/******************************************************************************

  *  Compilation:  javac MM1Queue.java

  *  Execution:    java MM1Queue lambda mu

  *  Dependencies: Queue.java Histogram.java

  *

  *  Simulate an M/M/1 queue where arrivals and departures are Poisson

  *  processes with arrival rate lambda and service rate mu.

  *

  *  % java MM1Queue .20 .33

  *

  *  % java MM1Queue .20 .25

  *

  *  % java MM1Queue .20 .21

  *

  *

  *  Remarks

  *  -------

  *   - We assume the interrarrival and service times are independent.

  *

  *

  ******************************************************************************/

 public class MM1Queue { 

     public static void main(String[] args) {

         double lambda = Double.parseDouble(args[0]);  // arrival rate

         double mu     = Double.parseDouble(args[1]);  // service rate

         Queue<Double> q = new Queue<Double>();            // arrival times of customers

         double nextArrival   = StdRandom.exp(lambda);     // time of next arrival

         double nextDeparture = Double.POSITIVE_INFINITY;  // time of next departure

         // histogram object

         Histogram hist = new Histogram(60);

         // simulate an M/M/1 queue

         while (true) {

             // it's an arrival

             if (nextArrival <= nextDeparture) {

                 if (q.isEmpty()) nextDeparture = nextArrival + StdRandom.exp(mu);

                 q.enqueue(nextArrival);

                 nextArrival += StdRandom.exp(lambda);

             }

             // it's a departure

             else {

                 double wait = nextDeparture - q.dequeue();

                 StdOut.printf("Wait = %6.2f, queue size = %d\n", wait, q.size());

                 hist.addDataPoint(Math.min(60,  (int) (Math.round(wait))));

                 hist.draw();

                 if (q.isEmpty()) nextDeparture = Double.POSITIVE_INFINITY;

                 else             nextDeparture += StdRandom.exp(mu);

             }

         }

     }

 }