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public void stopServing(int time) { System.out.printf("%s stopped serving client %s at time %d.%n", this, client, time); client = null; } public String toString() { return "Server " + "ABCDEFGHIJKLMNOPQRSTUVWXYZ".charAt(id); } }
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The startServing() method (lines 26 32) assigns a new client to the server, stores the start time in the Client object, computes and stores the stop time in its own stopTime field, and prints a report of those actions. The stopServing() method (lines 34 38) stores the stop time in the Client object and prints another report. For a simulation to be realistic, it must use randomly generated numbers to simulate the natural uncertainty of the real word. Those random numbers should have the same distribution as the natural uncertainties that they represent. Service times and time between client arrivals both tend to be distributed exponentially. That means that the probability that the time t is less than a number x is p = 1 e- x. But the Math.random() method returns numbers that are uniformly distributed in the range 0 p < 1. So to convert the random number p to the exponentially distributed random variable x, we solve the equation, obtaining x = (1/ ) ln(1 p). The constant 1/ is the mean of the distribution. Thus we code the nextDouble() method as shown at line 9:
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public class ExpRandom extends java.util.Random { private double mean; public ExpRandom(double mean) { this.mean = mean; } public double nextDouble() { return -mean*Math.log(1 - Math.random()); } public int nextInt() { return (int)Math.ceil(nextDouble()); } }
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The actual simulation is performed by the main class shown below. It sets four constants for the simulation at lines 2 5: the number of servers, the number of clients arriving for service, the mean service time among the servers, and the mean time between arrivals for the clients. The queue is to hold the clients that have arrived for service and are waiting for an unoccupied server. The simulation instantiates two random exponentially distributed number generators (lines 7 8) and separate arrays for the Server and Client objects (lines 9 10):
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public class Simulation { private static final int SERVERS = 3; private static final int CLIENTS = 20; private static final double MEAN_SERVICE_TIME = 25; private static final double MEAN_ARRIVAL_TIME = 4; private static Queue<Client> queue = new ArrayDeque<Client>(); private static ExpRandom randomService = new ExpRandom(MEAN_SERVICE_TIME); private static ExpRandom randomArrival = new ExpRandom(MEAN_ARRIVAL_TIME); private static Server[] servers = new Server[SERVERS]; private static Client[] clients = new Client[CLIENTS];
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public Simulation() { String fmt = "%-27s %6d%n"; System.out.printf(fmt, "Number of servers:", SERVERS); System.out.printf(fmt, "Number of clients:", CLIENTS); System.out.printf(fmt, "Mean service time:", MEAN_SERVICE_TIME); System.out.printf(fmt, "Mean interarrival time:", MEAN_ARRIVAL_TIME); for (int i=0; i<SERVERS; i++) { double meanServiceTime = randomService.nextDouble(); servers[i] = new Server(i, meanServiceTime); System.out.printf("Mean service time for %s: %4.1f%n", servers[i], servers[i].getMeanServiceTime()); } int nextArrivalTime = 0; for (int t=0, clientId=0; clientId < CLIENTS; t++) { if (t == nextArrivalTime) { nextArrivalTime = t + randomArrival.nextInt(); Client client = clients[clientId] = new Client(++clientId, t); queue.add(client); System.out.println("\tClient queue: " + queue); } for (Server server : servers) { if (t == server.getStopTime()) { server.stopServing(t); } if (server.isIdle() && !queue.isEmpty()) { Client client = (Client)queue.remove(); System.out.println("\tClient queue: " + queue); server.startServing(client,t); } } } } public static void main(String[] args) { new Simulation(); } }
The output for one run was:
Number of servers: Number of clients: Mean service time: Mean interarrival time: Mean service time for Server A: Mean service time for Server B: Mean service time for Server C: #1 arrived at time 0. Client queue: [#1] Client queue: [] Server A started serving client #2 arrived at time 2. Client queue: [#2] Client queue: [] Server B started serving client #3 arrived at time 4. Client queue: [#3] Client queue: [] 3 12 25 4 17.2 51.7 24.5
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