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Introduction to Discrete-Event Simulation and the SimPy Language Norm Matloff February 13, 2008 c 2006-2008, N.S. Matloff Contents 1 What Is Discrete-Event Simulation (DES)? 3 2 World Views in DES Programming 3 2.1 The Activity-Oriented Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 The Event-Oriented Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.3 The Process-Oriented Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Introduction to the SimPy Simulation Language 7 3.1 SimPy Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.2 Introduction to SimPy Programming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2.1 MachRep1.py: Our First SimPy Program . . . . . . . . . . . . . . . . . . . . . . . 10 3.2.2 MachRep2.py: Introducing the Resource Class . . . . . . . . . . . . . . . . . . . . 14 3.2.3 MachRep3.py: Introducing Passivate/Reactivate Operations . . . . . . . . . . . . . 16 3.2.4 MMk.py: “Do It Yourself” Queue Management . . . . . . . . . . . . . . . . . . . . 18 3.2.5 SMP.py: Simultaneous Possession of Resources . . . . . . . . . . . . . . . . . . . . 20 3.2.6 Cell.py: Dynamic Creation of Threads . . . . . . . . . . . . . . . . . . . . . . . . . 22 3.3 Note These Restrictions on PEMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4 SimPy Data Collection and Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.1 Introduction to Monitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.4.2 Time Averages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.4.3 The Function Monitor.timeAverage() . . . . . . . . . . . . . . . . . . . . . . . . . 27 3.4.4 But I Recommend That You Not Use This Function . . . . . . . . . . . . . . . . . . 27 1 3.4.5 3.5 Little’s Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 Other SimPy Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 A How to Obtain and Install SimPy 29 B Debugging and Verifying SimPy Programs 30 B.1 Debugging Tools . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 B.2 Know How Control Transfers in SimPy Programs . . . . . . . . . . . . . . . . . . . . . . . 30 B.3 Always Know What (Simulated) Time It Is . . . . . . . . . . . . . . . . . . . . . . . . . . 31 B.4 Starting Over . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B.5 Repeatability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B.6 Peeking at the SimPy’s Internal Event List . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 B.7 SimPy’s Invaluable Tracing Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 C Online Documentation for SimPy 33 2 1 What Is Discrete-Event Simulation (DES)? Consider simulation of some system which evolves through time. There is a huge variety of such applications. One can simulate a weather system, for instance. A key point, though, is that in that setting, the events being simulated would be continuous, meaning for example that if we were to graph temperature against time, the curve would be continuous, no breaks. By contrast, suppose we simulate the operation of a warehouse. Purchase orders come in and are filled, reducing inventory, but inventory is replenished from time to time. Here a typical variable would be the inventory itself, i.e. the number of items currently in stock for a given product. If we were to graph that number against time, we would get what mathematicians call a step function, i.e. a set of flat line segments with breaks between them. The events here—decreases and increases in the inventory—are discrete variables, not continuous ones. DES involves simulating such systems. 2 World Views in DES Programming Simulation programming can often be difficult—difficult to write the code, and difficult to debug. The reason for this is that it really is a form of parallel programming, with many different activities in progress simultaneously, and parallel programming can be challenging. For this reason, many people have tried to develop separate simulation languages, or at least simulation paradigms (i.e. programming styles) which enable to programmer to achieve clarity in simulation code. Special simulation languages have been invented in the past, notably SIMULA, which was invented in the 1960s and has significance today in that it was the language which invented the concept of object-oriented programmg that is so popular today. However, the trend today is to simply develop simulation libraries which can be called from ordinary languages such as C++, instead of inventing entire new languages.1 So, the central focus today is on the programming paradigms, not on language. In this section we will present an overview of the three major discrete-event simulation paradigms. Several world views have been developed for DES programming, as seen in the next few sections. 