The Bank (Object Oriented version)¶
Introduction¶
SimPy is used to develop a simple simulation of a bank with a number of tellers. This Python package provides Processes to model active components such as messages, customers, trucks, and planes. It has three classes to model facilities where congestion might occur: Resources for ordinary queues, Levels for the supply of quantities of material, and Stores for collections of individual items. Only examples of Resources are described here. It also provides Monitors and Tallys to record data like queue lengths and delay times and to calculate simple averages. It uses the standard Python random package to generate random numbers.
Starting with SimPy 2.0 an object-oriented programmer’s interface was added to the package and it is this version that is described here. It is quite compatible with the procedural approach. The object-oriented interface, however, can support the process of developing and extending a simulation model better than the procedural approach.
SimPy can be obtained from: https://github.com/SimPyClassic/SimPyClassic. This tutorial is best read with the SimPy Manual and CheatsheetOO at your side for reference.
Before attempting to use SimPy you should be familiar with the Python language. In particular you should be able to use classes. Python is free and available for most machine types. You can find out more about it at the Python web site. SimPy is compatible with Python version 2.3 and later.
A single Customer¶
In this tutorial we model a simple bank with customers arriving at
random. We develop the model step-by-step, starting out simply, and
producing a running program at each stage. The programs we develop are
available without line numbers and ready to go, in the
bankprograms_OO
directory. Please copy them, run them and improve
them - and in the tradition of open-source software suggest your
modifications to the SimPy users list. Object-orented versions of all
the models are included in the same directory.
A simulation should always be developed to answer a specific question; in these models we investigate how changing the number of bank servers or tellers might affect the waiting time for customers.
A Customer arriving at a fixed time¶
We first model a single customer who arrives at the bank for a visit, looks around at the decor for a time and then leaves. There is no queueing. First we will assume his arrival time and the time he spends in the bank are fixed.
Examine the following listing which is a complete runnable Python
script, except for the line numbers. We use comments to divide the
script up into sections. This makes for clarity later when the
programs get more complicated. Line 1 is a normal Python
documentation string; line 2 makes available the SimPy constructs
needed for this model: the Simulation
class, the Process
class,
and the hold
verb.
We define a Customer
class derived from the SimPy Process
class. We create a Customer
object, c
who arrives at the bank
at simulation time 5.0
and leaves after a fixed time of 10.0
minutes. The Customer
class definition, lines 5-12, defines our
customer class and has the required generator method (called
visit
) (line 9) having a yield
statement (line
11)). Such a method is called a Process Execution Method (PEM) in
SimPy.
The customer’s visit
PEM, lines 9-12, models his
activities. When he arrives (it will turn out to be a ‘he’ in this
model), he will print out the simulation time, self.sim.now()
,
and his name (line 10). self.sim
is a reference to the BankModel
simulation object where this customer exists. Every Process
instance
is linked to the simulation in which it is created by assigning to
its sim
parameter when it is created (see line 19).
The method now()
can be used at any
time in the simulation to find the current simulation time though it cannot be
changed by the programmer. The customer’s name will be set when the
customer is created later in the script (line 19).
He then stays in the bank for a fixed simulation time timeInBank
(line 11). This is achieved by the yield hold,self,timeInBank
statement.
This is the first of the special simulation commands that SimPy
offers.
After a simulation time of timeInBank
, the program’s execution
returns to the line after the yield
statement, line 12. The
customer then prints out the current simulation time and his
name. This completes the declaration of the Customer
class.
Though we do not do it here, it is also possible to define an
__init__()
method for a Process
if you need to give the
customer any attributes. Bear in mind that such an __init__
method must first call Process.__init__(self)
and can then
initialize any instance variables needed.
Lines 6 to 21 define a class BankModel
, composing a model of a bank from
the Simulation
class, a Customer
class and the global experiment data.
The definition class BankModel(Simulation)
gives an instance of a
BankModel
all the attributes of class Simulation
. (In OO terms,
BankModel
inherits from Simulation
.) Any instance of BankModel
is a Simulation
instance. This gives a BankModel
its own event list
and thus its own time axis. Also, it allows a BankModel
instance to
activate processes and to start the execution of a simulation on its time axis.
Lines 17 to 21 define a run
method; when called, it results in the
execution of a BankModel
instance, i.e. the performance of a
simulation experiment. Line 18 initializes this simulation, i.e. it
creates a new event list. L.19 creates a Customer
object. The
parameter assignment sim = self
ties the customer instance to this
and only this simulation. The customer does not exist outside this
simulation. L.20 activates the customer’s visit
process (PEM).
