Delay-Throughput Tradeoff with
Correlated Mobility in Ad-Hoc Networks
Shuochao Yao, Xinbing Wang
Department of Electronic Engineering, Shanghai Jiao Tong University,
China
Email: {sasukecao,xwang8}@sjtu.edu.cn
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
2
Motivations
 Kumar: Capacity of wireless network is not scalable: in a static wireless network
1
with nodes, the per-node capacity is O(
. Interference is the main
)[1]
n log n
reason behind.
[2]
 Grossglauser and Tse: Capcity can reach O(1) when moblity is introduce,
large delay, however, is needed
D
n
 Xiaojun Lin: Tradeoff under i.i.d slow mobility model can reach  3  O( log 3n)[3]
 Garetto: Correlated mobility may increase the tradeoff under Cluster Sparse
Regime[3]
[1] P. Gupta and P. R. Kumar, “The capacity of wireless networks”, in IEEE Transaction on Information
Theory, 2000.
[2] M. Grossglauser and D. Tse, \Mobility Increases the Capacity of Ad Hoc Wireless Networks,"
IEEE/ACM Transactions on Networking, vol. 10, no. 4, August 2002.
[3]X. Lin, N.B. Shroff, “The Fundamental Capacity-Delay Tradeoff in Large Mobile Ad Hoc Networks,” in
Proc. MedHoc’04.
[4]D. Ciullo, V. Martina, M. Garetto, E. Leonardi, “Impact of Correlated Mobility on Delay-Throughput
Performance in Mobile Ad-Hoc Networks”, in Proc. IEEE INFOCOM, Mar. 2010.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
3
Objectives
We study:
How does the correlated moblity model
influence the Delay-Throughput tradeoff ?
Especially the cluster dense and cluster cirtical
model (One is proved to have no fluence and the
other is not inclued in [3])
What is the Tradeoff under the correlated
moblity model?
We obtain:
 The Upper bound of Tradeoff under the correlated
mobility model.
 The achievable lower bound for get the Upper bound.
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
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
System model
n nodes move over a square with area n.
n nodes are divided into m  (n v ) groups, and
each group cover an circular area with radius
R  (n  )
Time is divided into time slots of unit duration
At each time slot, for node i in cluster j
 Center of cluster j's position are i.i.d and uniformly
chosen among the whole network area
 Node i's positon are i.i.d and unifromly chosen among
the area that cluster j cover.
Slow mobility
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
System model
Protocol model is used
Only communication between different clusters
are consider
Three regime of correlated mobility
 Cluster sparse regme when v  2  1 i.e. mR  o(n) m
clusters only cover a negligible fraction of whole
network area
 Cluster dense regime whenv  2  1 i.e. mR 2   (n) m
have a large probability to overlap
 Cluster critical regime whenv  2  1 i.e. mR2  (n)
2
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
System model
System Parameter
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Outline
 ntroduction
 System Models
 Tradeoff of Cluster Sparse Regime
 Upper bound of cluter sparse regime
 Detailed upper upper bound of sparse regime
 Lower bound of cluster sparse regime
 Tradeoff of Cluster Dense Regime and Cluster Critical Regime
 Summary
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
Scheduling policy
 s create Rs duplication nodes as relay in Cs with multicast
 When relays meet a cluster Ck (k=1,....Rcs, where Rcs is
the maximum number of clusters containing realy) not
containing duplication node, a duplication will be
created in Ck with one-hop unicast.
 New-created relay in Ck create Rk duplication nodes in
Ck with broadcast by opporitunity until message is
captured by Cd.
 When a relay meet Cd, a duplication will be created in Cd
with one-hop unicsat.
 New-created relay in Cd create about Rd duplication
nodes in Cd with broadcast by opportunity until message
is captured by destination.
 When Rd relays are captured by the destination with
range ls, the message will be transmitted to destination
with a hs-hop multihop transmission.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
 Lemma 3.1: Under cluster sparse regime, most intra-cluster duplication (the
duplication nodes in a certain cluster) {Rs,R1,...,RRc} will decrese the
throughput without decreaing the delay
A simplified shceduling policy
 When s and relays meet a cluster Ck (k=1,...Rcs), where
Rcs is the number inter-cluster duplication (the cluster
containing duplication node) not containing duplication
node, a duplication will be created in Ck with one-hop
unicast.
 When a relay meet Cd, a duplication will be created in Cd
with one-hop unicsat.
 New-created relay in Cd create Rds duplication nodes in
Cd with broadcast by opporitunity until message is
captured by Cd.
 When Rd relays are captured by the destination with
range ls, the message will be transmitted to destination
with a hs-hop multihop transmission.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
Basic tradeoff for delay
 DIs: delay of creating Rcs inter-cluster duplication
Rc s m
n
D  ( 2 (ln
  ))
mR
m  Rc s
s
I
 DIIs: delay of Rcs inter-cluster duplications transmitting
message to Cd
n
D  ( s 2 )
Rc R
s
II
 DIIIs: delay of transmission within Cd
R2
D  ( s 2 )
Rd l
s
III
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
Basic tradeoff for delay
 Total delay Ds under cluster sparse regime:
max{D I s , D II s , D III s }
 Lemma 3.2: Under the cluster sparse regime, the delay for a particular bit b
and its scheduling parameters comply thefollowing inequality
n
R2
c log nE[D ]  max{ 2
,
s
R E[R cb ] E[R s ]E[ls  mR 2
db
b
s
1
s
b
2
n2
}
]
 where c1s is a positive constant and variable Xbs denote the variable
X under cluster sparse regime for a particular bit b.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
Basic tradeoff for radio resource
 Protocol model will generate several disjoint circular area
with radius Δ|Xi-Xj|/2, where |Xi-Xj| is the
transmission range of two nodes.
 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.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
Basic tradeoff for radio resource
 Lemma 3.2: Under cluster sparse regime and concerning radio
resource, the throughput for a particular bit b and its scheduling
parameters comply the following inequality
 nT
 2 E[R d bs ]
 E[ 

