Binomial random variable

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 λ . 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 λ . You should keep track of each job to obtain the delay of the job. Choose λ = [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 λ = 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.

Java programming. Report should include the plot, and simulation code and annotations.

Taidot: Java

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