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from random import expovariate, gauss
from statistics import mean, median, stdev

average_arrival_interval = 5.6
average_service_time = 5.0
stdev_service_time = 0.5

num_waiting = 0
arrivals = []
starts = []
arrival = service_end = 0.0
for i in range(20000):
    if arrival <= service_end:
        num_waiting += 1
        arrival += expovariate(1.0 / average_arrival_interval)
        arrivals.append(arrival)
    else:
        num_waiting -= 1
        service_start = service_end if num_waiting else arrival
        service_time = gauss(average_service_time, stdev_service_time)
        service_end = service_start + service_time
        starts.append(service_start)

waits = [start - arrival for arrival, start in zip(arrivals, starts)]
print(f'Mean wait: {mean(waits):.1f}.  Stdev wait: {stdev(waits):.1f}.')
print(f'Median wait: {median(waits):.1f}.  Max wait: {max(waits):.1f}.')

# CREAT A 4X4 array of random numbers from normal distribution
import numpy as np
samples = np.random.normal(size=(4,4))

# Prints 10 Random Integers
import random

for i in range(10):
    x = random.random()
    print(x)

#Excerpt From: Charles R Severance. “Python for Everybody.” iBooks. 

# SIMULATES A RANDOM WALK
import random 
position = 0 
walk = [position] 
steps = 1000 
for i in range(steps): 
  step = 1 if random.randint(0,1) else -1 
  position += step 
  walk.append(position)

# RANDOM COIN FLIPS
nsteps = 1000
draws = np.random.randint(0,2,size=nsteps)
steps = np.where(draws > 0, 1, -1)
walk = steps.cumsum
walk.min()
walk.max()

# Calculate How Many Steps to Reach 10
(np.abs(walk) >= 10).argmax() # 

# FUNCTION FOR CREATING MULTIPLE RANDOM WALKS
nwalks = 5000
nsteps =1000
steps = np.where(draws > 0, 1, -1)
walk = steps.cumsum(1)
walks
walks.max()
walks.min()

# MINIMUM CROSSING TIME TO 30 OR -30
hits30 = (np.abs(walks) >= 30).any(1) 
hits30 
hits30.sum() # Number that hit 30 or -30 

#CROSSING TIME MEAN
crossing_times = (np.abs(walks[hits30]) >= 30).argmax(1)
crossing_times.mean()

# CREATE A DISTRIBUTION WITH A MEAN AND STDEV
steps = np.random.normal(loc=0, scale=.25,size=(nwalks, nsteps))