.. image:: images/sm_SimPy_Logo.png
   :align: left

=========================
 SimPy Manual
=========================

:Authors: - Tony Vignaux <Vignaux@users.sourceforge.net>
          - Klaus Muller <Muller@users.sourceforge.net>
:SimPy version: 1.4
:Web-site: http://simpy.sourceforge.net/

.. contents:: Contents
   :depth: 3
   
.. .. sectnum::
..    :depth: 2
 

SimPy is an efficient, process-based, open-source simulation language
using Python as a base. The facilities it offers are *Processes*,
*Resources*, and *Monitors*.
  
This describes version 1.4 of *SimPy*.


A Note for users of SimPy Version 1.3
-------------------------------------

There have been changes to Monitor. It is now incorporated into
Simulation.py. All old code should work but some old
methods, such as *tally* and *accum* are now deprecated and replaced
by *observe(y,t)*. Where we have used *x* as the observed value, now we
use *y* for compatibility with the plotting routines.

The Manual Appendix includes descriptions of a number of new SimPy
varieties, for plotting, interaction using a GUI, tracing,
event-stepping, and a real-time version.

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


*SimPy* is a Python-based discrete-event simulation system. It uses 
parallel processes to model active components such as messages,
customers, trucks, planes.

*SimPy* provides a number of facilities for the simulation programmer.
They include *Processes*, *Resources*, and, importantly, ways of recording the
histories of chosen variables in *Monitors*.

*Processes* are the basic component of a *SimPy* simulation script. A
Process models an active component (for example, a Truck, a Customer,
or a Message) which may have to queue for scarce Resources, to work
for fixed or random times, and to interact with other components.

A *SimPy* script consists of the declaration of one or more *Process*
classes and the instantiation of process objects from them.  Each such
process describes how the object behaves, elapses time, uses logic,
and waits for Resources. In addition, Resources and Monitors may be
defined and used.

Before attempting to use SimPy, you should know how to write Python
code. In particular, you should be able to use and define classes of
objects. Python is free and available on most machine types.  We do
not introduce it here. You can find out more about it and download it
from the *Python* web-site, http://www.Python.org

This document assumes *Python* 2.2 or later.  NOTE that if Python 2.2
is used, the following must be placed at the top of all *SimPy* scripts:
**from __future__ import generators** 
   

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

All discrete-event simulation programs automatically maintain the
current simulation time in a software clock. In *SimPy* this can be
accessed using the **now()** function. This is used in controlling the
simulation and in producing printed traces of its operation.

While a simulation program runs, time steps forward from one
*event* to the next. An event occurs whenever the state of the
simulated system changes. For example, an arrival of a customer is an
event. So is a departure.

To use the event scheduling mechanism of *SimPy* we must import the
Simulation module:
 
    **from SimPy.Simulation import *** 

Before any *SimPy* simulation statements, such as defining processes or
resources, are issued, the following statement must appear in the
script:
 
    **initialize()**
 
Then there will be some SimPy statements, creating and activating
objects. Execution of the timing mechanism itself starts when the
following statement appears in the script:
 
    **simulate(until=endtime)**
 
The simulation then starts, the timer routine seeking the first
scheduled event. The simulation will run until one of the following
states:
  
     * there are no more events to execute (*now()* == the time 
       of the last event)

     * the simulation time reaches *endtime* (*now() == endtime*)

     * the *stopSimulation()* command is executed (*now()* == the time
       when *stopSimulation()* was called).
   

The simulation can be stopped at any time using the command:
 
    **stopSimulation()**
 
which immediately stops the execution of the simulation.

Further statements can still be executed after exit from *simulate*.


The following  partial script shows only the *main* block in a simulation
program.  *Arrivals* is a Process class (previously defined) and *p*
is established as an object of that class. Activating *p* has the
effect of scheduling at least one event The *simulate(until=1000.0)*
starts the program start and it will immediately jump to that first
event. It will continue until it runs out of events to execute or
the simulation time reaches 1000.0::

	initialize()
	p = Arrivals(mean)
	activate(p,p.execute(),at=0.0)
	simulate(until=1000.0)

	Report()  #  when the simulation finishes


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

The active objects for discrete-event simulation in *SimPy* are of
classes that inherit from class *Process*.

For example, if we are simulating a messaging system we would model a
message as a *Process*.  A message arrives in a computing network; it
makes transitions between nodes, waits for service at each one, and
eventually leaves the system. The Message class describes these
actions in an *execute* method.  Individual messages are created as
the program runs and they go through their modelled lifetimes.
 

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

A process is a class that that inherits from the class
*Process*. For example here is the header of the definition of a
new Message process class:
 
* **class Message(Process):** 
 
The user must define two particular methods and may define any others.
 
* **__init__(self,...)**, where *...* indicates method arguments. This
  function initializes the Process object, setting values for any
  attributes.  The first line of this method must be a call to the
  Class *__init__()* in the form:
  **Process.__init__(self,name='a_process')**
 
  Then other commands can be used to initialize attributes of the
  object. The *__init__()* method is called automatically when a new
  message is created. 

  In this example of an  *__init__()* method for a *Message* class we
  give each new message  an integer identification number, *i*, and
  message length, *len* as instance variables::

       def __init__(self,i,len):
	   Process.__init__(self,name='Message'+str(i))
	   self.i = i
	   self.len = len
 
* **A process execution method (PEM)** This describes the actions of
  the process object and must contain at least one of the *yield*
  statements, described later, to make it a Python generator
  function. It can have arguments. Typically this can be called
  *execute()* or *run()* but any name may be chosen.

  The execution method  starts when the process is activated and the
  *simulate(until=...)* statement has been called.

  In this example of the process execution method  for the same  *Message*
  class, the message prints out the current time, its identification
  number and the word 'Starting'. After a simulated delay it then
  announces it has 'Arrived'::

       def go(self):
	   print now(), self.i, 'Starting'
	   yield hold,self,100.0
	   print now(), self.i, 'Arrived'

A Process must be *activated* in order to start it operating (see
`Starting and stopping SimPy Processes`_)

Following is a complete, runnable, SimPy script. We declare a *Message*
class and define *__init__()* and *go()* methods for it.  Two
*messages*, *p1* and *p2* are created. We do not actually use the
*len* attribute in this example. *p1* and *p2* are activated to start
at simulation times 0.0 and 6.0, respectively. Nothing happens until
the *simulate(until=200)* statement. When they have both
finished (at time 6.0+100.0=106.0) there will be no more events so the
simulation will stop at that time::

    from __future__ import generators
    from SimPy.Simulation import *

    class Message(Process):
       """ a simple Process """
       def __init__(self,i,len):
	   Process.__init__(self,name='Message'+str(i))
	   self.i = i
	   self.len = len

       def go(self):
	   print now(), self.i, 'Starting'
	   yield hold,self,100.0
	   print now(), self.i, 'Arrived'

    initialize()
    p1  = Message(1,203)
    activate(p1,p1.go())
    p2  = Message(2,33)
    activate(p2,p2.go(),at=6.0)
    simulate(until=200)
    print now() # will print 106.0



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

An execution method can cause time to elapse for a process using the
*yield hold* command:
 
* **yield hold,self,t** causes the object to wait for a delay of *t*
  time units (unless it is interrupted). It then continues its operation
  with the next statement.  During the hold the object is suspended.

* **yield passivate,self** suspends the process's operations
  indefinitely.
 

This example of an execution method (*buy*) for a *Customer* class
demonstrates that the method can have arguments which can be used in
the activation. The Customer also has an identification attribute
*id*. The *yield hold* is executed 4 times::

     def buy(self,budget=0):
	print 'Here I am at the shops ',self.id
	t = 5.0
	for i in range(4):
	    yield hold,self,t
	    print 'I just bought something ',self.id
	    budget -= 10.00
	print   'All I have left is ', budget,\
		' I am going home ',self.id,

     initialize()
     C = Customer(1)
     activate(C,C.buy(budget=100),at=10.0)
     simulate(until=100.0)



Starting and stopping SimPy Processes
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Once a Process object has been created, it is 'passive', i.e., it has no
event scheduled. It must be *activated* to start the process execution method:
 
* **activate(p,p.PEM(args)[,at=t][,delay=period][,prior=boolean])**
  will activate the execution method *p.PEM()* of Process instance,
  *p* with arguments *args*. The default action is to activate at the
  current time, otherwise one of the optional timing clauses
  operate. If *prior* is true, the process will be activated before
  any others at the specified time in the event list.

The process can be suspended and reactivated:

* **yield passivate,self** suspends the process itself. It becomes 'passive'.

* **reactivate(p,at=t,delay=period,prior=boolean)** will reactivate a
  passive process, *p*. It becomes 'active'. The optional timing clauses 
  work as for *activate*. A process cannot reactivate itself. If that is
  required, use *yield hold,self, . . .* instead.

* **self.cancel(p)** deletes all scheduled future events for process *p*.
  Only 'active' processes can be cancelled. A process cannot cancel itself. 
  If that is required, use *yield passivate,self* instead.
  *Note:* This new format replaces the *p.cancel()* form of earlier SimPy
  versions.


When all statements in a process execution method have been completed,
a process becomes 'terminated'. If the instance is still referenced, it 
becomes just a data container. Otherwise, it is automatically destroyed.

And, finally,

* **stopSimulation()** stops all simulation activity, even if some processes
  still have events scheduled.
 

Asynchronous interruptions
~~~~~~~~~~~~~~~~~~~~~~~~~~

One process (the *interrupter*) can interrupt another, active, process (the
*victim*). A process cannot interrupt itself. 

* **self.interrupt(victim)**

The interrupt is just a signal. After this statement, the
*interrupter* continues its current method.

The *victim* must be *active*. An *active* process is one that has an
event scheduled for it (that is, it is 'executing' a *yield
hold,self,t*). If the *victim* is not active (that is it is either
*passive* or *terminated*) the interrupt has no effect on it. As processes
queuing for resources are *passive*, they cannot be interrupted. *Active*
processes which have acquired a resource can be interrupted.

If interrupted, the *victim* returns from its *yield hold*
prematurely. It can sense if it has been interrupted by calling

* **self.interrupted()** which returns *True* if it has been
  interrupted. It can then either continue in the current activity or
  switch to an alternative, making sure it tidies up the current
  state, such as releasing any resources it owns. When this is True:

  * **self.interruptCause** is a reference to the *interrupter* instance.

  * **self.interruptLeft** gives the time remaining in the interrupted
    *yield hold,*

The interruption is reset at the *victim's* next call to a 
*yield hold,*. It can also be reset by calling

* **self.interruptReset()**

Here is a complete example of a simulation with interrupts. A bus is
subject to breakdowns which are modelled as interruptions. Notice that
in the first *yield hold*, interrupts may occur, so a reaction to the
interrupt (= repair) has been programmed::

     class Bus(Process):
       def __init__(self,name):
	  Process.__init__(self,name)

       def operate(self,repairduration,triplength):  # process execution method
	  tripleft = triplength
	  while tripleft > 0:
	     yield hold,self,tripleft                # try to get through trip
	     if self.interrupted():
		   print self.interruptCause.name, "at %s" %now() # breakdown
		   tripleft=self.interruptLeft 	     # yes; time to drive 
		   self.interruptReset()             # end interrupt state
		   reactivate(br,delay=repairduration) # delay any breakdowns 
		   yield hold,self,repairduration
		   print "Bus repaired at %s" %now()
	     else:
		   break                             # no breakdown, bus arrived
	     print "Bus has arrived at %s" %now()

     class Breakdown(Process):
	def __init__(self,myBus):
	    Process.__init__(self,name="Breakdown "+myBus.name)
	    self.bus=myBus

	def breakBus(self,interval):                 # process execution method 
	    while True:
	       yield hold,self,interval
	       if self.bus.terminated(): break
	       self.interrupt(self.bus)

     initialize()
     b=Bus("Bus")
     activate(b,b.operate(repairduration=20,triplength=1000))
     br=Breakdown(b)
     activate(br,br.breakBus(300))
     print simulate(until=4000)

The ouput from this example::

     Breakdown Bus at 300
     Bus repaired at 320
     Breakdown Bus at 620
     Bus repaired at 640
     Breakdown Bus at 940
     Bus repaired at 960
     Bus has arrived at 1060
     SimPy: No more events at time 1260

Where interrupts can occur, the process which may be the victim of
interrupts must test for interrupt occurrence after every "yield hold"
and react to it. If a process holds a resource when it gets
interrupted, it continues holding the resource.
 
Starting the simulation
~~~~~~~~~~~~~~~~~~~~~~~                           

Even activated  processes will not start until the following statement
has been executed:
 
* **simulate(until=T)** starts the simulation going and it will
  continue until time *T* unless it runs out of events to
  execute or the command *stopSimulation()* is executed.
 

 
.. ------example-------------

    Three messages are created and activated to start at different times.
    Message *m1*, length 3, is scheduled to start immediately . The
    absence of a time in the *schedule* arguments implies it should
    start now, at the current time. Message *m2* is of length 40 and
    will start at simulation time 100.0. Message *m3* is of length 50
    and will start 100.0 time units after the current time. Finally, the
    simulation is started by the call of *simulate()*::

	initialize()
	m1 = Message(1,30)
	m2 = Message(2,40)
	m3=  Message(3,50)
	activate(m1,m1.execute())
	activate(m1,m1.execute(),at=100.0)
	activate(m1,m1.execute(),delay=100.0)

	simulate(until=1000)

.. -----------------------------------------------------------------------



 
A complete *SimPy*  script
~~~~~~~~~~~~~~~~~~~~~~~~~~                           

This complete runnable script simulates a firework with a time fuse.
I have put in a few extra *yield hold* commands for added suspense::

    from __future__ import generators
    from SimPy.Simulation import *

    class Firework(Process):
       def __init__(self):
	   Process.__init__(self)

       def execute(self):
	   print now(), ' firework activated'
	   yield hold,self, 10.0
	   for i in range(10):
	       yield hold,self,1.0
	       print now(),  ' tick'
	   yield hold,self,10.0
	   print now(), ' Boom!!'

    initialize()
    f = Firework()
    activate(f,f.execute(),at=0.0)
    simulate(until=100)


The output from Example . No formatting of the
output was attempted so it looks a bit ragged::

    0.0  firework activated
    11.0  tick
    12.0  tick
    13.0  tick
    14.0  tick
    15.0  tick
    16.0  tick
    17.0  tick
    18.0  tick
    19.0  tick
    20.0  tick
    30.0  Boom!!


 
A source fragment
~~~~~~~~~~~~~~~~~~~                         

One useful program pattern is the *source*. This is an process with an
execution method that generates events or activates other processes as
a sequence -- it is a source of other processes. Random arrivals can
be modelled using random (exponential) intervals between activations.

The following example is of a source which activates a series of
*customers* to arrive at regular intervals of 10.0 units of time. The
sequence continues until the simulation time exceeds the specified
*finishTime*.  (Of course, to achieve *random'' arrivals of
*customer*s the *yield hold* method should use an *exponential* random
variate instead of, as here, a constant 10.0 value) The example
assumes that the *Customer* class has been defined with a PEM called
*run*::

     class Source(Process):
	def __init__(self,finish): 
	    Process.__init__(self)
	    self.finishTime = finish

	def execute(self):
	   while now() < self.finishTime:
	      c = Customer()          ## new customer
	      activate(c,c.run())     ## activate it now
	      print now(), ' customer'
	      yield hold,self,10.0

     initialize()
     g = Source(33.0)
     activate(g,g.execute(),at=0.0)   ## start the source
     simulate(until=100)

.. ------example-------------


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

A *resource* models a congestion point where there may be
queueing. For example in a manufacturing plant, a *Task* (modelled as
a *process*) needs work done at a *Machine* (modelled as a
*resource*). If a *Machine* unit is not available, the *Task* will
have to wait until one becomes free. The *Task* will then have the use
of it for however long it needs. It is not available for other *Tasks*
until released. These actions are all automatically taken care
of by the *SimPy* *resource*.
 
A resource can have a number of identical *units*. So there may be a
number of identical *Machine* units. A process gets service by
*requesting* a unit of the resource and, when it is finished,
*releasing* it. A resource maintains a queue of waiting processes and
another list of processes using it.  These are defined and updated
automatically.

A Resource is established by the following statement:
 
*  **r=Resource(capacity=1, name='a_resource',
   unitName='units', qType=FIFO, preemptable=0, monitored=False)**

   - *capacity* is the number of identical units of the resource
     available.  
   - *name* is the name by which the resource is known (eg *gasStation*) 
   - *unitName* is the name of a unit of the resource
     (eg *pump*)
   - *qType* describes the queue discipline of the waiting queue of
     processes; typically, this is *FIFO* (First-in, First-out). and
     this is the presumed value.  An alternative is *PriorityQ*
   - *preemptable* indicates, if it has a non-zero value, that a
     process being put into the *PriorityQ* may also pre-empt a
     lower-priority process already using a unit of the resource.
     This only has an effect when *qType == PriorityQ*
   - *monitored* indicates if the number of processes in the
     resource's queues (see below) are to
     be monitored (see Monitors_, below)
    
   A Resource, **r**,  has the following attributes:
 
   -  **r.n** The number of units that are currently free.

   -  **r.waitQ** A waiting queue (list) of processes (FIFO by default)
      The number of Processes waiting is **len(r.waitQ)**

   -  **r.activeQ** A queue (list) of processes holding units.
      The number of Processes in the active queue is
      **len(r.activeQ)**

   - **r.waitMon** A Monitor recording the number in *r.waitQ*
   - **r.actMon**  A Monitor recording the number in *r.activeQ*


A process can request and release a unit of resource, *r* using the
following yield commands:

 
* **yield request,self,r** requests a unit of resource,
  *r*. The process may be temporarily queued and suspended until
  one is available.
  
  If, or when, a unit is free, the requesting process will take one and continue
  its execution. The resource will record that the process is using a
  unit (that is, the process will be listed in *r.activeQ*)
  
  If one is not free , the the process will be automatically placed in
  the resource's waiting queue, *r.waitQ*, and suspended.  When a unit
  eventually becomes available, the first process in the waiting
  queue, taking account of the priority order, will be allowed to take
  it. That process is then reactivated.

  If the resource has been defined as being a *priorityQ* with
  *preemption == 1* then the requesting process can pre-empt a
  lower-priority process already using a unit. (see `Requesting a
  resource with preemptive priority`_, below)
  
* **yield release,self,r** releases the  unit of *r*. This may
  have the side-effect of allocating the released unit to the next
  process in the Resource's waiting queue.
 


  In this example, the current Process requests and, if necessary
  waits for, a unit of a Resource, *r*.  On acquisition it holds it
  while it pauses for a random time (exponentially distributed, mean
  20.0) and then releases it again::

      yield request,self,r
      yield hold,self,g.expovariate(1.0/20.0)
      yield release,self,r




Requesting resources with priority
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If a Resource, *r* is defined with *priority* queueing (that is
*qType==PriorityQ*) a request can be made for a unit by:

* **yield request,self,r,priority** requests a unit with priority.
  *priority* is real or integer.  Larger values of *priority*
  represent higher priorities and these will go to the head of the
  *r.waitQ* if there not enough units immediately.

An example of a complete script where priorities are used. Four
clients with different priorities request a resource unit from a
server at the same time. They get the resource in the order set by
their relative priorities::

    from __future__ import generators
    from SimPy.Simulation import *
    class Client(Process):
        inClients=[]
        outClients=[]

        def __init__(self,name):
           Process.__init__(self,name)

        def getserved(self,servtime,priority,myServer):
            Client.inClients.append(self.name)
            print self.name, 'requests 1 unit at t=',now()
            yield request, self, myServer, priority
            yield hold, self, servtime
            yield release, self,myServer
            print self.name,'done at t=',now()
            Client.outClients.append(self.name)

    initialize()
    server=Resource(capacity=1,qType=PriorityQ)
    c1=Client(name='c1') ; c2=Client(name='c2')
    c3=Client(name='c3') ; c4=Client(name='c4')
    activate(c1,c1.getserved(servtime=100,priority=1,myServer=server))
    activate(c2,c2.getserved(servtime=100,priority=2,myServer=server))
    activate(c3,c3.getserved(servtime=100,priority=3,myServer=server))
    activate(c4,c4.getserved(servtime=100,priority=4,myServer=server))
    simulate(until=500)
    print 'Request order: ',Client.inClients
    print 'Service order: ',Client.outClients


This program results in the following output::

    c1 requests 1 unit at t= 0
    c2 requests 1 unit at t= 0
    c3 requests 1 unit at t= 0
    c4 requests 1 unit at t= 0
    c1 done at t= 100
    c4 done at t= 200
    c3 done at t= 300
    c2 done at t= 400
    Request order:  ['c1', 'c2', 'c3', 'c4']
    Service order:  ['c1', 'c4', 'c3', 'c2']

.. ------example-------------

  Although *c1* has the lowest priority, it requests and gets the
  resource unit first.  When it completes, *c4* has the highest
  priority of all waiting processes and gets the resource next, etc.
  Note that there is no preemption of processes being served.

Requesting a resource with preemptive priority
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
                            
In some models, higher priority processes can preempt lower priority
processes when all resource units have been allocated. A resource with
preemption can be created by setting arguments  *qType==PriorityQ* and
*preemptable* non-zero.
 
When a process requests a unit of resource and all units are in use it
can preempt a lower priority process holding a resource unit. If there
are several processes already active (that is, in the *activeQ*), the
one with the lowest priority is suspended, put at the front of the
*waitQ* and the preempting process gets its resource unit and is
put into the *activeQ*. The preempted process is the next one to get a
resource unit (unless another preemption occurs).  The time for which
the preempted process had the resource unit is taken into account when
the process gets into the *activeQ* again. Thus, the total hold time
is always the same, regardless of whether or not a process gets
preempted.



An example of a complete script. Two clients of different priority
compete for the same resource unit::

      from __future__ import generators
      from SimPy.Simulation import *
      class Client(Process):
	  def __init__(self,name):
	     Process.__init__(self,name)

	  def getserved(self,servtime,priority,myServer):
	      print self.name, 'requests 1 unit at t=',now()
	      yield request, self, myServer, priority
	      yield hold, self, servtime
	      yield release, self,myServer
	      print self.name,'done at t=',now()

      initialize()
      server=Resource(capacity=1,qType=PriorityQ,preemptable=1)
      c1=Client(name='c1')
      c2=Client(name='c2')
      activate(c1,c1.getserved(servtime=100,priority=1,myServer=server),at=0)
      activate(c2,c2.getserved(servtime=100,priority=9,myServer=server),at=50)
      simulate(until=500)


The output from this program is::

    c1 requests 1 unit at t= 0
    c2 requests 1 unit at t= 50
    c2 done at t= 150
    c1 done at t= 200
 
Here, *c2*  preempted *c1* at *t=50*. At that time, *c1* had held the
resource for 50 of the total of 100 time units. *c1* got the resource
back when *c2* completed at *t=150*.

Monitoring a resource
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

If *monitored* is set *True* for a resource, *r*, the length of the
waiting queue, *len(r.waitQ)* and the active queue,*len(r.activeQ)*
are Both monitored automatically (see Monitors_, below). This solves a
problem, particularly for the waiting queue which cannot be monitored
externally to the resource. The monitors are called *r.waitMon* and
*r.actMon*, respectively. Complete time series for both queue lengths
are maintained so that statistics, such as the time average can be
found.

In this example, the resource, *server* is monitored and the
time-average of each is calculated::

   from SimPy.Simulation import *
   class Client(Process):
        inClients=[]
        outClients=[]

        def __init__(self,name):
           Process.__init__(self,name)

        def getserved(self,servtime,myServer):
            print self.name, 'requests 1 unit at t=',now()
            yield request, self, myServer
            yield hold, self, servtime
            yield release, self,myServer
            print self.name,'done at t=',now()

   initialize()
   server=Resource(capacity=1,monitored=True)
   c1=Client(name='c1') ; c2=Client(name='c2')
   c3=Client(name='c3') ; c4=Client(name='c4')
   activate(c1,c1.getserved(servtime=100,myServer=server))
   activate(c2,c2.getserved(servtime=100,myServer=server))
   activate(c3,c3.getserved(servtime=100,myServer=server))
   activate(c4,c4.getserved(servtime=100,myServer=server))
   simulate(until=500)
   print 'Average waiting',server.waitMon.timeAverage()
   print 'Average in service',server.actMon.timeAverage()
 

The output from this program is::

   c1 requests 1 unit at t= 0
   c2 requests 1 unit at t= 0
   c3 requests 1 unit at t= 0
   c4 requests 1 unit at t= 0
   c1 done at t= 100
   c2 done at t= 200
   c3 done at t= 300
   c4 done at t= 400
   Average waiting 1.5
   Average in service 1.0


.. ---------------------------------------------------------------------

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

Simulation usually needs pseudo-random numbers. *SimPy* uses the
standard *Python* *random* module. Its documentation should be
consulted for details.  We can have multiple random streams, as in
Simscript and ModSim.

One *imports* the Class and methods needed:
 
* **from random import Random**

You must define a random variable object using:

* **g = Random([seed])** sets up the random variable object *g* using
  *seed* to initialize the sequence. 

  For example, *g= Random(111333)*  sets up the random variable object
  *g* and initializes its seed to *111333*.
 

A good range of distributions is available. For example:
 
* **g.random()** returns the next random floating point number in the
  range [0.0, 1.0).
* **g.expovariate(lambd)** returns a sample from the exponential
  distribution. *lambd* is 1.0 divided by the desired mean. (The
  parameter would be called *lambda*, but that is a reserved word in
  Python.) Returned values range from 0 to positive infinity.
* **g.normalvariate(mu,sigma)** returns a sample from the normal
  distribution. *mu* is the mean, and *sigma* is the
  standard deviation.
 

This example uses exponential and normal random variables. The
*random* object, *g* is initialized with its initial seed set to
333555.  *X* and *Y* are pseudo-random variates from the two
distributions using the object *g*::

    from random import Random

    g = Random(333555)

    X = g.expovariate(10.0)
    Y = g.normalvariate(100.0, 5.0)



 
Monitors
----------------------------- 

A Monitor, a subclass of list, records a series of observed data
values, *y*, and associated times, *t*. Simple averages can then be
calculated from the series. Each Monitor observes one series of data
values. For example we might use one Monitor to record the waiting
times for customers and another to record the total number of
customers in the shop. Because SimPy is a discrete-event system, the
number of customers changes only at events and it is these that are
recorded.

Monitors are not intended as a substitute for real statistical
analysis but they have proved useful in developing simulations in
SimPy.
 
Monitors are included in the Simulation module of the SimPy package.
(In versions of SimPy 1.3 and earlier, the Monitor module was separate
from the Simulation module and had to be imported
independently. Previous programs still work as long as the *from
SimPy.Monitor import Monitor* occurs after the importation from
SimPy.Simulation)
 
To define a new Monitor object:

* **m=Monitor(name='', ylab='y', tlab='t')**, where *name* is the name
  of the monitor object, set to an empty string if it is missing. *ylab* and
  *tlab* are provided as labels for plotting graphs from the data held
  in the Monitor.

