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 Telecommunications, China

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 2 2 Outline Introduction  Motivations  Objectives System Models Tradeoff of Cluster Sparse Regime Tradeoff of Cluster Dense Regime and Cluster Critical Regime Summary

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Motivations  Ad-hoc Networks  Pessimistic 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. 3

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Objectives  Former work  Maximum throughput performance with corresponding delay.  Our Topic  Optimal delay-throughput performance under different node correlation. 4

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Outline Introduction System Models Tradeoff of Cluster Sparse Regime Tradeoff of Cluster Dense Regime and Cluster Critical Regime Summary 5

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks System Model-I/III  Network extension: a square with area n.  m clusters, each covers a circular area with radius 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. 6

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks System Model-II/III 7

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks System Model-III/III  Transmission protocol: protocol model  Communication among different clusters  Classify node correlation  Strong node correlation: cluster sparse regime; mR 2 ＜ n.  Weak node correlation: cluster dense regime; mR 2 ＞ n.  Medium node correlation: cluster critical regime; mR 2 = n. 8

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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. 9

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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 Critical Regime Summary 10

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Scheduling Policy  We regard that messages are first transmitted among cluster level until the cluster containing the destination, C d, capture the message.  Creating more relay in the clusters other than C d won't improve the delay-throughput tradeoff.  Causal scheduling policy is considered here; scheduler at time slot t can only obtain information before t. 11

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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 C d, more relay won't improve the asymptotic delay. 12

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime 13

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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 C d are denoted as intra- cluster duplication; this term refer to node. 14

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Lemma: Basic tradeoff for delay  Under the cluster sparse regime, the delay for bit b and its scheduling parameters comply the following inequality  where c 1 s is a positive constant, l b s denotes the capture range of the destination, R cb s denotes intra-cluster duplication, and D b s denotes the delay. 15

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Intuition:  Delay can be divided into two parts. Transmission delay after reaching C d and transmission delay before reaching C d.  For the part that before reaching C d, process can be further divided into creating relays in different clusters and transmitting messages to C d.  We solve these three parts separately to provide an intuitive answer to the question. 16

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Lemma: Basic tradeoff for radio resource  Under cluster sparse regime and concerning radio resource, the throughput for a particular bit b and its scheduling parameters comply the following inequality  where c 2 s is a positive constant, R db s denotes intra-cluster duplication, r b h is the transmission range of each hop, h = 1,..., h b s and λ s denotes the throughput. 17

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Intuition:  The area of radio resource is only Θ(mR 2 ) not Θ(n) because nodes only cover a certain part of area in the network  A certain cluster has only a probability of mR 2 /n to meet other clusters. So we need to offer system n/mR 2 chances for each inter-cluster operation. 18

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Lemma: Basic tradeoff for half duplex  No node can transmit and receive at same time and over same frequency, the following inequality holds  Lemma: Basic tradeoff for multihop  The following inequality holds for the nature of multihop 19

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Theorem:  Under cluster sparse regime, let D s denote the mean delay averaged over all bits and let λ s be the throughput of each source-destination pair. The following upper bound holds, 20

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime 21

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Upper bound of cluster sparse regime  Optimal values of key parameter  During our proof of upper bound, several inequalities are used. In order to get a tight bound, we need to let these inequalities equal. 22

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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 C d receive data from inter-cluster duplication, using one hop transmission manner with transmission range r b h.  R db s Intra-cluster duplications is created during this subslot, using multicast manner.  Intra-cluster duplication is captured by a range l b s and transmit to the destination, using h b s -hop multihop manner –All variables are selected from the optimal values of key parameter 23

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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. 24

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Outline Introduction System Models Tradeoff of Cluster Sparse Regime Tradeoff of Cluster Dense Regime and Cluster Critical Regime Tradeoff of Cluster Critical Regime Tradeoff of Cluster Dense Regime Summary 25

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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. 26

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Tradeoff of Cluster Dense Regime  Scheduling policy 27

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Tradeoff of Cluster Dense Regime  Some former policy about weak node correlation, cluster dense regime, cannot improve network performance. But our research found that 28

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 29 Outline Introduction System Models Tradeoff of Cluster Sparse Regime Tradeoff of Cluster Dense Regime and Cluster Critical Regime Summary

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks 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. 30

Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks Questions?  Thanks for listening. 31