![implementation: homogeneous case
def get_points_homogeneous(min_t, max_t, occurrence):
points = []
for _ in range(occurrence):
points.append(random.randint(min_t, max_t))
points.sort()
for point in points:
yield point](https://image.slidesharecdn.com/dummyloggenerationusingpoissonsampling-200203173521/85/Dummy-log-generation-using-poisson-sampling-7-320.jpg)
![implementation: nonhomogeneous case
def get_points_nonhomogeneous(min_t, max_t, occurrence):
points = []
max_bound = occurrence.get_max_bound(min_t, max_t)
for _ in range(max_bound):
points.append(random.randint(min_t, max_t))
points.sort()
for point in points:
keep_probability = occurrence.get(point) / max_bound
if keep_probability > random.random():
yield point](https://image.slidesharecdn.com/dummyloggenerationusingpoissonsampling-200203173521/85/Dummy-log-generation-using-poisson-sampling-11-320.jpg)
Dummy log generation using poisson sampling
- 1. dummy log generation using poisson sampling kyle (kwanghee choi)
- 2. problem definition - have to simulate fake logs based on log count per hour - data to fit: thumbor.buzzni.com
- 4. log modeling - count of logs per hour == frequency of logs appearing in a fixed interval of time
- 5. log modeling: poisson distribution - wikipedia: poisson distribution expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant rate λ and independently of the time since the last event.
- 6. log modeling: poisson process - wikipedia: poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space.
- 7. implementation: homogeneous case def get_points_homogeneous(min_t, max_t, occurrence): points = [] for _ in range(occurrence): points.append(random.randint(min_t, max_t)) points.sort() for point in points: yield point
- 8. log modeling - not a constant rate λ, but function of time λ(t)
- 9. log modeling: inhomogeneous poisson process
- 10. log modeling: inhomogeneous poisson process λmax keep discard maximum integer bound λ(t) t 65% discard probability 7% discard probability
- 11. implementation: nonhomogeneous case def get_points_nonhomogeneous(min_t, max_t, occurrence): points = [] max_bound = occurrence.get_max_bound(min_t, max_t) for _ in range(max_bound): points.append(random.randint(min_t, max_t)) points.sort() for point in points: keep_probability = occurrence.get(point) / max_bound if keep_probability > random.random(): yield point
- 12. results target function dummy log histogram
- 13. reference - Chiu, S. N., Stoyan, D., Kendall, W. S., & Mecke, J. (2013). Stochastic geometry and its applications (3rd ed.). The Atrium, Southern Gate, Chichester, West Sussex, United Kingdom: John Wiley & Sons. - Poisson distribution. (2019, February 16). Retrieved February 25, 2019, from https://en.wikipedia.org/wiki/Poisson_distribution - Poisson point process. (2019, February 20). Retrieved February 25, 2019, from https://en.wikipedia.org/wiki/Poisson_point_process