# Discrete Event Simulation CS1316: Representing Structure and Behavior.

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Discrete Event Simulation CS1316: Representing Structure and Behavior

Story Discrete event simulation Simulation time != real time Key ideas: A Queue A Queue is a queue, no matter how implemented. Different kinds of random Straightening time Inserting it into the right place Sorting it afterwards Building a discrete event simulation Graphics as the representation, not the real thing: The Model and the View

Imagine the simulation… There are three Trucks that bring product from the Factory. On average, they take 3 days to arrive. Each truck brings somewhere between 10 and 20 products—all equally likely. We’ve got five Distributors who pick up product from the Factory with orders. Usually they want from 5 to 25 products, all equally likely. It takes the Distributors an average of 2 days to get back to the market, and an average of 5 days to deliver the products. Question we might wonder: How much product gets sold like this?

Don’t use a Continuous Simulation We don’t want to wait that number of days in real time. We don’t even care about every day. There will certainly be timesteps (days) when nothing happens of interest. We’re dealing with different probability distributions. Some uniform, some normally distributed. Things can get out of synch A Truck may go back to the factory and get more product before a Distributor gets back. A Distributor may have to wait for multiple trucks to fulfill orders (and other Distributors might end up waiting in line)

We use a Discrete Event Simulation We don’t simulate every moment continuously. We simulate discrete events.

What’s the difference? No time loop In a discrete event simulation: There is no time loop. There are events that are scheduled. At each run step, the next scheduled event with the lowest time gets processed. The current time is then that time, the time that that event is supposed to occur. Key: We have to keep the list of scheduled events sorted (in order)

What’s the difference? Agents don’t act() In a discrete event simulations, agents don’t act(). Instead, they wait for events to occur. They schedule new events to correspond to the next thing that they’re going to do. Key: Events get scheduled according to different probabilities.

What’s the difference? Agents get blocked Agents can’t do everything that they want to do. If they want product (for example) and there isn’t any, they get blocked. They can’t schedule any new events until they get unblocked. Many agents may get blocked awaiting the same resource. More than one Distributor may be awaiting arrival of Trucks Key: We have to keep track of the Distributors waiting in line (in the queue)

Key Ideas A Queue A Queue is a queue, no matter how implemented. Different kinds of random Straightening time Inserting it into the right place Sorting it afterwards

Key idea #1: Introducing a Queue First-In-First-Out List First person in line is first person served I got here first! I got here second! I got here third! This is the front or head of the queue This is the tail of the queue

First-in-First-out New items only get added to the tail. Never in the middle Items only get removed from the head. I got here first! I got here second! I got here third! This is the front or head of the queue This is the tail of the queue

As items leave, the head shifts I got here first! AND NOW I’M UP! I got here second! I got here third! Now, this is the front or head of the queue This is the tail of the queue Served!

As new items come in, the tail shifts I got here second! I got here third! Now, this is the front or head of the queue Now, this is the tail of the queue I got here fourth!

What can we do with queues? push(anObject): Tack a new object onto the tail of the queue pop(): Pull the end (head) object off the queue. peek(): Get the head of the queue, but don’t remove it from the queue. size(): Return the size of the queue

Building a Queue > Queue line = new Queue(); > line.push("Fred"); > line.push("Mary"); > line.push("Jose"); > line.size() 3

Accessing a Queue > line.peek() "Fred" > line.pop() "Fred" > line.peek() "Mary" > line.pop() "Mary" > line.peek() "Jose" > line.pop() "Jose" > line.pop() java.util.NoSuchElementException: We don’t really want to peek() or pop() an empty queue, so we should probably check its size first.

Building a Queue import java.util.*; // LinkedList representation /** * Implements a simple queue **/ public class Queue { /** Where we'll store our elements */ public LinkedList elements; /// Constructor public Queue(){ elements = new LinkedList(); }

Queue methods /// Methods /** Push an object onto the Queue */ public void push(Object element){ elements.addFirst(element); } /** Peek at, but don't remove, top of queue */ public Object peek(){ return elements.getLast();} /** Pop an object from the Queue */ public Object pop(){ Object toReturn = this.peek(); elements.removeLast(); return toReturn; } /** Return the size of a queue */ public int size() { return elements.size();} We’re using a linked list to implement the Queue. The front of the LinkedList is the tail. The last of the LinkedList is the head.

