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 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.
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. Line 1 is a normal Python documentation string; line 2 imports the SimPy simulation code.
The Customer class definition, lines 6-12, 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, now(), and his name (line 10). 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 (line 22).
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.
Line 21 calls initialize() which sets up the simulation system ready to receive activate calls. In line 22, we create a customer, c, with name Klaus. All SimPy Processes have a name attribute. We activate Klaus in line 23 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) in line 24 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 in line 16.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | """ bank01: The single non-random Customer """
from SimPy.Simulation import *
## Model components -----------------------------
class Customer(Process):
""" Customer arrives, looks around and leaves """
def visit(self,timeInBank):
print now(),self.name," Here I am"
yield hold,self,timeInBank
print now(),self.name," I must leave"
## Experiment data ------------------------------
maxTime = 100.0 # minutes
timeInBank = 10.0 # minutes
## Model/Experiment ------------------------------
initialize()
c = Customer(name="Klaus")
activate(c,c.visit(timeInBank),at=5.0)
simulate(until=maxTime)
|
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 22, 25, and 26. 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. In line 22 we provide an initial seed of 99999. An exponential random variate, t, is generated in line 25. Note that the Python Random module’s expovariate function uses the rate (that is, 1.0/mean) as the argument. The generated random variate, t, is used in Line 26 as the at argument to the activate call.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 | """ bank05: The single Random Customer """
from SimPy.Simulation import *
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 now(), self.name," Here I am"
yield hold,self,timeInBank
print now(), self.name," I must leave"
## Experiment data -------------------------
maxTime = 100.0 # minutes
timeInBank = 10.0
## Model/Experiment ------------------------------
seed(99999)
initialize()
c = Customer(name = "Klaus")
t = expovariate(1.0/5.0)
activate(c,c.visit(timeInBank),at=t)
simulate(until=maxTime)
|
The result is shown below. The customer now arrives at time 10.5809. Changing the seed value would change that time.
10.5809228279 Klaus Here I am
20.5809228279 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 22-27 where we create, name, and activate three customers. We also increase the maximum simulation time to 400 (line 16 and referred to in line 29). 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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 | """ 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)
yield hold,self,timeInBank
print "%7.4f %s: I must leave"%(now(),self.name)
## Experiment data -------------------------
maxTime = 400.0 # minutes
## Model/Experiment ------------------------------
initialize()
c1 = Customer(name="Klaus")
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)
simulate(until=maxTime)
|
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 sequence of numbered Customers from 0 to (number-1), inclusive. We create a customer and give it a name in line 11. 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 13).
A Source, s, is created in line 32 and activated at line 33 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:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | """ bank03: Many non-random Customers """
from SimPy.Simulation import *
## 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,))
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"%(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()
activate(s,s.generate(number=maxNumber,
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 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 model routine (line 33). 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 33 but it is clear it could have been read in or manually entered on an input form.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 | """ 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)
yield hold,self,t
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)
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
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
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 38. This is provided as an argument to the Source (line 45) which, in turn, provides it to each customer it creates and activates (line 14).
The actions involving the service counter, k, 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 fixed timeInBank. During this period the customer is being served.
- 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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 | """ 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))
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() # arrival time
print "%8.3f %s: Here I am "%(now(),self.name)
yield request,self,res
wait = now()-arrive # waiting time
print "%8.3f %s: Waited %6.3f"%(now(),self.name,wait)
yield hold,self,timeInBank
yield release,self,res
print "%8.3f %s: Finished "%(now(),self.name)
## Experiment data -------------------------
maxNumber = 5
maxTime = 400.0 # minutes
ARRint = 10.0 # mean, minutes
k = Resource(name="Counter",unitName="Clerk")
## Model/Experiment ------------------------------
seed(99999)
initialize()
s = Source('Source')
activate(s,s.generate(number=maxNumber,
meanTBA=ARRint, resource=k),at=0.0)
simulate(until=maxTime)
|
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 35) so we cannot draw general conclusions.
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¶
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/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 31 to 42.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | """ 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)
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= 12345
## 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
8.7558 Customer01: Here I am
10.6770 Customer02: Here I am
22.7622 Customer03: Here I am
32.7477 Customer04: Here I am
55.0607 Customer00: Finished
55.0607 Customer01: Waited 46.305
61.8905 Customer01: Finished
61.8905 Customer02: Waited 51.213
83.7556 Customer02: Finished
83.7556 Customer03: Waited 60.993
108.7794 Customer03: Finished
108.7794 Customer04: Waited 76.032
118.8254 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 42. 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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 | """ 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 = 12345
## Model/Experiment ------------------------------
seed(theseed)
k = Resource(capacity=2,name="Counter",unitName="Clerk")
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 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
8.7558 Customer01: Here I am
8.7558 Customer01: Waited 0.000
10.6770 Customer02: Here I am
20.6626 Customer03: Here I am
23.2580 Customer01: Finished
23.2580 Customer02: Waited 12.581
30.0878 Customer02: Finished
30.0878 Customer03: Waited 9.425
37.0790 Customer04: Here I am
51.9528 Customer03: Finished
51.9528 Customer04: Waited 14.874
55.0607 Customer00: Finished
61.9988 Customer04: 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 30-32 (the variable choice).
The rest of the program is the same as before.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 | """ 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):
""" 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 = now()
Qlength = [NoInSystem(counters[i]) for i in range(Nc)]
print "%7.4f %s: Here I am. %s"%(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 = 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 = 12345
## Model/Experiment ------------------------------
seed(theseed)
kk = [Resource(name="Clerk0"),Resource(name="Clerk1")]
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 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
8.7558 Customer01: Here I am. [1, 0]
8.7558 Customer01: Waited 0.000
10.6770 Customer02: Here I am. [1, 1]
20.6626 Customer03: Here I am. [2, 1]
23.2580 Customer01: Finished
23.2580 Customer03: Waited 2.595
30.0878 Customer03: Finished
37.0790 Customer04: Here I am. [2, 0]
37.0790 Customer04: Waited 0.000
55.0607 Customer00: Finished
55.0607 Customer02: Waited 44.384
62.1029 Customer04: Finished
65.1067 Customer02: 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 42. It observes the waiting time mentioned in line 24. We run maxNumber=50 customers (in the call of generate in line 45) and have increased maxTime to 1000 minutes.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | """ 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)
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 = 12345
## Model/Experiment ----------------------
seed(theseed)
k = Resource(capacity=Nc,name="Clerk")
wM = Monitor()
initialize()
s = Source('Source')
activate(s,s.generate(number=maxNumber,interval=ARRint,
resource=k),at=0.0)
simulate(until=maxTime)
## Result ----------------------------------
result = wM.count(),wM.mean()
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 is:
Average wait for 50 completions was 2.466 minutes.
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 40-50). 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 43). 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 48) and then from the Source to the Customer (line 13).
model() is run for four different random-number seeds to get a set of replications (lines 54-57).
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 | """ 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))
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):
seed(runSeed)
k = Resource(capacity=Nc,name="Clerk")
wM = Monitor()
initialize()
s = Source('Source')
activate(s,s.generate(number=maxNumber,interval=ARRint,
resource=k,mon=wM),at=0.0)
simulate(until=maxTime)
return (wM.count(),wM.mean())
## Experiment/Result ----------------------------------
theseeds = [393939,31555999,777999555,319999771]
for Sd in theseeds:
result = model(Sd)
print "Average wait for %3d completions was %6.2f minutes."% result
|
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 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.
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, and Stores 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
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- The Bank: Examples of SimPy Simulation
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