Author: G A Vignaux
Date: 2004-05-23

# The Bank: an example of a SimPy Simulation

Author: | G A Vignaux
Date: | 2004-05-23
Version: | 1.11

Table Of Contents

- Introduction
- Our Bank
- A Customer
  - The non-random Customer
  - The Random Customer
- More Customers
  - Many non-random Customers
  - Many Random Customers
- A Counter
  - One Counter
  - A random service time
- Several Counters
  - Several Counters but a Single Queue
  - Several Counters with individual queues
- Monitors and Gathering Statistics
  - Monitors
  - Multiple runs
- Final Remarks
- Acknowledgments
- References

The Bank tutorial demonstrates the use of SimPy in developing and running a simple simulation of a practical problem, a multi-server bank.

# Introduction

This tutorial works through the development of a simulation of a bank using SimPy.

SimPy is a Python-based discrete-event simulation system. It uses parallel processes to model active components such as messages, customers, trucks, planes. It provides a number of facilities for the simulation programmer: Processes, Resources, and, just as important, ways of recording the average values of variables in Monitors.

Before attempting to use SimPy you should have some familiarity with the the Python language. In particular, you should be able to use and define classes of objects. Python is free and available on most machine types. You can find out more about it and download it from the Python web-site, http://www.Python.org. This document assumes Python 2.2 or later.

NOTE: If you use Python versions 2.2, you must place this import statement at the top of all SimPy scripts: `from __future __ import generators`

SimPy itself can be obtained from: http://sourceforge.net/projects/simpy.

# Our Bank

We are going to model a simple bank with a number of tellers and customers arriving at random. All simulations need to answer a question; in this case we are to investigate how increasing the number of tellers reduces the queueing time for customers.

We will develop the model step-by-step, starting out very simply.

# A Customer

We first model a single customer who arrives at the bank for a visit, looks around for a time and then leaves. There are no bank counters in this model. First we will assume his arrival time and time in the bank are known. Then we will allow the customer to arrive at a random time.

## The non-random Customer

We define a Customer class which will derive from the SimPy Process class. Examine the following listing which, except for the line numbers I have added, is a complete runnable Python script. The customer visits the bank at simulation time 5.0 and leaves after 10.0. We will take time units to be minutes

      1 #!/usr/bin/env python
      2 """ bank01: Simulate a single customer """
      3 from __future__ import generators
      4 from SimPy.Simulation  import *
      5
      6 class Customer(Process):
      7     """ Customer arrives, looks around and leaves """
      8     def __init__(self,name):
      9         Process.__init__(self)
     10         self.name = name
     11
     12     def visit(self,timeInBank=0):
     13         print "%7.4f %s: Here I am"%(now(),self.name)
     14         yield hold,self,timeInBank
     15         print "%7.4f %s: I must leave"%(now(),self.name)
     16
     17 def model():
     18     initialize()
     19     c=Customer(name="Klaus")
     20     activate(c,c.visit(timeInBank=10.0),delay=5.0)
     21     simulate(until=100.0)
     22
     23 model()

Line 1 is a Python comment indicating to the Unix shell which Python interpreter to use. Line 2 is a normal Python documentation string.

Line 3 imports generators (from the __future__ as Python 2.2 does not yet have generators built-in) and line 4 imports the the SimPy simulation code.

Now examine the Customer class definition, lines 6-15. It defines our customer and has the two required methods: an __init__() method (line 8) and an action method (visit) (line 12). An __init__ method must call Process.__init__(self) and can then initialize any instance variables needed by the class objects. Here, on line 9, we give the customer a name which will be used when we run the simulation.

The visit action method, lines 12-15, executes the customer's 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 13). The function now() can be used at any time in the simulation to find the current simulation time. The name will be set when the customer is created in the main() routine.

He then stays in the bank for a simulation period timeInBank (line 14). This is achieved in the yield hold,self,timeInBank statement. This is the first of the special simulation commands that SimPy offers. The yield statements shows that the customer's visit method is a Python generator.

After a simulation time of timeInBank, the program's execution returns to the line after the yield statement, line 15. Here he again print out the current simulation time and his name. This completes the declaration of the Customer class.

