702.sagews

import numpy
import pylab
# number of customers
n = 10000
# average time between arrivals
a = 1
# average time to serve each customer
b = 1
# Generate samples:
# inter-arrival times
at=numpy.random.exponential(a,n)
st=numpy.random.exponential(b,n)
for i in range(n-1):
    at[i+1]=at[i+1]+at[i]
ft=range(n)
ft[0]=at[0]+st[0]
for i in range(n-1):
    ft[i+1]=max(at[i+1]+st[i+1],ft[i]+st[i+1])

pylab.clf()
pylab.hist(ft-at)
pylab.savefig('sage.png')