.. meta::
  :description: Basic Manual SimPy Python Simulation Language
  :keywords: simulation python stochastic

.. highlight:: python
   :linenothreshold: 5

======================================================
Introduction to SimPy
======================================================

:Authors: G A Vignaux and Klaus Muller
:Date:  |today|
:SimPy release: |release|
:Python-Version: 2.6 and later

.. THIS WAS PUT UNDER SUBVERSION 2008/08/07

.. REPLACEMENTS ===================================================
.. |yrequest| replace:: ``yield request,self,``
.. |rrequest| replace:: ``yield (request,self,``\ *r [,P]*\ ``),``
.. |init| replace:: ``__init__``
.. ================================================================


.. contents:: Contents
   :depth: 2



..
    1  Introduction
    2  Simulation with SimPy
    3  Processes
      3.1  Defining a process
      3.2  Creating a process object
      3.3  Starting SimPy Process Objects
        3.3.1  activate
        3.3.2  start
        3.3.3  The standard PEM name, ACTIONS
      3.4  Elapsing time in a Process
        3.4.1  yield hold
      3.5  More about Processes
      3.6  A SimPy Program
    4  Resources
      4.1  Defining a Resource object
      4.2  Requesting and releasing a unit of a Resource
        4.2.1  yield request
        4.2.2  yield release
      4.3  Resource Example
    5  Levels
      5.1  Defining a Level
      5.2  Putting amounts into  a Level
      5.3  Getting amounts from a Level
    6  Random Number Generation
    7  Monitors and Recording Simulation Results
      7.1  Defining Monitors
      7.2  Observing data
      7.3  Data summaries
      7.4  Monitoring Resource Queues
      7.5  More on Monitors
    8  Appendices
      8.1  SimPy Contacts
      8.2  The Resource Example with Tracing



Introduction
---------------

The active elements (or *entities*) of a SimPy model are objects of a
class defined by the programmer (see Processes_, section 3). Each
entity has a standard method, a Process Execution Method (referred to
by SimPy programmers as a PEM) which specifies its actions in detail.
Each PEM runs in parallel with (and may interact with) the PEMs of
other entities.

The activity of an entity may be delayed for fixed or random times,
queued at resource facilities, and may be interrupted by or interact
in different ways with other entities and components. For example in a
gas station model, automobile entities (objects of an Automobile
Class) may have to wait at the gas station for a pump to become
available. On obtaining a pump it takes time to fill the tank. The
pump is then released for the next automobile in the queue if there is
one.

.. A SimPy program contains the declaration of one or more Process
   classes and the creation and activating of objects from them.


SimPy has three kinds of resource facilities (Resources, Levels, and
Stores). Each type models a congestion point where entities queue
while waiting to acquire or, in some cases, to deposit a
resource.SimPy automatically handles the queueing.

.. index:: resources


- Resources_ have one or more identical resource units, each of which
  can be held by entities. Extending the example above, the gas
  station might be modelled as a Resource with its pumps as resource
  units. When a car requests a pump the gas station resource
  automatically queues it until a pump becomes available (perhaps
  immediately). The car holds the pump until it finishes refuelling
  and then releases it for use by the next car.

.. index:: levels; definition

- ``Levels`` (not treated here) model the supply and consumption of a
  homogeneous undifferentiated "material". The Level holds an amount
  that is fully described by a non-negative number which can be
  increased or decreased by entities. For example, a gas station
  stores gas in large storage tanks. The tanks can be filled by
  tankers and emptied by cars refuelling. In contrast to the operation
  of a Resource, a car need not return the gas to the gas station.

.. index:: stores; definition

- ``Stores`` (not treated here) model the production and consumption of
  distinguishable items. A Store holds a list of items. Entities can
  insert or remove items from the list and these can be of any
  type. They can even be SimPy process objects. For example, the gas
  station holds spares of different types. A car might request a set
  of spares from the Store. The store is replenished by deliveries
  from a warehouse.

