CS485 Sylabus

### How to "better" avoid collision

• The goal of the back off algorithm

• Consider the non-persistent CSMA protocol:

• The goal of the back off algorithm is:

 Minimize the probability of collision between 2 or more waiting nodes

• Example:

• When nodes B and C both detect a busy channel:

and B and C pick different random numbers:

then C can sense B's transmission:

• Comment:

• If both nodes pick the same random number (duration), then:

 Their transmissions will collide

Because:

• The end-to-end propagation delay

• Definition:

• End-to-end propagation delay = the time it takes for signals to traverse:

 From one end of the network to the other end of the network

Graphically:

• Notation:

 τ = the end-to-end propagation delay

• Why do nodes wait (x × τ) delay before sensing the channel

• Fact:

• When 2 nodes delay for different (integer) random number × τ, then:

 The node that picks the larger integer is guaranteed to heard the other node's transmission

Proof:

• Suppose the nodes A and E hear a busy channel and backoff:

• Suppose:

 A and E pick 2 different integers that has the minimum difference possible (= 1)

Say:

 A picks x E picks x+1

• Then after x × τ , the node A starts to transmit:

Notice that:

 E can not hear A's transmission yet !!! E will start trying to transmit at time (x+1) × τ

• It take τ sec for the signal from A to reach node E

So at time: (x+1) × τ:

The transmission of A arrives at E in the nick of time !!!

When E starts its transmission attempt, E will hears A's transmission just in the nick of time !!!

• Conclusion:

 We must multiply the random integer value by the end-to-end propagation delay to ensure that the signal has enough time to reach all nodes to avoid collision !!!