Question

Consider a Bluetooth scatternet consisting of 2 piconets. What is the probability of a collision between packets of the two piconets? Assume nodes are not using CSMA. Remember that a successful transmission requires both a successful polling message to be sent from the master to slave, and then a successful message sent from slave to master. Assume there are 80 frequencies possible. All piconets constantly have packets they are trying to send and they are not using CSMA

Answer 1

The probability of a collision between packets of the two piconets in a Bluetooth scatternet can be calculated using the formula (1 - 1/6400)^2.

Step-by-step explanation:

In a Bluetooth scatternet consisting of 2 piconets with no CSMA, the probability of a collision between packets of the two piconets can be calculated as:

1. Calculate the probability of a successful transmission for each piconet: p(success) = (1/80)^2 = 1/6400
2. Calculate the probability of collision for each piconet: p(collision) = 1 - p(success)
3. Since the two piconets are independent, the probability of collision between the packets of the two piconets is the product of their individual collision probabilities: p(collision between piconets) = p(collision piconet 1) * p(collision piconet 2)

Therefore, the probability of a collision between packets of the two piconets is (1 - 1/6400)^2 = 0.9994222222, or approximately 0.9994.