SimPy also supplies Monitors and Tallys to record simulation
events. Monitors_ are used to compile summary statistics such as
waiting times and queue lengths. These statistics includes simple
averages and variances, time-weighted averages, or histograms. In
particular, data can be gathered on the queues associated with
Resources, Levels and Stores. For example we may collect data on the
average number of cars waiting at the gas station and the distribution
of their waiting times. Monitors preserve complete time-series records
that may later be used for more advanced post-simulation analyses. A
simpler version of a Monitor is a Tally which provides most of the
statistical facilities but does not retain a complete time-series
record. See the SimPy Manual for details on the Tally.



Simulation with SimPy
-------------------------

To use the SimPy simulation system in your Python program you must import its
``Simulation`` module using:

   ``from SimPy.Simulation import *``

We recommend that new users instead  import ``SimPy.SimulationTrace``,
which works the same but also automatically produces a timed listing of
events as the model executes. (An example of such a trace is shown in
`The Resource Example with Tracing`_):

   ``from SimPy.SimulationTrace import *``


Discrete-event simulation programs automatically maintain the current
simulation time in a software clock. This cannot be directly changed
by the user.  In SimPy the current clock value is returned by the
``now()`` function and you can access this or print it out. At the
start of the simulation it is set to 0.0.  While the simulation
program runs, simulation time steps forward from one *event* to the
next. An event occurs whenever the state of the simulated system
changes such as when a car arrives or departs from the gas station.

The ``initialize`` statement initialises global simulation variables and
sets the software clock to 0.0. It must appear in your program before
any SimPy process objects are activated.

   ``initialize()``

This is followed by SimPy statements creating and activating entities
(that is, SimPy process objects). Activation of entities adds events
to the simulation event schedule. Execution of the simulation itself
starts with the following statement:

   ``simulate(until=``\ *endtime*\ ``)``

The simulation then starts, and SimPy seeks and executes the first event in
the schedule.  Having executed that event, the simulation seeks and
executes the next event, and so on.

Typically a simulation terminates when there are no more events to
execute or when the *endtime* is reached but it can be stopped at any
time by the command:

   ``stopSimulation( )``

After the simulation stops, further statements can be executed.
``now()`` will retain the time of stopping and data held in Monitors
will be available for display or further analysis.

The following fragment shows only the *main* block in a simulation
program to illustrate the general structure. A complete `Example
Program`_ is shown later. Here ``Car`` is a Process class with a
``go`` as its PEM (described later) and ``c`` is made an entity of
that class, that is, a particular car. Activating ``c`` has the effect
of scheduling at least one event by starting ``c``\ 's PEM.  The
``simulate(until=1000.0)`` statement starts the simulation
itself. This immediately jumps to the first scheduled event. It will
continue executing events until it runs out of events to execute or
the simulation time reaches ``1000.0``. When the simulation stops the
``Report`` function is called to display the results::

  class Car(Process):
     def go(self):
        # PEM for a Car
        ...

  def Report():
     # print results when finished
     ...

  initialize()
  c = Car(name="Car23")
  activate(c,  c.go(), at=0.0)
  simulate(until=1000.0)

  Report()


In addition to *SimPy.Simulation* there are three alternative
simulation libraries with the same simulation capabilities but with
special facilities. Beside ``SimPy.SimulationTrace``, already
mentioned, there are ``SimPy.SimulationRT`` for real time
synchronisation and ``SimPy.SimulationStep`` for event-stepping through
a simulation. See the SimPy Manual for more information.


.. ==================================================================

.. index:: processes


Processes
-------------------

SimPy's active objects (entities) are process objects -- instances of
a class written by the user that inherits from SimPy's Process class.

For example, if we are simulating a gas station we might model each
car as an object of the class ``Car``. A car arrives at the gas
station (modelled as a Resource with ``pump``\s). It requests a pump
and may need to wait for it. Then it fills its tank and when it has
finished it releases the pump. It might also buy an item from the
station store. The ``Car`` class specifies the logic of these actions
in its Process Execution Method (PEM). The simulation creates a number
of cars as it runs and their evolutions are directed by their ``Car``
class's PEM.

