The Final Present
description
Transcript of The Final Present
The Final Present
Lee Jeng-Shiou
Computer Network of E.E
Outline Throughput Analysis Review for Single-hop Netw
orks Throughout Analysis for Multi-hop Networks Mathematical Analysis of the String Topology Analytical and Simulation Results An Alternative Mathematical Analysis of the Strin
g Topology Conclusion
Throughput Analysis Review for Single-hop Networks (s(t), b(t))
s(t): the backoff stage b(t): the backoff time counter p: the conditional collision probability τ: the probability that a station transmits in a generic slot time
Throughput Review for Single-hop Networks (cont~) The transmission probability τ in a randoml
y chosen ”generic” slot is
The collision probability is expressed by
Throughput S is obtained by
0
2(1 2 )
(1 2 )( 1) (1 (2 ) )
m
mi
p
p W pW p
11 (1 )np
cstrsstrtr
str
TPPTPPP
PEPPS
)1()1(
][
Throughout Analysis for Multi-hop Networks We concentrate on the impact of the hidden node
problem. We analyze the throughput based on a single
station’s point of view. The analysis method is similar to the single-hop
case. Obtaining the stationary probability τ using a Markov
model. Expressing the throughput as function of τ by studying
the events that can occur within a generic slot time.
Throughout Analysis for Multi-hop Networks Assumption:
All packets are destined for neighbor nodes.
There is no capture effect. Each station always has packets to trans
mit.
A Simplified Condition The carrier sense range is equal to the
transmission range.
BA
R=r
A1
A Simplified Condition (cont~)
A Simplified Condition (cont~) The simulations have been done by the network si
mulator - ns2. Simulation area 1500x1500 m2. We consider five topology scenarios and each sce
nario includes four traffic patterns. Each node generates packets based on CBR model
with packet sizes 256, 512, 1024 and 2048 bytes. They correspond to packet arrival interval of 0.001
3, 0.0026, 0.0052 and 0.01 sec.
A Simplified Condition (cont~)
A Simplified Condition (cont~)
A Simplified Condition (cont~)
A Realistic Carrier Sense Range The carrier sense range is 550 meters and th
e transmission range is 250 meters.
BA
R
r
A1
A Realistic Carrier Sense Range (cont~)
A Realistic Carrier Sense Range (cont~)
A Realistic Carrier Sense Range (cont~)
Throughout Analysis for Single-hop Networks (cont~)
Throughout Analysis for Single-hop Networks (cont~)
Conclusions The throughput performance of the IEEE
802.11 DCF scheme in multi-hop ad hoc networks is analyzed.
It also shows the proposed model is accurate when degenerated into single-hop networks.
The throughput of a single station is decreased as the number of stations increases.
The total throughout almost stays at a constant value.
Conclusions (cont~) The total network throughput is decreased
as much as by 55% when the carrier sense range is equal to 550 meters.
The larger packet size results in the higher network throughput.
For spatial reuse factor, the results shows that there no clear relationship with the number of stations and packet size.
Mathematical Analysis of the String Topology
6 4 2 0 1 3 5
Mathematical Analysis of the String Topology (cont.)
Six possible situations observed by station 0 at the beginning of a slot.
Node 0 “idle” (1-τ) (cont.)
One of n1 and n2 Tx (P2) (assume n1 Tx)
(2)
0 1
0 1 3
Success(n2 idle)
Collided byhidden node
(n2 tx during Tv)
1/2
1/2
Psucc
Pcoll
T2_1_succ
1/2
1/2
0 12
0 12
T2_1_1_coll
T2_1_2_coll
0 12
0 12
1/2
1/2
T2_2_1_coll
T2_2_2_coll
n2 idle
n2 tx during Tv
T2_2_succPsucc
Pcoll
0 1 324
0 1 324
success: n2 idle during
collision: n2 Tx during Tv
0 1 324
Mathematical Analysis of the String Topology (cont.)
1 1 1
2 2 2_1_ 2_1_ 2_1_ 2 _1_1_ 2 _1_ 2_
2 _ 2_ 2 _ 2_ 2_ 2_ 2 _ 2_1_ 2 _ 2_ 2_
3 3 3
4 4 4_ 4 _
(1 )
1 1 1(1 ) { [ ( )]
2 2 21 1 1
[ ( )]}2 2 2(1 )
[
succ succ coll coll coll
succ succ coll coll coll
succ s
L P T
L P P T P T T
P T P T T
L P T
L P P T
4 _ 4_
5 5 5_1 5_ 2_ 5_ 2_ 5_ 2 _ 5_ 2 _ 5_ 3
5_ 4_ 5_ 4 _ 5_ 4 _ 5_ 4 _
6 6 6
]
1 1 1{ [ ]
4 4 41
[ ]}4
ucc coll coll
succ succ coll coll
succ succ coll coll
P T
L P T P T P T T
P T P T
L P T
4 4_ 5 5_ 2_ 5_ 4_
1 2 3 4 5 6
1[ [ ] ( [ ] [ ])]
4succ succ succP P E P P P E P P E PS
L L L L L L
26
Analytical and Simulation Results (cont.)
The simulation throughput (13 stations) and the analytical throughput.
An Alternative Mathematical Analysis of the String Topology
One directional traffic between two stations
No collisions
->
0 1
min
1The avg. backoff time
2 3 ec10 s
CW aSlotTime
An Alternative Mathematical Analysis of the String Topology (cont.)