Finally the call of simulate(until=maxTime)
in line 24 starts the
simulation. It will run until the simulation time is maxTime
unless stopped beforehand either by the stopSimulation()
command
or by running out of events to execute (as will happen
here). maxTime
was set to 100.0
in line 25.
Note
If model classes like the``BankModel`` are to be given any other
attributes, they must have an __init__
method in which these
attributes are assigned with the syntax self.attrib1 =
. . .
. Such an __init__
method must first call
Simulation.__init__(self)
to also initialize the
Simulation
class from which the model inherits.
The simulation model is executed by line 32. BankModel()
constructs the
model, and .run()
executes it. This is just a short form of:
bM = BankModel()
bM.run()
""" bank01_OO: The single non-random Customer """
from SimPy.Simulation import Simulation, Process, hold # 1
# Model components -----------------------------
class Customer(Process): # 2
""" Customer arrives, looks around and leaves """
def visit(self, timeInBank):
print("%2.1f %s Here I am" %
(self.sim.now(), self.name))
yield hold, self, timeInBank
print("%2.1f %s I must leave" %
(self.sim.now(), self.name))
# Model ----------------------------------------
class BankModel(Simulation): # 3
def run(self):
""" An independent simulation object """
c = Customer(name="Klaus", sim=self) # 4
self.activate(c, c.visit(timeInBank), at=tArrival)
self.simulate(until=maxTime) # 5
# Experiment data ------------------------------
maxTime = 100.0 # minutes #6
timeInBank = 10.0 # minutes
tArrival = 5.0 # minutes
# Experiment -----------------------------------
mymodel = BankModel() # 7
mymodel.run() # 8
The short trace printed out by the print
statements shows the
result. The program finishes at simulation time 15.0
because there are
no further events to be executed. At the end of the visit
routine,
the customer has no more actions and no other objects or customers are
active.
5.0 Klaus Here I am
15.0 Klaus I must leave
A Customer arriving at random¶
Now we extend the model to allow our customer to arrive at a random simulated time though we will keep the time in the bank at 10.0, as before.
The change occurs in line 3 of the program and in lines 19, 21,
23, 31 and 35. In line 3 we import from the standard
Python random
module to give us expovariate
to generate the
random time of arrival. We also import the seed
function to
initialize the random number stream to allow control of the random
numbers. The run
method is given a parameter aseed
for the
initial seed (line 19) .In line 31 we provide an initial seed of
99999
. An exponential random variate, t
, is generated in line 23. Note
that the Python Random module’s expovariate
function uses the rate
(here, 1.0/tMeanArrival
) as the argument. The generated random variate,
t
, is used in line 24 as the at
argument to the
activate
call. tMeanArrival
is assigned a value of 5.0
minutes
at line 31.
In line 35, the BankModel
entity is generated and its run
function
called with parameter assignment aseed=seedVal
.
""" bank05_OO: The single Random Customer """
from SimPy.Simulation import Simulation, Process, hold
from random import expovariate, seed
# Model components ------------------------
class Customer(Process):
""" Customer arrives at a random time,
looks around and then leaves """
def visit(self, timeInBank):
print("%f %s Here I am" % (self.sim.now(), self.name))
yield hold, self, timeInBank
print("%f %s I must leave" % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self, aseed):
""" PEM """
seed(aseed)
c = Customer(name="Klaus", sim=self)
t = expovariate(1.0 / tMeanArrival)
self.activate(c, c.visit(timeInBank), at=t)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxTime = 100.0 # minutes
timeInBank = 10.0 # minutes
tMeanArrival = 5.0 # minutes
seedVal = 99999
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run(aseed=seedVal)
The result is shown below. The customer now arrives at time 10.5809. Changing the seed value would change that time.
0.641954 Klaus Here I am
10.641954 Klaus I must leave
The display looks pretty untidy. In the next example I will try and make it tidier.
More Customers¶
Our simulation does little so far. To consider a simulation with
several customers we return to the simple deterministic model and add
more Customers
.
The program is almost as easy as the first example (A Customer
arriving at a fixed time). The main change is in lines
19-24 where we create, name, and activate three
customers. We also increase the maximum simulation time to 400
(line 29 and referred to in line 25). Observe that we need
only one definition of the Customer
class and create several
objects of that class. These will act quite independently in this
model.
Each customer stays for a different timeInBank
so, instead of
setting a common value for this we set it for each customer. The
customers are started at different times (using at=
). Tony's
activation time occurs before Klaus's
, so Tony
will arrive
first even though his activation statement appears later in the
script.
As promised, the print statements have been changed to use Python string formatting (lines 10 and 12). The statements look complicated but the output is much nicer.
