Introduction Discrete-Event Simulation Using SimPy

Introduction toDiscrete-Event

SimulationUsing SimPy

Chun-ChiehHuangjjhuang

What isSimulation andWhen to Use it?

What isDiscrete-EventSimulation?

Example toIllustrate WorldViews

Introduction toSimPy

SimPy Example

References

Introduction to Discrete-Event SimulationUsing SimPy

Chun-Chieh Huangjjhuang

DSP and Algorithm Design DepartmentMetanoia Communications Inc.<[email protected]>

June 9, 2012








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Outline

1 What is Simulation and When to Use it?

2 What is Discrete-Event Simulation?

3 Example to Illustrate World Views

4 Introduction to SimPy

5 SimPy Example








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What is Simulation and When to Use it?

Simulationa computer program that creates a virtual environmentin order to study physical problems








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When to use simulationhard to do real experiment,e.g. battle field, or banking system








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When to use simulationhard to do real experiment,e.g. battle field, or banking systemcheaper to do simulation,e.g. RTL simulation for IC design,or highway/freeway route planning








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When to use simulationhard to do real experiment,e.g. battle field, or banking systemcheaper to do simulation,e.g. RTL simulation for IC design,or highway/freeway route planninganalyzing bottleneck of current workflow








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When not to use simulationmore expensive to do simulation,e.g. simple harmonic motion








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When not to use simulationmore expensive to do simulation,e.g. simple harmonic motionproblems that can be analyzed by pencil and paper








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Categories of Simulation

Continuous or discretestate variable is continuous, e.g. weather systemsstate variable is discrete, e.g. number of customers








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Static or dynamicStatic: represents a system at a particular point of time

representation of time is unnecessary [1]sometimes called Monte-Carlo simulation [2]

Dynamic: represents systems as they change over time

e.g. banking system from 9:00 AM to 5:00 PM








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Static or dynamicStatic: represents a system at a particular point of time

representation of time is unnecessary [1]sometimes called Monte-Carlo simulation [2]

Dynamic: represents systems as they change over time

e.g. banking system from 9:00 AM to 5:00 PM

Deterministic or stochasticDeterministic: contains no random variableStochastic: has one or more random variables








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What is Discrete-Event Simulation?

Discrete-Event Simulation isDiscreteDynamicStochastic

Simulation for queueing in a post office is DES

Mostly, but not limited to, queueing systemsfactory work flowfreeway traffic simulationnetwork traffic simulation








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Discrete-Event Simulation World Views

Activity-orientedfixed increment of timetime-consuming








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Event-orientedon each event, generate next event andput into event queue and sortsimulation time advances to next closest eventfaster than activity-oriented








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Process-orientedabstract one object into a processeasier to maintain in the end








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Process-orientedabstract one object into a processeasier to maintain in the endSimPy belongs here!








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Example to Illustrate World Views

Simulating a post office with only one clerk

Customers come in at random timeand wait if the clerk is already serving

Clerk serves each customer for a random period of time








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Activity-Oriented Discrete-Event Simulation

0 1 2 3 4 5 6 7 8 90

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Simulation starts at 2.0!

Gen 1st arr at 2.6

Check events: 1st arr at 2.6, no action








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0 1 2 3 4 5 6 7 8 90

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Check events: 1st arr at 2.6, no action








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0 1 2 3 4 5 6 7 8 90

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Check events: 1st arr at 2.6, process now








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0 1 2 3 4 5 6 7 8 90

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First arrival!








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0 1 2 3 4 5 6 7 8 90

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Calculate next arrival at 3.5

Calculate service time, end at 4.0








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0 1 2 3 4 5 6 7 8 90

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Check events: 2nd arrival at 3.5, no action








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0 1 2 3 4 5 6 7 8 90

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Check events: 2nd arrival at 3.5, process now








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0 1 2 3 4 5 6 7 8 90

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Second arrival!








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0 1 2 3 4 5 6 7 8 90

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Calculate next arrival at ...








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0 1 2 3 4 5 6 7 8 90

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Check events: service end at 4.0, no action








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0 1 2 3 4 5 6 7 8 90

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Check events: service end at 4.0, no action...








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Event-Oriented Discrete-Event Simulation

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62.6: 1st arr

Simulation starts!








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0 1 2 3 4 5 6 7 8 90

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62.6: 1st arr

First arrival!








