Consider N = 5 servers, where each server completes a job with probability µ = 0

Question

Consider N = 5 servers, where each server completes a job with probability µ  = 0:5 in each
time slot. Assume that the number of jobs that arrive in each time slot is a Binomial random
variable with parameters N and . When each job arrives, let the job join the queue with
the fewest number of waiting jobs, i.e., join the shortest queue. If multiple jobs arrive in a
time slot, do this for one job at a time, update the queue lengths, and then do this again for
the next job.
Plot the mean delay as a function of . You should keep track of each job to obtain
the delay of the job. Choose = [0.2; 0.3; 0.4; 0.45; 0.49; 0.495]. You should run the
simulations for 10^6 time slots.
Plot a histogram of the delays for = 0.45, i.e., the x-axis would be the possible delays,
1 time slot, 2 time slots, etc. The y-axis would be the fraction of jobs that experience a
delay of 1 time slot, 2 time slots, 3 time slots, etc.

Note:
Choose one programming language to do the simulation from C/C++, Matlab, Python,
Java, and R.
Report should include the plot, and simulation code and annotations.

Explanation / Answer

i use the DDA line approach to plot the graph with x and y axes taking input from user  

#include <graphics.h>

#include <iostream.h>

#include <math.h>

#include <dos.h>

void main( )

{

    float x,y,x1,y1,x2,y2,dx,dy,step;

    int i,gd=DETECT,gm;

    initgraph(&gd,&gm,"c:\turboc3\bgi");

    cout<<"Enter the value of x1 and y1 : ";

    cin>>x1>>y1;

    cout<<"Enter the value of x2 and y2: ";

    cin>>x2>>y2;

    dx=abs(x2-x1);

    dy=abs(y2-y1);

    if(dx>=dy)

        step=dx;

    else

        step=dy;

    dx=dx/step;

    dy=dy/step;

    x=x1;

    y=y1;

    i=1;

    while(i<=step)

    {

        putpixel(x,y,5);

        x=x+dx;

        y=y+dy;

        i=i+1;

        delay(100);

    }

    closegraph();

}

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