Lines 17-23 declare the model routine and then call it. The name of this function could be anything, of course, (for example main(), or bank()). Indeed, the code could even have been written in-line rather than embedded in a function but when we come to carry out series of experiments we will find it is better to structure the model this way.

Line 18 calls initialize() which sets up the simulation system ready to receive activate calls. Then, in line 19, we create a customer with name Klaus. We activate Klaus in line 20. We specify the active object(c) to be activated, the call of the action routine (c.visit(timeInBank=10.0)) and the time it is to be activated (with, here, a after=5.0). This will activate klaus after a delay from the current time, in this case at the start of the simulation, 0.0, of 5.0 minutes. 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=100.0 in line 21 will start the simulation. It will run until the simulation time is 100.0 unless stopped beforehand. A simulation can be stopped, either by the command stopSimulation() or by running out of events to execute (as will happen here).

So far we have been declaring a class, its methods, and one routine. The call of model() in line 23 starts the script running. The trace printed out by the print commands 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.

The output from the program is

     5.0000 Klaus: Here I am
    15.0000 Klaus: I must leave

## The Random Customer

Now we extend the model to allow our customer to arrive at a random simulated time. We modify the previous model:

      1 #!/usr/bin/env python
      2 """ bank05: A single customer arrives at random time"""
      3 from __future__ import generators
      4 from SimPy.Simulation  import *
      5 from random import Random
      6
      7 class Customer(Process):
      8     """ Customer arrives at a random time,
      9     looks around  and then leaves
     10     """
     11     def __init__(self,name):
     12         Process.__init__(self)
     13         self.name = name
     14
     15     def visit(self,timeInBank=0):
     16         print "%7.4f %s: Here I am"%(now(),self.name)
     17         yield hold,self,timeInBank
     18         print "%7.4f %s: I must leave"%(now(),self.name)
     19
     20 def model():
     21     rv = Random(99999)
     22     initialize()
     23     c=Customer(name="Klaus")
     24     t = rv.expovariate(1.0/5.0)
     25     activate(c,c.visit(timeInBank=10.0),delay=t)
     26     simulate(until=100.0)
     27
     28 model()

The change occurs in lines 5, 21, 24, and 25 of model(). In line 5 we import from the standard Python random module. We need Random to create a random variable object -- this is done in line 21 using a random number seed of 99999. In later models we will use the seed as an argument to the model routine. We need expovariate to generate an exponential random variate from that object -- this is done in line 24 and the random sample, t, is used in Line 25 as the delay argument to the activate call.

The result is shown below where we see the customer now arrives at time 10.5809. Changing the seed value would change that time.

    10.5809 Klaus: Here I am
    20.5809 Klaus: I must leave

# More Customers

Our simulation does little so far. Eventually, we need multiple customers to arrive at random and be served for times that can also be random. Let us next consider several customers. We first go back to the simple deterministic model and add more Customers.

      1 #!/usr/bin/env python
      2 """ bank01: Simulate a single customer """
      3 from __future__ import generators
      4 from SimPy.Simulation  import *
      5
      6 class Customer(Process):
      7     """ Customer arrives, looks around and leaves """
      8     def __init__(self,name):
      9         Process.__init__(self)
     10         self.name = name
     11
     12     def visit(self,timeInBank=0):
     13         print "%7.4f %s: Here I am"%(now(),self.name)
     14         yield hold,self,timeInBank
     15         print "%7.4f %s: I must leave"%(now(),self.name)
     16
     17 def model():
     18     initialize()
     19     c1=Customer(name="Klaus")
     20     activate(c1,c1.visit(timeInBank=10.0),delay=5.0)
     21     c2=Customer(name="Tony")
     22     activate(c2,c2.visit(timeInBank=8.0),delay=2.0)
     23     c3=Customer(name="Evelyn")
     24     activate(c3,c3.visit(timeInBank=20.0),delay=12.0)
     25     simulate(until=400.0)
     26
     27 model()

The program is almost as easy as The non-random Customer. The only change is in lines 19-24 where we create, name, and activate three customers in model() and a change in the argument of simulate(until=100). Customer Tony is created second but as it is activated at simulation time 2.0 he will start before Customer Klaus. Each of the customers stays for a different timeinbank.

The trace produced by the program is shown below. Again the simulation finishes before the till=100.0 of the simulate call.