.. index:: process; defining


Defining a process
~~~~~~~~~~~~~~~~~~~~~~~~~

Each Process class inherits from SimPy's ``Process`` class. For example
the header of the definition of a ``Car`` Process class would
be:

   ``class Car(Process):``


At least one Process Execution Method (PEM) must be defined in each
Process class (though an entity can have only one PEM active).  A PEM
may have arguments in addition to the required ``self`` argument
needed by all Python class methods. Naturally, other methods and, in
particular, an ``__init__``, may be defined.


.. _PEM:

* ``A Process Execution Method (PEM)`` defines the actions that are
  performed by its process objects. *Each PEM must contain at least
  one of the special ``yield`` statements, described later*. This
  makes the PEM  a Python generator function so that it has resumable
  execution -- it can be restarted again after the yield statement
  without losing its current state.  A PEM may have any name of your
  choice. For example it may be called ``execute( )`` or ``run(
  )``. However, if a PEM is called ``ACTIONS``, SimPy recognises this
  as a PEM. This can simplify the ``start`` method as explained below.



  The ``yield`` statements are simulation commands which affect an
  ongoing life cycle of Process objects. These statements control the
  execution and synchronisation of multiple processes. They can delay
  a process, put it to sleep, request a shared resource or provide a
  resource. They can add new events to the simulation event schedule,
  cancel existing ones, or cause processes to wait for a change in the
  simulated system's state.


  For example, here is a  Process Execution Method, ``go(self)``,
  for the simple ``Car`` class that does no more than delay for a
  time.  As soon as it is activated it prints out the current time,
  the car object's name and the word ``Starting``. After a
  simulated delay of 100.0 time units (in the ``yield hold, ...``
  statement) it announces that this car has "Arrived"::

      def go(self):
          print("%s %s %s" % (now(), self.name, 'Starting'))
          yield hold, self, 100.0
          print("%s %s %s" % (now(), self.name, 'Arrived'))

  A process object's PEM starts execution when the object is
  activated, provided the ``simulate(until=``\ *endtime*\ ``)``
  statement has been executed.


* **__init__(self, ...)**, where *...* indicates other arguments. This
  method is optional but is useful to initialise the process object,
  setting values for its attributes.  As for any sub-class in Python,
  the first line of this method must call the ``Process`` class's
  ``__init__( )`` method in the form:

      ``Process.__init__(self)``

  You can then use additional commands to initialise attributes of the
  Process class's objects. You can also override the standard ``name``
  attribute of the object.

  If present, the ``__init__( )`` method is always called whenever
  you create a new process object. If you do not wish to provide for
  any attributes other than a ``name``, the ``__init__`` method may be
  dispensed with. An example of an ``__init__( )`` method is shown in
  the `Example Program`_.

.. index:: process; creation


Creating a process object
~~~~~~~~~~~~~~~~~~~~~~~~~~~

An entity (process object) is created in the usual Python manner by
calling the Class. Process classes have a single attribute, ``name``
which can be specified even if no |init| method is defined. ``name``
defaults to ``'a_process'`` unless the user specified a different one.

For example to create a new ``Car`` object with a name ``Car23``:

   ``c = Car(name="Car23")``





.. index:: process; starting

.. =================================================================

Starting SimPy Process Objects
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

An entity (process object) is "passive" when first created, i.e., it
has no events scheduled for it. It must be *activated* to start its
Process Execution Method. To do this you can use either the
``activate`` function or the ``start`` method of the Process.

.. index::
   single: process object; activation


activate
+++++++++

.. |arguments| replace:: \ ``[,{at=now()|delay=0}][,prior=False])``
.. |arguments2| replace:: \ ``[,{at=now()|delay=0}])``
.. |arguments3| replace:: \ ``[,{at=``\ *t*\ ``|delay=``\ *period*\ ``}])``

Activating an entity by using the SimPy ``activate`` function:

-    ``activate(``\ *p, p.pemname([args])*\ |arguments3|

     activates process object *p*, provides its Process Execution
     Method *p.pemname( )* with the arguments *args* and possibly assigns
     values to the other optional parameters. You must choose one (or
     neither) of ``at=``\ *t* and ``delay=``\ *period*. The default is
     to activate at the current time (``at=now( )``) and with no delay
     (``delay=0``).

