Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective

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Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective

Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective

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指導老師指導老師 : : 林永松教授林永松教授

d96725002 d96725002 蕭鉢蕭鉢d96725011 d96725011 黃文莉黃文莉r96725035 r96725035 林意婷林意婷

指導老師指導老師 : : 林永松教授林永松教授

Gaurav Sharma,Ravi Mazumdar,Ness ShroffIEEE/ACM Transaction on Networking, Vol 15,No 5. 2007, pp981-991


Is node mobility a “liability” or an “asset” in ad hoc networks?


Liability Hand-off protocols for cellular networks [Toh & Akyol] Adverse effect on the performance of traditional ad hoc routing

protocols [Bai, Sadagopan and Helmy]

Asset Grossglauser and Tse showed node mobility can increase the

capacity of an ad hoc network, if properly exploited. The delay related issues were not considered.


To Provide better understanding of

the delay and capacity trade-offs

in mobile ad hoc networks (MANET)

from a global perspective


OutlinesOutlines

Introduction Capacity scaling of ad hoc networks Mobility can increase capacity Main contributions Main Results Overview

The Models Hybrid random walk model i.i.d mobility model Random walk model Hybrid random direction model Discrete random direction model Brownian motion mobility

Critical Delay and 2-hops Delay Critical Delay and 2-hops Delay Under Various Mobility Models

Lower bound on critical delay for hybrid random walk models Upper bound on critical delay for hybrid random walk models Lower bound on critical delay for discrete random direction models Upper bound on critical delay for discrete random direction models

Discussion Characteristic path length

Conclusion


IntroductionIntroduction


Capacity scaling of ad hoc networksCapacity scaling of ad hoc networks

Study fundamental properties of large wireless networks [Gupta & Kumar]

Derive asymptotic bounds for throughput capacity To derive upper bounds, use:

Interference penalty—nodes within range need to be silenced for successful communication

Multi-hop relaying penalty— a node that traverses a distance of d needs to use order of d hops.

To derive constructive lower bounds, use: Geographic routing strategic along great circles Greedy coloring schedules.


Capacity scaling of ad hoc networksCapacity scaling of ad hoc networks

Number of nodes

Per-node Capacity

[Gupta & Kumar]-Nodes static-Interference model: protocol or physical model-Common power level across network

)log

1(

nn

[Francheschetti &Dousse] - Nodes static - Power control allowed

)1

(n

[Grossglauser & Tse] - Nodes are mobile

)1(


Mobility can increase capacityMobility can increase capacity

[Grossglauser & Tse] achieve constant capacity scaling by two-hop relaying

[Gupta & Kumar] allow for constant capacity scaling if the traffic pattern is purely local.

Source uses one of all possible mobile nodes as a relay. Source splits stream uniformly across all relays. When a mobile forwarder nears the destination, it hands off packet.


Mobility can increase capacityMobility can increase capacity

Why does mobility increase capacity? By choosing a random intermediate relay, the traffic is diffused uniformly

throughout the network. Thus, on average, every mobile node has a packet for every other destination

and can schedule a packet to a nearby destination in every slot. (For those who took randomized algorithms, this is akin to permutation

routing algorithms)

Catch: forwarding strategy improves capacity at the expense of introducing delay.

Need to study the delay-capacity tradeoff!!


Main contributionsMain contributions

Delay-capacity tradeoff: increasing the maximum allowable average delay increases the capacity.

Delay-capacity tradeoff depends on network setting, mobility patterns.

Different mobility models have been studied in the literature i.i.d Brownian motion Random way-point Random walk

Difficult to compare results across paper because network setting are quite different.

How does the mobility model affect the delay capacity trade-off?


Main Results: Notion of critical delay to compare mobility modes

Main Results: Notion of critical delay to compare mobility modes

For each mobility model, there is a critical delay below which node mobility cannot be exploited for improving capacity.

Critical delay depends mainly on mobility pattern, not on network setting


OverviewOverview

Mobility can increase capacity. Delay-capacity tradeoff depends on network setting, mobility

models. Some questions arises

How representative are these mobility models in this study? Can the delay-capacity relationship be significantly different under the

mobility models? What sort of delay-capacity trade-off are we likely to see in real world

scenario?