A queue is a queue, no matter what lies beneath. Our description of the queue minus the implementation is an example of an abstract data type (ADT). An abstract type is a description of the methods that a data structure knows and what the methods do. We can actually write programs that use the abstract data type without specifying the implementation. There are actually many implementations that will work for the given ADT. Some are better than others.

Array-oriented Queue /** * Implements a simple queue **/ public class Queue2 { private static int ARRAYSIZE = 20; /** Where we'll store our elements */ private Object[] elements; /** The indices of the head and tail */ private int head; private int tail;

Queue = array + head index + tail index /// Constructor public Queue2(){ elements = new Object[ARRAYSIZE]; head = 0; tail = 0; }

Queue2 methods /** Push an object onto the Queue */ public void push(Object element){ if ((tail + 1) >= ARRAYSIZE) { System.out.println("Queue underlying implementation failed"); } else { // Store at the tail, // then increment to a new open position elements[tail] = element; tail++; } } /** Peek at, but don't remove, top of queue */ public Object peek(){ return elements[head];} /** Pop an object from the Queue */ public Object pop(){ Object toReturn = this.peek(); if (((head + 1) >= ARRAYSIZE) || (head > tail)) { System.out.println("Queue underlying implementation failed."); return toReturn; } else { // Increment the head forward, too. head++; return toReturn;}} /** Return the size of a queue */ public int size() { return tail-head;} As the queue gets pushed and popped, it moves down the array.

Same methods, same behavior Welcome to DrJava. > Queue2 line = new Queue2(); > line.push("Mary") > line.push("Kim") > line.push("Ron") > line.peek() "Mary" > line.pop() "Mary" > line.peek() "Kim" > line.size() 2 > line.pop() "Kim" > line.pop() "Ron" But can only handle up to 20 elements in the queue! Less if pushing and popping. Could shift elements to always allow 20. Not as good an implementation as the linked list implementation. (But uses less memory.)

Key idea #2: Different kinds of random We’ve been dealing with uniform random distributions up until now, but those are the least likely random distribution in real life. How can we generate some other distributions, including some that are more realistic?

Visualizing a uniform distribution import java.util.*; // Need this for Random import java.io.*; // For BufferedWriter public class GenerateUniform { public static void main(String[] args) { Random rng = new Random(); // Random Number Generator BufferedWriter output=null; // file for writing // Try to open the file try { // create a writer output = new BufferedWriter(new FileWriter("D:/cs1316/uniform.txt")); } catch (Exception ex) { System.out.println("Trouble opening the file."); } // Fill it with 500 numbers between 0.0 and 1.0, uniformly distributed for (int i=0; i < 500; i++){ try{ output.write("\t"+rng.nextFloat()); output.newLine(); } catch (Exception ex) { System.out.println("Couldn't write the data!"); System.out.println(ex.getMessage()); } // Close the file try{ output.close();} catch (Exception ex) {System.out.println("Something went wrong closing the file");} } By writing out a tab and the integer, we don’t have to do the string conversion.

How do we view a distribution? A Histogram

Then graph the result

A Uniform Distribution

A Normal Distribution // Fill it with 500 numbers between -1.0 and 1.0, normally distributed for (int i=0; i < 500; i++){ try{ output.write("\t"+rng.nextGaussian()); output.newLine(); } catch (Exception ex) { System.out.println("Couldn't write the data!"); System.out.println(ex.getMessage()); }

Graphing the normal distribution The end aren’t actually high— the tails go further.

How do we shift the distribution where we want it? // Fill it with 500 numbers with a mean of 5.0 and a //larger spread, normally distributed for (int i=0; i < 500; i++){ try{ output.write("\t"+((range * rng.nextGaussian())+mean)); output.newLine(); } catch (Exception ex) { System.out.println("Couldn't write the data!"); System.out.println(ex.getMessage()); } Multiply the random nextGaussian() by the range you want, then add the mean to shift it where you want it.

