The Bank: Examples of SimPy Simulation¶
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. It is quite compatible with the current procedural approach which is used in the models described here.
SimPy can be obtained from: http://sourceforge.net/projects/simpy. The examples run with SimPy version 1.5 and later. This tutorial is best read with the SimPy Manual or Cheatsheet 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
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 bankprobrams_OO sub 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.
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.
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. At line 1 is a normal Python documentation string; 2 imports the SimPy simulation code.
The Customer
class definition at 3 defines our customer class and has
the required generator method (called visit
4) having a yield
statement 6. Such a method is called a Process Execution Method (PEM) in
SimPy.
The customer’s visit
PEM at 4, models his activities. When he
arrives (it will turn out to be a ‘he’ in this model), he will print out the
simulation time, now()
, and his name at 5. The function 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 at 10.
He then stays in the bank for a fixed simulation time timeInBank
6.
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 at 6. The
customer then prints out the current simulation time and his
name at 7. This completes the declaration of the Customer
class.
The call initialize()
at 9 sets up the simulation
system ready to receive activate
calls. At 10, we create
a customer, c
, with name Klaus
. All SimPy Processes have a
name
attribute. We activate
Klaus
at 11
specifying the object (c
) to be activated, the call of the action
routine (c.visit(timeInBank = 10.0)
) and that it is to be activated
at time 5 (at = 5.0
). This will activate
Klaus
exactly 5
minutes after the current time, in this case
after the start of the simulation at 0.0
. The call of an action
routine such as c.visit
can specify the values of arguments, here
the timeInBank
.
Finally the call of simulate(until=maxTime)
at 12 will
start the simulation. This 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
at 8.
""" bank01: The single non-random Customer """ # (1)
from SimPy.Simulation import * # (2)
## Model components -----------------------------
class Customer(Process): # (3)
""" Customer arrives, looks around and leaves """
def visit(self, timeInBank): # (4)
print("%2.1f %s Here I am" % (now(), self.name)) # (5)
yield hold, self, timeInBank # (6)
print("%2.1f %s I must leave" % (now(), self.name)) # (7)
## Experiment data ------------------------------
maxTime = 100.0 # minutes (8)
timeInBank = 10.0 # minutes
## Model/Experiment ------------------------------
initialize() # (9)
c = Customer(name="Klaus") # (10)
activate(c, c.visit(timeInBank), at=5.0) # (11)
simulate(until=maxTime) # (12)
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 1 of the program and in lines 2,
3, and 4. In line 1 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. In line 2 we provide an initial seed of 99999
. An
exponential random variate, t
, is generated in line 3. Note
that the Python Random module’s expovariate
function uses the
average rate (that is, 1.0/mean
) as the argument. The generated
random variate, t
, is used in line 4 as the at
argument
to the activate
call.
""" bank05: The single Random Customer """
from SimPy.Simulation import *
from random import expovariate, seed # (1)
## 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" % (now(), self.name))
yield hold, self, timeInBank
print("%f %s I must leave" % (now(), self.name))
## Experiment data -------------------------
maxTime = 100.0 # minutes
timeInBank = 10.0
## Model/Experiment ------------------------------
seed(99999) # (2)
initialize()
c = Customer(name="Klaus")
t = expovariate(1.0 / 5.0) # (3)
activate(c, c.visit(timeInBank), at=t) # (4)
simulate(until=maxTime)
The result is shown below. The customer now arrives at about 0.64195, (or 10.58092 if you are not using Python 3). 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.
If you are not using Python 3, you output may differ. The output for Python 2 is given in Appendix A.
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
4 to 5 where we create, name, and activate three
customers. We also increase the maximum simulation time to 400
(line 3 and referred to in line 6). 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 1 and 2). The statements look complicated but the output is much nicer.
""" bank02: More Customers """
from SimPy.Simulation import *
## Model components ------------------------
class Customer(Process):
""" Customer arrives, looks around and leaves """
def visit(self, timeInBank):
print("%7.4f %s: Here I am" % (now(), self.name)) # (1)
yield hold, self, timeInBank
print("%7.4f %s: I must leave" % (now(), self.name)) # (2)
## Experiment data -------------------------
maxTime = 400.0 # minutes # (3)
## Model/Experiment ------------------------------
initialize()
c1 = Customer(name="Klaus") # (4)
activate(c1, c1.visit(timeInBank=10.0), at=5.0)
c2 = Customer(name="Tony")
activate(c2, c2.visit(timeInBank=7.0), at=2.0)
c3 = Customer(name="Evelyn")
activate(c3, c3.visit(timeInBank=20.0), at=12.0) # (5)
simulate(until=maxTime) # (6)
The trace produced by the program is shown below. Again the
simulation finishes before the 400.0
specified in the simulate
call as it has run out of events.
