What Is The Collision Possibility Of Car Remote Control

What Is The Collision Possibility Of Car Remote Control


by cawan (cawan[at]ieee.org or chuiyewleong[at]hotmail.com)

on 26/11/2013


Assume there are a number of car remote controls which are operating in
315 MHz where each of them will occupy 50 ms for any button being
pressed. If each of the car remote control be pressed for every 1 second
randomly, then what is the number of the car remote control should
have to induce the collision possibility to 0.5 ? Well, that's almost similar
to birthday paradox which is the fundamental of ancient syn flood attack.

In one second (1000 ms), there are 1000/50 = 20 of 50 ms time slots.
While there are only 2 car remote controls, the possibility they don't
collide each other is 20/20 x 19/20. Yes, the possibility seems high.
However, while the number of car remote controls go up to 6, the
possibility they don't collide each other become

20/20 x 19/20 x 18/20 x 17/20 x 16/20 x 15/20 = 0.44

So, the possibility they will collide each other is 1 - 0.44 = 0.56. Thus,
the possibility for the 6 car remote controls will collide each other in
1 second is higher than 0.5. Well, this might not an issue at all because
while the first press has no response, just press the second time and it
should trigger. For those who looking for jamming the system, simply
fill all the time slots, it should work.