Download coe041-451 LAN/MAN Performance

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 22-144
Ext. 1724
Email: [email protected]
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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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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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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).
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CSMA is useful if propagation delay << packet
transmission time.
Carrier sense reduces the length of collision
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intervals.
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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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Architecture
•BUS:
Baseband.
Passive network.
Both directions (Coax/TP/FO) from station.
Prevent reflection.
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Architecture
•Tree:
Broadband:
Active repeaters.
Directional transmission (repeaters).
EX: CATV.
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Architecture
Major difference:
baseband propagation delays << broadband delays
(due to directional transmission)
This chapter is on baseband network.
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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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Random Access Network (Example)
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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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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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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
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0.368 for G=1.
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Throughput of S-ALOHA for an
infinite Population
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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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Throughput of S-ALOHA for finite
Population:
For station # i Let:
Probability of a station i successfully transmits is:
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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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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= 0.368 is a good approximation for M>20.
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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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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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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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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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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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Delay Analysis of S-ALOHA):
•The probabilities qn and qt are determined in the Appendix:
III-
Notice that:
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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
However, using
reduced to
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(III). (more accurate than
)
implies
.
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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
Where
as function of G and K only, we obtain:
IV
and
Steps:
Solve IV for S(G,k)
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Delay Analysis of S-ALOHA):
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Delay Analysis of S-ALOHA):
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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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Delay Analysis of S-ALOHA):
We can plot n as a function of S for values of K.
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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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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
(load line) with negative slope =
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=> straight line
.
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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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Stability Consideration
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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 P2.
P2 is unstable.
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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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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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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):
If channel is sensed idle then transmit packet
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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Flow diagram of CSMA.
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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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Throughput Analysis CSMA
Throughput Analysis CSMA
ST may transmit
No. Stations may transmit
ST
t  t
t 
t
t  t  
P1
ST1
t
Y
Pk Assume Last Attempt
t1(Time where ST
senses medium & free)
STk
t
Y
t 
t  y  t
t  y  t  z
STk
Heard by all
Busy Period B
Idle
1 Cycle
Throughput Analysis CSMA
U
S
BI
B Includes both U and another
(1)
U  t * e
 G
t
( t ) K e   t
G
, 
 t 
P(k arrival in 0,t) =
K!
t
G
G 0  ( t  )
( ) e
P(0 arrival in ) =
t
0!
U  t * Prob( o arrival in  )
G
(
U  t * e t )
Throughput Analysis CSMA
Random Variable
(2) B  t    Y
First moment
B  t    y
CDF Fy (y) = Prob (Y  y)
For y, no arrival in period(t+)
0
Fy ( y )  e
y

 G (  y )
t
Py (y) = Prob (Y > y)
=1 – Fy (y) = 1  e
 G (  y )
t
0 arrival in  -y
Throughput Analysis CSMA

y   y (1  e
 G (  y )
t
0
t
y    (1  e
G
)dy
 G .
t
)
Throughput Analysis CSMA
(3)
I
End of bzi interval
Connected prob of arrival + Arrival rate
G
t
Arrival Rate
t
G
Inter-Arrival Rate
(Reciprocal)
Shrink to   t
y 
0
0
No collisions
On Average time wait for its equal to interarrival
Collisions
Throughput Analysis CSMA
I
S
t
G
 G (  y )
t
t.e
 G .
t
t
t    (  (1  e t )) 
G
G
Multiplying and Dividing by
G
t
 G .
t
G.e
S
 G .
2
G (1  )  e t )
t
 0 , S = G/G+1
 0 & G >>1, S=1
Throughput Analysis CSMA
Notes:
As a become small S=> limit of carrier sensing.
S=1 can be achieved for G=∞.
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Throughput Analysis CSMA
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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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Throughput Analysis CSMA
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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. ppersistent is optimized for a given (a)
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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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Avg. Normalized Delay VS Throughput
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Flow chart of CSMA/CD:
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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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Performance Analysis CSMA/CD
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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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Performance Analysis CSMA/CD
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Performance Analysis CSMA/CD
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Performance Analysis CSMA/CD
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Performance Analysis CSMA/CD
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Performance Analysis CSMA/CD
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