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 1 to 4
define a Source
class. Its PEM, here called generate
, is
defined in lines 2 to 4. 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 sequence
of numbered Customers
from 0
to (number-1)
, inclusive. We
create a customer and give it a name in line 3. It is
then activated at the current simulation time (the final argument of
the activate
statement is missing so that the default value of
now()
is used as the time). 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 4).
A Source
, s
, is created in line 5 and activated at line
6 where the number of customers to be generated is set to
maxNumber = 5
and the interval between customers to ARRint =
10.0
. Once started at time 0.0
it creates customers at intervals
and each customer then operates independently of the others:
""" bank03: Many non-random Customers """
from SimPy.Simulation import *
## Model components ------------------------
class Source(Process): # (1)
""" Source generates customers regularly """
def generate(self, number, TBA): # (2)
for i in range(number):
c = Customer(name="Customer%02d" % (i)) # (3)
activate(c, c.visit(timeInBank=12.0))
yield hold, self, TBA # (4)
class Customer(Process):
""" Customer arrives, looks around and leaves """
def visit(self, timeInBank):
print("%7.4f %s: Here I am" % (now(), self.name))
yield hold, self, timeInBank
print("%7.4f %s: I must leave" % (now(), self.name))
## Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
ARRint = 10.0 # time between arrivals, minutes
## Model/Experiment ------------------------------
initialize()
s = Source() # (5)
activate(s, s.generate(number=maxNumber, # (6)
TBA=ARRint), at=0.0)
simulate(until=maxTime)
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 1 with
meanTBA
as the mean Time Between Arrivals and used in line
2. 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 model
routine (line 3). 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 3
but it is clear it could have been read in or manually entered on an
input form.
""" bank06: Many Random Customers """
from SimPy.Simulation import *
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))
activate(c, c.visit(timeInBank=12.0))
t = expovariate(1.0 / meanTBA) # (1)
yield hold, self, t # (2)
class Customer(Process):
""" Customer arrives, looks around and leaves """
def visit(self, timeInBank=0):
print("%7.4f %s: Here I am" % (now(), self.name))
yield hold, self, timeInBank
print("%7.4f %s: I must leave" % (now(), self.name))
## Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
ARRint = 10.0 # mean arrival interval, minutes
## Model/Experiment ------------------------------
seed(99999) # (3)
initialize()
s = Source(name='Source')
activate(s, s.generate(number=maxNumber,
meanTBA=ARRint), at=0.0)
simulate(until=maxTime)
with 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 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). If there is no
free clerk the customer joins the queue (managed by the resource
object) until it is their turn to be served. As each customer
completes service and releases
the unit, the clerk can start
serving the next in line.
One Service counter¶
The service counter is created as a Resource
(k
) in
line 8. This is provided as an argument to the Source
(line 9)
which, in turn, provides it to each customer it creates and activates
(line 1).
The actions involving the service counter, k
, in the customer’s
PEM are:
- the
yield request
statement in line 3. If the server is free then the customer can start service immediately and the code moves on to line 4. If the server is busy, the customer is automatically queued by the Resource. When it eventually comes available the PEM moves on to line 4. - the
yield hold
statement in line 5 where the operation of the service counter is modelled. Here the service time is a fixedtimeInBank
. During this period the customer is being served. - the
yield release
statement in line 6. 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 2 to record when the customer
arrived and line 4 to record the time between arrival in the
bank and starting service. Line 4 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: One Counter,random arrivals """
from SimPy.Simulation import *
from random import expovariate, seed
## Model components ------------------------
class Source(Process):
""" Source generates customers randomly """
def generate(self, number, meanTBA, resource):
for i in range(number):
c = Customer(name="Customer%02d" % (i))
activate(c, c.visit(timeInBank=12.0,
res=resource)) # (1)
t = expovariate(1.0 / meanTBA)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, timeInBank, res):
arrive = now() # (2) arrival time
print("%8.3f %s: Here I am" % (now(), self.name))
yield request, self, res # (3)
wait = now() - arrive # (4) waiting time
print("%8.3f %s: Waited %6.3f" % (now(), self.name, wait))
yield hold, self, timeInBank # (5)
yield release, self, res # (6)
print("%8.3f %s: Finished" % (now(), self.name))
## Experiment data -------------------------
maxNumber = 5 # (7)
maxTime = 400.0 # minutes
ARRint = 10.0 # mean, minutes
k = Resource(name="Counter", unitName="Clerk") # (8)
## Model/Experiment ------------------------------
seed(99999)
initialize()
s = Source('Source')
activate(s, s.generate(number=maxNumber,
meanTBA=ARRint, resource=k), at=0.0) # (9)
simulate(until=maxTime)
Examining the trace we see that the first, and last, customers get instant service but the others have to wait. We still only have five customers (line 4) 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
1 and used in line 2. The argument to be used in the call
of expovariate
is not the mean of the distribution,
timeInBank
, but is the rate 1/timeInBank
.
