- 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:
- When nodes B and
C
both detect
a busy channel:
- Comment:
- If both nodes
pick the same random number
(duration), then:
- Their transmissions will collide
Because:
- If both nodes
pick the same random number
(duration), then:
- 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:
- End-to-end propagation delay =
the time it takes for
signals to
traverse:
- Notation:
- τ = the end-to-end propagation delay
- 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
- E
can not hear
A's transmission
yet !!!
- 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 !!!
- When 2 nodes
delay for different (integer)
random number × τ, then:
- 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 !!!