LV08** (the default model) uses
constant factors that are intended to capture common effects such as slow-start, the fact that TCP headers reduce the
*effective* bandwidth, or TCP's ACK messages. **SMPI** uses more advanced factors that also capture the MPI-specific
effects such as the switch between the eager vs. rendez-vous communication modes. You can :ref:`choose the
model<options_model_select>` on command line, and these models can be :ref:`further configured<options_model>`.

The LMM solver is then used as described above to compute the effect of contention on the communication time that is
computed by the TCP model. For sake of realism, the sharing on saturated links is not necessarily a fair sharing.
Instead, flows receive an amount of bandwidth inversely proportional to their round trip time.

Regardless of the used TCP model, the latency is paid beforehand. It is as if the communication only starts after a
little delay corresponding to the latency. During that time, the communication has no impact on the links (the other
communications are not slowed down, because there is no contention yet).

In addition to these LMM-based models, you can use the :ref:`ns-3 simulator as a network model <models_ns3>`. It is much
more detailed than the pure SimGrid models and thus slower, but it is easier to get more accurate results. Concerning
the speed, both simulators are linear in the size of their input, but ns-3 has a much larger input in case of large
steady communications. On the other hand, the SimGrid models must be carefully :ref:`calibrated <models_calibration>` if
accuracy is really important to your study, while ns-3 models are less demanding with that regard.

.. _understanding_cm02:

CM02
====

This is a simple model of TCP performance, where the sender stops sending packets when its TCP window is full. If the
acknowledgment packets are returned in time to the sender, the TCP window has no impact on the performance that then is
only limited by the link bandwidth. Otherwise, late acknowledgments will reduce the bandwidth.

SimGrid models this mechanism as follows: :math:`real\_BW = min(physical\_BW, \frac{TCP\_GAMMA}{2\times latency})` The used
bandwidth is either the physical bandwidth that is configured in the platform, or a value representing the bandwidth
limit due to late acknowledgments. This value is the maximal TCP window size (noted TCP Gamma in SimGrid) over the
round-trip time (i.e. twice the one-way latency). The default value of TCP Gamma is 4194304. This can be changed with
the :ref:`network/TCP-gamma <cfg=network/TCP-gamma>` configuration item.

If you want to disable this mechanism altogether (to model e.g. UDP or memory movements), you should set TCP-gamma
to 0. Otherwise, the time it takes to send 10 Gib of data over a 10 Gib/s link that is otherwise unused is computed as
follows. This is always given by :math:`latency + \frac{size}{bandwidth}`, but the bandwidth to use may be the physical
one (10Gb/s) or the one induced by the TCP window, depending on the latency.

 - If the link latency is 0, the communication obviously takes one second.
 - If the link latency is 0.00001s, :math:`\frac{gamma}{2\times lat}=209,715,200,000 \approx 209Gib/s` which is larger than the
   physical bandwidth. So the physical bandwidth is used (you fully use the link) and the communication takes 1.00001s
 - If the link latency is 0.001s, :math:`\frac{gamma}{2\times lat}=2,097,152,000 \approx 2Gib/s`, which is smalled than the
   physical bandwidth. The communication thus fails to fully use the link, and takes about 4.77s.
 - With a link latency of 0.1s, :math:`gamma/2\times lat \approx 21Mb/s`, so the communication takes about 476.84 + 0.1 seconds!
 - More cases are tested and enforced by the test ``teshsuite/models/cm02-tcpgamma/cm02-tcpgamma.tesh``

For more details, please refer to "A Network Model for Simulation of Grid Application" by Henri Casanova and Loris
Marchal (published in 2002, thus the model name).