     2.0000 Tony: Here I am
     5.0000 Klaus: Here I am
    10.0000 Tony: I must leave
    12.0000 Evelyn: Here I am
    15.0000 Klaus: I must leave
    32.0000 Evelyn: I must leave

## Many non-random Customers

Another change will allow us to have multiple customers. As it is tedious to give a specially chosen name to each customer, we will instead call them Customer00, Customer01, .... We will also use a separate class to create and activate these customers. We will call this class a Source.

      1 #!/usr/bin/env python
      2 """ bank01: Simulate several customers using a Source """
      3 from __future__ import generators
      4 from SimPy.Simulation  import *
      5
      6 class Source(Process):
      7     """ Source generates customers regularly"""
      8     def __init__(self):
      9         Process.__init__(self)
     10
     11     def generate(self,number,interval):
     12         for i in range(number):
     13             c = Customer(name = "Customer%02d"%(i,))
     14             activate(c,c.visit(timeInBank=12.0))
     15             yield hold,self,interval
     16
     17 class Customer(Process):
     18     """ Customer arrives, looks round and leaves """
     19     def __init__(self,name):
     20         Process.__init__(self)
     21         self.name = name
     22
     23     def visit(self,timeInBank=0):
     24         print "%7.4f %s: Here I am"%(now(),self.name)
     25         yield hold,self,timeInBank
     26         print "%7.4f %s: I must leave"%(now(),self.name)
     27
     28 def model():
     29     initialize()
     30     source=Source()
     31     activate(source,source.generate(5,10.0),0.0)
     32     simulate(until=400.0)
     33
     34 model()
     35

The listing shows the new program. Lines 6-15 show the Source class. There is the compulsory __init__ method (lines 8-9) and a Python generator, here called generate (lines 11-15). This method has a couple of arguments, number and interval, the time between customer arrivals. It consists of a loop that creates a sequence of numbered Customers from 0 to number-1. Upon creation each is activated at the current simulation time (the final argument of the activate statement is missing). We also specify how long the customer is to stay in the bank. To keep it simple, all customers will stay exactly 12 minutes. When a new customer is activated, the Source holds for a fixed time (yield hold,self, interval) before creating the next one.

The Source is created in line 30 and activated at line 31 where the number of customers is set to 5 and the interval to 10.0. Once it starts, at time 0.0 it creates customers at intervals and each customer then operates independently of others:

>      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 extend this model to allow our customers to arrive at random. In simulation this is usually interpreted as meaning that the times between customer arrivals are distributed as exponential random variates. Thus there is little change in our program:

      1 #!/usr/bin/env python
      2 """ bank06: Simulate several customers arriving
      3             at random, using a Source
      4 """
      5 from __future__ import generators
      6 from SimPy.Simulation  import *
      7 from random import Random
      8
      9 class Source(Process):
     10     """ Source generates customers randomly"""
     11     def __init__(self,seed=333):
     12         Process.__init__(self)
     13         self.SEED = seed
     14
     15     def generate(self,number,interval):
     16         rv = Random(self.SEED)
     17         for i in range(number):
     18             c = Customer(name = "Customer%02d"%(i,))
     19             activate(c,c.visit(timeInBank=12.0))
     20             t = rv.expovariate(1.0/interval)
     21             yield hold,self,t
     22
     23 class Customer(Process):
     24     """ Customer arrives, looks round and leaves """
     25     def __init__(self,name):
     26         Process.__init__(self)
     27         self.name = name
     28
     29     def visit(self,timeInBank=0):
     30         print "%7.4f %s: Here I am"%(now(),self.name)
     31         yield hold,self,timeInBank
     32         print "%7.4f %s: I must leave"%(now(),self.name)
     33
     34 def model():
     35     initialize()
     36     source=Source(seed = 99999)
     37     activate(source,source.generate(5,10.0),0.0)
     38     simulate(until=400.0)
     39
     40 model()

We import the random routines we need in line 7. I decided to set up the random number used to generate the customers as an attribute of the Source class, with its seed being supplied by the user when a Source is created (lines 11, 13, and 36). The random variate itself is created when the generate method is activated (line 16). The exponential random variate is generated in line 20 using interval as the mean of the distribution and used in line 21. This gives an exponential delay between two arrivals and hence pseudo-random arrivals, as specified. In this model the first customer arrives at time 0.