Methods of the Monitor class include:
 
* **m.observe(y [,t])** records the current value of the variable, *y*
  and time *t* (the current time, *now()*, if *t* is missing).  
* **m.reset([t])** resets the observations. The recorded time series
  is set to the empty list, *[]* and the starting time to *t* or, if
  it is missing, to the current simulation time, *now()*.

 
the Monitor object, **m**, holds the recorded data as a list of data
pairs. Each pair, *[t,y]*, records the time and the value of one
observation. Simple data summaries can be obtained from such a
*Monitor* object:

* **m[i]** holds the **i** th observation as a list, *[ti, yi]*
* **m.yseries()** returns a list of the recorded data values.
* **m.tseries()** returns a list of the recorded times.
* **m.total()** returns the sum of the *y* values
* **m.count()** returns the current number of observations. This is
  the same as *len(m)*.
* **m.mean()** returns the simple average of the observations (see the
  left-hand picture below) If there are no observations, the message: 
  'SimPy: No observations  for mean' is printed.
* **m.var()** returns the simple variance of the observations. If
  there are no observations, the message: 
  'SimPy: No observations for sample variance' is printed.

* **m.timeAverage([t])** returns the time-average of the integrated *y*
  values, calculated from time 0 (or the last time *m.reset([t])* was
  called) to time *t* (the current simulation time if *t* is missing).
  It is assumed that *y* is
  continuous in time but changes in steps at the times that
  *observe(y)* is called. In calculating the time-average the area
  under the graph is calculated as shown in the right-hand figure
  below. If there are no observations, the message 'SimPy: No observations
  for timeAverage'. If no time has elapsed, the message 'SimPy: No
  elapsed time for timeAverage' is printed. 

.. figure:: images/Mon001.png 
   :scale: 60
   :alt: Different averages


* **m.__str__()** is a string that briefly describes the current state
  of the monitor. This can be used in a print statement.
 
* **m.histogram(low=0.0,high=100.0,nbins=10)** is a *histogram* object
  (a derived class of *list*) which contains the number of *y* values
  in each of its bins. It is calculated from the monitored *y*
  values. A *histogram* can be graphed using the *plotHistogram*
  method in the `SimPlot`_ package.

  - *low* is the lowest value of the histogram
  - *high* is the highest value of the histogram

  - *nbins* is the number of bins beween *low* and *high* into which
    the histogram is to be divided. The number of *y* values in each
    of the divisions is counted into the appropriate bin. Another 2
    bins are constructed, counting the number of *y* values *under*
    the *low* value and the number *over* the *high* value. There
    are *nbins+2* counts altogether.


Note: The following methods are retained for backwards compatibility
but are not recommended. They may be removed in future releases of
SimPy.

* **m.tally(y)** records the current value of *y* and the current
  time, *now()*.
* **m.accum(y [,t])** records the current value of *y* and time *t* (the current
  time, *now()*, if *t* is missing).


In this example we establish a Monitor to estimate the mean and
variance of 1000 observations of an exponential random variate. A
histogram with 30 bins (plus an *under* and an *over* count is also
returned.::

    from SimPy.Simulation import *
    from random import Random

    M = Monitor()
    g = Random()

    for i in range(1000):
       y = g.expovariate(0.1)
       M.observe(y)

    print 'mean= ',M.mean(), 'var= ',M.var()
    h = M.histogram(low=0.0, high=20, nbins=30)

In this example,  the number in the system, recorded as *N*,  is being monitored to
estimate the average number in the system (This example is only fragmentary)::

    from SimPy.Simulation import *

    M = Monitor()

       ...   # upon an arrival of a job, increment N
             # the time used is now()
       N = N +1
       M.observe(N)
       ...

       ...   # upon a departure of a job
       N = N -1
       M.observe(N) 

    print 'mean= ',M.timeAverage()

.. -------------------------------------------------------------------------

Other Links
-------------------

Several `SimPy models`_ are included with the SimPy code distribution.

.. _`SimPy models`: LISTOFMODELS.html 

Klaus MŸller and Tony Vignaux, *SimPy: Simulating Systems in Python*,
O'Reilly ONLamp.com, 2003-Feb-27,  http://www.onlamp.com/pub/a/python/2003/02/27/simpy.html

Norman Matloff, *Introduction to the SimPy Discrete-Event Simulation
Package*, U Cal: Davis, 2003,
http://heather.cs.ucdavis.edu/~matloff/simpy.html

David Mertz, *Charming Python: SimPy simplifies complex models*, IBM
Developer Works, Dec 2002,
http://www-106.ibm.com/developerworks/linux/library/l-simpy.html



Acknowledgments
-------------------

We will be grateful for any corrections or suggestions for improvements
to the document.