""" bank02_OO: More Customers """
from SimPy.Simulation import Simulation, Process, hold
# Model components ------------------------
class Customer(Process):
""" Customer arrives, looks around and leaves """
def visit(self, timeInBank=0):
print("%7.4f %s: Here I am" % (self.sim.now(), self.name))
yield hold, self, timeInBank
print("%7.4f %s: I must leave" % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self):
""" PEM """
c1 = Customer(name="Klaus", sim=self)
self.activate(c1, c1.visit(timeInBank=10.0), at=5.0)
c2 = Customer(name="Tony", sim=self)
self.activate(c2, c2.visit(timeInBank=7.0), at=2.0)
c3 = Customer(name="Evelyn", sim=self)
self.activate(c3, c3.visit(timeInBank=20.0), at=12.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxTime = 400.0 # minutes
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run()
The trace produced by the program is shown below. Again the
simulation finishes before the 400.0
specified in the simulate
call.
2.0000 Tony: Here I am
5.0000 Klaus: Here I am
9.0000 Tony: I must leave
12.0000 Evelyn: Here I am
15.0000 Klaus: I must leave
32.0000 Evelyn: I must leave
Many Customers¶
Another change will allow us to have more customers. As it is
tedious to give a specially chosen name to each one, we will
call them Customer00, Customer01,...
and use a separate
Source
class to create and activate them. To make things clearer
we do not use the random numbers in this model.
The following listing shows the new program. Lines 6-13
define a Source
class. Its PEM, here called generate
, is
defined in lines 9-13. This PEM has a couple of arguments:
the number
of customers to be generated and the Time Between
Arrivals, TBA
. It consists of a loop that creates a stream
of numbered Customers
from 0
to (number-1)
, inclusive. We
create a customer and give it a name in line 11. The parameter
assignment sim = self.sim
ties the customers to the BankModel
to which the Source
belongs. The customer is
then activated at the current simulation time (the final argument of
the activate
statement is missing so that the default value of
self.sim.now()
, the current simulation time for the instance of
BankModel
, is used as the time; here, it is 0.0
). We also specify
how long the customer
is to stay in the bank. To keep it simple, all customers stay
exactly 12
minutes. After each new customer is activated, the
Source
holds for a fixed time (yield hold,self,TBA
)
before creating the next one (line 13).
class BankModel(Simulation)
(line 24) provides a run
method
which executes this model consisting of a customer source and the global data.
As BankModel
inherits from Simulation
, it has its own event list which gets
initialized as empty in line 26.
A Source
, s
, is created in line 27 and activated at line
28 where the number of customers to be generated is set to
maxNumber = 5
and the interval between customers to ARRint = 10.0
.
The parameter assignment sim = self
links the Source
process
to this BankModel
instance. Once started at time 0.0
, s
creates
customers at intervals and each customer then operates independently of the others.
In line 40, a BankModel
object is created and its run
method executed:
""" bank03_OO: Many non-random Customers """
from SimPy.Simulation import Simulation, Process, hold
# Model components ------------------------
class Source(Process):
""" Source generates customers regularly """
def generate(self, number, TBA):
for i in range(number):
c = Customer(name="Customer%02d" % (i), sim=self.sim)
self.sim.activate(c, c.visit(timeInBank=12.0))
yield hold, self, TBA
class Customer(Process):
""" Customer arrives, looks around and leaves """
def visit(self, timeInBank):
print("%7.4f %s: Here I am" % (self.sim.now(), self.name))
yield hold, self, timeInBank
print("%7.4f %s: I must leave" % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self):
""" PEM """
s = Source(sim=self)
self.activate(s, s.generate(number=maxNumber,
TBA=ARRint), at=0.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
ARRint = 10.0 # time between arrivals, minutes
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run()
The output is:
0.0000 Customer00: Here I am
10.0000 Customer01: Here I am
12.0000 Customer00: I must leave
20.0000 Customer02: Here I am
22.0000 Customer01: I must leave
30.0000 Customer03: Here I am
32.0000 Customer02: I must leave
40.0000 Customer04: Here I am
42.0000 Customer03: I must leave
52.0000 Customer04: I must leave
Many Random Customers¶
We now extend this model to allow arrivals at random. In simulation this
is usually interpreted as meaning that the times between customer
arrivals are distributed as exponential random variates. There is
little change in our program, we use a Source
object, as before.
The exponential random variate is generated in line 14 with
meanTBA
as the mean Time Between Arrivals and used in line
15. Note that this parameter is not exactly intuitive. As already
mentioned, the Python expovariate
method uses the rate of
arrivals as the parameter not the average interval between them. The
exponential delay between two arrivals gives pseudo-random
arrivals. In this model the first customer arrives at time 0.0
.
