Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks

Rice Networks Grouphttp://www.ece.rice.edu/networks

Michele GarettoJingpu Shi

Edward W. Knightly

Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks

MobiCom 2005

Garetto, Shi, Knightly

Motivation

Multi-hop wireless networks employing CSMA/CA protocols exhibit complex behavior and are difficult to analyze– Root cause: different and incomplete channel state

information among flows– Most of existing modeling techniques only consider the

case in which all stations are in radio range

When stations are not all in radio range, severe unfairness can occur among flows:– Long-term unfairness : some flows can starve

completely– Short-term unfairness : flows alternate phases in which

dominate each other in terms of throughput


Our contribution

We decompose a large-scale network into embedded subgraphs, each consisting of four nodes and two flow pairs

We identify all possible two-flow scenarios and propose a novel classification of them

We compute the occurrence probability of each scenario under random nodes deployment

We accurately study the performance of random access in all cases not analyzed so far in the literature


Basic two-flow, four-node layout

A

ba

BAB

Ab

aB

AB

Senders A, B Receivers a, b A-a, B-b must be connected

(= in radio range)

Nodes from one flow may hear nodes from the other

Four possible connections that can exist – or not

24 = 16 combinations Ab, Ba interchangeable 4 redundant scenarios


Twelve possible scenarios

A

ba

BA

ba

BA

ba

BA

ba

BAb

A

ba

B

ab

A

ba

BAb

A

ba

BABA

ba

BAB

A

ba

B

ab

A

ba

BA

ba

B

ab

Ab

aB

A

ba

BAB AB AB

AB

Ab Ab

aB

aB aBaB

ab

ab ab

aB aB


Example topologies

bB

aA

bBaA bB aA

bB aA

bB

aAbBa A

bBaA

b B

aAbBaA b

B

aAbBaA


Spatial analysis We assume nodes uniformly distributed in the area We compute the occurrence probability of each

scenario We discard the case in which flows are completely

isolated from each other normalized probabilities – insensitive to area size (no border effects)– insensitive to node density


0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Prob

abili

ty (c

ondi

tione

d)

Normalized distance between tx and rx

scenario 2scenario 3scenario 4scenario 5scenario 6

scenario 7scenario 8scenario 9

scenario 10scenario 11scenario 12

Scenario Likelihood


Performance simulations with CSMA/CA protocol

Throughput measurements every 400 ms X = two-way handshake = four-way handshake


Scenarios classification : 3 groups

A

ba

BAb

aB

A

ba

BA

ba

BAb

aBab

A

ba

BA

ba

B

aBaB

ab

A

ba

BAB

Senders Connected (SC)

Symmetric Incomplete State

(SIS)

Asymmetric Incomplete State

(AIS)


00.10.20.30.40.50.60.70.80.9

1

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Prob

abili

ty (c

ondi

tione

d)

Normalized distance between tx and rx

SCAISSIS

Probabilities of 3 groups of scenarios


Hop distance distribution in a multi-hop network

0

0.1

0.2

0.3

0.4

0.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Prob

abili

ty

Hop distance / TX range

300 nodes - 2000 m x 2000 m – Random waypoint – DSDV

Most of actively used hops are close to the maximum

TX range !


Probabilities of 3 groups of scenarios

00.10.20.30.40.50.60.70.80.9

1

1 1.5 2 2.5 3

Prob

abili

ty (c

ondi

tione

d)

Ratio between sensing range and transmission range

SCAISSIS

Hop distance = TX range ; variable Sensing Range


Analysis of Asimmetric Incomplete State scenarios (AIS)

Known to be highly problematic for random access protocols: flow A a starves – V. Bharghavan, A. J. Demers, S. Shenker, L. Zhang, MACAW: A Media Access Protocol for Wireless LAN's, SIGCOMM ‘94

RTS/CTS does not solve the problem RRTS does not help Not yet modeled analytically

bB

aAbB

aA aA Aa

B b b

B


Decoupling technique (valid for general topologies)

The channel “private view” of a node:

… …

Node’s transmission is

successfulidle slot

Node’s transmission

collides

t

channel is busy because of activity

of other nodes

Modelled as a renewal-reward process

Throughput (pkt/s) = P [event Ts occurs]

Average duration of an event (s)



Flow A a does not know when to contend: it has to discover an available gap in the activity of flow B b randomly, where to place an entire RTS or DATA packet