     For example: to activate an entity, ``cust`` at time 10.0
     using its PEM called ``lifetime``::

       cust = Customer()
       activate(cust, cust.lifetime(), at=10.0)

.. index:: 
   pair: process; start

start
+++++++++

An alternative to the ``activate()`` function is the ``start`` method
of Process objects:

-    *p.*\ ``start(``\ *p.pemname([args])*\ |arguments3|

     Here *p* is a Process object.  Its PEM, *pemname*, can have any
     identifier (such as ``run``, ``lifecycle``, etc) and any
     arguments *args*.

     For example, to activate the process object ``cust`` using the PEM
     with identifier ``lifetime`` at time 10.0 we would use::

         cust.start(cust.lifetime(),at=10.0)

The standard PEM name, ACTIONS
+++++++++++++++++++++++++++++++++

The identifier ``ACTIONS`` is recognised by SimPy as a PEM name and
can be used (or implied) in the ``start`` method.

-    *p.*\ ``start([``\ *p.*\ ``ACTIONS()]`` |arguments3|

     ``ACTIONS`` *cannot* have parameters. The call *p.*\ ``ACTIONS()``
     is optional but may make your code clearer.

     For example, to activate the Process object ``cust`` with a PEM
     called ``ACTIONS`` at time 10.0, the following are equivalent
     (and the second version more convenient)::

       cust.start(cust.ACTIONS(), at=10.0)
       cust.start(at=10.0)

*A reminder*: Even activated process objects will not actually start
operating until the ``simulate()`` statement is executed.



Elapsing time in a Process
~~~~~~~~~~~~~~~~~~~~~~~~~~

A PEM_ uses the ``yield hold`` command to temporarily delay a process
object's operations. This might represent a service time for the
entity. (Waiting is handled automatically by the resource facilities
and is not modelled by ``yield hold``)

.. index:: 
   pair: yield; hold

yield hold
++++++++++++

    ``yield hold,self,``\ *t*

    Causes the entity to delay *t* time units.  After the delay, it
    continues  with the next statement in its PEM.  During the ``hold`` the
    entity's operations are suspended.

Paradoxically, in the model world, the entity is considered to be
*busy* during this simulated time. For example, it might be involved
in filling up with gas or driving.  In this state it can be
interrupted by other entities.


More about Processes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. index:: 
   pair: yield; passivate
   single: sleep a process
   single: process; sleep


An entity (Process object) can be "put to sleep" or passivated using

     ``yield passivate,self`` 

(and it can be reactivated by another entity
using ``reactivate``), or permanently removed from the future event
queue by the command ``self.cancel()``. Active entities can be
``interrupt``\ed by other entities. Examine the full SimPy Manual for
details.

------

A SimPy Program
~~~~~~~~~~~~~~~~

.. index:: example;car

.. _`Example Program`:


This is a complete SimPy script. We define a ``Car`` class with a PEM
called ``go( )``. We also (for interest) define an ``__init__( )``
method to provide individual cars with an identification name and
engine size, ``cc``. The ``cc`` attribute is not used in this very
simple example.

Two cars, ``p1`` and ``p2`` are created. ``p1`` and ``p2`` are
activated to start at simulation times 0.6 and 0.0, respectively. Note
that these will *not* start in the order they appear in the program
listing. ``p2`` actually starts first in the simulation. Nothing
happens until the ``simulate(until=200)`` statement at which point the
event scheduler starts operating by finding the first event to
execute. When both cars have finished (at time ``6.0+100.0=106.0``)
there will be no more events so the simulation will stop::

..  .. literalinclude:: programs/car.py

Running this program gives the following output::

..  .. literalinclude:: programs/car.out

If, instead one chose to import ``SimPy.SimulateTrace`` at the start
of the program one would obtain the following output. (The meaning of
the phrase ``prior : False`` in the first two lines is described in
the full SimPy Manual. ``prior`` is an advanced technique for fine control
of PEM priorities but seldom affects simulated operations and so
normally can be ignored/)

.. include:: programs/carT.out
   :literal:

-------

.. ==================================================================

.. index:: !resources


Resources
-------------------

The three resource facilities provided by SimPy are Resources_,
``Levels`` and ``Stores``. Each models a congestion point where process
objects may have to queue up to access resources. This section
describes the Resource type of resource facility. ``Levels`` and
``Stores`` are not treated in this introduction.