.. _understanding_lv08:

LV08 (default)
==============

This model builds upon CM02 to model TCP windowing. It also introduces corrections factors for further realism. Lets
consider the following platform:

.. code-block:: xml

   <host id="A" speed="1Gf" />
   <host id="B" speed="1Gf" />

   <link id="link1" latency="10ms" bandwidth="1Mbps" />

   <route src="A" dst="B">
     <link_ctn id="link1" />
   </route>

If host `A` sends ``100kB`` (a hundred kilobytes) to host `B`, one can expect that this communication would take `0.81`
seconds to complete according to a simple latency-plus-size-divided-by-bandwidth model (0.01 + 8e5/1e6 = 0.81) since the
latency is small enough to ensure that the physical bandwidth is used (see the discussion on CM02 above). However, the
LV08 model is more complex to account for three phenomena that directly impact the simulation time:

  - The size of a message at the application level (i.e., 100kB in this example) is not the size that is actually
    transferred over the network. To mimic the fact that TCP and IP headers are added to each packet of the original
    payload, the TCP model of SimGrid empirically considers that `only 97% of the nominal bandwidth` are available. In
    other words, the size of your message is increased by a few percents, whatever this size be.

  - In the real world, the TCP protocol is not able to fully exploit the bandwidth of a link from the emission of the
    first packet. To reflect this `slow start` phenomenon, the latency declared in the platform file is multiplied by
    `a factor of 13.01`. Here again, this is an empirically determined value that may not correspond to every TCP
    implementations on every networks. It can be tuned when more realistic simulated times for the transfer of short
    messages are needed though.

  - When data is transferred from A to B, some TCP ACK messages travel in the opposite direction. To reflect the impact
    of this `cross-traffic`, SimGrid simulates a flow from B to A that represents an additional bandwidth consumption
    of `0.05%`. The route from B to A is implicitly declared in the platform file and uses the same link `link1` as if
    the two hosts were connected through a communication bus. The bandwidth share allocated to a data transfer from A
    to B is then the available bandwidth of `link1` (i.e., 97% of the nominal bandwidth of 1Mb/s) divided by 1.05
    (i.e., the total consumption). This feature, activated by default, can be disabled by adding the
    ``--cfg=network/crosstraffic:0`` flag to the command line.

As a consequence, the time to transfer 100kB from A to B as simulated by the default TCP model of SimGrid is not 0.81
seconds but

.. code-block:: python

    0.01 * 13.01 + 800000 / ((0.97 * 1e6) / 1.05) =  0.996079 seconds.

For more details, please refer to "Accuracy study and improvement of network simulation in the SimGrid framework" by
Arnaud Legrand and Pedro Velho.

.. _models_l07:

Parallel tasks (L07)
********************

This model is rather distinct from the other LMM models because it uses another objective function called *bottleneck*.
This is because this model is intended to be used for parallel tasks that are actions mixing flops and bytes while the
Max-Min objective function requires that all variables are expressed using the same unit. This is also why in reality,
we have one LMM system per resource kind in the simulation, but the idea remains similar.

Use the :ref:`relevant configuration <options_model_select>` to select this model in your simulation.

.. _models_wifi:

WiFi zones
**********

In SimGrid, WiFi networks are modeled with WiFi zones, where a zone contains the access point of the WiFi network and
the hosts connected to it (called `stations` in the WiFi world). The network inside a WiFi zone is modeled by declaring
a single regular link with a specific attribute. This link is then added to the routes to and from the stations within
this WiFi zone. The main difference of WiFi networks is that their performance is not determined by some link bandwidth
and latency but by both the access point WiFi characteristics and the distance between that access point and a given
station.

Such WiFi zones can be used with the LMM-based model or ns-3, and are supposed to behave similarly in both cases.

Declaring a WiFi zone
=====================

To declare a new WiFi network, simply declare a network zone with the ``WIFI`` routing attribute.

.. code-block:: xml

        <zone id="SSID_1" routing="WIFI">

Inside this zone you must declare which host or router will be the access point of the WiFi network.

.. code-block:: xml

        <prop id="access_point" value="alice"/>

Then simply declare the stations (hosts) and routers inside the WiFi network. Remember that one must have the same name
as the "access point" property.

.. code-block:: xml

        <router id="alice" speed="1Gf"/>
        <host id="STA0-0" speed="1Gf"/>
        <host id="STA0-1" speed="1Gf"/>

Finally, close the WiFi zone.

.. code-block:: xml

        </zone>

The WiFi zone may be connected to another zone using a traditional link and a zoneRoute. Note that the connection between two
zones is always wired.