A number of different ways of handling the random variables could have been chosen. For example, set up the random variable in the model routine and pass it to the Source as an argument either in the __init__ method or in the generate call on line 37. Or, somewhat less elegantly, establish the random variable as a global object. The important factor is that if we wish to do serious comparisons of systems, we need control over the random variates and hence control over the seeds. Thus we must be able to run identical models with different seeds or different models with identical seeds. This requires us to be able to provide the seeds as control parameters of the run. Here, of course it is just assigned in line 36 but it is clear it could have been read in or provided in a GUI form.

     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 Counter

Now we extend the bank, and the activities of the customers by installing a counter with a clerk where banking takes place. So far, it has been more like an art gallery, the customers entering, looking around, and leaving. We need a object to represent the counter and SimPy provides a Resource class for this purpose. The actions of a Resource are simple: customers request a clerk, if she is free he gets service but others are blocked until the clerk becomes free again. This happens when the customer completes service and releases the clerk. If a customer requests service and the clerk is busy, the customer joins a queue until it is their turn to be served.

## One Counter

The next model is a development of the previous one with random arrivals but they need to use a single counter for a fixed time. Here customers arrive randomly to be served at a single counter.

      1 #!/usr/bin/env python
      2 """ bank07: Simulate customers arriving
      3             at random, using a Source
      4             requesting service from a clerk.
      5 """
      6 from __future__ import generators
      7 from SimPy.Simulation  import *
      8 from random import Random
      9
     10 class Source(Process):
     11     """ Source generates customers randomly"""
     12     def __init__(self,seed=333):
     13         Process.__init__(self)
     14         self.SEED = seed
     15
     16     def generate(self,number,interval):
     17         rv = Random(self.SEED)
     18         for i in range(number):
     19             c = Customer(name = "Customer%02d"%(i,))
     20             activate(c,c.visit(timeInBank=12.0))
     21             t = rv.expovariate(1.0/interval)
     22             yield hold,self,t
     23
     24 class Customer(Process):
     25     """ Customer arrives, is served and  leaves """
     26     def __init__(self,name):
     27         Process.__init__(self)
     28         self.name = name
     29
     30     def visit(self,timeInBank=0):
     31         arrive=now()
     32         print "%7.4f %s: Here I am     "%(now(),self.name)
     33         yield request,self,counter
     34         wait=now()-arrive
     35         print "%7.4f %s: Waited %6.3f"%(now(),self.name,wait)
     36         yield hold,self,timeInBank
     37         yield release,self,counter
     38         print "%7.4f %s: Finished      "%(now(),self.name)
     39
     40 def model():
     41     global counter
     42     counter = Resource(name="Karen")
     43     initialize()
     44     source=Source(seed = 99999)
     45     activate(source,source.generate(5,10.0),0.0)
     46     simulate(until=400.0)
     47
     48 model()

The counter is created in lines 41-42. I have chosen to make this a global object so it can be referred to by the Customer class. An alternative would have been to create it globally outside model or to carry it as an argument of the Customer class.

The actions involving the counter are the yield statements in lines 33 and 37 where we request it and then, later release it.

To show the effect of the counter on the activities of the customers, I have added line 31 that records when the customer arrived and line 34 that records the time between arrival and getting the counter. Line 34 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 service-time. Queueing may have taken place and wait will record how long the customer waited. This technique of saving the arrival time in a variable to record the time taken in systems is common in simulations. So the print statement also prints out how long the customer waited and we see that, except for the first customer (we still only have five customers, see line 45) all the customers have to wait. Here is the output:

     0.0000 Customer00: Here I am
     0.0000 Customer00: Waited  0.000
    12.0000 Customer00: Finished
    21.1618 Customer01: Here I am
    21.1618 Customer01: Waited  0.000
    32.8968 Customer02: Here I am
    33.1618 Customer01: Finished
    33.1618 Customer02: Waited  0.265
    33.3790 Customer03: Here I am
    36.3979 Customer04: Here I am
    45.1618 Customer02: Finished
    45.1618 Customer03: Waited 11.783
    57.1618 Customer03: Finished
    57.1618 Customer04: Waited 20.764
    69.1618 Customer04: Finished

## A random service time

We retain the one counter but bring in another source of variability: we make the service time a random variable as well as the inter-arrival time. As is traditional in the study of queues we first assume an exponential service time with a mean of timeInBank. This time we will define the random variable to be used for the service time in the model function. We will set the seed for this random variable as an argument to model in anticipation of future use.