An example of queueing for a Resource might be a manufacturing plant
in which a ``Task`` (modelled as an entity or *Process object*) needs
work done by a ``Machine`` (modelled as a *Resource object*). If all
of the ``Machines`` are currently being used, the ``Task`` must wait
until one becomes free. A SimPy Resource can have a number of
identical ``units``, such as a number of identical ``machine``
units. An entity obtains a unit of the Resource by ``requesting`` it
and, when it is finished, ``releasing`` it. A Resource maintains a
list (the ``waitQ``) of entities that have requested but not yet
received one of the Resource's units, and another list (the
``activeQ``) of entities that are currently using a unit.  SimPy
creates and updates these queues itself -- the user can read their
values, but should not change them.

.. index:: resource; define


Defining a Resource object
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A Resource object, ``r``,  is established by the following statement::

 r = Resource(capacity=1,
              name='a_resource', unitName='units',
              monitored=False)

where

.. index:: resource; capacity

- ``capacity`` (positive integer) specifies the total
  number of identical units in Resource object ``r``.

.. index:: resource; name

- ``name`` (string) the name for this Resource object (e.g.,
  ``'gasStation'``).

.. index:: resource; unitName

- ``unitName`` (string) the name for a unit of the resource (e.g.,
  ``'pump'``).

.. index:: resource; monitored

- ``monitored`` (``False`` or ``True``) If set to ``True``, then
  information is gathered on the sizes of ``r``'s ``waitQ`` and
  ``activeQ``, otherwise not.


For example, in the model of a 2-pump gas-station we might define::

   gasstation = Resource(capacity=2,name='gasStation',unitName='pump')

.. index:: resource; attributes

Each Resource object, ``r``,  has the following additional attributes:

.. index:: resource; n

- ``r.n``,  the number of units that are currently free.

.. index:: resource; waitQ

- ``r.waitQ``, a queue (list) of processes that have requested but
  not yet received a unit of ``r``, so ``len(r.waitQ)`` is the
  number of process objects currently waiting.

.. index:: resource; activeQ

- ``r.activeQ``, a queue (list) of process objects currently using
  one of the Resource's units, so ``len(r.activeQ)`` is the number of
  units that are currently in use.

.. index:: resource; waitMon

- ``r.waitMon``, the record (made by a ``Monitor`` whenever
  ``monitored==True``) of the activity in ``r.waitQ``. So, for
  example, ``r.waitMon.timeaverage()`` is the average number of
  processes in ``r.waitQ``.  See `Data Summaries`_
  for an example.

.. index:: resource; actMon

- ``r.actMon``, the record (made by a ``Monitor`` whenever
  ``monitored==True``) of the activity in ``r.activeQ``.



Requesting and releasing a unit of a Resource
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

A process can request and later release a unit of the Resource object,
``r``, by using the following yield commands in a Process Execution
Method:

.. index:: 
   single: yield; request a resource
   pair: yield; request

yield request
+++++++++++++++


- |yrequest|\ *r*

Requests a unit of Resource *r*

If a Resource unit is free when the request is made, the requesting
entity takes it and moves on to the next statement in its PEM. It is
added to the Resource's ``activeQ``.

If no Resource unit is available when the request is made, the
requesting entity is appended to the Resource's ``waitQ`` and
suspended.  The next time a unit becomes available the first entity in
the ``r.waitQ`` takes it and continues its execution.

For example, a ``Car`` might request a ``pump``::

  yield request,self,gasstation

(It is actually requesting a *unit* of the ``gasstation``, i.e. a
``pump``.) An entity holds a resource unit until it releases it.