We have also collected together a number of constants by defining a number of appropriate variables and giving them values. These are in lines 3 to 4.
""" bank08: A counter with a random service time """
from SimPy.Simulation import *
from random import expovariate, seed
## Model components ------------------------
class Source(Process):
""" Source generates customers randomly """
def generate(self, number, meanTBA, resource):
for i in range(number):
c = Customer(name="Customer%02d" % (i,))
activate(c, c.visit(b=resource))
t = expovariate(1.0 / meanTBA)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b):
arrive = now()
print("%8.4f %s: Here I am " % (now(), self.name))
yield request, self, b
wait = now() - arrive
print("%8.4f %s: Waited %6.3f" % (now(), self.name, wait))
tib = expovariate(1.0 / timeInBank) # (1)
yield hold, self, tib # (2)
yield release, self, b
print("%8.4f %s: Finished " % (now(), self.name))
## Experiment data -------------------------
maxNumber = 5 # (3)
maxTime = 400.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
theseed = 99999 # (4)
## Model/Experiment ------------------------------
seed(theseed)
k = Resource(name="Counter", unitName="Clerk")
initialize()
s = Source('Source')
activate(s, s.generate(number=maxNumber, meanTBA=ARRint,
resource=k), at=0.0)
simulate(until=maxTime)
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 1. We have provided two counters by increasing the
capacity of the counter
resource to 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
.
""" bank09: Several Counters but a Single Queue """
from SimPy.Simulation import *
from random import expovariate, seed
## Model components ------------------------
class Source(Process):
""" Source generates customers randomly """
def generate(self, number, meanTBA, resource):
for i in range(number):
c = Customer(name="Customer%02d" % (i))
activate(c, c.visit(b=resource))
t = expovariate(1.0 / meanTBA)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b):
arrive = now()
print("%8.4f %s: Here I am " % (now(), self.name))
yield request, self, b
wait = now() - arrive
print("%8.4f %s: Waited %6.3f" % (now(), self.name, wait))
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, b
print("%8.4f %s: Finished " % (now(), self.name))
## Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
theseed = 99999
## Model/Experiment ------------------------------
seed(theseed)
k = Resource(capacity=2, name="Counter", unitName="Clerk") # (1)
initialize()
s = Source('Source')
activate(s, s.generate(number=maxNumber, meanTBA=ARRint,
resource=k), at=0.0)
simulate(until=maxTime)
The waiting times in this model are very different from those for the single service counter. For example, none of the customers had to wait. But, again, we have observed too few customers 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 now has its own queue. The programming is more complicated because the customer has to decide which one 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 7).
In practice, a customer will join the shortest queue. So we define
a Python function, NoInSystem(R)
(lines 1 to 2) to
return the sum of the number waiting and the number being served for
a particular counter, R
. This function is used in line 3 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 4 to display the state of the system when
the customer arrives. We choose the shortest queue in lines
5 to 6 (using the variable choice
).
The rest of the program is the same as before.
