1. King Fahd University of Petroleum & Minerals Computer Engineering Dept
COE 541 – Design and Analysis of Local Area Networks
Term 071
Dr. Ashraf S. Hasan Mahmoud Rm
Ext. 1724
2/22/2019
Dr. Ashraf S. Hasan Mahmoud

2. Dr. Ashraf S. Hasan Mahmoud
Random Access Network:
Random access network is characterized by the absence of access control mechanism. A station can transmit at a time (arbitrary) but it can not determine if another station is transmitting at nearly the same time.
Pure ALOHA: a station can transmit at any time (collision interval) is 2 Δt, where Δt is the one way propagation delay.
Slotted ALOHA (S-ALOHA): (refinement from pure aloha) all stations must be synchronized to transmit in the beginning of a time slot, all packets have the same length, and then there is a decrease in the collision interval to Δt :
“Packets may collide completely or not at all”
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Dr. Ashraf S. Hasan Mahmoud

3. Dr. Ashraf S. Hasan Mahmoud
Random Access Network:
Under light load, a user can access the network after a reasonable waiting time.
No central control, a station can be added deleted easily. Network has some good fault tolerance.
S-Aloha is not appropriate for networks for which there is long propagation delay like radio or satellite networks.
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Dr. Ashraf S. Hasan Mahmoud

4. Dr. Ashraf S. Hasan Mahmoud
Random Access Network:
Other networks with shorter propagation delay are benefiting from this strategy.
In this case, a station can listen (carrier sensing) to medium (CSMA) and transmits if medium is not busy.
CSMA is useless for network for which the propagation delay is greater than the packet transmission time like radio or satellite network (useful only when propagation delay is a small fraction of packet transmission time).
CSMA is useful if propagation delay << packet transmission time.
Carrier sense reduces the length of collision intervals.
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Dr. Ashraf S. Hasan Mahmoud

5. Dr. Ashraf S. Hasan Mahmoud
Random Access Network:
CSMA/CD: Listen (for 2 Δt) while transmitting if collision is detected then stop immediately (corrupted transmission can be easily detected) and transmit a jamming signal.
Collision detection gives performance to CSMA/CD than CSMA. However, CSMA/CD are difficult to analyze for the delay. But for Slotted ALOHA (class of random access) a delay analyze is possible.
This is comparable to non-persistent CSMA/CD in terms of general efforts on performance.
Also stability analysis is taken for slotted ALOHA too.
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Dr. Ashraf S. Hasan Mahmoud

6. Dr. Ashraf S. Hasan Mahmoud
Architecture
BUS:
Baseband.
Passive network.
Both directions (Coax/TP/FO) from station.
Prevent reflection.
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7. Dr. Ashraf S. Hasan Mahmoud
Architecture
Tree:
Broadband:
Active repeaters.
Directional transmission (repeaters).
EX: CATV.
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Dr. Ashraf S. Hasan Mahmoud

8. Dr. Ashraf S. Hasan Mahmoud
Architecture
Major difference:
baseband propagation delays << broadband delays
(due to directional transmission)
This chapter is on baseband network.
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9. Dr. Ashraf S. Hasan Mahmoud
Random Access Network (Example)
Signal propagation over a 500 m Coax/TP where signal propagate at a speed of 0.65*C (C= 3*108 m/s) or 5 µs/Km.
The Number of bits transmitted before a collision is detected:
Ncoll = 2*L*5 µs/Km*R b/µs.
R= 1Gbps or 103 b/µs.
Ncoll = 2*0.5 Km*5 µs/Km *103 b/µs= 5 Kbits.
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Dr. Ashraf S. Hasan Mahmoud

10. Dr. Ashraf S. Hasan Mahmoud
Random Access Network (Example)
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11. Dr. Ashraf S. Hasan Mahmoud
The Slotted ALOHA (S-ALOHA):
S-ALOHA can be used for LAN even if it was designed for station channels.
Time is segmented into Δt, where Δt=X/R is the packet
transmission time.
Every packet transmitted must fit in a Δt interval.
Stations must delay transmission until beginning of a Δt.
We assume a bus medium.
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Dr. Ashraf S. Hasan Mahmoud

12. Dr. Ashraf S. Hasan Mahmoud
The Slotted ALOHA (S-ALOHA):
State (station):
transmitting :( a packet is trans. In Δt= ).
Backoff: (results from a collision where a station selects each with a probability of , then back off time is )
After a time equal to two ways propagation delay the sender receives an ACK (on a separate channel) indicating no collision.
If there is a collision, no ACK will be received after the two way propagation delay, the station decides to back-off and select a new integer i.
The procedure is repeated as needed until successful transmission.
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Dr. Ashraf S. Hasan Mahmoud

13. Dr. Ashraf S. Hasan Mahmoud
Throughput of S-ALOHA for an
infinite Population
Consider an infinite population (∞ # of stations) which is a good approximate for finite population case.
Assume Poisson arrivals with:
S (Throughput): avg. # of successful trans. /
G (Offered load): avg. # of Attempts /
Smax = 1/e for G=1.
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Dr. Ashraf S. Hasan Mahmoud

14. Dr. Ashraf S. Hasan Mahmoud
Throughput of S-ALOHA for an
infinite Population
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15. Dr. Ashraf S. Hasan Mahmoud
Throughput of S-ALOHA for finite
Population:
Assume:
M independent stations that are using S-ALOHA.
Transmissions form a sequence of independent Bernoulli trials.
All transmissions originate from one arrival process.
Do not account for delays due to backoff because of collisions.
From probability theory: M independent Bernoulli, each with G/M arrivals, approaches a Poisson Distribution.
With parameter:
G as M
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16. Dr. Ashraf S. Hasan Mahmoud
Throughput of S-ALOHA for finite
Population:
For station # i Let:
Probability of a station i successfully transmits is:
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17. Dr. Ashraf S. Hasan Mahmoud
Throughput of S-ALOHA for finite
Population:
If all station shares the load: Si = S/M and Gi=G/M which gives:
(network throughput Snet=N*Sst).
Since then
This is similar to the previous results of large value of M.
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Dr. Ashraf S. Hasan Mahmoud

18. Dr. Ashraf S. Hasan Mahmoud
Throughput of S-ALOHA for finite
Population:
we may evaluate the maximum throughput Smax by differentiating S w.r.t. G:
which gives Smax for G=1 (in each slot one station is trying).
Thus, which evaluate as follows:
Notice that: Smax decreases as M increases ( ).
Therefore, Smax= is a good approximation for M>20.
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Dr. Ashraf S. Hasan Mahmoud

19. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
S-ALOHA provides an approximate analysis.
Analysis assumes that:
New and collided packets come from the same process.
Newly and retransmitted packets are separate variables.
This will give better accuracy than :
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Dr. Ashraf S. Hasan Mahmoud

20. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
Process Assumptions:
Infinite population
New Arrivals to the network: Poisson distribution with avg. rate S packets/slot or λ packet /s where S=λ*
Total arrivals of the process (new and retransmitted) have Poisson distribution with G packets/slot.
Stations have always one packet ready for transmission (new and retransmitted).
Bus end to end propagation delay is τ seconds.
A station knows about its successful transmission after waiting for a time of r slots( ) following the transmission of a packet in .
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21. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
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Delay Analysis of S-ALOHA):
Time to transmit a packet (assume 1 retransmission):
The total transfer delay is:
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Dr. Ashraf S. Hasan Mahmoud

23. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
Evaluation of the number of retransmissions:
Assume:
qn: is the probability of a successful transmission for a new packet.
qt: is the probability of a successful transmission for a retransmitted packet.
The probability (Pi) that a packet takes i attempts to transmit is:
Where:
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Dr. Ashraf S. Hasan Mahmoud

24. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
The average number of retransmissions is:
Therefore,
Thus the transfer delay is:
The normalized transfer delay is:
where
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Dr. Ashraf S. Hasan Mahmoud

25. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
The probabilities qn and qt are determined in the Appendix: I-
II-
Notice that:
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Dr. Ashraf S. Hasan Mahmoud

26. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
Since S/G (ratio of # of success/ # of attempts) is the probability of successful transmission. the G/S is the avg. # of times a packet is retransmitted until success:
1+h = G/S, we have
Then (III). (more accurate than )
However, using implies
reduced to
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Dr. Ashraf S. Hasan Mahmoud

27. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
Equations I,II and III are non-linear and transcendental equations.
Since it is difficult to eliminate , we may have a numerical solution as follows:
and use as function of G and K only, we obtain: IV
Where and
Steps:
Solve IV for S(G,k)
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28. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
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Delay Analysis of S-ALOHA):
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30. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
Average number of back logged stations:
The backlogged delay is similar to queuing delay.
Using little law:
The arrival rate is packet /s (normalized –input rate = output rate-).
where (n ≤ m) ,
is the avg. time a station is in the backlog state (waiting) and is 2-way prop. Delay.
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31. Dr. Ashraf S. Hasan Mahmoud
Delay Analysis of S-ALOHA):
We can plot n as a function of S for values of K.
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32. Dr. Ashraf S. Hasan Mahmoud
Stability Consideration
We notice the relationship (G => S => => h).
In G => S each value of S has 2 values for G.
In S => each value of S has 2 values for
This contradiction is explained by using the stability consideration for ALOHA.
Under statistical Equilibrium the major issues are M (# of Stations) and the avg. backlogged time which determine the stability.
The infinite population is adequate model for finite population behavior when M is large enough (M > 20).
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33. Dr. Ashraf S. Hasan Mahmoud
Stability Consideration
Only under equilibrium we have
Thus S must be the normalized throughput that is equal to normalized input rate.
Consider a finite (M station) with n # of them in the backlogged state, then:
M-n stations can generate packets.
σ probability of a free station generates a packet.
The total input rate => straight line (load line) with negative slope = .
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Dr. Ashraf S. Hasan Mahmoud

34. Dr. Ashraf S. Hasan Mahmoud
Stability Consideration
Network is:
Stable: if the load line intersects (non-tangentially) to throughput in one and only one point (otherwise channel is unstable).
Stable Equilibrium: it remains at or at about that point for a finite period of time.
Globally stable: if this point is the only stable equilibrium point.
Locally stable: there more than one stable equilibrium point. each is locally stable.
Unstable: operation immediately drift away from the point.
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Dr. Ashraf S. Hasan Mahmoud

35. Dr. Ashraf S. Hasan Mahmoud
Stability Consideration
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36. Dr. Ashraf S. Hasan Mahmoud
Stability Consideration
For Case a:
Move left from P => n . since load >throughput =>n => back to P.
Move Right from P => n . since load < throughput =>n => back to P.
P is locally stable. Since there is only one intersection => stable network.
For Case b:
P1: Same as P in Case a. P1 is locally stable.
P2:
Move left from P2 => n . since load < throughput => n => drift away from P2.
Move Rig. from P2 =>n . since load > throughput => n => drift away from P P2 is unstable.
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Dr. Ashraf S. Hasan Mahmoud

37. Dr. Ashraf S. Hasan Mahmoud
Stability Consideration
For Case b (cont.)
P3:
Same as P in Case a. P3 is locally stable.
For Case c:
Same as P in Case a. Q is locally stable. Since there is only one intersection => stable network but overloaded.
For Case d:
Q1:
Same as P in Case a. Q1 is locally stable.
Q2:
Same as P2 in Case b. Q2 is unstable.
=>Unstable network.
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38. Dr. Ashraf S. Hasan Mahmoud
Stabilizing the network:
The network is bi-stable (3- intersections) for Backoff=K1.
Increase from K1 to K2 => the only intersection is Q1.=>
Stable network however throughput is decreased (P1->Q1) and backlog increased and so for the delay.
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Dr. Ashraf S. Hasan Mahmoud

39. Dr. Ashraf S. Hasan Mahmoud
CSMA
Non-persistent CSMA (NP):
If channel is sensed idle then transmit packet
Else (channel busy) use backoff algorithm to delay transmission.
1-persistent CSMA (p-persistent and P=1):
Else (channel busy) keep spin sensing until channel is ideal in which case repeat the algorithm.
p-persistent CSMA (NP):
If channel is sensed idle then Transmit packet with probability of p.
Else Wait for end to end delay (time slot) with probability
(1-p) & repeat.
Else (channel busy) keep spin sensing until channel is idle in which case repeat the algorithm.
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40. Dr. Ashraf S. Hasan Mahmoud
Flow diagram of CSMA.
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41. Dr. Ashraf S. Hasan Mahmoud
Throughput Analysis CSMA
Assumption for throughput analysis:
Infinite # of station, arrivals are following possion distribution.
Propagation delay between stations is τ. That is the one –way propagation delay for bus.
Fixed packet length and transmission time is Δt.
Each ST has at most one packet ready for transmission
In the case of slotted protocols Δt = k τ. Where k is integer.
No overhead for sensing, channel is noiseless.
Any packet time overlap is destructive.
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Dr. Ashraf S. Hasan Mahmoud