The seed
method is called to initialize the random number stream
in the run
routine of BankModel
(line 30). It uses the value
provided by parameter aseed
. It is possible to leave this
call out but if we wish to do serious comparisons of systems, we must
have control over the random variates and therefore control over the
seeds. Then we can run identical models with different seeds or
different models with identical seeds. We provide the seeds as
control parameters of the run. Here a seed is assigned in line 41
but it is clear it could have been read in or manually entered on an
input form.
The BankModel
is generated in line 45 and its run
method called with
the seed value as parameter.
""" bank06: Many Random Customers """
from SimPy.Simulation import Simulation, Process, hold
from random import expovariate, seed
# Model components ------------------------
class Source(Process):
""" Source generates customers at random """
def generate(self, number, meanTBA):
for i in range(number):
c = Customer(name="Customer%02d" % (i), sim=self.sim)
self.sim.activate(c, c.visit(timeInBank=12.0))
t = expovariate(1.0 / meanTBA)
yield hold, self, t
class Customer(Process):
""" Customer arrives, looks round and leaves """
def visit(self, timeInBank=0):
print("%7.4f %s: Here I am" % (self.sim.now(), self.name))
yield hold, self, timeInBank
print("%7.4f %s: I must leave" % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self, aseed):
""" PEM """
seed(aseed)
s = Source(name='Source', sim=self)
self.activate(s, s.generate(number=maxNumber,
meanTBA=ARRint), at=0.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
ARRint = 10.0 # mean arrival interval, minutes
seedVal = 99999
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run(aseed=seedVal)
This generates the following output:
0.0000 Customer00: Here I am
1.2839 Customer01: Here I am
4.9842 Customer02: Here I am
12.0000 Customer00: I must leave
13.2839 Customer01: I must leave
16.9842 Customer02: I must leave
35.5432 Customer03: Here I am
47.5432 Customer03: I must leave
48.9918 Customer04: Here I am
60.9918 Customer04: I must leave
A Service counter¶
So far, the model bank has been more like an art gallery, the customers
entering, looking around, and leaving. Now they are going to require
service from the bank clerk. We extend the model to include a service
counter which will be modelled as an object of SimPy’s Resource
class with a single resource unit. The actions of a Resource
are
simple: a customer requests
a unit of the resource (a clerk). If
one is free he gets service (and removes the unit, i.e., makes it busy).
If there is no
free clerk the customer joins the queue (managed by the resource
object) until it is his turn to be served. As each customer
completes service and releases
the unit, the clerk automatically
starts serving the next in line. This is done by reactivating that customer’s
process where it had been blocked.
One Service counter¶
As this model is built with the Resource
class from SimPy.Simulation
,
it and the related request
and release
verbs are mported, in addition
to the imports made in the previous programs
(line 2).
The service counter is created as a Resource
attribute self.k
of the BankModel
(line 39). The resource exists in the BankModel
,
and this is indicated by the parameter assignment sim = self
.
The Source
PEM generate
can access this attribute by
self.sim.k
, its BankModel
’s resource attribute (line 14).
The actions involving the Counter
referred to by the parameter
res
in the customer’s PEM are:
- the
yield request
statement in line 25. If the server is free then the customer can start service immediately and the code moves on to line 26. If the server is busy, the customer is automatically queued by the Resource. When it eventually comes available the PEM moves on to line 26. - the
yield hold
statement in line 28 where the operation of the service counter is modelled. Here the service time is a fixedtimeInBank
. During this period the customer is being served and the resource (the counter) is busy. - the
yield release
statement in line 29. The current customer completes service and the service counter becomes available for any remaining customers in the queue.
Observe that the service counter is used with the pattern (yield
request..
; yield hold..
; yield release..
).
To show the effect of the service counter on the activities of the
customers, I have added line 22 to record when the customer
arrived and line 26 to record the time between arrival in the
bank and starting service. Line 26 is after the yield
request
command and will be reached only when the request is
satisfied. It is before the yield hold
that corresponds to the
start of service. The variable wait
will record how long the
customer waited and will be 0 if he received service at once. This
technique of saving the arrival time in a variable is common. So the
print
statement also prints out how long the customer waited in
the bank before starting service.