Main Results A new hybrid random walk model


Propose and study a new family on hybrid random walk models, indexed by a parameter in [0, ].

For the hybrid random walk model with parameter ,critical delay is

As approaches 0, the hybrid random walk model approaches an i.i.d mobility model.

As approaches , the hybrid random walk model approaches a random walk mobility model.

2

1

)( 2n

21




Number of nodes

Critical Delay

i.i.d )1(

random walk model

)(n

0

1

2

1

Hybrid random walk model )( 2n


Main Results A new hybrid random direction model


Propose and study a new family on hybrid random direction models, indexed by a parameter in [0, ].

For the hybrid random direction model with parameter , the critical delay is

As approaches 0, this hybrid random direction model approaches a random way-point model.

As approaches , this hybrid random direction model approaches a Brownian mobility model.

21

)( 2

1 n

21




Number of nodes

Critical Delay

Brownian mobility

)(n

1

Hybrid random direction model

)( 21 n

Random Way-point

)( n

0

21


The ModelsThe Models


Hybrid random walk modelHybrid random walk model

Divide the unit square into cells of area Divide each cell into sub cells of area In each time slot, a node is in one of sub cells in a cell. At the beginning of a slot, node jumps uniformly to one of the sub

cells of an “Adjacent cell”

2n 2

1

n21n n

1

nn


i.i.d mobility modeli.i.d mobility model

As approaches 0, we get i.i.d mobility. One big cell with n sub-cells. In each slot, a node is in one of the sub-cells. At the beginning of a time slot, a node jumps uniformly to one of

the n subcells.


Random walk modelRandom walk model

As approaches , we get the random walk. n cells, one sub-cell in each cell. In any slot, a node is in particular cell. At the beginning of a slot, node jumps uniformly to one of the

adjacent cells.

21


Hybrid random direction modelHybrid random direction model

Motion of a node is divided into trips. In a trip, node chooses a direction in [0,360] and moves a distance

Speed of movement (for scaling reasons).

n)

1(

nVn

The average neighborhood size scales as )1

(n

Vn


Discrete random direction model.Discrete random direction model.

Divide the square into cells of area tours of size Time divided into equal duration slots At the beginning of a slot, a node jumps uniformly to an adjacent

cell. During a slot, the node chooses a start and end point uniformly

inside the cell, and moves from start to end. Velocity of motion is made inversely proportional to distance.

2n 21

n

)( 21 n

nn


Brownian motion mobilityBrownian motion mobility

For , the discretized random direction model degenerates to the random walk discrete equivalent of a Brownian motion with variance

2

1

n

1


Critical delay and 2-hop delayCritical delay and 2-hop delay


Definition of critical delayDefinition of critical delay

We know that in the static node case, per node capacity is . Capacity achieving scheme is the multi-hop relaying scheme of Gupta & Kumar.

If mobility is allowed, the two-hop relaying strategy achieves per node capacity of [Grossglauser & Tse]

The two hop relaying strategy has an average delay of , under most mobility models.

Mobility increase capacity at the expense of delay.

)1

(n

)1(

)(n


Definition of critical delay (conti)Definition of critical delay (conti)

Suppose we impose the constraint that the average delay can not exceed .

Under this constraint, relaying strategy that use mobility will achieve a capacity , somewhere between and

For some critical delay bound , this capacity will be equal to capacity of static node networks.

Below this critical delay , there is no benefit from using mobility based relaying.

)(nt

)(nct )1( )1

(n

)(ntc )(nctc


An illustration of critical delayAn illustration of critical delay

Maximum average delay

Capacity

Two hop delay

[Grossglauser & Tse]

[Gupta & Kumar]

Critical delay

Critical delay is the minimum delay that must be tolerated

2 hop relaying scheme has been shown to incur an average delay of about under many different mobility models


More on the critical delayMore on the critical delay

It depends on the mobility mode. It provides a basic to compare mobility model. If mobility model A has lower critical delay than mobility

model B , then A provides more leeway to achieve capacity gains from mobility than B.

Critical delay also depends on what scheduling strategies are allowed.