B b…t

…B b B b B b

A a ?

bB

aAbB

aA aA Aa

B b b

B

RTS/DATA



B bA a

B b B b

B bA a

B b B b

B b A a B b B b

• The collision probability of flow A a can be accurately computed assuming that the first packet arrives at a random point in time • The collision probability of flow B b is zero


AIS scenario – model vs simulation

0

200

400

600

800

1000

200 400 600 800 1000 1200 1400

Pack

et T

hrou

ghpu

t (pk

t/s)

Data Payload Size (bytes)

ns - Flow Bmodel - Flow B

ns - Flow Amodel - Flow A

0

200

400

600

800

1000

200 400 600 800 1000 1200 1400



with RTS/CTS basic access (no RTS/CTS)


AIS scenario – model vs simulation

0

50

100

150

200

250

300

350

400

450

500

0 100 200 300 400 500 600

Pack

et T

hrou

ghpu

t (pk

t/s)

Arrival rate of flow B (pkt/s)

Flow A backlogged – Flow B not backlogged




Analysis of Symmetric Incomplete State scenarios (SIS)

Long term fair, but short term unfair One flow dominates over the other, until they switch

their role (randomly) RTS/CTS does not help, and can even make things

worse Not yet modeled analytically As a special case, the receiver can be in common:

b B

aAbB

aAb BaA

AP= the classic “hidden-terminal” scenario


Simulation of short term unfairness – SC vs SIS

05

101520253035404550

50 51 52 53 54 55 56 57 58 59 60

thro

ughp

ut d

urin

g 10

0 m

s

Time (s)

Time (s)

RTS/CTS – 7 backoff stages

05

101520253035404550

50 51 52 53 54 55 56 57 58 59 60 thro

ughp

ut d

urin

g 10

0 m

s basic access – 4 backoff stages

05

101520253035404550

50 51 52 53 54 55 56 57 58 59 60Time (s)

basic access – 7 backoff stages

05

101520253035404550

50 51 52 53 54 55 56 57 58 59 60Time (s)

RTS/CTS – 9 backoff stages



To capture short-term behavior, we cannot apply the decoupling technique (independent states) States of the two flows are tightly correlated !

We use a markov model in which the state is:

The computation of the collision probability is the key point

b B

aAbB

aAb BaA

{ backoff stage of A, backoff stage of B }



Steady-state distribution of Markov Chain:

01

23

45

6

0 1 2 3 4 5 6stage A

00.020.040.060.08

0.10.12

Prob

abili

ty

stage B

0.140.16

Time-scale of short term unfairness


SIS scenario – model vs simulation

Case Throughput(pkt/s)

Collision probability

Time scale of unfairness (ms)

RTS/CTS7 stages

218216

0.250.25

235223

RTS/CTS9 stages

229230

0.110.09

9821156

Basic access4 stages

125107

0.690.75

1515

Basic access7 stages

222220

0.370.38

5960

nsmodel

nsmodel

nsmodel

nsmodel

Thanks !

Backup slides


Modeling Media Access

Event probabilities:

… …t

Define the probabilities = probability that the node sends out a packet in a slot= conditional collision probability= conditional busy channel probability


The unknown variables are:

(a decreasing function of p )

The throughput of a node decreases if either: is large (if so, is small, also) is large (large fraction of busy time)

Throughput formula:

Modeling Media Access


Short term unfairness – simulation

0

5

10

15

20

25

30

35

40

45

50

50 51 52 53 54 55 56 57 58 59 60

thr

ough

put d

urin

g 10

0 m

s

Time (s)

SCSIS


0

5

10

15

20

25

30

35

40

45

50

50 51 52 53 54 55 56 57 58 59 60Time (s)

thro

ughp

ut d

urin

g 10

0 m

sShort term unfairness – simulation

SCSIS


0

5

10

15

20

25

30

35

40

45

50

50 51 52 53 54 55 56 57 58 59 60

thro

ughp

ut d

urin

g 10

0 m

s

Time (s)


SCSIS


0

5

10

15

20

25

30

35

40

45

50

50 51 52 53 54 55 56 57 58 59 60

thro

ughp

ut d

urin

g 10

0 m

s

Time (s)


SCSIS

Documents

Modeling Media Access in Embedded Two-Flow Topologies of Multi-hop Wireless Networks