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

Here are some

A1. SimPy Error Messages
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Advisory messages
+++++++++++++++++++

These messages are returned by *simulate()*, as in
*message=simulate(until=123)*.

Upon a normal end of a simulation, *simulate()* returns the message:

- **SimPy: Normal exit**. This means that no errors have occurred and 
  the simulation has run to the time specified by the *until* parameter.

The following messages, returned by *simulate()*, are produced at a premature
termination of the simulation but allow continuation of the program.

- **SimPy: No more events at time x**. All processes were completed prior
  to the endtime given in *simulate(until=endtime)*.

- **SimPy: No activities scheduled**. No activities were scheduled
  when *simulate()* was called.
	
Fatal error messages
++++++++++++++++++++++

These messages are generated when SimPy-related fatal  exceptions occur.
They end the SimPy program. Fatal SimPy error messages are output to 
*sysout*.

- **Fatal SimPy error: activating function which is not a generator (contains no 'yield')**.
  A process tried to (re)activate a function which is not a
  SimPy process (=Python generator). SimPy processes must contain
  at least one *yield . . .* statement.

- **Fatal SimPy error: Simulation not initialized**. The SimPy program
  called *simulate()* before calling *initialize()*.

'Monitor' error messages
++++++++++++++++++++++++++

- **SimPy: No observations for mean**. No observations were made by the
  monitor before attempting to calculate the mean.

- **SimPy: No observations for sample variance**. No observations were made by the
  monitor before attempting to calculate the sample variance.

- **SimPy: No observations for timeAverage**, No observations
    were made by the monitor before attempting to calculate the time-average.

- **SimPy: No elapsed time for timeAverage**. No simulation
  time has elapsed before attempting to calculate the time-average.



A2. SimPy Process States
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From the point of the model builder, at any time, a SimPy process, *p*,
can be in one of the following states:
   
- **Active**: Waiting for a scheduled event. This state simulates an
  activity in the model.  Simulated time passes in this
  state. The process state *p.active()* returns *True*.

- **Passive**: Not active or terminated. Awaiting *(re-)activation* by
  another process.  This state simulates a real world process which
  has not finished and is waiting for some trigger to continue. Does
  not change simulation time.  *p.passive()* returns *True*.

- **Terminated**: The process has executed all its action statements
  and continues as a data instance, if referenced. *p.terminated()*
  returns *True*

Initially (upon creation of the Process instance), a process returns *passive*.

In addition, a SimPy process, *p*,  can be in the following (sub)states:

- **Interrupted**: Active process has been interrupted by another
   process. It can immediately respond to the interrupt. This
   simulates an interruption of a simulated activity before its
   scheduled completion time.  *p.interrupted()* returns *True*.

- **Queuing**: Active process has requested a busy resource and is
  waiting (passive) to be reactivated upon resource
  availability. *p.queuing(a_resource)* returns *True*.


.. -------------------------------------------------------------------------


A3. SimPlot, The Simpy plotting utility
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

SimPlot_ provides an easy way to graph the results of simulation runs.

.. _`SimPlot`: SimPlotManual/ManualPlotting.html


A4. SimGUI, The Simpy Graphical User Interface
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

SimGUI_  provides a  way for users to interact with a SimPy program,
changing its parameters and examining the output.

.. _`SimGUI`: SimGUIManual/SimGUImanual.html



A5. SimulationTrace, the SimPy tracing utility
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`SimulationTrace`_ has been developed to give users insight into the
dynamics of the execution of SimPy simulation programs. It can help
developers with testing and users with explaining SimPy models to themselves
and others (e.g. for documentation or teaching purposes). 

.. _`SimulationTrace`: Tracing.html


A6. SimulationStep, the SimPy event stepping utility
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`SimulationStep`_ can assist with debugging models, interacting with them on
an event-by-event basis, getting event-by-event output from a model (e.g.
for plotting purposes), etc.

It caters for:

    - running a simulation model, with calling a user-defined procedure after every event,
    - running a simulation model one event at a time by repeated calls,
    - starting and stopping the event stepping mode under program control.

.. _`SimulationStep`: SimStepManual/SimStepManual.html

A7. SimulationRT, a real-time synchronizing utility
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`SimulationRT`_ allows synchronizing simulation time and real (wallclock) time. 
This capability can be used to implement e.g. interactive game applications or
to demonstrate a model's execution in real time.

.. _`SimulationRT`: SimRTManual.html 

:Revision:  $Revision: 1.0 $  
:Date: $Date: 2004-05-15 11:09:20+02 $ gav
:Python-Version: 2.2, 2.3
:Created: 2003-April-6


..
   Local Variables:
   mode: indented-text
   indent-tabs-mode: nil
   sentence-end-double-space: t
   fill-column: 70 
   End:
