import numpy as np
import random
import matplotlib.pyplot as plt

def simulating(start_point, lambd, time):
    cli = start_point
    clients = [cli]
    visit_time = []
    new_visit_time = random.expovariate(lambd)
    while new_visit_time <= time:
        visit_time.append(new_visit_time)
        new_visit_time += random.expovariate(lambd)
    s = 0   # порядок клиента
    l = 1   # номер шага
    while s < len(visit_time) - 1:
        if tau[l] >= visit_time[s]:
                cli += 1
                s += 1
        clients.append(cli)
        l += 1
    else:
        for i in range(len(clients),len(tau)):
            clients.append(cli)
    return clients


start_point = 0
lambd = 3
time = 5
ns = 1000
tau = np.linspace(0,time,(time * ns) +1)
print (simulating(start_point, lambd, time))
plt.plot(tau,simulating(start_point, lambd, time))