1. Consider N = 5 servers, where each server completes a job with probability = 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 106 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.