1. Medium Access Control Protocols
CMPE 252A: SET 4:
Medium Access Control Protocols

2. Persistence after Carrier Sensing
Problem: Non-persistent carrier sensing forces stations to back off too much when the channel is lightly loaded.
Approach: Have stations persist with their transmissions immediately after detecting that the channel is busy, and deal with collisions after they occur.
Examples: CSMA, CSMA/CD, CSMA/CA, Ethernet adopts 1-persistent CSMA/CD.

3. 1-Persistent Carrier Sensing
Definition: Any node that has a local DATA packet to send will persist to sense the channel until no carrier is detected. At that time, with probability 1 the node will transmit the packet.
ongoing transmission
collision

4. Markov Chains
A random process is a Markov process if the future of the process given the present is independent of the past.
For arbitrary times we have
The above is called the “Markov property,” and the pmf or pdf of a Markov process that is conditioned on several instants of time always reduces to a pmf or pdf conditioned only on the most recent time instant.

5. Markov Chains Example:
The Poisson process is a continuous-time Markov process, because:

6. Markov Chains An integer-valued Markov process is a Markov chain.
The value of X(t) at time t is called the state of the process at time t.
The probability is called a (state) transition probability.
Transition probabilities must satisfy:

7. Markov Chains
The probability that X(t) assumes a given value at time t is called a state probability.
In all our cases, the probability of state j approaches a constant independent of time and the initial state probabilities, i.e.,
State probabilities become limiting probabilities, steady-state probabilities, or stationary probabilities.
Steady-state probabilities can be interpreted as the proportion of time the system visits a given state.
It must be true that

8. Markov Chains In practice, We can obtain transition probabilities.
From them we obtain steady-state probabilities by means of a system of simultaneous equations that include the sum to 1 of steady-state or transition probabilities.

9. 1-Persistent Carrier Sensing
Definition: Any node that has a local DATA packet to send will persist to sense the channel until no carrier is detected. At that time, with probability 1 the node will transmit the packet.
ongoing transmission
collision

10. 1-persistent CSMA
All the assumptions made for the analysis of non persistent protocols are valid here as well.
Divide time into transmission periods (TP)
The type of a TP that follows another TP depends on the number of those persistent users waiting for the current TP to end!
time
TP 0
TP 1
TP 2
Nodes detect carrier

11. Throughput Analysis
The state of the system at the beginning of a transmission period is the type of that transmission period,
The knowledge of the system at the beginning of a transmission period and the scheduling points of packets during the transmission period determines the state of the system at the beginning of the next transmission period.
We have three states:
Transmission period of type 0 (TP 0): No packets are transmitted at the beginning of the TP.
TP 1: Only one packet is transmitted at the beginning of the TP, and it succeeds if there are no arrivals within tau sec after that.
TP 2: Two or more packets are transmitted at the beginning of the TP.

12. Throughput Analysis
The states correspond to a three-state Markov chain embedded at the beginning of the TP.
The throughput of the system is given by the proportion of time spent in state 1 having a success divided by the average time spent in all three states: 2 1 P 00 01 10 21 12 22 11 20
(a)

13. Throughput Analysis
The average length of TP 0 is the same as in non-persistent CSMA:
A transmission period of type 1 and 2 have the same average length, which is determined by the last packet arriving in the TP, just as in np-CSMA:
The value of Y is:
From the state diagram we have:
(b)

14. Throughput Analysis
Once in TP0, the system leaves to TP1 with probability 1, because we consider all the idle period as a single TP0 (and because arrivals are Poisson!)
If no packets arrive during a TP 1 or TP 2, the next transmission period is TP 0.
If only one packet arrives τ seconds after a TP 1 or TP 2 starts, the next TP is a TP 1.
If two or more packets arrive τ seconds after the start of a TP 1 or TP 2, the next period is a TP 2.
This implies:
(c)

15. Throughput Analysis
(c)
(b)
Using Eqs. (b) and (c) we can obtain:

16. Throughput Analysis
time
FIRST
LAST
START
Y= y
TP 1:
NEXT TP
0 arrivals => TP 0 next
1 arrival => TP 1 next τ τ
Arrivals after the vulnerability period of first packet in TP determine the type of the next TP.
Let Y = y, then:
We know the CDF of Y, and taking the derivative:

17. Throughput Analysis TP 1: NEXT TP τ τ Unconditioning we obtain: time
FIRST
LAST
START
Y= y
TP 1:
NEXT TP
0 arrivals => TP 0 next
1 arrival => TP 1 next τ τ
Unconditioning we obtain:

18. Throughput Analysis TP 1: NEXT TP τ τ Let Y = y, then:
time
FIRST
LAST
START
Y= y
TP 1:
NEXT TP
0 arrivals => TP 0 next
1 arrival => TP 1 next τ τ
Let Y = y, then:
Unconditioning we obtain:

19. Throughput Analysis
Substituting in Eq. (a) we obtain: