1 /****************************************************************************** 2 * Compilation: javac MM1Queue.java 3 * Execution: java MM1Queue lambda mu 4 * Dependencies: Queue.java Histogram.java 5 * 6 * Simulate an M/M/1 queue where arrivals and departures are Poisson 7 * processes with arrival rate lambda and service rate mu. 8 * 9 * % java MM1Queue .20 .33 10 * 11 * % java MM1Queue .20 .25 12 * 13 * % java MM1Queue .20 .21 14 * 15 * 16 * Remarks 17 * ------- 18 * - We assume the interrarrival and service times are independent. 19 * 20 * 21 ******************************************************************************/ 22 23 public class MM1Queue { 24 25 public static void main(String[] args) { 26 double lambda = Double.parseDouble(args[0]); // arrival rate 27 double mu = Double.parseDouble(args[1]); // service rate 28 29 Queue<Double> q = new Queue<Double>(); // arrival times of customers 30 double nextArrival = StdRandom.exp(lambda); // time of next arrival 31 double nextDeparture = Double.POSITIVE_INFINITY; // time of next departure 32 33 // histogram object 34 Histogram hist = new Histogram(60); 35 36 // simulate an M/M/1 queue 37 while (true) { 38 39 // it's an arrival 40 if (nextArrival <= nextDeparture) { 41 if (q.isEmpty()) nextDeparture = nextArrival + StdRandom.exp(mu); 42 q.enqueue(nextArrival); 43 nextArrival += StdRandom.exp(lambda); 44 } 45 46 // it's a departure 47 else { 48 double wait = nextDeparture - q.dequeue(); 49 StdOut.printf("Wait = %6.2f, queue size = %d\n", wait, q.size()); 50 hist.addDataPoint(Math.min(60, (int) (Math.round(wait)))); 51 hist.draw(); 52 if (q.isEmpty()) nextDeparture = Double.POSITIVE_INFINITY; 53 else nextDeparture += StdRandom.exp(mu); 54 55 } 56 } 57 58 } 59 60 }