The normalized throughput of the basic access scheme when there is one traffic.
PktSize
(byte)
DIFS + Avg. Backoff + Time + Data + SIFS + ACK
Total(μsec)
Normalized
Throughput
Max.Throughpu
t(backoff=0)
256 50+310+342*8/2+10+152 1890 0.601058 0.718987
512 50+310+598*8/2+10+152 2914 0.741249 0.829493
1024 50+310+1110*8/2+10+152 4962 0.848045 0.904557
2048 50+310+2134*8/2+10+152 9058 0.916759 0.949246
An Alternative Mathematical Analysis of the String Topology (cont.)
The normalized throughput of the RTS/CTS access scheme when there is one traffic.
PktSize(byt
e)
DIFS + Avg. Backoff + Time + RTS + CTS
+ Data + SIFS + ACK
Total(μse
c)
Normalized
Throughput
Max.Throughpu
t(backoff=
0)
25650+310+176+10+152+10+342*8
/2+10+1522238 0.507596 0.589212
51250+310+176+10+152+10+598*8
/2+10+1523262 0.662170 0.731707
1024
50+310+176+10+152+10+1110*8/2+10+152
5310 0.792467 0.841600
2048
50+310+176+10+152+10+2134*8/2+10+152
9406 0.882841 0.912929
An Alternative Mathematical Analysis of the String Topology (cont.)
Bi-directional traffic between two stations
Collisions may occur. Evaluating the average backoff time
All newly generated backoff values, such as X ,Y ,and M ,are identically distributed from uniform distribution.
where A represents the CWmin
0 1
1( ) , ( ) , 0X X
xf x F x x A
A A
An Alternative Mathematical Analysis of the String Topology (cont.)
Let Z=|X-Y|. We have
A newly generated backoff value is M with the probability distribution as X, and Y. Let W=|M-Z|. We have
-> Z and W are identical distribution. The expected backoff interval is
2( ) (1 ), 0Z
zf z z A
A A
2( ) (1 ), 0W
wf w w A
A A
min( , ), 4
sec4
155
U
AU X Z m
AaSlotTime
An Alternative Mathematical Analysis of the String Topology (cont.)
Evaluating the collision probability2 1
[collision] [ 1] (1 )2
2[succes
2
3129
3s
1] 1
31
P P wA A
P
An Alternative Mathematical Analysis of the String Topology (cont.)
The normalized throughput of the basic access scheme considering the collisions when there is two traffic.
PktSize(byt
e)
DIFS + Avg. Backoff + Time + Data + SIFS + ACK
Total(μsec)
Normalized
Throughput
Max.Throughp
ut(backoff=
0)
Simulation
Throughput
25629/31*(50+155+342*8/2+10+1
52+50) +2/31*(50+155+342*8/2+162)
1781.77
0.596433 0.653262 0.649542
51229/31*(50+155+598*8/2+10+1
52+50) +2/31*(50+155+598*8/2+162)
2805.77
0.720174 0.762285 0.770645
1024
29/31*(50+155+1110*8/2+10+152+50)
+2/31*(50+155+1110*8/2+162)
4853.77
0.811022 0.837775 0.853088
2048
29/31*(50+155+2134*8/2+10+152+50)
+2/31*(50+155+2134*8/2+162)
8949.77
0.867984 0.883281 0.899572
An Alternative Mathematical Analysis of the String Topology (cont.)
The normalized throughput of the RTS/CTS access scheme considering the collisions when there is two traffic.
PktSize(byt
e)
DIFS + Avg. Backoff + Time + RTS + CTS + Data + SIFS + ACK
Total(μsec)
Normalized
Through-put
Max.Throughp
ut(backoff
=0)
Simulation
Through-put
256
29/31*(50+155+176+10+152+10+342*8/2
+10+152+50) +2/31*(50+155+176+162)
2030.42
0.523394
0.566652 0.55067
6
512
29/31*(50+155+176+10+152+10+598*8/2
+10+152+50)+2/31*(50+155+176+162)
2988.35
0.676173
0.713163 0.69984
0
1024
29/31*(50+155+176+10+152+10+1110*8/2
+10+152+50)+2/31*(50+155+176+162)
4904.23
0.802678
0.828875 0.81963
4
2048
29/31*(50+155+176+10+152+10+2134*8/2
+10+152+50)+2/31*(50+155+176+162)
8735.97
0.889227
0.905289 0.89957
2
Appendix (simulation results)
Appendix (simulation results)
Appendix (simulation results)
Appendix (simulation results)
Conclusions We first analyze the transmission behavior of stations in
a string topology in the multi-hop environment. In the presence of the hidden and exposed terminal
problems, the mathematical analysis is more complicated compared to the single-hop wireless network.
From the analytical and simulation results, we find that a larger packet size can increase the normalized throughput.
Conclusions (cont.) For future research, we will proceed with the
alternative mathematical analysis. We may discuss the behavior under the
assumption that the carrier sensing range is much larger than the transmission range, and the capture effect may be included.
Besides, we may extend our one-dimension topology to different types of topology.
Conclusion
What we have done We propose a new method to improve
IEEE 802.11 performance and establish a model for analysis.
Simulation and comparison What we are going to do
A general equation (even solution) for our model
More simulation