Critical Delay and 2-hops Delay Under Various Mobility Models

Critical Delay and 2-hops Delay Under Various Mobility Models


Lower bound on critical delay for hybrid random walk models

Lower bound on critical delay for hybrid random walk models

Obtain a value such that if average delay is below this value than (on average) packets travel a constant distance using wireless transmissions before reaching their destinations. For the hybrid random walk model , this value is

Show that if packets are on average relayed over constant distance using wireless transmission, this results in a throughput of ,with the protocol model of the interference.

Thus, the critical delay can not be any lower than this value.

n

n

log

2

)1

(n


Lower bound on critical delay for hybrid random walk models (cont)

Lower bound on critical delay for hybrid random walk models (cont)

Step1: Establish a lower bound on the first exit time from a disc of radius

Step2: If average delay is smaller than , than packets must on average be relayed over a distance no smaller than Pigeonhole argument Exit lemma Union Bound Motion arguments for successful relaying.

81

2

24

1

,

4)

log1024(

nn

nP E

n

nf

log2048

20

2400

10 f

100f


Upper bound on critical delay for hybrid random walk models

Upper bound on critical delay for hybrid random walk models

Develop a scheduling and relaying scheme that provides a throughput of while incurring a delay of

Consider a scheme where relay node transfer the packet to destination when it is in the same cell as destination

Delay=(approx) time for delay node to move into destination node’s cell. Packet arrivals are independent of mobility delay is the same as mean first

hitting time on a torus of size This first hitting time=

)1(n

)log( 2 nn

nn

)log( 2 nn


Upper bound on critical delay for hybrid random walk models (conti)

Upper bound on critical delay for hybrid random walk models (conti)

With this strategy, multi-hop relaying is only used once we reach the destination’s cell, ie., at most distance

Each hop travels a distance Throughput loss from multihop relaying = Since each wireless transmission travels ,nodes within this

range must stay silent. An additional throughput loss of Combining the two, throughput=

)1

( n

)log

(n

n

)log

(2/1

n

nO

)log

(n

n

)(log n

)1

()log

(2

1

nn

n


Discussion on hybrid random walk modelsDiscussion on hybrid random walk models

As increases, the critical delay increases, thereby shrinking the delay-capacity trade-off region.

Two extreme cases: i.i.d model: when the static node capacity can be achieved even with a

constant delay constraint. Random walk model: where delay on the order of is required to

achieve the static node capacity.

)log

(n

n


Lower bound on critical delay for hybrid discretized random direction models

Lower bound on critical delay for hybrid discretized random direction models

Same approach as before to obtain lower bound on critical delay as

Step1: derive a lower bound on exit time from a disc of radius 8 under the random direction model

Step2: If average delay is smaller than packets must on average be relayed over a distance on smaller than

)log

(2

1

n

n

2

21

41

,

4)

log768(

nn

CnP E

n

nCf

log2048

2

1

0

100f


Upper bound on critical delay for hybrid discretized random direction models

Upper bound on critical delay for hybrid discretized random direction models

Same strategy as before Replicate and give to relay node Relay node hands off to destination when it is in the cell of the destination

Can obtain a throughput of with a delay of Provides an upper bound on critical delay for discreted random

direction model.

)1

(n

)log( 2

1

nn


DiscussionDiscussion


Discussion : Characteristic path lengthDiscussion : Characteristic path length

Critical delay seems to be inversely proportion to characteristic path length of a mobility model.

Characteristic path length is the average distance traveled before changing direction under the model.

For example, with hybrid discretized random ditection model, characteristic path length is and the critical delay is n

2

1

n


Discussion : Characteristic path length(cont)

Discussion : Characteristic path length(cont)

Thus, a scenario with nodes moving long distance before changing direction provides more opportunities to harness delay-capacity trade-off, e.g., random way point model vs. Brownian model.


ConclusionConclusion


Conclusion Conclusion

Motivate capacity-delay tradeoff in MANET （ Mobile Ad-hoc NETworks ） .

Define critical delay to compare capacity-delay tradeoff region across mobility models.

Define a parameterized set of hybrid random walk models and hybrid random direction models that exhibit continuous critical delay behavior from minimum possible to maximum possible.


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Delay and Capacity Trade-offs in Mobile Ad Hoc Networks: A Global Perspective