Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks

Shuochao Yao*, Xinbing Wang*, Xiaohua Tian*‡, Qian Zhang†

*Department of Electronic Engineering, Shanghai Jiao Tong University, China

†Dept. of Computer Science and Engineering, Hong Kong University of Science and Technology, China‡State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunic

ations, China

Email: {sasukecao,xwang8,xtain}@sjtu.edu.cn qianzh@cse.ust.hk

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 22

Outline

Introduction Motivations Objectives

System Models

Tradeoff of Cluster Sparse Regime

Tradeoff of Cluster Dense Regime and Cluster Critic

al Regime

Summary

Motivations

Ad-hoc NetworksPessimistic throughput performance for static

networks.Delay-Throughput Tradeoff

Mobility increase throughput & Tradeoff exist.Mobility Pattern

Important role in tradeoff.Correlated Mobility

Study the impact of node correlation.

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Objectives

Former workMaximum throughput performance with corres

ponding delay.

Our TopicOptimal delay-throughput performance under

different node correlation.

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Outline

Introduction

System Models

Tradeoff of Cluster Sparse Regime

Tradeoff of Cluster Dense Regime and Cluste

r Critical Regime

Summary

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System Model-I/III

Network extension: a square with area n.m clusters, each covers a circular area with radiu

s R.Each cluster contain Θ(n/m) nodes.Mobility model

Each cluster relocates its position uniformly i.i.d. in the whole network area.

Each node relocates its position uniformly i.i.d. in the its cluster.

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System Model-II/III

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System Model-III/III

Transmission protocol: protocol modelCommunication among different clustersClassify node correlation

Strong node correlation: cluster sparse regime; mR2 ＜ n.

Weak node correlation: cluster dense regime; mR2 ＞ n.

Medium node correlation: cluster critical regime; mR2=n.

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Asymptotic Capacity & Delay

Asymptotic per-node capacity Θ(n) of the network is said to be Θ(g(n)) if there exist two positive constants c and c' such that:

Asymptotic delay is similarly defined.

1))(Pr(lim

achievableisncfn

1))('Pr(lim

achievableisnfcn

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Outline Introduction

System Models

Tradeoff of Cluster Sparse Regime

Upper bound of cluster sparse regime

Low bound of cluster spare regime

Tradeoff of Cluster Dense Regime and Cluster Critica

l Regime

Summary10

Upper bound of cluster sparse regime

Scheduling PolicyWe regard that messages are first transmitted a

mong cluster level until the cluster containing the destination, Cd, capture the message.

Creating more relay in the clusters other than Cd won't improve the delay-throughput tradeoff.

Causal scheduling policy is considered here; scheduler at time slot t can only obtain information before t.

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Upper bound of cluster sparse regime

Lemma: Creating relay in cluster other than the cluster containing the destination decreasing the asymptotic throughput without decreasing the asymptotic delay.

Intuition: Nodes are located in a certain cluster with radius R. Before messages being transmitted to Cd, more relay won't improve the asymptotic delay.

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Upper bound of cluster sparse regime

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Upper bound of cluster sparse regime

Definition: Cluster contain relay is denoted as inter-cluster duplication; this term refer to cluster.

Definition: Relays in the Cd are denoted as intra-cluster duplication; this term refer to node.

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Upper bound of cluster sparse regime

Lemma: Basic tradeoff for delayUnder the cluster sparse regime, the delay for

bit b and its scheduling parameters comply the following inequality

where c1s is a positive constant, lb

s denotes the capture range of the destination, Rcb

s denotes intra-cluster duplication, and Db

s denotes the delay.

2

1 2 2 2log [D ] max ,

[R ] [R ]E[l / n]s s

b s s scb d b b

n Rc nE

R E E mR

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Upper bound of cluster sparse regime

Intuition: Delay can be divided into two parts. Transmissi

on delay after reaching Cd and transmission delay before reaching Cd.

For the part that before reaching Cd, process can be further divided into creating relays in different clusters and transmitting messages to Cd.

We solve these three parts separately to provide an intuitive answer to the question.

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Upper bound of cluster sparse regime

Lemma: Basic tradeoff for radio resourceUnder cluster sparse regime and concerning ra

dio resource, the throughput for a particular bit b and its scheduling parameters comply the following inequality

where c2s is a positive constant, Rdb

s denotes intra-cluster duplication, rb

h is the transmission range of each hop, h = 1, ..., hb

s and λs denotes the throughput.

2/( ) 22 2

221 1 1

[R ][ ] c logn

4 4

s ss sb cbh nR mRs hnT nT

sd b b

b b h

E rE WT

n mR

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Upper bound of cluster sparse regime

Intuition: The area of radio resource is only Θ(mR2)

not Θ(n) because nodes only cover a certain part of area in the network

A certain cluster has only a probability of mR2/n to meet other clusters. So we need to offer system n/mR2 chances for each inter-cluster operation.

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Upper bound of cluster sparse regime

Lemma: Basic tradeoff for half duplexNo node can transmit and receive at same time

and over same frequency, the following inequality holds

Lemma: Basic tradeoff for multihopThe following inequality holds for the nature of

multihop

2/( )

1 1

12

s ssb cbh nR mRnT

b h

WTn

1 1

ssbhnT

h sb b

b h

r l

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Upper bound of cluster sparse regime

Theorem:Under cluster sparse regime, let Ds denote the

mean delay averaged over all bits and let λs be the throughput of each source-destination pair. The following upper bound holds,

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3 3

43

2

( ) ( log n)

( log )

ss s s

III II

ss s s

III II

mDD D

n

mR Dn D D

n

Upper bound of cluster sparse regime

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Upper bound of cluster sparse regime

Optimal values of key parameterDuring our proof of upper bound, several

inequalities are used. In order to get a tight bound, we need to let these inequalities equal.

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Lower bound of cluster sparse regime

Tradeoff achieving scheme:– normal time slot are divided into three subslots

The nodes create inter-cluster duplications and the destination cluster Cd receive data from inter-cluster duplication, using one hop transmission manner with transmission range rb

h .Rdb

s Intra-cluster duplications is created during this subslot, using multicast manner.

Intra-cluster duplication is captured by a range lb

s and transmit to the destination, using hbs-ho

p multihop manner– All variables are selected from the optimal values of key paramete

r

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Lower bound of cluster sparse regime

Intuition: Sophisticated policy cannot improve the tradeoff performance more than polynomial of log n. So we use a direct time slot division method to construct a tradeoff achieving scheme.

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Outline Introduction

System Models

Tradeoff of Cluster Sparse Regime

Tradeoff of Cluster Dense Regime and Cluster Critica

l Regime

Tradeoff of Cluster Critical Regime

Tradeoff of Cluster Dense Regime

Summary25

Tradeoff of Cluster Critical Regime

Intuition:The upper and lower bound of the cluster critical regime (v+2β = 1) can be derived from the similar analysis.

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Tradeoff of Cluster Dense Regime

Scheduling policy

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Tradeoff of Cluster Dense Regime

Some former policy about weak node correlation, cluster dense regime, cannot improve network performance. But our research found that

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Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 2929

Outline

Introduction

System Models

Tradeoff of Cluster Sparse Regime

Tradeoff of Cluster Dense Regime and Cluste

r Critical Regime

Summary

Summary

Cluster sparse regime may suffer a maximum throughput constraint, cluster dense regime, however, does not.

Tradeoff of cluster sparse, critical, and dense regime are continuous.

Node correlation can increase the tradeoff for both cluster sparse regime and cluster dense regime.

Medium node correlation can improve the network performance best.

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Questions?

Thanks for listening.

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