#AJ

import random                                                                                                                                                                                                                                                                   import math
                                                                                                                                                                                                                                                                                def sample_exp(p):
    # random in U(0, 1)                                                                                                                                                                                                                                                             uniform_sample  = random.random()
    return -1.0 * math.log(uniform_sample) /  p;
def n_samples(n, p):                                                                                                                                                                                                                                                                return [sample_exp(p) for i in range(n)]
                                                                                                                                                                                                                                                                                def simulate(mu, lmbda):
    job_sizes = n_samples(2000, mu)                                                                                                                                                                                                                                                 inter_times = n_samples(2000, lmbda)
                                                                                                                                                                                                                                                                                    queue_delay = 0
    for i in range(2000):                                                                                                                                                                                                                                                               queue_delay  = max(0, queue_delay + job_sizes[i] - inter_times[i])

    return queue_delay

def simulate_n(n, mu, lmbda):
    samples = [simulate(mu, lmbda) for i in range(n)]
    print(sum(samples)/n)

simulate_n(200, 1.0, 0.5)
simulate_n(200, 1.0, 0.7)
simulate_n(200, 1.0, 0.9)