expected blocktime by random time selection

gistfile1.txt

#!/usr/bin/env python3

from numpy import *

nblocks = 10000
nsamples= 10000

def random_block_duration(_acc=1, _steps=512):
    nz = nonzero(random.poisson(1/600., size=_steps))[0]
    return _acc + nz[0] if len(nz) else random_block_duration(_acc + _steps, _steps)
intervals = array([random_block_duration() for _ in range(nblocks)])
block_times = cumsum(intervals)
def block_length_at_time(t):
    return intervals[searchsorted(block_times, t)]
sample_times = random.random(size=nsamples) * block_times[-1]
sample_lengths = vectorize(block_length_at_time)(sample_times)

def p(what, xs):
    print('%d %s, average = %f seconds, min = %f, max = %f' % 
        (len(xs), what, average(xs), min(xs), max(xs)))
p('blocks created', intervals)
p('times sampled', sample_lengths)


--

~/work/blocktime/% ./blocktime.py  
1000 blocks created, average = 620.926000 seconds, min = 4.000000, max = 4677.000000
10000 times sampled, average = 1181.791000 seconds, min = 6.000000, max = 4677.000000
~/work/blocktime/% ./blocktime.py
1000 blocks created, average = 613.377000 seconds, min = 1.000000, max = 4307.000000
10000 times sampled, average = 1230.157100 seconds, min = 4.000000, max = 4307.000000
~/work/blocktime/% ./blocktime.py
1000 blocks created, average = 596.308000 seconds, min = 3.000000, max = 4532.000000
10000 times sampled, average = 1126.356100 seconds, min = 14.000000, max = 4532.000000