2.1 The Activity-Oriented Paradigm Let us think of simulating a queuing system. Jobs arrive at random times, and the job server takes a random time for each service. The time between arrivals of jobs, and the time needed to serve a job, will be continuous random variables, possibly having exponential or other continuous distributions. For concreteness, think of an example in which the server is an ATM cash machine and the jobs are customers waiting in line. Under the activity-oriented paradigm, we would break time into tiny increments. If for instance the mean interarrival time were, say 20 seconds, we might break time into increments of size 0.001. At each time point, our code would look around at all the activities, e.g. currently-active job servicing, and check for the possible occurrence of events, e.g. completion of service. Our goal is to find the long-run average job wait 1 These libraries are often called “languages” anyway, and I will do so too. 3 time. Let SimTime represent current simulated time. Our simulation code in the queue example above would look something like this: 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 QueueLength = 0 NJobsServed = 0 SumResidenceTimes = 0 ServerBusy = false generate NextArrivalTime // random # generation NIncrements = MaxSimTime / 0.001 for SimTime = 1*0.001 to NIncrements*0.001 do if SimTime = NextArrivalTime then add new jobobject to queue QueueLength++ generate NextArrivalTime // random # generation if not ServerBusy then ServerBusy = true jobobject.ArrivalTime = SimTime generate ServiceFinishedtime currentjob = jobobject delete head of queue and assign to currentjob QueueLength-else if SimTime = ServiceFinishedtime then NJobsServed++ SumResidenceTimes += SimTime - currentjob.ArrivalTime if QueueLength > 0 then generate ServiceFinishedtime // random # generation delete currentjob from queue QueueLength-else ServerBusy = false print out SumResidenceTimes / NJobsServed 2.2 The Event-Oriented Paradigm Clearly, an activity-oriented simulation program is going to be very slow to execute. Most time increments will produce no state change to the system at all, i.e. no new arrivals to the queue and no completions of service by the server. Thus the activity checks will be wasted processor time. This is a big issue, because in general simulation code often needs a very long time to run. (Electronic chip manufacturers use DES for chip simulation. A simulation can take days to run.) Inspection of the above pseudocode, though, shows a way to dramatically increase simulation speed. Instead of having time “creep along” so slowly, why not take a “shortcut” to the next event? What we could do is something like the following: Instead of having the simulated time advance via the code 1 for SimTime = 1*0.001 to NIncrements*0.001 do we could advance simulated time directly to the time of the next event: 4 1 2 3 4 5 if ServerBusy and NextArrivalTime < ServiceFinishedtime or not ServerBusy then SimTime = NextArrivalTime else SimTime = ServiceFinishedtime (The reason for checking ServerBusy is that ServiceFinishedtime will be undefined if ServerBusy is false.) The entire pseudocode would then be 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 QueueLength = 0 NJobsServed = 0 SumResidenceTimes = 0 ServerBusy = false generate NextArrivalTime SimTime = 0.0; while (1) do if ServerBusy and NextArrivalTime < ServiceFinishedtime or not ServerBusy then SimTime = NextArrivalTime else SimTime = ServiceFinishedtime if SimTime > MaxSimTime then break if SimTime = NextArrivalTime then QueueLength++ generate NextArrivalTime if not ServerBusy then ServerBusy = true jobobject.ArrivalTime = SimTime currentjob = jobobject generate ServiceFinishedtime QueueLength-else // the case SimTime = ServiceFinishedtime NJobsServed++ SumResidenceTimes += SimTime - currentjob.ArrivalTime if QueueLength > 0 then generate ServiceFinishedtime QueueLength-else ServerBusy = false print out SumResidenceTimes / NJobsServed The event-oriented paradigm formalizes this idea. We store an event set, which is the set of all pending events. In our queue example above, for instance, there will always be at least one event pending, namely the next arrival, and sometimes a second pending event, namely the completion of a service. Our code above simply inspects the scheduled event times of all pending events (again, there will be either one or two of them in our example here), and updates SimTime to the minimum among them. In the general case, there may be many events in the event set, but the principle is still the same—in each iteration of the while loop, we update SimTime to the minimum among the scheduled event times. Note also that in each iteration of the while loop, a new event is generated and added to the set; be sure to look at the pseudocode above and verify this. 5 Thus a major portion of the execution time for the program will consist of a find-minimum operation within the event set. Accordingly, it is desirable to choose a data structure for the set which will facilitate this operation, such as a heap-based priority queue. In many event-oriented packages, though, the event set is implemented simply as a linearly-linked list. This will be sufficiently efficient as long as there usually aren’t too many events in the event set; again, in the queue example above, the maximum size of the event set is 2. (We will return to the issue of efficient event lists in a later unit.) Again, note the contrast between this and continuous simulation models. The shortcut which is the heart of the event-oriented paradigm was only possible because of the discrete nature of system change. So this paradigm is not possible in models in which the states are continuous in nature. The event-oriented paradigm was common in the earlier years of simulation, used in packages in which code in a general-purpose programming language such as C called functions in a simulation library. It still has some popularity today. Compared to the main alternative, the process-oriented paradigm, the chief virtues of the event-oriented approach are: • Ease of implementation. The process-oriented approach requires something like threads, and in those early days there were no thread packages available. One needed to write