
Simulate discrete simultaneous events for fun and profit
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Level: Introductory
David Mertz (mertz@gnosis.cx), Simulacrum, Gnosis Software, Inc.
01 Dec 2002
The stochastic behavior of real-world systems is often difficult to understand or predict. Sometimes it is possible rigorously to demonstrate statistical properties of systems, such as average, worst-case, and best-case performance features. But at other times, pitfalls of concrete designs only become evident when you actually run (or simulate) a system. In this article, David takes a look at SimPy, a Python package that allows you to very easily create models of discrete event systems.
I learned of the SimPy package when I
was contacted by one of its creators, Klaus Müller. Dr. Müller
had read the Charming Python installments that
presented techniques for using Python 2.2+ generators to implement
semi-coroutines and "weightless" threads. In particular -- and much to my
gratification -- he found that these techniques were useful for
implementing Simula-67 style simulations in Python.
It turned out that Tony Vignaux and Chang Chui had previously created
another Python library that was conceptually closer to Simscript, and that
used standard threading rather than my semi-coroutine technique. Working
together, the group determined that the generator-based style was much
more efficient and recently launched a GPL'd project on SourceForge,
called SimPy (see Resources for a link to the SimPy home page), currently
at beta status. Professor Vignaux hopes to use the unified SimPy package in his future university
teaching at the University of Victoria at Wellington;
I believe the library is also quite applicable to a variety of
applied problems.
Prior to my recent correspondence and investigation, I admit I had no
background in simulation as a programming field. I suspect most readers
of this installment share my limitation. Although there is some novelty
involved in the way one thinks about this style of programming,
simulations are useful for understanding the behavior of resource-limited
real-life systems. Whether you are interested in limited bandwidth
networks, automobile traffic behavior, market and commercial optimization,
biological/evolutionary interactions, or other "stochastic" systems, SimPy provides a simple Python tool for such
modeling.
stochastic, from the Greek stokhastikos (adj)
1) Of, relating to, or characterized by conjecture; conjectural.
2) In statistics: Involving or containing a random variable or
variables, or involving chance or probability.
Source: Dictionary.com
In this column, I'll be using the fairly simple example of a grocery store
can ask questions about the economic and wait-time implications of various
modifications to scanner technologies, shopper habits, staffing needs, and
so on. The nice thing about this modeling is that it lets you make policy
decisions in advance while having a clear idea of the implications of
changes made. Obviously, most readers will not run a grocery store
specifically, but the techniques can be widely applied to a large variety
of systems.
Simulation concepts
There are just three abstract/parent classes provided by the SimPy library, and they correspond to the
three basic concepts of a simulation. A number of other general functions
and constants are used to control the run of a simulation, but the
important concepts are tied to the classes.
The central concept in a simulation is a process. A process is
simply an object that does something, then sometimes waits for a while
before it is ready to do a next thing. In SimPy you can also "passivate" a process,
which means that it will not do anything further unless called upon to do
so by another process. It is often useful to think of a process as trying
to complete a goal. Often a process is programmed as a loop in which
multiple actions are performed. Between each action, you insert a Python
"yield" statement, which lets the simulation scheduler carry out the
actions of each waiting process before returning control.
Many of the actions that processes perform depend on the use of
resources. A resource is simply anything that is limited in
availability. In a biological model, a resource might be a food supply;
in a network model, a resource could be a router or a finite-bandwidth
channel; in our market simulation, a resource is a checkout aisle. The
only thing a resource does is restrict its usage to one particular process
at any given time. Under the SimPy
programming model, a process alone determines how long it wants to retain
a resource, the resource itself is just passive. In a real-life system,
the SimPy model may or may not fit the
conceptual scheme; it is easy to imagine a resource that inherently
limits its utilization (for example, a server computer that severs a connection if
it does not get a satisfactory response in a required timeframe). But as
a programming matter, it does not matter greatly whether a process or a
resource is the "active" party (just make sure you understand your
intention).
The final SimPy class is a
monitor. A monitor is not really essential, it is merely a
convenience. All a monitor does is record events reported to it, and save
statistics about those events (averages, counts, variances, etc). The
provided Monitor class is a useful tool for
logging simulation measures, but you could record events by any other
technique you wished also. In fact, my example subclasses Monitor to provide some (slight) enhanced
capabilities.
Monitor
Setting up shop: programming a simulation
Most of the time in my articles, I present sample applications all at
once, but in this case I think it is more useful to walk you through each
step of the grocery store application instead. You can clip together each
portion if you wish; the SimPy authors
will include my example in future releases.
The first step in a SimPy simulation is
a few general import statements:
#!/usr/bin/env python
from __future__ import generators
from SimPy import Simulation
from SimPy.Simulation import hold, request, release, now
from SimPy.Monitor import Monitor
import random
from math import sqrt
Some of the examples accompanying SimPy use an import * style, but I prefer to be more explicit about the namespaces I populate. For Python 2.2 (the minimum version needed for SimPy-) you will need to import the generators feature as indicated. After Python 2.3, this will not be necessary.
import *
For my application, I define a few runtime constants that describe the
scenarios I am interested in during a particular simulation run. As I
change the scenario, I must edit these constants within the main script.
If this were a more fleshed-out application, I might configure these
parameters with command-line options, environment variables, or a
configuration file. But for now, this style is adequate:
AISLES = 5 # Number of open aisles
ITEMTIME = 0.1 # Time to ring up one item
AVGITEMS = 20 # Average number of items purchased
CLOSING = 60*12 # Minutes from store open to store close
AVGCUST = 1500 # Average number of daily customers
RUNS = 10 # Number of times to run the simulation
The main thing our simulation needs to do is define one or more processes.
For the grocery store simulation, the process we are interested in is a
customer who checks out at an aisle.
class Customer(Simulation.Process):
def __init__(self):
Simulation.Process.__init__(self)
# Randomly pick how many items this customer is buying
self.items = 1 + int(random.expovariate(1.0/AVGITEMS))
def checkout(self):
start = now() # Customer decides to check out
yield request, self, checkout_aisle
at_checkout = now() # Customer gets to front of line
waittime.tally(at_checkout-start)
yield hold, self, self.items*ITEMTIME
leaving = now() # Customer completes purchase
yield release, self, checkout_aisle
Each customer has decided to purchase a certain number of items. (Our
simulation does not cover the selection of items from the grocery aisles; customers simply arrive at checkout with their carts). I am not confident
that exponential-variate distribution is genuinely an accurate model here.
At the low end it feels right, but I feel like there should be a fuzzy top
limit on how many items a real-life shopper ever buys. In any case, you
can see how easy it would be to adjust our simulation should better model
information become available.
The actions a customer takes is the thing to focus on. The "execution
method" of a customer is .checkout(). This
process method is often named .run() or .execute(), but in my example, .checkout() seemed most descriptive. You can use
whatever name you wish. The only real actions taken by a Customer object are checking the simulated time at a
couple of points, and logging some durations to the waittime and checkouttime
monitors. But in between the actions are the crucial yield statements. In the first case, the customer
requests a resource (a checkout aisle). Customers cannot do anything
else until they get the needed resource. Once at the checkout
aisle, the customer actually checks out -- which takes an amount of time
proportionate to the number of items purchased. Finally, once through the checkout, the customer releases the resource so that other
customers can use it.
.run()
.execute()
Customer
waittime
yield
The above code defines what a Customer class does, but we need to create
some actual customer objects before we run a simulation. We could
generate a customer object for each customer who will shop during the day,
and assign each one an appropriate checkout time. But a more parsimonious
approach is to let a factory object generate the needed customer objects
"as each customer enters the store." The simulation is not really
interested simultaneously in all the customers that will shop during a
day, but only in the ones who contend for checkout aisles at the same
time. Notice that the Customer_Factory class
is itself part of the simulation -- it is a process. Despite possible
associations with manufactured robot workers, a la Fritz Lang's
Metropolis, you should just think of the
customer factory as a programming convenience; it does not correspond
directly to anything in the modeled domain.
Customer_Factory
class Customer_Factory(Simulation.Process):
def run(self):
while 1:
c = Customer()
Simulation.activate(c, c.checkout())
arrival = random.expovariate(float(AVGCUST)/CLOSING)
yield hold, self, arrival
As I mentioned earlier, I want to collect some statistics that the current
SimPy Monitor
class does not address. Namely, I am not just interested in the average
checkout time, but also in the worst case in a given scenario. So I
created an enhanced monitor that collects minimum and maximum tallied
values.
class Monitor2(Monitor):
def __init__(self):
Monitor.__init__(self)
self.min, self.max = (int(2**31-1),0)
def tally(self, x):
Monitor.tally(self, x)
self.min = min(self.min, x)
self.max = max(self.max, x)
The final step in our simulation is, of course, to run it. In most
of the standard examples, a simulation is run just once. But for my
grocery store, I decided to loop through several simulations, each one
corresponding to a day of business. This turns out to be a good idea,
since some statistics differ fairly significantly from day to day (as
different random values are used for customer arrivals and item counts).