42. Throughput Analysis CSMA

43. Throughput Analysis CSMA
ST may transmit
No. Stations may transmit ST t P1
ST1 t Y
Pk Assume Last Attempt
t1(Time where ST senses medium & free)
STk t Y
Heard by all
STk
Busy Period B
Idle
1 Cycle

44. Throughput Analysis CSMA
Includes both U and another
(1)
P(k arrival in 0,t) =
P(0 arrival in ) =
Prob( o arrival in )

45. Throughput Analysis CSMA
Random Variable
(2)
First moment
CDF Fy (y) = Prob (Y y)
For y, no arrival in period(t+ ) y
0 arrival in -y
Py (y) = Prob (Y > y)
=1 – Fy (y) =

46. Throughput Analysis CSMA

47. Throughput Analysis CSMA
End of bzi interval
Connected prob of arrival + Arrival rate
(3)
Arrival Rate
Inter-Arrival Rate (Reciprocal)
Shrink to
No collisions
On Average time wait for its equal to interarrival
Collisions

48. Throughput Analysis CSMA
0 , S = G/G+1
0 & G >>1, S=1
Multiplying and Dividing by

49. Dr. Ashraf S. Hasan Mahmoud
Throughput Analysis CSMA
Notes:
As a become small S=> limit of carrier sensing.
S=1 can be achieved for G=∞.
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50. Dr. Ashraf S. Hasan Mahmoud
Throughput Analysis CSMA
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51. Dr. Ashraf S. Hasan Mahmoud
Throughput Analysis CSMA
Notes:
For small G the persistent CSMA is the best.
For large G the non persistent CSMA is the best.
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52. Dr. Ashraf S. Hasan Mahmoud
Throughput Analysis CSMA
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53. Dr. Ashraf S. Hasan Mahmoud
Throughput Analysis CSMA
Notes:
ALOHA protocols are not sensitive to varying (a) since it does not depend on it (constant).
1-persistant (slotted/un-slotted) are not sensitive to varying (a) for small (a). however, as (a) increases the sensitivity increases as well-this goes for non-persistent also-.
For large (a) ALOHA gives highest S because sensing became useless as 2τ is very large.
p-persistent performance is between S-NP & NP. p-persistent is optimized for a given (a)
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54. Dr. Ashraf S. Hasan Mahmoud
Stability of CSMA
Stability of CSMA is very comparable to that of S-Aloha for a=0.01.
CSMA with M<103 with proper backoff provides excellent stability in performance.
For each value of S, (a) is optimized w.r.t. mean backoff time.
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55. Dr. Ashraf S. Hasan Mahmoud
Avg. Normalized Delay VS Throughput
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56. Dr. Ashraf S. Hasan Mahmoud
Flow chart of CSMA/CD:
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57. Dr. Ashraf S. Hasan Mahmoud
Timing diagram of CSMA /CD:
Notes:
Time during which channel is idle as seen by each station is :
Where J is jamming time
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58. Dr. Ashraf S. Hasan Mahmoud
Performance Analysis CSMA/CD
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59. Dr. Ashraf S. Hasan Mahmoud
Performance Analysis CSMA/CD
Notes:
γ is normalized Jamming time (in plot γ=1).
SNP is better for low value of (a) (slotted is good for high G).
Slotting time has negligible effect for low G.
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60. Dr. Ashraf S. Hasan Mahmoud
Performance Analysis CSMA/CD
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61. Dr. Ashraf S. Hasan Mahmoud
Performance Analysis CSMA/CD
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62. Dr. Ashraf S. Hasan Mahmoud
Performance Analysis CSMA/CD
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63. Dr. Ashraf S. Hasan Mahmoud
Performance Analysis CSMA/CD
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64. Dr. Ashraf S. Hasan Mahmoud
Performance Analysis CSMA/CD
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Dr. Ashraf S. Hasan Mahmoud