""" bank10: Several Counters with individual queues"""
from SimPy.Simulation import *
from random import expovariate, seed
## Model components ------------------------
class Source(Process):
""" Source generates customers randomly"""
def generate(self, number, interval, counters):
for i in range(number):
c = Customer(name="Customer%02d" % (i))
activate(c, c.visit(counters))
t = expovariate(1.0 / interval)
yield hold, self, t
def NoInSystem(R): # (1)
""" Total number of customers in the resource R"""
return (len(R.waitQ) + len(R.activeQ)) # (2)
class Customer(Process):
""" Customer arrives, chooses the shortest queue
is served and leaves
"""
def visit(self, counters):
arrive = now()
Qlength = [NoInSystem(counters[i]) for i in range(Nc)] # (3)
print("%7.4f %s: Here I am. %s" % (now(), self.name, Qlength)) # (4)
for i in range(Nc): # (5)
if Qlength[i] == 0 or Qlength[i] == min(Qlength):
choice = i # the index of the shortest line
break # (6)
yield request, self, counters[choice]
wait = now() - arrive
print("%7.4f %s: Waited %6.3f" % (now(), self.name, wait))
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, counters[choice]
print("%7.4f %s: Finished" % (now(), self.name))
## Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
Nc = 2 # number of counters
theseed = 787878
## Model/Experiment ------------------------------
seed(theseed)
kk = [Resource(name="Clerk0"), Resource(name="Clerk1")] # (7)
initialize()
s = Source('Source')
activate(s, s.generate(number=maxNumber, interval=ARRint,
counters=kk), at=0.0)
simulate(until=maxTime)
The results show how the customers choose the counter with the
smallest number. Unlucky Customer03
who joins the wrong queue has
to wait until Customer01
finishes before his service can be
started. 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.
A Monitor, wM
, is created in line 2. It observes
and
records the waiting time mentioned in line 1. We run
maxNumber=50
customers (in the call of generate
in line
3) and have increased maxTime
to 1000
minutes. Brief
statistics are given by the Monitor methods count()
and mean()
in line 4.
""" bank11: The bank with a Monitor"""
from SimPy.Simulation import *
from random import expovariate, seed
## Model components ------------------------
class Source(Process):
""" Source generates customers randomly"""
def generate(self, number, interval, resource):
for i in range(number):
c = Customer(name="Customer%02d" % (i))
activate(c, c.visit(b=resource))
t = expovariate(1.0 / interval)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b):
arrive = now()
yield request, self, b
wait = now() - arrive
wM.observe(wait) # (1)
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, b
## Experiment data -------------------------
maxNumber = 50
maxTime = 1000.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
Nc = 2 # number of counters
theseed = 99999
## Model/Experiment ----------------------
seed(theseed)
k = Resource(capacity=Nc, name="Clerk")
wM = Monitor() # (2)
initialize()
s = Source('Source')
activate(s, s.generate(number=maxNumber, interval=ARRint,
resource=k), at=0.0) # (3)
simulate(until=maxTime)
## Result ----------------------------------
result = wM.count(), wM.mean() # (4)
print("Average wait for %3d completions was %5.3f minutes." % result)
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 (using Python 3.2) is:
Average wait for 50 completions was 8.941 minutes.
Result for Python 2.x is given in Appendix A.
Multiple runs¶
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 so the Monitor and Resources must be redefined for each run. We can no longer allow them to be global objects as we have before.
We will define a function, model
with a parameter runSeed
so
that the random number seed can be different for different runs (lines
2 to 5). The contents of the function are the same as the
Model/Experiment
section in the previous program except for one
vital change.
This is required since the Monitor, wM
, is defined inside the
model
function (line 3). A customer can no longer refer to
it. In the spirit of quality computer programming we will pass wM
as a function argument. Unfortunately we have to do this in two steps,
first to the Source
(line 4) and then from the Source
to
the Customer
(line 1).
model()
is run for four different random-number seeds to get a set
of replications (lines 6 to 7).
""" bank12: Multiple runs of the bank with a Monitor"""
from SimPy.Simulation import *
from random import expovariate, seed
## Model components ------------------------
class Source(Process):
""" Source generates customers randomly"""
def generate(self, number, interval, resource, mon):
for i in range(number):
c = Customer(name="Customer%02d" % (i))
activate(c, c.visit(b=resource, M=mon)) # (1)
t = expovariate(1.0 / interval)
yield hold, self, t
class Customer(Process):
""" Customer arrives, is served and leaves """
def visit(self, b, M):
arrive = now()
yield request, self, b
wait = now() - arrive
M.observe(wait)
tib = expovariate(1.0 / timeInBank)
yield hold, self, tib
yield release, self, b
## Experiment data -------------------------
maxNumber = 50
maxTime = 2000.0 # minutes
timeInBank = 12.0 # mean, minutes
ARRint = 10.0 # mean, minutes
Nc = 2 # number of counters
theSeed = 393939
## Model ----------------------------------
def model(runSeed=theSeed): # (2)
seed(runSeed)
k = Resource(capacity=Nc, name="Clerk")
wM = Monitor() # (3)
initialize()
s = Source('Source')
activate(s, s.generate(number=maxNumber, interval=ARRint,
resource=k, mon=wM), at=0.0) # (4)
simulate(until=maxTime)
return (wM.count(), wM.mean()) # (5)
## Experiment/Result ----------------------------------
theseeds = [393939, 31555999, 777999555, 319999771] # (6)
for Sd in theseeds:
result = model(Sd)
print("Average wait for %3d completions was %6.2f minutes." % result) # (7)
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.
