Simulating multiple Poisson processes

Question

I have N processes and a different Poisson rate for each. I would like to simulate arrival times from all N processes. If N =1 I can do this

t = 0
N = 1
for i in range(1,10):
   t+= random.expovariate(15)
   print N, t

However if I have N = 5 and a list of rates

rates =  [10,1,15,4,2]

I would like somehow for the loop to output the arrival times of all N processes in the right order. That is I would still like only two numbers per line (the ID of the process and the arrival time) but globally sorted by arrival time.

I could just make N lists and merge them afterwards but I would like the arrival times to be outputted in the right order in the first place.

Update. One problem is that if you just sample a fixed number of arrivals from each process, you get only early times from the high rate processes. So I think I need to sample from a fixed time interval for each process so the number of samples varies depending on the rate.

Answer 1

If I'm understanding you correctly:

import random
import itertools

def arrivalGenerator(rate):
    t = 0
    while True:
        t += random.expovariate(rate)
        yield t

rates = [10, 1, 15, 4, 2]
t = [(i, 0) for i in range(0, len(rates))]
arrivals = []
for i in range(len(rates)):
    t = 0
    generator = arrivalGenerator(rates[i])
    arrivals += [(i, arrival) \
                 for arrival in itertools.takewhile(lambda t: t < 100, generator)]


sorted_arrivals = sorted(arrivals, key=lambda x: x[1])
for arrival in sorted_arrivals:
    print arrival[0], arrival[1]

Note that your initial logic was generating a fixed number of arrivals for each process. What you really want is a specific time window, and to keep generating for a given process until you exceed that time window.