      1 #!/usr/bin/env python
      2 """ bank08: Simulate customers arriving
      3     at random, using a Source, requesting service
      4     from a clerk, with a random servicetime
      5 """
      6 from __future__ import generators
      7 from SimPy.Simulation  import *
      8 from random import Random
      9
     10 class Source(Process):
     11     """ Source generates customers randomly"""
     12     def __init__(self,seed=333):
     13         Process.__init__(self)
     14         self.SEED = seed
     15
     16     def generate(self,number,interval):
     17         rv = Random(self.SEED)
     18         for i in range(number):
     19             c = Customer(name = "Customer%02d"%(i,))
     20             activate(c,c.visit(timeInBank=12.0))
     21             t = rv.expovariate(1.0/interval)
     22             yield hold,self,t
     23
     24 class Customer(Process):
     25     """ Customer arrives, is served and leaves """
     26     def __init__(self,name):
     27         Process.__init__(self)
     28         self.name = name
     29
     30     def visit(self,timeInBank=0):
     31         arrive=now()
     32         print "%7.4f %s: Here I am     "%(now(),self.name)
     33         yield request,self,counter
     34         wait=now()-arrive
     35         print "%7.4f %s: Waited %6.3f"%(now(),self.name,wait)
     36         tib = counterRV.expovariate(1.0/timeInBank)
     37         yield hold,self,tib
     38         yield release,self,counter
     39         print "%7.4f %s: Finished      "%(now(),self.name)
     40
     41 def model(counterseed=393939):
     42     global counter,counterRV
     43     counter = Resource(name="Karen")
     44     counterRV = Random(counterseed)
     45     initialize()
     46     sourceseed = 99999
     47     source = Source(seed = sourceseed)
     48     activate(source,source.generate(5,10.0),0.0)
     49     simulate(until=400.0)
     50
     51 model()

The argument, counterseed is set up in line 41. The corresponding random variable, counterRV is created in line 44. I have declared it global in line 42 so we can use it in the Customer class without passing it as a parameter through the Source and the Customer calls.

It is used in lines 36-37 of the visit() method of Customer. We obtain a sample (tib) in line 36 and use it in line 37. Here is the trace from this program.

     0.0000 Customer00: Here I am
     0.0000 Customer00: Waited  0.000
    21.1618 Customer01: Here I am
    26.6477 Customer00: Finished
    26.6477 Customer01: Waited  5.486
    32.8968 Customer02: Here I am
    33.3790 Customer03: Here I am
    33.4806 Customer01: Finished
    33.4806 Customer02: Waited  0.584
    36.3979 Customer04: Here I am
    45.6262 Customer02: Finished
    45.6262 Customer03: Waited 12.247
    53.6001 Customer03: Finished
    53.6001 Customer04: Waited 17.202
    56.2820 Customer04: Finished

This model with random arrivals and exponential service times is known as the M/M/1 queue and can be solved analytically.

# Several Counters

When we introduce several counters we must decide the 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 lanes (jockey)? We look first at a single-queue with several counters then at several isolated queues.

## Several Counters but a Single Queue

The bank model with customers who arrive randomly to be served at a group of counters taking a random time for service. A single queue is assumed.