""" bank07_OO: One Counter,random arrivals """
from SimPy.Simulation import (Simulation, Process, hold, Resource, request,
release)
from random import expovariate, seed
# Model components ------------------------
class Source(Process):
""" Source generates customers randomly """
def generate(self, number, meanTBA):
for i in range(number):
c = Customer(name="Customer%02d" % (i), sim=self.sim)
self.sim.activate(c, c.visit(timeInBank=12.0,
res=self.sim.k))
t = expovariate(1.0 / meanTBA)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, timeInBank=0, res=None):
arrive = self.sim.now() # arrival time
print("%8.3f %s: Here I am" % (self.sim.now(), self.name))
yield request, self, res
wait = self.sim.now() - arrive # waiting time
print("%8.3f %s: Waited %6.3f" % (self.sim.now(), self.name, wait))
yield hold, self, timeInBank
yield release, self, res
print("%8.3f %s: Finished" % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self, aseed):
""" PEM """
seed(aseed)
self.k = Resource(name="Counter", unitName="Clerk", sim=self)
s = Source('Source', sim=self)
self.activate(s, s.generate(number=maxNumber, meanTBA=ARRint), at=0.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
ARRint = 10.0 # mean, minutes
seedVal = 99999
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run(aseed=seedVal)
Examining the trace we see that the first two customers get instant service but the others have to wait. We still only have five customers (line 44) so we cannot draw general conclusions.
0.000 Customer00: Here I am
0.000 Customer00: Waited 0.000
1.284 Customer01: Here I am
4.984 Customer02: Here I am
12.000 Customer00: Finished
12.000 Customer01: Waited 10.716
24.000 Customer01: Finished
24.000 Customer02: Waited 19.016
35.543 Customer03: Here I am
36.000 Customer02: Finished
36.000 Customer03: Waited 0.457
48.000 Customer03: Finished
48.992 Customer04: Here I am
48.992 Customer04: Waited 0.000
60.992 Customer04: Finished
A server with a random service time¶
This is a simple change to the model in that we retain the single
service counter but make the customer service time a random variable. As
is traditional in the study of simple queues we first assume an exponential service
time and set the mean to timeInBank
.
The service time random variable, tib
, is generated in line
26 and used in line 27. The argument to be used in the call
of expovariate
is not the mean of the distribution,
timeInBank
, but is the rate 1.0/timeInBank
.
We have put together the exeriment data by defining a number of appropriate variables and giving them values. These are in lines 44 to 48.
""" bank08_OO: A counter with a random service time """
from SimPy.Simulation import (Simulation, Process, Resource, hold, request,
release)
from random import expovariate, seed
# Model components ------------------------
class Source(Process):
""" Source generates customers randomly """
def generate(self, number, meanTBA):
for i in range(number):
c = Customer(name="Customer%02d" % (i), sim=self.sim)
self.sim.activate(c, c.visit(b=self.sim.k))
t = expovariate(1.0 / meanTBA)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b):
arrive = self.sim.now()
print("%8.4f %s: Here I am " % (self.sim.now(), self.name))
yield request, self, b
wait = self.sim.now() - arrive
print("%8.4f %s: Waited %6.3f" % (self.sim.now(), self.name, wait))
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, b
print("%8.4f %s: Finished " % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self, aseed):
""" PEM """
seed(aseed)
self.k = Resource(name="Counter", unitName="Clerk", sim=self)
s = Source('Source', sim=self)
self.activate(s, s.generate(number=maxNumber, meanTBA=ARRint), at=0.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
seedVal = 99999
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run(aseed=seedVal)
And the output:
0.0000 Customer00: Here I am
0.0000 Customer00: Waited 0.000
1.2839 Customer01: Here I am
4.4403 Customer00: Finished
4.4403 Customer01: Waited 3.156
20.5786 Customer01: Finished
31.8430 Customer02: Here I am
31.8430 Customer02: Waited 0.000
34.5594 Customer02: Finished
36.2308 Customer03: Here I am
36.2308 Customer03: Waited 0.000
41.4313 Customer04: Here I am
67.1315 Customer03: Finished
67.1315 Customer04: Waited 25.700
87.9241 Customer04: Finished
This model with random arrivals and exponential service times is an example of an M/M/1 queue and could rather easily be solved analytically to calculate the steady-state mean waiting time and other operating characteristics. (But not so easily solved for its transient behavior.)
Several Service Counters¶
When we introduce several counters we must decide on a queue discipline. Are customers going to make one queue or are they going to form separate queues in front of each counter? Then there are complications - will they be allowed to switch lines (jockey)? We first consider a single queue with several counters and later consider separate isolated queues. We will not look at jockeying.
Several Counters but a Single Queue¶
Here we model a bank whose customers arrive randomly and are to be served at a group of counters, taking a random time for service, where we assume that waiting customers form a single first-in first-out queue.