.. code-block:: xml

        <link id="wireline" bandwidth="100Mbps" latency="2ms" sharing_policy="SHARED"/>

        <zoneRoute src="SSID_1" dst="SSID_2" gw_src="alice" gw_dst="bob">
            <link_ctn id="wireline"/>
        </zoneRoute>

WiFi network performance
========================

The performance of a wifi network is controlled by the three following properties:

 * ``mcs`` (`Modulation and Coding Scheme <https://en.wikipedia.org/wiki/Link_adaptation>`_)
   is a property of the WiFi zone. Roughly speaking, it defines the speed at which the access point is exchanging data
   with all the stations. It depends on the access point's model and configuration. Possible values for the MCS can be
   found on Wikipedia for example.
   |br| By default, ``mcs=3``.
 * ``nss`` (Number of Spatial Streams, or `number of antennas <https://en.wikipedia.org/wiki/IEEE_802.11n-2009#Number_of_antennas>`_) is another property of the WiFi zone. It defines the amount of simultaneous data streams that the access
   point can sustain. Not all values of MCS and NSS are valid nor compatible (cf. `802.11n standard <https://en.wikipedia.org/wiki/IEEE_802.11n-2009#Data_rates>`_).
   |br| By default, ``nss=1``.
 * ``wifi_distance`` is the distance from a station to the access point. Each station can have its own specific value.
   It is thus a property of the stations declared inside the WiFi zone.
   |br| By default, ``wifi_distance=10``.

Here is an example of a zone with non-default ``mcs`` and ``nss`` values.

.. code-block:: xml

        <zone id="SSID_1" routing="WIFI">
            <prop id="access_point" value="alice"/>
            <prop id="mcs" value="2"/>
            <prop id="nss" value="2"/>
        ...
        </zone>

Here is an example of setting the ``wifi_distance`` of a given station.

.. code-block:: xml

        <host id="STA0-0" speed="1Gf">
            <prop id="wifi_distance" value="37"/>
        </host>

Constant-time model
*******************

This simplistic network model is one of the few SimGrid network model that is not based on the LMM solver. In this
model, all communication take a constant time (one second by default). It provides the lowest level of realism, but is
marginally faster and much simpler to understand. This model may reveal interesting if you plan to study abstract
distributed algorithms such as leader election or causal broadcast.

.. _models_ns3:

ns-3 as a SimGrid model
***********************

The **ns-3 based model** is the most accurate network model that you can get in SimGrid. It relies on the well-known
`ns-3 packet-level network simulator <http://www.nsnam.org>`_ to compute every timing information related to the network
transfers of your simulation. For instance, this may be used to investigate the validity of a simulation. Note that this
model is much slower than the LMM-based models, because ns-3 simulates the movement of every network packet involved in
every communication while SimGrid only recomputes the respective instantaneous speeds of the currently ongoing
communications when one communication starts or stops.

You need to install ns-3 and recompile SimGrid accordingly to use this model.

The SimGrid/ns-3 binding only contains features that are common to both systems. Not all ns-3 models are available from
SimGrid (only the TCP and WiFi ones are), while not all SimGrid platform files can be used in conjunction with ns-3
(routes must be of length 1). Also, the platform built in ns-3 from the SimGrid
description is very basic. Finally, communicating from a host to
itself is forbidden in ns-3, so every such communication completes
immediately upon startup.


Compiling the ns-3/SimGrid binding
==================================

Installing ns-3
---------------

SimGrid requires ns-3 version 3.26 or higher, and you probably want the most
recent version of both SimGrid and ns-3. While the Debian package of SimGrid
does not have the ns-3 bindings activated, you can still use the packaged version
of ns-3 by grabbing the ``libns3-dev ns3`` packages. Alternatively, you can
install ns-3 from scratch (see the `ns-3 documentation <http://www.nsnam.org>`_).

Enabling ns-3 in SimGrid
------------------------

SimGrid must be recompiled with the ``enable_ns3`` option activated in cmake.
Optionally, use ``NS3_HINT`` to tell cmake where ns3 is installed on
your disk.

.. code-block:: console

   $ cmake . -Denable_ns3=ON -DNS3_HINT=/opt/ns3 # or change the path if needed

By the end of the configuration, cmake reports whether ns-3 was found,
and this information is also available in ``include/simgrid/config.h``
If your local copy defines the variable ``SIMGRID_HAVE_NS3`` to 1, then ns-3
was correctly detected. Otherwise, explore ``CMakeFiles/CMakeOutput.log`` and
``CMakeFiles/CMakeError.log`` to diagnose the problem.

Test that ns-3 was successfully integrated with the following command (executed from your SimGrid
build directory). It will run all SimGrid tests that are related to the ns-3
integration. If no test is run at all, then ns-3 is disabled in cmake.

.. code-block:: console

   $ ctest -R ns3

Troubleshooting
---------------

If you use a version of ns-3 that is not known to SimGrid yet, edit
``tools/cmake/Modules/FindNS3.cmake`` in your SimGrid tree, according to the
comments on top of this file. Conversely, if something goes wrong with an old
version of either SimGrid or ns-3, try upgrading everything.

Note that there is a known bug with the version 3.31 of ns3 when it is built with
MPI support, like it is with the libns3-dev package in Debian 11 « Bullseye ».
A simple workaround is to edit the file
``/usr/include/ns3.31/ns3/point-to-point-helper.h`` to remove the ``#ifdef NS3_MPI``
include guard.  This can be achieved with the following command (as root):

.. code-block:: console

   # sed -i '/^#ifdef NS3_MPI/,+2s,^#,//&,' /usr/include/ns3.31/ns3/point-to-point-helper.h

.. _ns3_use:

Using ns-3 from SimGrid
=======================

Platform files compatibility
----------------------------

Any route longer than one will be ignored when using ns-3. They are
harmless, but you still need to connect your hosts using one-hop routes.
The best solution is to add routers to split your route. Here is an
example of an invalid platform:

.. code-block:: xml

   <?xml version='1.0'?>
   <!DOCTYPE platform SYSTEM "https://simgrid.org/simgrid.dtd">
   <platform version="4.1">
     <zone id="zone0" routing="Floyd">
       <host id="alice" speed="1Gf" />
       <host id="bob"   speed="1Gf" />

       <link id="l1" bandwidth="1Mbps" latency="5ms" />
       <link id="l2" bandwidth="1Mbps" latency="5ms" />

       <route src="alice" dst="bob">
         <link_ctn id="l1"/>            <!-- !!!! IGNORED WHEN USED WITH ns-3       !!!! -->
         <link_ctn id="l2"/>            <!-- !!!! ROUTES MUST CONTAIN ONE LINK ONLY !!!! -->
       </route>
     </zone>
   </platform>

This can be reformulated as follows to make it usable with the ns-3 binding.
There is no direct connection from alice to bob, but that's OK because ns-3
automatically routes from point to point (using
``ns3::Ipv4GlobalRoutingHelper::PopulateRoutingTables``).

.. code-block:: xml

   <?xml version='1.0'?>
   <!DOCTYPE platform SYSTEM "https://simgrid.org/simgrid.dtd">
   <platform version="4.1">
     <zone id="zone0" routing="Full">
       <host id="alice" speed="1Gf" />
       <host id="bob"   speed="1Gf" />

       <router id="r1" /> <!-- routers are compute-less hosts -->

       <link id="l1" bandwidth="1Mbps" latency="5ms"/>
       <link id="l2" bandwidth="1Mbps" latency="5ms"/>

       <route src="alice" dst="r1">
         <link_ctn id="l1"/>
       </route>

       <route src="r1" dst="bob">
         <link_ctn id="l2"/>
       </route>
     </zone>
   </platform>

Once your platform is OK, just change the :ref:`network/model
<options_model_select>` configuration option to `ns-3` as follows. The other
options can be used as usual.