      1 #!/usr/bin/env python
      2 """ bank09: Simulate customers arriving
      3     at random, using a Source requesting service
      4     from several clerks but a single queue
      5     with a random servicetime
      6 """
      7 from __future__ import generators
      8 from SimPy.Simulation  import *
      9 from random import Random
     10
     11 class Source(Process):
     12     """ Source generates customers randomly"""
     13     def __init__(self,seed=333):
     14         Process.__init__(self)
     15         self.SEED = seed
     16
     17     def generate(self,number,interval):
     18         rv = Random(self.SEED)
     19         for i in range(number):
     20             c = Customer(name = "Customer%02d"%(i,))
     21             activate(c,c.visit(timeInBank=12.0))
     22             t = rv.expovariate(1.0/interval)
     23             yield hold,self,t
     24
     25 class Customer(Process):
     26     """ Customer arrives, is served and leaves """
     27     def __init__(self,name):
     28         Process.__init__(self)
     29         self.name = name
     30
     31     def visit(self,timeInBank=0):
     32         arrive=now()
     33         print "%7.4f %s: Here I am "%(now(),self.name)
     34         yield request,self,counter
     35         wait=now()-arrive
     36         print "%7.4f %s: Waited %6.3f"%(now(),self.name,wait)
     37         tib = counterRV.expovariate(1.0/timeInBank)
     38         yield hold,self,tib
     39         yield release,self,counter
     40         print "%7.4f %s: Finished"%(now(),self.name)
     41
     42 def model(counterseed=393939):
     43     global counter,counterRV
     44     counter = Resource(name="Clerk",capacity = 2)
     45     counterRV = Random(counterseed)
     46     initialize()
     47     sourceseed = 99999
     48     source = Source(seed = sourceseed)
     49     activate(source,source.generate(5,10.0),0.0)
     50     simulate(until=400.0)
     51
     52 model()

The only difference between this model and the single-server model is in line 44. I have increased the capacity of the counter resource to 2 and, because both clerks cannot be called Karen, I have specified the name Clerk. The waiting times, however, are very different. The second server has cut the waiting times down considerably:

     0.0000 Customer00: Here I am
     0.0000 Customer00: Waited  0.000
    21.1618 Customer01: Here I am
    21.1618 Customer01: Waited  0.000
    26.6477 Customer00: Finished
    27.9948 Customer01: Finished
    32.8968 Customer02: Here I am
    32.8968 Customer02: Waited  0.000
    33.3790 Customer03: Here I am
    33.3790 Customer03: Waited  0.000
    36.3979 Customer04: Here I am
    41.3528 Customer03: Finished
    41.3528 Customer04: Waited  4.955
    44.0348 Customer04: Finished
    45.0424 Customer02: Finished

## Several Counters with individual queues

Each counter is now assumed to have its own queue. The obvious modelling technique therefore is to make each counter a separate resource. Then we have to decide how a customer will choose which queue to join. In practice, a customer will join the counter with the fewest customers. An alternative (and one that can be handled analytically) is to allow him to join a queue ''at random''. This may mean that one queue is long while another server is idle. Here we allow the customer to choose the counter with the fewest customers. If there are more than one that satisfies this criterion he will choose the first.

      1 #!/usr/bin/env python
      2 """ bank10: Simulate customers arriving
      3     at random, using a Source, requesting service
      4     from two counters each with their own queue
      5     random servicetime
      6 """
      7 from __future__ import generators
      8 from SimPy.Simulation  import *
      9 from random import Random
     10
     11 class Source(Process):
     12     """ Source generates customers randomly"""
     13     def __init__(self,seed=333):
     14         Process.__init__(self)
     15         self.SEED = seed
     16
     17     def generate(self,number,interval):
     18         rv = Random(self.SEED)
     19         for i in range(number):
     20             c = Customer(name = "Customer%02d"%(i,))
     21             activate(c,c.visit(timeInBank=12.0))
     22             t = rv.expovariate(1.0/interval)
     23             yield hold,self,t
     24
     25 def NoInSystem(R):
     26     """ The number of customers in the resource R
     27     in waitQ and active Q"""
     28     return (len(R.waitQ)+len(R.activeQ))
     29
     30 class Customer(Process):
     31     """ Customer arrives, is served and leaves """
     32     def __init__(self,name):
     33         Process.__init__(self)
     34         self.name = name
     35
     36     def visit(self,timeInBank=0):
     37         arrive=now()
     38         Qlength = [NoInSystem(counter[i]) for i in range(Nc)]
     39         print "%7.4f %s: Here I am. %s   "%(now(),self.name,Qlength)
     40         for i in range(Nc):
     41             if Qlength[i] ==0 or Qlength[i]==min(Qlength): join =i ; break
     42         yield request,self,counter[join]
     43         wait=now()-arrive
     44         print "%7.4f %s: Waited %6.3f"%(now(),self.name,wait)
     45         tib = counterRV.expovariate(1.0/timeInBank)
     46         yield hold,self,tib
     47         yield release,self,counter[join]
     48         print "%7.4f %s: Finished    "%(now(),self.name)
     49
     50 def model(counterseed=393939):
     51     global Nc,counter,counterRV
     52     Nc = 2
     53     counter = [Resource(name="Clerk0"),Resource(name="Clerk1")]
     54     counterRV = Random(counterseed)
     55     initialize()
     56     sourceseed = 99999
     57     source = Source(seed = sourceseed)
     58     activate(source,source.generate(5,10.0),0.0)
     59     simulate(until=400.0)
     60
     61 model()