The only difference between this model and the single-server model
is in line 37. We have provided two counters by increasing the
capacity of the counter
resource to 2. This value is set in line 50
(Nc = 2
). These units of the
resource correspond to the two counters. Because both clerks cannot be
called Karen
, we have used a general name of Clerk
as resource
unit.
""" bank09_OO: Several Counters but a Single Queue """
from SimPy.Simulation import (Simulation, Process, Resource, hold, request,
release)
from random import expovariate, seed
# Model components ------------------------
class Source(Process):
""" Source generates customers randomly """
def generate(self, number, meanTBA):
for i in range(number):
c = Customer(name="Customer%02d" % (i), sim=self.sim)
self.sim.activate(c, c.visit(b=self.sim.k))
t = expovariate(1.0 / meanTBA)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b):
arrive = self.sim.now()
print("%8.4f %s: Here I am " % (self.sim.now(), self.name))
yield request, self, b
wait = self.sim.now() - arrive
print("%8.4f %s: Waited %6.3f" % (self.sim.now(), self.name, wait))
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, b
print("%8.4f %s: Finished " % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self, aseed):
""" PEM """
seed(aseed)
self.k = Resource(capacity=Nc, name="Counter", unitName="Clerk",
sim=self)
s = Source('Source', sim=self)
self.activate(s, s.generate(number=maxNumber, meanTBA=ARRint), at=0.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxNumber = 5 # of customers
maxTime = 400.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
Nc = 2 # of clerks/counters
seedVal = 99999
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run(aseed=seedVal)
The waiting times in this model are much shorter than those for the
single service counter. For example, the waiting time for
Customer02
has been reduced from 51.213
to 12.581
minutes. Again we have too few customers processed to draw general
conclusions.
0.0000 Customer00: Here I am
0.0000 Customer00: Waited 0.000
1.2839 Customer01: Here I am
1.2839 Customer01: Waited 0.000
4.4403 Customer00: Finished
17.4222 Customer01: Finished
31.8430 Customer02: Here I am
31.8430 Customer02: Waited 0.000
34.5594 Customer02: Finished
36.2308 Customer03: Here I am
36.2308 Customer03: Waited 0.000
41.4313 Customer04: Here I am
41.4313 Customer04: Waited 0.000
62.2239 Customer04: Finished
67.1315 Customer03: Finished
Several Counters with individual queues¶
Each counter is now assumed to have its own queue. The programming is more complicated because the customer has to decide which queue to join. The obvious technique is to make each counter a separate resource and it is useful to make a list of resource objects (line 56).
In practice, a customer will join the shortest queue. So we define
the Python function, NoInSystem(R)
(lines 17-19) which
returns the sum of the number waiting and the number being served for
a particular counter, R
. This function is used in line 28 to
list the numbers at each counter. It is then easy to find which
counter the arriving customer should join. We have also modified the
trace printout, line 29 to display the state of the system when
the customer arrives. We choose the shortest queue in lines
30-33 (the variable choice
).
The rest of the program is the same as before.
""" bank10_OO: Several Counters with individual queues"""
from SimPy.Simulation import (Simulation, Process, Resource, hold, request,
release)
from random import expovariate, seed
# Model components ------------------------
class Source(Process):
""" Source generates customers randomly"""
def generate(self, number, interval):
for i in range(number):
c = Customer(name="Customer%02d" % (i,), sim=self.sim)
self.sim.activate(c, c.visit(counters=self.sim.kk))
t = expovariate(1.0 / interval)
yield hold, self, t
def NoInSystem(R):
""" Total number of customers in the resource R"""
return (len(R.waitQ) + len(R.activeQ))
class Customer(Process):
""" Customer arrives, chooses the shortest queue
is served and leaves
"""
def visit(self, counters):
arrive = self.sim.now()
Qlength = [NoInSystem(counters[i]) for i in range(Nc)]
print("%7.4f %s: Here I am. %s" % (self.sim.now(), self.name, Qlength))
for i in range(Nc):
if Qlength[i] == 0 or Qlength[i] == min(Qlength):
choice = i # the chosen queue number
break
yield request, self, counters[choice]
wait = self.sim.now() - arrive
print("%7.4f %s: Waited %6.3f" % (self.sim.now(), self.name, wait))
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, counters[choice]
print("%7.4f %s: Finished" % (self.sim.now(), self.name))
# Model -----------------------------------
class BankModel(Simulation):
def run(self, aseed):
""" PEM """
seed(aseed)
self.kk = [Resource(name="Clerk0", sim=self),
Resource(name="Clerk1", sim=self)]
s = Source('Source', sim=self)
self.activate(s, s.generate(number=maxNumber, interval=ARRint), at=0.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
Nc = 2 # number of counters
seedVal = 787878
# Experiment ------------------------------
mymodel = BankModel()
mymodel.run(aseed=seedVal)
The results show how the customers choose the counter with the
smallest number. Unlucky Customer02
who joins the wrong queue has
to wait until Customer00
finishes at time 55.067
. There are,
however, too few arrivals in these runs, limited as they are to five
customers, to draw any general conclusions about the relative
efficiencies of the two systems.