Entities can use a priority system for queueing. They can also preempt
(that is, interrupt) others already in the system. They can also
*renege* from the ``waitQ`` (that is, abandon the queue if it takes
too long). This is achieved by an extension to the ``yield request``
command. See the main SimPy Manual.


.. index:: yield; release a resource
   pair: yield; release

yield release
+++++++++++++++

  ``yield release,self,r``

Releases the  unit of ``r``.


The entity is removed from ``r.activeQ`` and continues with its next
statement. If, when the unit of ``r`` is released, another entity is
waiting (in ``waitQ``) it will take the unit, leave the ``waitQ`` and
move into the ``activeQ`` and go one with its PEM.

For example the ``Car`` might release the ``pump`` unit of the
gasstation::

  yield release,self,gasstation



------------

.. index:: resource; example
.. index:: example;resource
.. index:: example;cars

Resource Example
~~~~~~~~~~~~~~~~~

In this complete script, the ``gasstation`` Resource object is given
two resource units (``capacity=2``). Four cars arrive at the times
specified in the program (not in the order they are listed). They all
request a ``pump`` and use it for 100 time units:

.. literalinclude:: programs/cars.py
   :language: python
   :linenos:


This program results in the following output:

.. literalinclude:: programs/cars.out


And, if we use ``SimPy.SimulationTrace`` to get an automatic trace we
get the result shown in Appendix `The Resource Example with Tracing`_.
(It is rather long to be inserted here).

-------


.. ==========================================================================

.. index:: !random number generation

Random Number Generation
-------------------------

Simulations usually need random numbers. By design, SimPy does not
provide its own random number generators, so users need to import them
from some other source.  Perhaps the most convenient is the standard
`Python random module`_.  It can generate random variates from the
following continuous distributions: uniform, beta, exponential, gamma,
normal, log-normal, Weibull, and vonMises.  It can also generate
random variates from some discrete distributions. Consult the module's
documentation for details.  Excellent brief descriptions of these
distributions, and many others, can be found in the `Wikipedia
<http://www.wikipedia.com/>`_.

Python's ``random`` module can be used in two ways: you can import the
methods directly or you can import the ``Random`` class and make your
own random objects. In the second method, each object gives a
different random number sequence, thus providing multiple random
streams as in some other simulation languages such as Simscript and
ModSim.

Here the first method is illustrated. A single pseudo-random sequence
is used for all calls. You ``import`` the methods you need from the
``random`` module. For example::

 from random import seed, random, expovariate, normalvariate

In simulation it is good practice to set the initial ``seed`` for the
pseudo-random sequence at the start of each run. You then have good
control over the random numbers used. Replications and comparisons are
easier and, together with variance reduction techniques, can provide
more accurate estimates. In the following code snippet we set the
initial seed to ``333555``.  ``X`` and ``Y`` are pseudo-random
variates from the two distributions. Both distributions have the same
mean::

   from random import seed, expovariate, normalvariate

   seed(333555)
   X = expovariate(0.1)
   Y = normalvariate(10.0, 1.0)


.. ============================================================================

.. index:: Monitors
.. index:: Recording Simulation Results


Monitors and Recording Simulation Results
---------------------------------------------



A Monitor enables us to observe a particular variable of interest and
to hold a time series of its values. It can return a simple data
summary either during or at the completion of a simulation run.

For example we might use one Monitor to record the waiting time for
each of a series of customers and another to record the total number
of customers in the shop. In a discrete-event system the number of
customers changes only at arrival or departure events and it is at
those events that the number in the shop must be observed. A Monitor
provides simple statistics useful either alone or as the start of a
more sophisticated statistical analysis.

When Resources are defined, a Monitor can be set up to automatically
observe the lengths of each of their queues.

The simpler version, the Tally, is not covered in this document. See
the SimPy Manual for more details.

.. index:: monitors; defining

Defining Monitors
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


The ``Monitor`` class preserves a complete time-series of the observed
data values, ``y``, and their associated times, ``t``. The data are held
in a list of two-item sub-lists, ``[t,y]``. Monitors calculate data
summaries using this time-series when your program requests them. In
long simulations their memory demands may be a disadvantage

To define a new Monitor object:

* ``m = Monitor(name='a_Monitor')``

  where ``name`` is a descriptive name for the Monitor object. The
  descriptive name is used when the data is graphed or tabulated.

For example, to record the waiting times of cars in the gas station we
might use a Monitor::

  waittimes = Monitor(name='Waiting times')


.. index:: monitors; observe
.. index:: observing data


Observing data
~~~~~~~~~~~~~~~~~