We need to find the total number of customers at each counter. To make the programming clearer, I define a Python function, NoInSystem(R) (lines 25-28) which returns the sum of the number waiting and the number being served for a particular counter, R. This function is used in line 38 to get a list of the numbers at each counter. I have modified the trace printout, line 39 to display the state of the system when the customer arrives. It is then obvious which counter he will join. We then choose the shortest queue in lines 40-41 (the variable join). The remaining program is the same as before.

     0.0000 Customer00: Here I am. [0, 0]
     0.0000 Customer00: Waited  0.000
    21.1618 Customer01: Here I am. [1, 0]
    21.1618 Customer01: Waited  0.000
    26.6477 Customer00: Finished
    27.9948 Customer01: Finished
    32.8968 Customer02: Here I am. [0, 0]
    32.8968 Customer02: Waited  0.000
    33.3790 Customer03: Here I am. [1, 0]
    33.3790 Customer03: Waited  0.000
    36.3979 Customer04: Here I am. [1, 1]
    41.3528 Customer03: Finished
    45.0424 Customer02: Finished
    45.0424 Customer04: Waited  8.645
    47.7244 Customer04: Finished

The results show how the customers choose the counter with the smallest number. For this sample, the fifth customer waits 17.827 minutes which is longer than the 3.088 minutes he waited in the previous 2-server model, There are, however, too few arrivals in these runs, limited to five customers, to draw any general conclusions about the relative efficiencies of the two systems.

# 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 gather 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.

Another useful way of dealing with the results is to provide a graphical output. I do not have space to examine this thoroughly here (but see the comments in Final Remarks).

## Monitors

SimPy offers an easy way to gather a few simple statistics such as averages: the Monitor class. These record the values of chosen variables as time series.

To demonstrate the use of Monitors let us observe the average waiting times for our customers. In the following program I have commented out the old trace statements because I will run the simulations for many more arrivals. In practice, I would make the printouts controlled by a variable, say, TRACE which is set in model(). This would aid in debugging but would not complicate the data analysis. However, I have not done this here.

The bank model with customers who arrive randomly to be served at two counters taking a random time for service. A customer chooses the shortest queue to join. A Monitor variable records some statistics.

      1 #!/usr/bin/env python
      2 """ bank11: Simulate customers arriving
      3     at random, using a Source, requesting service
      4     from two counters each with their own queue
      5     random servicetime.
      6     Uses a Monitor object to record waiting times
      7
      8 """
      9 from __future__ import generators   # not needed for Python 2.3+
     10 from SimPy.Simulation  import *
     11 from random import Random
     12
     13 class Source(Process):
     14     """ Source generates customers randomly"""
     15     def __init__(self,seed=333):
     16         Process.__init__(self)
     17         self.SEED = seed
     18
     19     def generate(self,number,interval):
     20         rv = Random(self.SEED)
     21         for i in range(number):
     22             c = Customer(name = "Customer%02d"%(i,))
     23             activate(c,c.visit(timeInBank=12.0))
     24             t = rv.expovariate(1.0/interval)
     25             yield hold,self,t
     26
     27 def NoInSystem(R):
     28     """ The number of customers in the resource R
     29     in waitQ and active Q"""
     30     return (len(R.waitQ)+len(R.activeQ))
     31
     32 class Customer(Process):
     33     """ Customer arrives, is served and leaves """
     34     def __init__(self,name):
     35         Process.__init__(self)
     36         self.name = name
     37
     38     def visit(self,timeInBank=0):
     39         arrive=now()
     40         Qlength = [NoInSystem(counter[i]) for i in range(Nc)]
     41         for i in range(Nc):
     42             if Qlength[i] ==0 or Qlength[i]==min(Qlength): join =i ; break
     43         yield request,self,counter[join]
     44         wait=now()-arrive
     45         waitMonitor.observe(wait)
     46         tib = counterRV.expovariate(1.0/timeInBank)
     47         yield hold,self,tib
     48         yield release,self,counter[join]
     49
     50 def model(counterseed=393939):
     51     global Nc,counter,counterRV,waitMonitor
     52     Nc = 2
     53     counter = [Resource(name="Clerk0"),Resource(name="Clerk1")]
     54     counterRV = Random(counterseed)
     55     waitMonitor = Monitor()
     56     initialize()
     57     sourceseed = 99999
     58     source = Source(seed = sourceseed)
     59     activate(source,source.generate(50,10.0),0.0)
     60     simulate(until=2000.0)
     61     return (waitMonitor.count(),waitMonitor.mean())
     62
     63 result = model(393939)
     64 print "Average wait for %4d was %6.2f"% result

