The time between the arrival at a traffic light (or at a highway toll booth) of a car and the arrival of the next car,  the time between the arrival of one phone call and the other at the switchboard for a television broadcast, … are example of the negative exponential distribution. The "zombies" example remembers them.

 Zombies A 1 long wall; a W wide hole in the wall; every second a zombie arrives in a completely random position of the wall.  Let W be 1/10; let's simulate 1 hour. The waiting times between a pass through the hole of a zombie and the next pass:

17, 10, 8, 36, 7, 21, 1, 6, 2, 8, 3, 5, 7, 3, 7, 2, 2, 6, 2, 15, 12, 10, 2, 18, 1, 19, 14, 22, 6, 2, 2, 7, 4, 8, 12, 6, 12, 2, 17, 4, 1, 3, 5, 15, 11, 1, 4, 16, 6, 11, 6, 20, 2, 14, 1, 15, 38, 1, 7, 23, 10, 4, 25, 1, 1, 4, 11, 7, 1, 4, 2, 6, 7, 15, 4, 20, 17, 3, 15, 8, 16, 2, 15, 3, 3, 3, 30, 13, 23, 19, 38, 18, 4, 17, 1, 1, 1, 21, 5, 45, 11, 3, 5, 2, 19, 9, 5, 16, 5, 1, 1, 35, 12, 6, 22, 29, 16, 13, 8, 9, 12, 4, 4, 1, 10, 1, 2, 10, 22, 2, 2, 16, 20, 12, 5, 5, 2, 12, 1, 9, 1, 26, 37, 1, 6, 2, 8, 7, 6, 1, 5, 8, 6, 6, 19, 4, 23, 12, 33, 4, 3, 8, 4, 2, 28, 20, 10, 15, 15, 4, 5, 2, 3, 1, 1, 18, 4, 2, 15, 10, 6, 1, 9, 5, 32, 1, 31, 20, 10, 5, 23, 1, 9, 11, 3, 20, 14, 5, 5, 5, 1, 18, 3, 23, 7, 10, 10, 14, 3, 8, 9, 3, 8, 1, 21, 3, 5, 2, 31, 1, 31, 1, 3, 37, 5, 7, 4, 21, 7, 7, 2, 13, 4, 4, 1, 1, 8, 25, 18, 4, 5, 6, 14, 17, 2, 11, 6, 5, 6, 8, 1, 9, 1, 6, 9, 4, 1, 5, 1, 14, 6, 12, 3, 3, 7, 6, 3, 10, 31, 3, 3, 4, 8, 4, 12, 5, 1, 3, 1, 18, 25, 6, 24, 14, 2, 1, 29, 23, 31, 15, 24, 2, 2, 5, 4, 5, 15, 3, 3, 14, 11, 5, 2, 9, 45, 3, 4, 4, 21, 9, 16, 4, 12, 17, 12, 4, 14, 3, 4, 20, 5, 8, 8, 6, 21, 19, 4, 5, 5, 5, 28, 18, 9, 10, 3, 12, 2, 2, 4, 15, 2, 7, 3, 4, 8, 6, 10, 14, 7, 14, 13, 9, 4, 5, 12, 1, 3, 4, 14, 8, 1, 6, 3, 16, 1, 6, 9, 2, 3, 6, 21, 15, 2, 20, 18, 9, 7, 3, 5, 7, 18

The distribution (in 5 sec intervals) of the waiting times. With this script  (hist.htm)  I get:

[the histogram tends to have the graph of  x → W·exp(−W·x)  as profile]

The number of zombies that pass through the hole in 60 sec:

3, 2, 6, 9, 5, 3, 8, 7, 6, 4, 3, 3, 3, 4, 9, 3, 4, 4, 2, 2, 0, 1, 6, 2, 0, 2, 6, 5, 3, 1, 4, 8, 4, 5, 5, 0, 4, 8, 3, 4, 4, 3, 8, 8, 2, 0, 2, 5, 6, 5, 6, 8, 2, 1, 6, 4, 6, 4, 6, 12, 6, 5, 10, 2, 3, 3, 1, 5, 7, 3, 4, 2, 4, 5, 5, 3, 4, 7, 8, 5, 7, 8, 5, 4, 5

The distribution of them. With this script  (hist.htm)  I get:

[the histogram tends to have the graph of the Poisson distribution (with the same mean) as profile]

Using these outputs (waiting times), with this script  (istog_4.htm)  I get:

between 0 and 5 s, 7.24% of passages per second, ...
The curve:  y = 0.1·e−0.1·x

Using these outputs (zombies that pass), with this script  (istog_5.htm)  I get:

The Poisson distribution (with the same mean: M = 4.47)
n → Mn·exp(-M)/n!