Average wait for 50 completions was 3.66 minutes.
Average wait for 50 completions was 2.62 minutes.
Average wait for 50 completions was 8.97 minutes.
Average wait for 50 completions was 5.34 minutes.
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: http://www.Python.org
- SimPy website: http://sourceforge.net/projects/simpy
Appendix A¶
With Python 3 the definition of expovariate changed. In some cases this was back ported to some distributions of Python 2.7. Because of this the output for the bank programs varies. This section just contains the older output.
A Customer arriving at a fixed time
5.0 Klaus Here I am
15.0 Klaus I must leave
A Customer arriving at random
10.580923 Klaus Here I am
20.580923 Klaus I must leave
More Customers
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
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
0.0000 Customer00: Here I am
12.0000 Customer00: I must leave
21.1618 Customer01: Here I am
32.8968 Customer02: Here I am
33.1618 Customer01: I must leave
33.3790 Customer03: Here I am
36.3979 Customer04: Here I am
44.8968 Customer02: I must leave
45.3790 Customer03: I must leave
48.3979 Customer04: I must leave
One Service Counter
0.000 Customer00: Here I am
0.000 Customer00: Waited 0.000
12.000 Customer00: Finished
21.162 Customer01: Here I am
21.162 Customer01: Waited 0.000
32.897 Customer02: Here I am
33.162 Customer01: Finished
33.162 Customer02: Waited 0.265
33.379 Customer03: Here I am
36.398 Customer04: Here I am
45.162 Customer02: Finished
45.162 Customer03: Waited 11.783
57.162 Customer03: Finished
57.162 Customer04: Waited 20.764
69.162 Customer04: Finished
A server with a random service time
0.0000 Customer00: Here I am
0.0000 Customer00: Waited 0.000
14.0819 Customer00: Finished
21.1618 Customer01: Here I am
21.1618 Customer01: Waited 0.000
21.6441 Customer02: Here I am
24.7845 Customer01: Finished
24.7845 Customer02: Waited 3.140
31.9954 Customer03: Here I am
41.0215 Customer04: Here I am
43.9441 Customer02: Finished
43.9441 Customer03: Waited 11.949
49.9552 Customer03: Finished
49.9552 Customer04: Waited 8.934
52.2900 Customer04: Finished
Several Counters but a Single Queue
0.0000 Customer00: Here I am
0.0000 Customer00: Waited 0.000
14.0819 Customer00: Finished
21.1618 Customer01: Here I am
21.1618 Customer01: Waited 0.000
21.6441 Customer02: Here I am
21.6441 Customer02: Waited 0.000
24.7845 Customer01: Finished
31.9954 Customer03: Here I am
31.9954 Customer03: Waited 0.000
32.9459 Customer03: Finished
40.8037 Customer02: Finished
41.0215 Customer04: Here I am
41.0215 Customer04: Waited 0.000
43.3562 Customer04: Finished
Several Counters with individual queues
0.0000 Customer00: Here I am. [0, 0]
0.0000 Customer00: Waited 0.000
3.5483 Customer01: Here I am. [1, 0]
3.5483 Customer01: Waited 0.000
4.4169 Customer01: Finished
6.4349 Customer02: Here I am. [1, 0]
6.4349 Customer02: Waited 0.000
7.0368 Customer00: Finished
9.7200 Customer02: Finished
9.8846 Customer03: Here I am. [0, 0]
9.8846 Customer03: Waited 0.000
19.8340 Customer03: Finished
26.2357 Customer04: Here I am. [0, 0]
26.2357 Customer04: Waited 0.000
29.8709 Customer04: Finished
The Bank with a Monitor
Average wait for 50 completions was 3.430 minutes.
Multiple runs
Average wait for 50 completions was 2.75 minutes.
Average wait for 50 completions was 6.01 minutes.
Average wait for 50 completions was 5.53 minutes.
Average wait for 50 completions was 3.76 minutes.