Monitors use their ``observe`` method to record data.  Here and in the
next section, ``m`` is a Monitor object:

* ``m.observe(y [,``\ *t*\ ``])``

  records the current value of the variable, ``y`` and time *t* (or
  the current time, ``now()``, if *t* is missing). A Monitor retains
  the two values as a sub-list ``[t,y]``.

For example, using the Monitor in the previous example, we might
record the waiting times of the cars as shown in the following
fragment of the PEM of a ``Car``::

  startwaiting = now()             # start wait
  yield request, self, gasstation
  waitingtime = now() - startwaiting # time spent waiting

  waittimes.observe(waitingtime)

The first three lines measure the waiting time (from the time of the
request to the time the ``pump`` is obtained). The last records the
waiting time in the ``waittimes`` Monitor.

.. index:: 
   pair: monitors; reset

The data recording can be ``reset`` to start at any time in the
simulation:

* ``m.reset([``\ *t*\ ``])``

  resets the observations. The recorded data is re-initialised, and
  the observation starting time is set to *t*, or to the current
  simulation time, ``now( )``, if *t* is missing.



.. index:: monitors; data summaries


Data summaries
~~~~~~~~~~~~~~~~~

The following simple data summaries are available from Monitors at
any time during or after the simulation run:


* ``m[i]`` holds the ``i``\-th observation as a two-item list, *[ti,
  yi]*

.. index:: 
   pair: monitors; yseries

* ``m.yseries( )`` is a list of the recorded data values, *yi*

.. index:: 
   pair: monitors; tseries

* ``m.tseries( )`` is a list of the recorded times, *ti*


.. index:: 
   pair: monitors; count

* ``m.count( )``, the current number of observations. (This is the
  same as ``len(r)``).

.. index::
   pair: monitors; total

* ``m.total( )``, the sum of the ``y`` values

.. index:: 
   pair: monitors; mean

* ``m.mean( )``, the simple numerical average of the observed *y*
  values, *ignoring the times at which they were made*.  This is
  ``m.total( )/m.count( )``.

  .. figure:: /_static/images/Mon004.*
     :alt: Standard mean value
     :figwidth: 400
     :align: center

     ``m.mean`` is the simple average of the *y* values observed.

.. index:: 
   pair: monitors; var

* ``m.var( )`` the *sample* variance of the observations, ignoring the
  times at which they were made. If an unbiased estimate of the
  *population* variance is desired, the sample variance should be
  multiplied by *n/(n-1)*, where *n = m.count( )*.  In either case the
  standard deviation is, of course, the square-root of the variance


.. index:: 
   pair monitors; timeAverage

* ``m.timeAverage(``\ *[t]*\ ``)`` the time-weighted average of ``y``,
  calculated from time 0 (or the last time ``m.reset(``\ *[t]*\ ``)``
  was called) to time *t* (or to the current simulation time,
  ``now()``, if *t* is missing).

  This is intended to measure the average of a quantity that always
  exists, such as the length of a queue or the amount in a Level [#]_.
  In discrete-event simulation such quantity changes are always
  instantaneous jumps occurring at events. The recorded times and new
  levels are sufficient information to calculate the average over
  time. The graph shown in the figure below illustrates the calculation. The
  total area under the line is calculated and divided by the total
  time of observation.  For accurate time-average results *y* must be
  piecewise constant like this and observed *just after* each change
  in its value. That is, the *y* value observed must be the *new*
  value after the state change.


  .. figure:: /_static/images/Mon005.*
     :alt: Time Average
     :figwidth: 400
     :align:  center

     ``m.timeAverage([t])`` is the time-weighted average of the observed
     ``y`` values. Each ``y`` value is weighted by the time for which
     it exists. The average is the area under the above curve divided
     by the total time, *t*.


  .. [#] ``timeAverage`` is not intended to measure instantaneous