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0 1 2 3 4 5 6 7 8 90

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Calculate next arrival at 3.5

Calculate service time, end at 4.0

3.5: 2nd arr 4.0: 1st arr end








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0 1 2 3 4 5 6 7 8 90

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63.5: 2nd arr 4.0: 1st arr end

Second arrival!








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0 1 2 3 4 5 6 7 8 90

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64.0: 1st arr end








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0 1 2 3 4 5 6 7 8 90

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64.0: 1st arr end

End service of 1st arrival.








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Process-orientedabstract one object into a process

Arrival process for customers, or AClerk process, or S

easier to maintain in the end








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Process-Oriented Discrete-Event Simulation

Arrival is an infinite loop of the followingCalculate next arrival timeSleep until next arrivalAdd customer into queue

Clerk is an infinite loop of the followingSleep until waken up by customersServe the customer on waken upuntil there is no customer in line








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0 1 2 3 4 5 6 7 8 90

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A: Gen 1st arr at 2.6

S:

Simulation starts!








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0 1 2 3 4 5 6 7 8 90

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First arrival!

A: Add customer to queue

S:








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0 1 2 3 4 5 6 7 8 90

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A: Calc next arr at 3.5

S:








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0 1 2 3 4 5 6 7 8 90

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A:

S: Serv, calc serv T at 4.0








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0 1 2 3 4 5 6 7 8 90

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A: Add customer to queue

S:

Second arrival!








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0 1 2 3 4 5 6 7 8 90

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A: Calc next arr at ...

S:

Calc next arrival at ...








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0 1 2 3 4 5 6 7 8 90

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A:

S: 1st arr end serv. Call next.








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0 1 2 3 4 5 6 7 8 90

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A:

S: Serv 2nd arr. Calc end time at ...








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Implementing Discrete-Event Simulation

Use your own C/C++ implementationtakes time to write simulation engine and algorithm codehard to debug when both are not verifiednot very convincing








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Use generalized simulation library, or languageSIMULA programming languageC++SIM or JavaSIM [3]SimEvents in Simulink/MATLABSimPy [4]








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Use generalized simulation library, or languageSIMULA programming languageC++SIM or JavaSIM [3]SimEvents in Simulink/MATLABSimPy [4]

Use special purpose simulation packagesns-3 for network simulation [5]








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Introduction to SimPy

Uses Python for modelingPython is a scripting language like MATLAB, but faster!Python is free!Python is very easy to write and beautiful!








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Process-oriented Discrete-Event Simulation Languageis easier to write modelprovides proven event manager implementationlets you focus on algorithm code








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Process-oriented Discrete-Event Simulation Languageis easier to write modelprovides proven event manager implementationlets you focus on algorithm code

Uses coroutine to suspend/resume processguarantees order of executioncannot run on parallel machine for a single simulation








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SimPy Terminology: Classes

Processsimulates an entity which evolves in time, e.g.a clerk that serves customersrefered to as thread in [6]








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SimPy Terminology: Classes

Processsimulates an entity which evolves in time, e.g.a clerk that serves customersrefered to as thread in [6]

Resourcesimulates something to be requested andqueued if not available nowe.g. a wash machine








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SimPy Terimnology: Functions

activate() used to mark a thread as runnable when it is firstcreated








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simulate() starts the simulation








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yield hold put current thread into suspension for a certainamount of time








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yield passivate put current thread into suspension andwait until awakened by some other thread








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reactivate() awakes a previously-passivated thread








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cancel() cancels all the events associated with apreviously-passivated thread








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cancel() cancels all the events associated with apreviously-passivated thread

yield request requests for a given resource

yield release used to indicate that current thread no longer needthe given resource








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SimPy Example

ScenarioA post office with only one clerk.Customer arrival is a poisson process,i.e. inter-arrival time is exponential distribution.Service time is also a poisson process.Classical M/M/1 problem in queueing theory

ProcessArrivalClerk

Queue is managed by ourselvesSo that we can extend to M/M/m later, i.e. m clerks








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Arrival Pseudo Code

Arrival is an infinite loop of the followingCalculate next arrival timeSleep until next arrivalAdd customer into queue








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Arrival Process

1 class Ar r i va lC lass ( Process ) :2 " " " An a r r i v a l maintenance class " " "3 Ar r i va lRa te = 1 /1 .0 # r e c i p r o c a l o f mean i n t e r a r r i v a l t ime4 def __ in i t__ ( se l f , name ) :5 Process . __ in i t__ ( s e l f )6 s e l f .name = name78 def Run( s e l f ) :9 while True :

10 I n t e r A r r i v a l T i m e = G. Rnd . expovar ia te ( A r r i va lC lass . A r r i va lRa te )11 y i e l d hold , se l f , I n t e r A r r i v a l T i m e12 C = Customer ( )13 ClerkClass . Queue . append (C) # a customer a r r i v e s14 G. NumCustomers += 115 i f ClerkClass . I d l e != [ ] : # Is there any c l e r k i d l e ?16 r e a c t i v a t e ( ClerkClass . I d l e [ 0 ] ) # Yes , wake him / her up








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Clerk Pseudo Code

Clerk is an infinite loop of the followingSleep until waken up by customersServe the customer on waken upuntil there is no customer in line








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Clerk Process

1 class ClerkClass ( Process ) :2 " " " A server process , or c l e r k i n the post o f f i c e " " "3 ServiceRate = 1 /1 .2 # r e c i p r o c a l o f mean se rv i ce t ime4 MaxQueueLength = 05 Queue = [ ] # customer queue6 I d l e = [ ] # i d l e c l e r k l i s t7 Busy = [ ] # busy c l e r k l i s t8 NumDone = 0 # No . of customers being serviced9 def __ in i t__ ( s e l f ) :

10 Process . __ in i t__ ( s e l f )11 ClerkClass . I d l e . append ( s e l f ) # I n i t i a l l y i d l e12 def Run( s e l f ) :13 while True :14 y i e l d passivate , s e l f # wa i t u n t i l awaken by customers15 ClerkClass . I d l e . remove ( s e l f )16 ClerkClass . Busy . append( s e l f ) # going to be busy17 while ClerkClass . Queue != [ ] :18 i f len ( ClerkClass . Queue ) > ClerkClass . MaxQueueLength :19 ClerkClass . MaxQueueLength = len ( ClerkClass . Queue )20 C = ClerkClass . Queue . pop ( ) # c a l l next customer in l i n e21 # S t a r t se rv i ce the customer22 ServiceTime = G. Rnd . expovar ia te ( ClerkClass . ServiceRate )23 y i e l d hold , se l f , ServiceTime # s t a r t to serve24 C. endService ( ) # end of se rv i ce25 G. Tota lWai t ingTime += now ( ) − C. Ar r i va lT ime26 ClerkClass .NumDone += 127 del C # customer i s gone28 ClerkClass . Busy . remove ( s e l f )29 ClerkClass . I d l e . append( s e l f )








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Simulation Main Loop

1 i f DEBUG:2 from SimPy . Simulat ionTrace import ∗

3 else :4 from SimPy . Simulat ion import ∗

56 def main ( ) :7 i n i t i a l i z e ( ) # I n i t i a l i z e s s imu la to r8 A = Ar r i va lC lass (name=" A r r i v a l " )9 a c t i v a t e (A ,A. Run ( ) ) # Act i va te a r r i v a l

1011 S = ClerkClass (name=" Clerk " )12 a c t i v a t e (S ,S. Run ( ) ) # Act i va te c l e r k1314 simulate ( u n t i l =MaxSimTime) # S t a r t to simulate !1516 i f __name__ == ’ __main__ ’ :17 main ( )








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Concluding Remarks

Simulation is a powerful tool to study physical problems atcheaper cost.

SimPy provides process-oriendted DES frameworkto write simulation easily and reasonably fast.

And SimPy is free!








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References

[1] R. E. Nance, “A history of discrete event simulationprogramming languages,” in The second ACM SIGPLANconference on History of programming languages, ser.HOPL-II. New York, NY, USA: ACM, 1993, pp. 149–175.[Online]. Available: http://doi.acm.org/10.1145/154766.155368

[2] J. Banks, J. S. Carson, B. L. Nelson, and D. M. Nicol,Discrete-Event System Simulation (5th Edition). PrenticeHall, 2009.

[3] C++SIM and JavaSim, “http://javasim.codehaus.org/.”

[4] S. S. Package, “http://simpy.sourceforge.net/.”

[5] ns-3 Network Simulator, “http://www.nsnam.org/.”

[6] N. Matloff, “A discrete-event simulation course based on thesimpy language,” Davis, 2006.

http://doi.acm.org/10.1145/154766.155368








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