one’s own threads mechanisms, by writing highly platform-dependent assembly-language routines for stack manipulation. • Execution speed. The threads machinery of process-oriented simulation really slows down execution speed (even if user-level threads are used). • Flexibility. If for example one event will trigger two others, it is easy to write this into the application code. 2.3 The Process-Oriented Paradigm Here each simulation activity is modeled by a process. The idea of a process is similar to the notion by the same name in Unix, and indeed one could write process-oriented simulations using Unix processes. However, these would be inconvenient to write, difficult to debug, and above all they would be slow. As noted earlier, the old process-oriented software such as SIMULA and later CSIM were highly platformdependent, due to the need for stack manipulation. However, these days this problem no longer exists, due to the fact that modern systems include threads packages (e.g. pthreads in Unix, Java threads, Windows threads and so on). Threads are sometimes called “lightweight” processes. If we were to simulate a queuing system as above, but using the process-oriented paradigm, we would have two threads, one simulating the arrivals and the other simulating the operation of the server. Those would be the application-specific threads (so NumActiveAppThreads = 2 in the code below), and we would also have a general thread to manage the event set. Our arrivals thread would look something like 1 2 3 4 5 6 NumActiveAppThreads++ while SimTime < MaxSimTime do generate NextArrivalTime add an arrival event for time NextArrivalTime to the event set sleep until wakened by the event-set manager jobobject.ArrivalTime = SimTime 6 7 8 add jobobject to the machine queue thread exit The server thread would look something like 1 2 3 4 5 6 7 8 9 10 11 12 NumActiveAppThreads++ while SimTime < MaxSimTime do sleep until QueueLength > 0 while QueueLength > 0 do remove queue head and assign to jobobject QueueLength-generate ServiceFinishedtime add a service-done event for time ServiceFinishedtime to the event set sleep until wakened by the event-set manager SumResidenceTimes += SimTime - jobobject.ArrivalTime NJobsServed++ thread exit The event set manager thread would look something like 1 2 3 4 5 6 while SimTime < MaxSimTime do sleep until event set is nonempty delete the minimum-time event E from the event set update SimTime to the time scheduled for E wake whichever thread had added E to the event set thread exit The function main() would look something like this: 1 2 3 4 5 6 7 QueueLength = 0 NJobsServed = 0 SumResidenceTimes = 0 ServerBusy = false start the 3 threads sleep until all 3 threads exit print out SumResidenceTimes / NJobsServed Note that the event set manager would be library code, while the other modules shown above would be application code. Two widely used oper-source process-oriented packages are C++SIM, available at http://cxxsim. ncl.ac.uk and SimPy, available at http://simpy.sourceforge.net. The process-oriented paradigm produces more modular code. This is probably easier to write and easier for others to read. It is considered more elegant, and is the more popular of the two main world views today. 3 Introduction to the SimPy Simulation Language SimPy (rhymes with “Blimpie”) is a package for process-oriented discrete-event simulation. It is written in, and called from, Python. I like the clean manner in which it is designed, and the use of Python generators— 7 and for that matter, Python itself—is a really strong point. If you haven’t used Python before, you can learn enough about it to use SimPy quite quickly; see my quick introduction to Python, at my Python tutorials page, http://heather.cs.ucdavis.edu/˜matloff/python.html. Instructions on how to obtain and install SimPy are given in Appendix A. Instead of using threads, as is the case for most process-oriented simulation packages, SimPy makes novel use of Python’s generators capability.2 Generators allow the programmer to specify that a function can be prematurely exited and then later re-entered at the point of last exit, enabling coroutines, meaning functions that alternate execution with each other. The exit/re-entry points are marked by Python’s yield keyword. Each new call to the function causes a resumption of execution of the function at the point immediately following the last yield executed in that function. As you will see below, that is exactly what we need for DES. For convenience, I will refer to each coroutine (or, more accurately, each instance of a coroutine), as a thread.3 3.1 SimPy Overview Here are the major SimPy classes which we will cover in this introduction:4 • Process: simulates an entity which evolves in time, e.g. one customer who needs to be served by an ATM machine; we will refer to it as a thread, even though it is not a formal Python thread • Resource: simulates something to be queued for, e.g. the machine Here are the major SimPy operations/function calls we will cover in this introduction: • activate(): used to mark a thread as runnable when it is first created • simulate(): starts the simulation • yield hold: used to indicate the passage of a certain amount of time within a thread; yield is a Python operator whose first operand is a function to be called, in this case a code for a function that performs the hold operation in the SimPy library • yield request: used to cause a thread to join a queue for a given resource (and start using it immediately if no other jobs are waiting for the resource) • yield release: used to indicate that the thread is done using the given resource, thus enabling the next thread in the queue, if any, to use the resource • yield passivate: used to have a thread wait until “awakened” by some other thread 2 Python 2.2 or better is required. See my Python generators tutorial at the above URL if you wish to learn about generators, but you do not need to know about them to use SimPy. 