         values such as a service time or a waiting time. ``m.mean()``
         is used for that.

.. index:: 
   pair: monitors; timeVarience

* ``m.timeVariance([t])`` the time-weighted variance of the ``y``
  values calculated from time 0 (or the last time ``m.reset([t])`` was
  called) to time *t* (or to the current simulation time, ``now()``,
  if *t* is missing).


.. index:: 
   pair: monitors; current state

* ``m.__str__( )`` is a string that briefly describes the current state
  of the monitor. This can be used in a print statement.

.. index:: resource queue; monitoring
.. index:: monitoring; resource queues

Monitoring Resource Queues
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If a Resource, ``m``, (and similarly for a Level or a Store) is
defined with ``monitored=True``, SimPy automatically records the
lengths of its associated queues (i.e. ``waitQ`` and ``activeQ`` for
Resources, and the analogous queues for Levels and Stores). These
records are kept in Monitors ``m.waitMon`` for the ``waitQ`` and
``m.actMon`` for the ``activeQ`` (and analogously for the other
resource types). This solves a problem, particularly for the ``waitQ``
which cannot easily be recorded externally to the resource.

Complete time series for queue lengths are maintained and can be used
for advanced post-simulation statistical analyses and to display
summary statistics.


.. index::
  pair: monitors; histogram
  pair: monitor; allMonitors
  pair: monitor; startCollection

More on Monitors
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


When a Monitor is defined it is automatically entered into a global
list ``allMonitors``. Each Monitor also has a descriptive label for
its variable values, ``y``, and their corresponding times, ``t``, that can
be used when the data are plotted.  The function ``startCollection()``
can be called to initialise all the Monitors in ``allMonitors`` at a
certain simulation time. This is helpful when a simulation needs a
'warmup' period to achieve steady state before measurements are
started.  A Monitor can also generate a ``Histogram`` of the data
(The SimPy ``Tally`` is an alternative to ``Monitor`` that does essentially
the same job but uses less storage space at some cost of speed and
flexibility. See the SimPy Manual for more information on these options.)




Appendices
---------------

.. index:: example; resource with tracing
.. index:: SimulationTrace

The Resource Example with Tracing
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

This is the trace produced in the Resource example when
``SimPy.SimulationTrace`` is imported at the head of the program. The
relevance of the phrases ```prior: False``` and ```priority:
default``` refer to advanced but seldom-needed methods for
fine-grained control of event timing, as explained in the SimPy Manual. The
trace contains the results of all the ``print`` output specifically
called for by the user's program (for example, line 5) but adds a line
for every event executed. (The ``request`` at time ``3.0``, for
example, lists the contents of the ``waitQ`` and the ``activeQ`` for
the ``gasstation``.)

.. literalinclude:: programs/carsT.out
   :linenos:

..
   .. image:: http://sourceforge.net/sflogo.php?group_id=62366&type=4
      :width: 125
      :alt:  SourceForge Logo
      :height: 37

.. ------------------------------------------------------------------------
.. some useful stuff used above


.. _`simpydownload`: http://sourceforge.net/projects/simpy/
.. _`Python web-site` : http://www.Python.org


.. _`SimPy.SimulationRT`: http://simpy.sourceforge.net/SimPyDocs/SimRTManual.html
.. _`SimPy.SimulationStep`: http://simpy.sourceforge.net/SimPyDocs/SimStepManual/SimStepManual.html
.. _`The Bank`: http://simpy.sourceforge.net/SimPyDocs/TheBank.html


.. .. _Top: Contents_

.. _monitors: `Monitors and Recording Simulation Results`_


.. _`Python random module`: http://www.python.org/doc/current/lib/module-random.html
.. _Python: http://www.Python.org




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