<<<<<<< TheBankOrig.txt The monitor waitMonitor is created in line 55 and declared to be global in line 51. It gathers statistics about the waiting times in line 45 where it observes them. At the end of the model function, line 61, the simple results are returned. model is run in line 63 and the results printed in line 64. Here I ran 50 customers (in the call of generate in line 59) and have increased the until argument in line 60 to 2000. ======= The Monitor class is imported with the import statement in line 10. The monitor waitMonitor is created in line 55 and declared to be global in line 51. It gathers statistics about the waiting times in line 45 where it observes them. At the end of the model function, line 61, the simple results are returned. model is run in line 63 and the results printed in line 64. Here I ran 50 customers (in the call of generate in line 59) and have increased the until argument in line 60 to 2000. >>>>>>> 1.11

    Average wait for   50 was   5.83

The average waiting time for 50 customers in a 2-counter, 2-queue system is more reliable than the times we measured before but it is not very convincing. We should replicate the runs using different random number seeds.

## Multiple runs

The advantage of the way the programs have been set up with the main part of the program in a model() routine will now become apparent. We will not need to make any changes to run a series of replications:

The bank model with customers who arrive randomly to be served at two counters taking a random time for service. A customer chooses the shortest queue to join. A Monitor variable records some statistics. A number of replications are (The partial listing of bank12.py only shows the model, where there was no change, and its call.).

     51     global Nc,counter,counterRV,waitMonitor
     52     Nc = 2
     53     counter = [Resource(name="Clerk0"),Resource(name="Clerk1")]
     54     counterRV = Random(counterseed)
     55     waitMonitor = Monitor()
     56     initialize()
     57     sourceseed = 99999
     58     source = Source(seed = sourceseed)
     59     activate(source,source.generate(50,10.0),0.0)
     60     simulate(until=2000.0)
     61     return (waitMonitor.count(),waitMonitor.mean())
     62
     63
     64 # now carry out a number of replications
     65 counterseed = [393939,31555999,777999555,319999771]
     66 for i in range(4):
     67     result = model(counterseed[i])
     68     print "Average wait for %4d was %6.2f"% result
     69

The change is in lines 65-68. model() is now run for four different random-number seeds to get a set of replications. The results are printed with a limited number of significant digits.

    Average wait for   50 was   5.83
    Average wait for   50 was   3.19
    Average wait for   50 was   4.52
    Average wait for   50 was   3.70

The results show variation. Remember, though, that the system is only operating for 50 customers so the system may not be in steady-state.

# 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 other documents:

- GUI input. Graphical input of simulation parameters could be an advantage in many 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.
- Statistical Output. The Monitor class is of some value 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.
- Interactions between processes. Often the simple-minded Resource model is insufficient. For example a tug may be needed to carry out many tasks in a port model but demands on it may have to be queued. Here we can drop back to the older, Simula inspired, methods of process interaction. In these methods a process suspends itself after joining a waiting queue (modelled as a simple Python list) and is reactivated when the tug, say, is available.

# Acknowledgments

I thank those developers and users of SimPy who have improved this document by sending their comments. I will be grateful for further corrections or suggestions. Could you send them to me: vignaux at users.sourceforge.net.

# References

- Python website: http://www.Python.org
- SimPy website: http://sourceforge.net/projects/simpy