0.0000 Customer00: Here I am. [0, 0]
0.0000 Customer00: Waited 0.000
9.7519 Customer00: Finished
12.0829 Customer01: Here I am. [0, 0]
12.0829 Customer01: Waited 0.000
25.9167 Customer02: Here I am. [1, 0]
25.9167 Customer02: Waited 0.000
38.2349 Customer03: Here I am. [1, 1]
40.4032 Customer04: Here I am. [2, 1]
43.0677 Customer02: Finished
43.0677 Customer04: Waited 2.664
44.0242 Customer01: Finished
44.0242 Customer03: Waited 5.789
60.1271 Customer03: Finished
70.2500 Customer04: Finished
Monitors and Gathering Statistics¶
The traces of output that have been displayed so far are valuable for checking that the simulation is operating correctly but would become too much if we simulate a whole day. We do need to get results from our simulation to answer the original questions. What, then, is the best way to summarize the results?
One way is to analyze the traces elsewhere, piping the trace output, or a modified version of it, into a real statistical program such as R for statistical analysis, or into a file for later examination by a spreadsheet. We do not have space to examine this thoroughly here. Another way of presenting the results is to provide graphical output.
SimPy offers an easy way to gather a few simple statistics such as
averages: the Monitor
and Tally
classes. The Monitor
records the values of chosen variables as time series.
(but see the comments in Final Remarks).
The Bank with a Monitor¶
We now demonstrate a Monitor
that records the average waiting
times for our customers. We return to the system with random arrivals,
random service times and a single queue and remove the old trace
statements. In practice, we would make the printouts controlled by a
variable, say, TRACE
which is set in the experimental data (or
read in as a program option - but that is a different story). This
would aid in debugging and would not complicate the data analysis. We
will run the simulations for many more arrivals.
In addition to the imports in the programs shown before, we now have
to import the Monitor
class (line 2).
A Monitor, wM
, is created in line 37. We make the monitor an
attribute of the BankModel
by the assignment to self.wM
.
The monitor observes
the
waiting time mentioned in line 25. As the monitor is an attribute
of the BankModel
to which the customer belongs,
self.sim.wM
can refere to it. We run
maxNumber = 50
customers (in the call of generate
in line
39) and have increased maxTime
to 1000.0
minutes.
""" bank11: The bank with a Monitor"""
from SimPy.Simulation import Simulation, Process, Resource, Monitor, hold,\
request, release
from random import expovariate, seed
# Model components ------------------------
class Source(Process):
""" Source generates customers randomly"""
def generate(self, number, interval):
for i in range(number):
c = Customer(name="Customer%02d" % (i), sim=self.sim)
self.sim.activate(c, c.visit(b=self.sim.k))
t = expovariate(1.0 / interval)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b):
arrive = self.sim.now()
yield request, self, b
wait = self.sim.now() - arrive
self.sim.wM.observe(wait)
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, b
# Model -----------------------------------
class BankModel(Simulation):
def run(self, aseed):
""" PEM """
seed(aseed)
self.k = Resource(capacity=Nc, name="Clerk", sim=self)
self.wM = Monitor(sim=self)
s = Source('Source', sim=self)
self.activate(s, s.generate(number=maxNumber, interval=ARRint), at=0.0)
self.simulate(until=maxTime)
# Experiment data -------------------------
maxNumber = 50
maxTime = 1000.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
Nc = 2 # number of counters
seedVal = 99999
# Experiment -----------------------------
experi = BankModel()
experi.run(aseed=seedVal)
# Result ----------------------------------
result = experi.wM.count(), experi.wM.mean()
print("Average wait for %3d completions was %5.3f minutes." % result)
In previous programs, we have generated the BankModel
anonymously. Here, we do it differently: we assign the BankModel
object to the variable experi
(line 53). This way,
we can reference its monitor attribute by experi.wM
(line 58).
The average waiting time for 50 customers in this 2-counter system is
more reliable (i.e., less subject to random simulation effects) than
the times we measured before but it is still not sufficiently reliable for
real-world decisions. We should also replicate the runs using different
random number seeds. The result of this run is:
Average wait for 50 completions was 8.941 minutes.