A new normal distribution

Key idea #3: Straightening Time Straightening time Inserting it into the right place Sorting it afterwards We’ll actually do these in reverse order: We’ll add a new event, then sort it. Then we’ll insert it into the right place.

Exercising an EventQueue public class EventQueueExercisor { public static void main(String[] args){ // Make an EventQueue EventQueue queue = new EventQueue(); // Now, stuff it full of events, out of order. SimEvent event = new SimEvent(); event.setTime(5.0); queue.add(event); event = new SimEvent(); event.setTime(2.0); queue.add(event); event = new SimEvent(); event.setTime(7.0); queue.add(event); event = new SimEvent(); event.setTime(0.5); queue.add(event); event = new SimEvent(); event.setTime(1.0); queue.add(event); // Get the events back, hopefull in order! for (int i=0; i < 5; i++) { event = queue.pop(); System.out.println("Popped event time:"+event.getTime()); } We’re stuffing the EventQueue with events whose times are out of order.

If it works right, should look like this: Welcome to DrJava. > java EventQueueExercisor Popped event time:0.5 Popped event time:1.0 Popped event time:2.0 Popped event time:5.0 Popped event time:7.0

Implementing an EventQueue import java.util.*; /** * EventQueue * It's called an event "queue," but it's not really. * Instead, it's a list (could be an array, could be a linked list) * that always keeps its elements in time sorted order. * When you get the nextEvent, you KNOW that it's the one * with the lowest time in the EventQueue **/ public class EventQueue { private LinkedList elements; /// Constructor public EventQueue(){ elements = new LinkedList(); }

Mostly, it’s a queue public SimEvent peek(){ return (SimEvent) elements.getFirst();} public SimEvent pop(){ SimEvent toReturn = this.peek(); elements.removeFirst(); return toReturn;} public int size(){return elements.size();} public boolean empty(){return this.size()==0;}

Two options for add() /** * Add the event. * The Queue MUST remain in order, from lowest time to highest. **/ public void add(SimEvent myEvent){ // Option one: Add then sort elements.add(myEvent); this.sort(); //Option two: Insert into order //this.insertInOrder(myEvent); }

There are lots of sorts! Lots of ways to keep things in order. Some are faster – best are O(n log n) Some are slower – they’re always O(n 2 ) Some are O(n 2 ) in the worst case, but on average, they’re better than that. We’re going to try an insertion sort

How an insertion sort works Consider the event at some position (1..n) Compare it to all the events before that position backwards—towards 0. If the comparison event time is LESS THAN the considered event time, then shift the comparison event down to make room. Wherever we stop, that’s where the considered event goes. Consider the next event…until done

Insertion Sort public void sort(){ // Perform an insertion sort // For comparing to elements at smaller indices SimEvent considered = null; SimEvent compareEvent = null; // Just for use in loop // Smaller index we're comparing to int compare; // Start out assuming that position 0 is "sorted" // When position==1, compare elements at indices 0 and 1 // When position==2, compare at indices 0, 1, and 2, etc. for (int position=1; position < elements.size(); position++){ considered = (SimEvent) elements.get(position); // Now, we look at "considered" versus the elements // less than "compare" compare = position; // While the considered event is greater than the compared event, // it's in the wrong place, so move the elements up one. compareEvent = (SimEvent) elements.get(compare-1); while (compareEvent.getTime() > considered.getTime()) { elements.set(compare,elements.get(compar e-1)); compare = compare-1; // If we get to the end of the array, stop if (compare <= 0) {break;} // else get ready for the next time through the loop else {compareEvent = (SimEvent) elements.get(compare-1);} } // Wherever we stopped, this is where "considered" belongs elements.set(compare,considered); } // for all positions 1 to the end } // end of sort() Trace this out to convince yourself it works!

Useful Links on Sorting http://ciips.ee.uwa.edu.au/~morris/Year2 /PLDS210/sorting.html http://ciips.ee.uwa.edu.au/~morris/Year2 /PLDS210/sorting.html http://www.cs.ubc.ca/spider/harrison/Jav a/sorting-demo.html http://www.cs.ubc.ca/spider/harrison/Jav a/sorting-demo.html http://www.cs.brockport.edu/cs/java/apps /sorters/insertsort.html http://www.cs.brockport.edu/cs/java/apps /sorters/insertsort.html These include animations that help to see how it’s all working Recommended

Option #2: Put it in the right place /** * Add the event. * The Queue MUST remain in order, from lowest time to highest. **/ public void add(SimEvent myEvent){ // Option one: Add then sort //elements.add(myEvent); //this.sort(); //Option two: Insert into order this.insertInOrder(myEvent); }

insertInOrder() /** * Put thisEvent into elements, assuming * that it's already in order. **/ public void insertInOrder(SimEvent thisEvent){ SimEvent comparison = null; // Have we inserted yet? boolean inserted = false; for (int i=0; i < elements.size(); i++){ comparison = (SimEvent) elements.get(i); // Assume elements from 0..i are less than thisEvent // If the element time is GREATER, insert here and // shift the rest down if (thisEvent.getTime() < comparison.getTime()) { //Insert it here inserted = true; elements.add(i,thisEvent); break; // We can stop the search loop } } // end for // Did we get through the list without finding something // greater? Must be greater than any currently there! if (!inserted) { // Insert it at the end elements.addLast(thisEvent);} } Again, trace it out to convince yourself that it works!

Finally: A Discrete Event Simulation Now, we can assemble queues, different kinds of random, and a sorted EventQueue to create a discrete event simulation.

Running a DESimulation Welcome to DrJava. > FactorySimulation fs = new FactorySimulation(); > fs.openFrames("D:/temp/"); > fs.run(25.0)

What we see (not much)

The detail tells the story Time:1.7078547183397625Distributor: 0 Arrived at warehouse Time:1.7078547183397625Distributor: 0 is blocking >>> Timestep: 1 Time:1.727166341118611Distributor: 3 Arrived at warehouse Time:1.727166341118611Distributor: 3 is blocking >>> Timestep: 1 Time:1.8778754913001443Distributor: 4 Arrived at warehouse Time:1.8778754913001443Distributor: 4 is blocking >>> Timestep: 1 Time:1.889475045031698Distributor: 2 Arrived at warehouse Time:1.889475045031698Distributor: 2 is blocking >>> Timestep: 1 Time:3.064560375192933Distributor: 1 Arrived at warehouse Time:3.064560375192933Distributor: 1 is blocking >>> Timestep: 3 Time:3.444420374970288Truck: 2 Arrived at warehouse with load 13 Time:3.444420374970288Distributor: 0 unblocked! Time:3.444420374970288Distributor: 0 Gathered product for orders of 11 >>> Timestep: 3 Time:3.8869697922832698Truck: 0 Arrived at warehouse with load 18 Time:3.8869697922832698Distributor: 3 unblocked! Time:3.8869697922832698Distributor: 3 Gathered product for orders of 12 >>> Timestep: 3 Time:4.095930381479024Distributor: 0 Arrived at market >>> Timestep: 4 Time:4.572840072576855Truck: 1 Arrived at warehouse with load 20 Time:4.572840072576855Distributor: 4 unblocked! Time:4.572840072576855Distributor: 4 Gathered product for orders of 19 Notice that time 2 never occurs!

What questions we can answer How long do distributors wait? Subtract the time that they unblock from the time that they block How much product sits in the warehouse? At each time a distributor leaves, figure out how much is left in the warehouse. How long does the line get at the warehouse? At each block, count the size of the queue. Can we move more product by having more distributors or more trucks? Try it!

How DESimulation works

FactorySimulation: Extend a few classes

DESimulation: Sets the Stage DESimulation calls setUp to create agents and schedule the first events. It provides log for writing things out to the console and a text file. When it run()’s, it processes each event in the event queue and tells the corresponding agent to process a particular message.

What a DESimulation does: // While we're not yet at the stop time, // and there are more events to process while ((now < stopTime) && (!events.empty())) { topEvent = events.pop(); // Whatever event is next, that time is now now = topEvent.getTime(); // Let the agent now that its event has occurred topAgent = topEvent.getAgent(); topAgent.processEvent(topEvent.getMessage()); // repaint the world to show the movement // IF there is a world if (world != null) { world.repaint();} // Do the end of step processing this.endStep((int) now); } As long as there are events in the queue, and we’re not at the stopTime: Grab an event. Make it’s time “now” Process the event.

What’s an Event (SimEvent)? /** * SimulationEvent (SimEvent) -- an event that occurs in a simulation, * like a truck arriving at a factory, or a salesperson leaving the * market **/ public class SimEvent{ /// Fields /// /** When does this event occur? */ public double time; /** To whom does it occur? Who should be informed when it occurred? */ public DEAgent whom; /** What is the event? We'll use integers to represent the meaning * of the event -- the "message" of the event. * Each agent will know the meaning of the integer for themselves. **/ public int message; It’s a time, an Agent, and an integer that the Agent will understand as a message

DEAgent: Process events, block if needed DEAgents define the constants for messages: What will be the main events for this agent? If the agent needs a resource, it asks to see if it’s available, and if not, it blocks itself. It will be told to unblock when it’s ready. Agents are responsible for scheduling their OWN next event!

An Example: A Truck /** * Truck -- delivers product from Factory * to Warehouse. **/ public class Truck extends DEAgent { /////// Constants for Messages public static final int FACTORY_ARRIVE = 0; public static final int WAREHOUSE_ARRIVE = 1; ////// Fields ///// /** * Amount of product being carried **/ public int load;

How Trucks start /** * Set up the truck * Start out at the factory **/ public void init(Simulation thisSim){ // Do the default init super.init(thisSim); this.setPenDown(false); // Pen up this.setBodyColor(Color.green); // Let green deliver! // Show the truck at the factory this.moveTo(30,350); // Load up at the factory, and set off for the warehouse load = this.newLoad(); ((DESimulation) thisSim).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); } The truck gets a load, then schedules itself to arrive at the Warehouse.

tripTime() uses the normal distribution /** A trip distance averages 3 days */ public double tripTime(){ double delay = randNumGen.nextGaussian()+3; if (delay < 1) // Must take at least one day {return 1.0+((DESimulation) simulation).getTime();} else {return delay+((DESimulation) simulation).getTime();} }

newLoad() uses uniform /** A new load is between 10 and 20 on a uniform distribution */ public int newLoad(){ return 10+randNumGen.nextInt(11); }

How a Truck processes Events /** * Process an event. * Default is to do nothing with it. **/ public void processEvent(int message){ switch(message){ case FACTORY_ARRIVE: // Show the truck at the factory ((DESimulation) simulation).log(this.getName()+"\t Arrived at factory"); this.moveTo(30,350); // Load up at the factory, and set off for the warehouse load = this.newLoad(); ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); break;

Truck Arriving at the Warehouse case WAREHOUSE_ARRIVE: // Show the truck at the warehouse ((DESimulation) simulation).log(this.getName()+"\t Arrived at warehouse with load \t"+load); this.moveTo(50,50); // Unload product -- takes zero time (unrealistic!) ((FactorySimulation) simulation).getProduct().add(load); load = 0; // Head back to factory ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),FACTORY_ARRIVE)); break;

What Resources do They keep track of what amount they have available (of whatever the resource is). They keep a queue of agents that are blocked on this resource. They can add to the resource, or have it consume(d). When more resource comes in, the head of the queue gets asked if it’s enough. If so, it can unblock.

How Resources alert agents /** * Add more produced resource. * Is there enough to unblock the first * Agent in the Queue? **/ public void add(int production) { amount = amount + production; if (!blocked.empty()){ // Ask the next Agent in the queue if it can be unblocked DEAgent topOne = (DEAgent) blocked.peek(); // Is it ready to run given this resource? if (topOne.isReady(this)) { // Remove it from the queue topOne = (DEAgent) blocked.pop(); // And tell it it’s unblocked topOne.unblocked(this); }

An example blocking agent: Distributor /** * Distributor -- takes orders from Market to Warehouse, * fills them, and returns with product. **/ public class Distributor extends DEAgent { /////// Constants for Messages public static final int MARKET_ARRIVE = 0; public static final int MARKET_LEAVE = 1; public static final int WAREHOUSE_ARRIVE = 2; /** AmountOrdered so-far */ int amountOrdered;

Distributors start in the Market public void init(Simulation thisSim){ //First, do the normal stuff super.init(thisSim); this.setPenDown(false); // Pen up this.setBodyColor(Color.blue); // Go Blue! // Show the distributor in the market this.moveTo(600,460); // At far right // Get the orders, and set off for the warehouse amountOrdered = this.newOrders(); ((DESimulation) thisSim).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); }

Distributors have 3 events Arrive in Market: Schedule how long it’ll take to deliver. Leave Market: Schedule arrive at the Factory Arrive at Warehouse: Is there enough product available? If not, block and wait for trucks to bring enough product.

Processing Distributor Events /** * Process an event. * Default is to do nothing with it. **/ public void processEvent(int message){ switch(message){ case MARKET_ARRIVE: // Show the distributor at the market, far left ((DESimulation) simulation).log(this.getName()+"\t Arrived at market"); this.moveTo(210,460); // Schedule time to deliver ((DESimulation) simulation).addEvent( new SimEvent(this,timeToDeliver(),MARKET_LEAVE)); break;

Leaving the Market case MARKET_LEAVE: // Show the distributor at the market, far right ((DESimulation) simulation).log(this.getName()+"\t Leaving market"); this.moveTo(600,460); // Get the orders, and set off for the warehouse amountOrdered = this.newOrders(); ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),WAREHOUSE_ARRIVE)); break;

Arriving at the Warehouse case WAREHOUSE_ARRIVE: // Show the distributor at the warehouse ((DESimulation) simulation).log(this.getName()+"\t Arrived at warehouse"); this.moveTo(600,50); // Is there enough product available? Resource warehouseProduct = ((FactorySimulation) simulation).getProduct(); if (warehouseProduct.amountAvailable() >= amountOrdered) { // Consume the resource for the orders warehouseProduct.consume(amountOrdered); // Zero time to load? ((DESimulation) simulation).log(this.getName()+"\t Gathered product for orders of \t"+amountOrdered); // Schedule myself to arrive at the Market ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),MARKET_ARRIVE)); } else {// We have to wait until more product arrives! ((DESimulation) simulation).log(this.getName()+"\t is blocking"); waitFor(((FactorySimulation) simulation).getProduct());} break;

Is there enough product? /** Are we ready to be unlocked? */ public boolean isReady(Resource res) { // Is the amount in the factory more than our orders? return ((FactorySimulation) simulation).getProduct().amountAvailable() >= amountOrdered;}

If so, we’ll be unblocked /** * I've been unblocked! * @param resource the desired resource **/ public void unblocked(Resource resource){ super.unblocked(resource); // Consume the resource for the orders ((DESimulation) simulation).log(this.getName()+"\t unblocked!"); resource.consume(amountOrdered); // Zero time to load? ((DESimulation) simulation).log(this.getName()+"\t Gathered product for orders of \t"+amountOrdered); // Schedule myself to arrive at the Market ((DESimulation) simulation).addEvent( new SimEvent(this,tripTime(),MARKET_ARRIVE)); }

The Overall Factory Simulation /** * FactorySimulation -- set up the whole simulation, * including creation of the Trucks and Distributors. **/ public class FactorySimulation extends DESimulation { private Resource product; /** * Accessor for factory **/ public FactoryProduct getFactory(){return factory;}

Setting up the Factory Simulation public void setUp(){ // Let the world be setup super.setUp(); // Give the world a reasonable background FileChooser.setMediaPath("D:/cs1316/MediaSources/"); world.setPicture(new Picture( FileChooser.getMediaPath("EconomyBackground.jpg")) ); // Create a warehouse resource product = new Resource(); //Track product // Create three trucks Truck myTruck = null; for (int i=0; i<3; i++){ myTruck = new Truck(world,this); myTruck.setName("Truck: "+i);} // Create five Distributors Distributor sales = null; for (int i=0; i<5; i++){ sales = new Distributor(world,this); sales.setName("Distributor: "+i);} }

The Master Data Structure List: We use almost everything here! Queues: For storing the agents waiting in line. EventQueues: For storing the events scheduled to occur. LinkedList: For storing all the agents.

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