3 This tutorial does not assume the reader has a background in threads programming. In fact, readers who do have that background will have to unlearn some of what they did before, because our threads here will be non-preemptive, unlike the preemptive type one sees in most major threads packages. 4 Others will be covered in our followup tutorial at AdvancedSimpy.pdf. 8 • reactivate(): does the “awakening” of a previously-passivated thread • cancel(): cancels all the events associated with a previously-passivated thread Here is how the flow of control goes from one function to another: • When main() calls simulate() main() blocks. The simulation itself then begins, and main() will not run again until the simulation ends. (When main() resumes, typically it will print out the results of the simulation.) • Anytime a thread executes yield, that thread will pause. SimPy’s internal functions will then run, and will restart some thread (possibly the same thread). • When a thread is finally restarted, its execution will resume right after whichever yield statement was executed last in this thread. Note that activate(), reactivate() and cancel do NOT result in a pause to the calling function. Such a pause occurs only when yield is invoked. Those with extensive experience in threads programming (which, as mentioned, we do NOT assume here) will recognize this the non-preemptive approach to threads. In my opinion, this is a huge advantage, for two reasons: • Your code is not cluttered up with a lot of lock/unlock operations. • Execution is deterministic, which makes both writing and debugging the program much easier. (A disadvantage is that SimPy, in fact Python in general, cannot run in a parallel manner on multiprocessor machines.) 3.2 Introduction to SimPy Programming We will demonstrate the usage of SimPy by presenting three variations on a machine-repair model. In each case, we are modeling a system consisting of two machines which are subject to breakdown, but with different repair patterns: • MachRep1.py: There are two repairpersons, so that the two machines can be repaired simultaneously if they are both down at once. • MachRep2.py: Here there is only one repairperson, so if both machines are down then one machine must queue for the repairperson while the other machine is being repaired. • MachRep3.py: Here there is only one repairperson, and he/she is not summoned until both machines are down. In all cases, the up times and repair times are assumed to be exponentially distributed with means 1.0 and 0.5, respectively. Now, let’s look at the three programs.5 5 You can make your own copies of these programs by downloading the raw .tex file for this tutorial, and then editing out the material other than the program you want. 9 3.2.1 MachRep1.py: Our First SimPy Program Here is the code: 1 #!/usr/bin/env python 2 3 # MachRep1.py 4 5 6 7 8 9 # # # # # Introductory SimPy example: Two machines, which sometimes break down. Up time is exponentially distributed with mean 1.0, and repair time is exponentially distributed with mean 0.5. There are two repairpersons, so the two machines can be repaired simultaneously if they are down at the same time. 10 11 12 # Output is long-run proportion of up time. # 0.66. Should get value of about 13 14 15 import SimPy.Simulation import random # required 16 17 18 class G: # global variables Rnd = random.Random(12345) 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 class MachineClass(SimPy.Simulation.Process): UpRate = 1/1.0 # reciprocal of mean up time RepairRate = 1/0.5 # reciprocal of mean repair time TotalUpTime = 0.0 # total up time for all machines NextID = 0 # next available ID number for MachineClass objects def __init__(self): # required constructor SimPy.Simulation.Process.__init__(self) # must call parent constructor # instance variables self.StartUpTime = 0.0 # time the current up period started self.ID = MachineClass.NextID # ID for this MachineClass object MachineClass.NextID += 1 def Run(self): # required constructor while 1: # record current time, now(), so can see how long machine is up self.StartUpTime = SimPy.Simulation.now() # hold for exponentially distributed up time UpTime = G.Rnd.expovariate(MachineClass.UpRate) yield SimPy.Simulation.hold,self,UpTime # simulate UpTime # update up time total MachineClass.TotalUpTime += SimPy.Simulation.now() - self.StartUpTime RepairTime = G.Rnd.expovariate(MachineClass.RepairRate) # hold for exponentially distributed repair time yield SimPy.Simulation.hold,self,RepairTime 43 44 45 46 47 48 49 50 51 52 53 54 55 56 def main(): SimPy.Simulation.initialize() # required # set up the two machine threads for I in range(2): # create a MachineClass object M = MachineClass() # register thread M, executing M’s Run() method, SimPy.Simulation.activate(M,M.Run()) # required # run until simulated time 10000 MaxSimtime = 10000.0 SimPy.Simulation.simulate(until=MaxSimtime) # required print "the percentage of up time was", \ MachineClass.TotalUpTime/(2*MaxSimtime) 57 58 if __name__ == ’__main__’: main() First, some style issues: 10