.. code-block:: console

   $ ./network-ns3 --cfg=network/model:ns-3 (other parameters)

Many other files from the ``examples/platform`` directory are usable with the
ns-3 model, such as `examples/platforms/dogbone.xml <https://framagit.org/simgrid/simgrid/tree/master/examples/platforms/dogbone.xml>`_.
Check the file  `examples/cpp/network-ns3/network-ns3.tesh <https://framagit.org/simgrid/simgrid/tree/master/examples/cpp/network-ns3/network-ns3.tesh>`_
to see which ones are used in our regression tests.

Alternatively, you can manually modify the ns-3 settings by retrieving
the ns-3 node from any given host with the
:cpp:func:`simgrid::get_ns3node_from_sghost` function (defined in
``simgrid/plugins/ns3.hpp``).

.. doxygenfunction:: simgrid::get_ns3node_from_sghost

Random seed
-----------
It is possible to define a fixed or random seed to the ns3 random number generator using the config tag.

.. code-block:: xml

        <?xml version='1.0'?><!DOCTYPE platform SYSTEM "https://simgrid.org/simgrid.dtd">
        <platform version="4.1">
            <config>
                    <prop id = "network/model" value = "ns-3" />
                    <prop id = "ns3/seed" value = "time" />
            </config>
        ...
        </platform>

The first property defines that this platform will be used with the ns3 model.
The second property defines the seed that will be used. Defined to ``time``,
it will use a random seed, defined to a number it will use this number as
the seed.

Limitations
===========

A ns-3 platform is automatically created from the provided SimGrid
platform. However, there are some known caveats:

  * The default values (e.g., TCP parameters) are the ns-3 default values.
  * ns-3 networks are routed using the shortest path algorithm, using ``ns3::Ipv4GlobalRoutingHelper::PopulateRoutingTables``.
  * End hosts cannot have more than one interface card. So, your SimGrid hosts
    should be connected to the platform through only one link. Otherwise, your
    SimGrid host will be considered as a router (FIXME: is it still true?).

Our goal is to keep the ns-3 plugin of SimGrid as easy (and hopefully readable)
as possible. If the current state does not fit your needs, you should modify
this plugin, and/or create your own plugin from the existing one. If you come up
with interesting improvements, please contribute them back.

Troubleshooting
===============

If your simulation hangs in a communication, this is probably because one host
is sending data that is not routable in your platform. Make sure that you only
use routes of length 1, and that any host is connected to the platform.
Arguably, SimGrid could detect this situation and report it, but unfortunately,
this still has to be done.

FMI-based models
****************

`FMI <https://fmi-standard.org/>`_ is a standard to exchange models between simulators. If you want to plug such a model
into SimGrid, you need the `SimGrid-FMI external plugin <https://framagit.org/simgrid/simgrid-FMI>`_.
There is a specific `documentation <https://simgrid.frama.io/simgrid-FMI/index.html>`_ available for the plugin.
This was used to accurately study a *Smart grid* through co-simulation: `PandaPower <http://www.pandapower.org/>`_ was
used to simulate the power grid, `ns-3 <https://nsnam.org/>`_ was used to simulate the communication network while SimGrid was
used to simulate the IT infrastructure. Please also refer to the `relevant publication <https://hal.science/hal-03217562>`_
for more details.

.. _models_other:

Other kind of models
********************

As for any simulator, models are very important components of the SimGrid toolkit. Several kind of models are used in
SimGrid beyond the performance models described above:

The **routing models** constitute advanced elements of the platform description. This description naturally entails
:ref:`components<platform>` that are very related to the performance models. For instance, determining the execution
time of a task obviously depends on the characteristics of the machine that executes this task. Furthermore, networking
zones can be interconnected to compose larger platforms `in a scalable way <http://hal.inria.fr/hal-00650233/>`_. Each
of these zones can be given a specific :ref:`routing model<platform_routing>` that efficiently computes the list of
links forming a network path between two given hosts.

The model checker uses an abstraction of the performance simulations. Mc SimGrid explores every causally possible
execution paths of the application, completely abstracting the performance away. The simulated time is not even
computed in this mode! The abstraction involved in this process also models the mutual impacts among actions, to not
re-explore histories that only differ by the order of independent and unrelated actions. As with the rest of the model
checker, these models are unfortunately still to be documented properly.


.. |br| raw:: html

   <br />