Multiple runs¶
This example demonstrates the power of the object-oriented approach. To get a number of independent measurements we must replicate the runs using different random number seeds. Each replication must be independent of previous ones both in the random numbers and in the data collection so capability of creating independent simulation models within one program is useful.
We do a standard from SimPy.Simulation import ...
at #1. We define
Source
and Customer
as subclasses of `Process
. These
differ in detail from the way they are defined in the classic
procedure-oriented version of SimPy. Each must refer to the simulation
environment it is running in, here the sim
argument. Thus the
current time is returned by the self.sim.now()
method (at #5
We define a BankModel
as a sub-class of Simulation
(at #8) and
create an object, mymodel
, of that class (at #14). A BankModel
object has a run
method and this is used for each independent
replication (at #16). Note that the BankModel
is only generated
once (line 54). This is sufficient, as the run
method freshly
generates an empty event list, a new counter resource, a new monitor,
and a new source. This way, all iterations are independent of each
other.
The random number seeds are stored in a list, seedVals
and the
for
loop walks through this list and executes mymodel
’s
run
method for each entry to get a set of replications.
""" bank12_OO: Multiple runs of the bank with a Monitor"""
from SimPy.Simulation import Simulation, Process, \
Resource, Monitor, hold, request, release # 1
from random import expovariate, seed
# Model components ------------------------
class Source(Process):
""" Source generates customers randomly"""
def generate(self, number, interval): # 2
for i in range(number):
c = Customer(name="Customer%02d" % (i),
sim=self.sim) # 3
self.sim.activate(c, c.visit(b=self.sim.k)) # 4
t = expovariate(1.0 / interval)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b):
arrive = self.sim.now() # 5
yield request, self, b
wait = self.sim.now() - arrive # 6
self.sim.wM.observe(wait)
tib = expovariate(1.0 / timeInBank) # 7
yield hold, self, tib
yield release, self, b
# Simulation Model ----------------------------------
class BankModel(Simulation): # 8
def run(self, aseed):
self.initialize() # 9
seed(aseed)
self.k = Resource(capacity=Nc, name="Clerk",
sim=self) # 10
self.wM = Monitor(sim=self) # 11
s = Source('Source', sim=self) # 12
self.activate(s, s.generate(number=maxNumber,
interval=ARRint), at=0.0)
self.simulate(until=maxTime) # 13
return (self.wM.count(), self.wM.mean())
# Experiment data -------------------------
maxNumber = 50
maxTime = 2000.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
Nc = 2 # number of counters
seedVals = [393939, 31555999, 777999555, 319999771]
# Experiment/Result ----------------------------------
mymodel = BankModel() # 14
for Sd in seedVals: # 15
mymodel.run(aseed=Sd) # 16
moni = mymodel.wM # 17
print("Avge wait for %3d completions was %6.2f min." %
(moni.count(), moni.mean()))
The results show some variation. Remember, though, that the system is still only operating for 50 customers so the system may not be in steady-state.
Avge wait for 50 completions was 3.66 min.
Avge wait for 50 completions was 2.62 min.
Avge wait for 50 completions was 8.97 min.
Avge wait for 50 completions was 5.34 min.
Final Remarks¶
This introduction is too long and the examples are getting longer. There is much more to say about simulation with SimPy but no space. I finish with a list of topics for further study:
- GUI input. Graphical input of simulation parameters could be an
advantage in some cases. SimPy allows this and programs using
these facilities have been developed (see, for example, program
MM1.py
in the examples in the SimPy distribution) - Graphical Output. Similarly, graphical output of results can also be of value, not least in debugging simulation programs and checking for steady-state conditions. SimPlot is useful here.
- Statistical Output. The
Monitor
class is useful in presenting results but more powerful methods of analysis are often needed. One solution is to output a trace and read that into a large-scale statistical system such as R. - Priorities and Reneging in queues. SimPy allows processes to request units of resources under a priority queue discipline (preemptive or not). It also allows processes to renege from a queue.
- Other forms of Resource Facilities. SimPy has two other
resource structures:
Levels
to hold bulk commodities, andStores
to contain an inventory of different object types. - Advanced synchronization/scheduling commands. SimPy allows process synchronization by events and signals.
Acknowledgements¶
I thank Klaus Muller, Bob Helmbold, Mukhlis Matti and other developers and users of SimPy for improving this document by sending their comments. I would be grateful for further suggestions or corrections. Please send them to: vignaux at users.sourceforge.net.
References¶
- Python website: https://www.python.org
- SimPy website: https://github.com/SimPyClassic/SimPyClassic