for run in range(RUNS):
waittime = Monitor2()
Simulation.initialize()
cf = Customer_Factory()
Simulation.activate(cf, cf.run(), 0.0)
Simulation.simulate(until=CLOSING)
#print "Customers:", checkouttime.count()
print "Waiting time average: %.1f" % waittime.mean(), \
"(std dev %.1f, maximum %.1f)" % (sqrt(waittime.var()),waittime.max)
#print "Checkout time average: %1f" % checkouttime.mean(), \
# "(standard deviation %.1f)" % sqrt(checkouttime.var())
print 'AISLES:', AISLES, ' ITEM TIME:', ITEMTIME
Three's a crowd: some outcomes (and what they mean)
When I first thought of my grocery store model, I thought a simulation
would answer a few direct questions. For example, I imagined that an
owner might have a choice between buying improved scanners (reducing ITEMTIME) or hiring more clerks (increasing AISLES). I thought I would just run the simulation
under each scenario -- assuming given labor and technology costs -- and
determine which was cheaper.
ITEMTIME
AISLES
Once I played with the simulation, I realized something that is probably
more interesting than I had anticipated. Looking at all my collected
data, I noticed that I did not know what it was I was trying to
optimize. For example, is it more important to reduce average
checkout time, or to reduce the worst case time? Which makes for
better overall customer satisfaction? Moreover, how do I compare the time
a customer spends waiting to arrive at a checkout aisle with the time
spent ringing up the items? In my personal experience, I get impatient
waiting in the line, but I feel less worried once my items are being rung
up (even if it takes a while).
Not owning a grocery store, of course, I don't know the answer to all
these questions. But the simulation does let me determine exactly what
the tradeoffs are; and it is simple enough to tweak behaviors (including
those not yet explicitly parameterized -- for example, "do customers really
arrive consistently throughout the day?").
Let me show just one closing example that illustrates the value of the
model. I wrote above that the behavior of complex systems is hard to
conceptualize. Here is something I consider a proof of that fact. What
do you think happens when available aisles are reduced from six to five
(with other parameters constant)? I would initially expect
slightly worst checkout times. The reality is different:
% python Market.py
Waiting time average: 0.5 (std dev 0.9, maximum 4.5)
Waiting time average: 0.3 (std dev 0.6, maximum 3.7)
Waiting time average: 0.4 (std dev 0.8, maximum 5.6)
Waiting time average: 0.4 (std dev 0.8, maximum 5.2)
Waiting time average: 0.4 (std dev 0.8, maximum 5.8)
Waiting time average: 0.3 (std dev 0.6, maximum 5.2)
Waiting time average: 0.5 (std dev 1.1, maximum 5.2)
Waiting time average: 0.5 (std dev 1.0, maximum 5.4)
AISLES: 6 ITEM TIME: 0.1
% python Market.py
Waiting time average: 2.1 (std dev 2.3, maximum 9.5)
Waiting time average: 1.8 (std dev 2.3, maximum 10.9)
Waiting time average: 1.3 (std dev 1.7, maximum 7.3)
Waiting time average: 1.7 (std dev 2.1, maximum 9.5)
Waiting time average: 4.2 (std dev 5.6, maximum 21.3)
Waiting time average: 1.6 (std dev 2.6, maximum 12.0)
Waiting time average: 1.3 (std dev 1.6, maximum 7.5)
Waiting time average: 1.5 (std dev 2.1, maximum 11.2)
AISLES: 5 ITEM TIME: 0.1
Rather than being 1/5 worse or something like that, eliminating one
checkout aisle causes average waiting time to increase by around 4 times.
Moreover, the unluckiest customer (during these particular runs) goes from
a 6 minute wait to a 21 minute wait. If I were the manager, I think
knowing this threshold condition would be extremely important to customer
satisfaction. Who would have known?
Resources
About the author
David Mertz exists virtually. With a bit of disappointment, he suspects
that Neuromancer-style direct interfaces
between brain and net will not quite come around during his lifetime; but
with a bit of dread, he imagines the civil liberties implications of what
will happen in 50 years. David may be reached at mertz@gnosis.cx; his
life pored over at.
Suggestions and recommendations on this, past, or future columns are
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