n
b 1 4
b 1
 nT
s
s
hbs 
nRcbs
mR2

h 1
 2 rbh 2
4 mR
s
]

c
WT logn
2
2
 where c2s is a positive number, hbs is the number of transmission
hops after message being captured by destination node, and rbh
is the transmission range of each hop, h = 1;..., hbs
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
Basic tradeoff for half duplex
 No node can transmit and receive at same time and over
same frequency, the following inequality holds
 s nT
hbs 
nRcbs
mR2
 
b 1
h 1
WT
1
n
2
Basic tradeoff for multihop
 The following inequality holds for the nature of
multihop
s
 s nT hb
h
s
r

l
 b b
b 1 h 1
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
Upper bound
 Theorem 3.1: 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,
s
mD
(  s ) 3  (
log 3n) DIIIs  DIIs
n
mR 4 D s
s
3
s
s
  (
log
n
)
D

D
III
II
n2
{
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
DIIIs>DIIs
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
DIIIs<DIIs
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Upper bound of cluster sparse regime
 Red line is tradeoff of Xiaojun Lin
 Blue line is tradeoff of our cluster sparse regime
 Green line is the maximum throughput of cluster sparse
regime
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed 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. The value of key parameters
can be deduced
 Optimal values of key parameter when DIIIs>DIIs
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster sparse regime
Optimal values of key parameter
 Optimal values of key parameter when DIIIs<DIIs
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster sparse regime
Detailed upper bound
 Expression of upper bound contain a blurry separation
for two tradeoff
mD s
(  )  (
log 3n) DIIIs  DIIs
n
mR 4 D s
s
3
s
s
  (
log
n
)
D

D
III
II
n2
s 3
{
 A detailed upper bound with clear separation expression
can be derived by applying the optimal values of key
paramters
s
mD
5
log 3n) d   v  6 
n
2
mR 4 D s
5
s
3
  (
log
n
)
d

 v  6
2
n
2
(  s ) 3  (
{
 assuming Ds=nd
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Lower bound of cluster sparse regime
Tradeoff achieving scheme:
– normal are divided into three subslots
 The nodes (source node or duplication) create intercluster duplications and the destination cluster Cd
receive data from inter-cluster duplication, using one
hop transmission manner with transmission range rbh .
 Rdbs Intra-cluster duplications is created during this
subslot, using multicast manner.
 Intra-cluster is captured by a range lbs and transmit tothe
destination, using hbs-hop multihop manner.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Lower bound of cluster sparse regime
Tradeoff achieving scheme:
– We show the operations of each subslot below noticing that TDMA
are as the transmission scheme
 In the 1st subslot, we divide each cluster into n1-v equalarea cells. Asuume that each message'length is
λs/log2n≤mR2/(nRcbs), so a node can send at least
nRcbs/(mR2) packets each transmission. We know that
each node have a chance of mR2/(nlogn) to transmit. At
least Rcbs/logn parckets can be sent per second, so
networkcan sustain throughput of λs/log2n. If each time
netwotk cannot sustain mR2/n per-node throghput of
inter-cluster communcaiton, we call this ErrorIs. If a
message cannot be sent to its Cd during Θ(DIIs) time
slots, w call this ErrorIIs.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Lower bound of cluster sparse regime
 In the 2rd and 3th subslot, all messgaes are transmtted in
their Cd. Nodes in a certain cluster follow the uniform
distribution. The achievable lower bound under uniform
condition have been studied widely. The only problem is
more than a certian number of clusters overlap at a
certain area which are denoted as ErrorIIIs
 Theorem 5.1: Under cluster sparse regime,P[ErrorIs]→0,
P[ErrorIIs]→0, and P[ErrorIIIs]→0, as n→∞
 Chernoff bound is a effective method to solve this quetion
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
 Detailed upper upper bound of dense regime
 Lower bound of cluster dense regime
 Summary
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Several properties of cluster dense regime
 Every point in the network is covered by Θ(mR2/n)
cluster w.h.p, which seems to be helpful but not indeed
 Lemma 6.1: Under cluster dense regime, an area of Θ(R2) is
covered by Θ(mR2/n) cluster.
 Lemma 6.2: The probability that a source cluster send a message
to a certain cluster is independent of the number of nodes in
source cluster containing the message, assuming transmitting
range r = o(R).
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
U times broadcast
 u times broadcast with broadcast area Ad is applied, for
the reason that
 Lemma 6.3: If we have already created inter-cluster duplications in
Rx ≤(m) cluster, each point will still be covered by at least mR2=(m)
clusters not containing duplication.
Scheduling policy
 Nodes containing a certain message create inter-cluster
duplications with u times broadcast until it is captured.
 When inter-cluster relays are captured by any node in Cd
with range l1d, message will be transmitted to the node
with a h1d-hop multihop transmission.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Scheduling policy
 New-created relay in Cd create Rdd duplications in Cd
with broadcast until it is captured.
 When Rdd relays are captured by the destination with
range l2d, the message will be transmitted to destination
with a h2d-hop multihop transmission.
Scheduling division
 In the following analysis, we divide our schedule into two
parts. One is 1)-2) (Part I) and the other is 3)-4) (Part II).
We will analyse them respectively
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Basic tradeoff for delay of Part I
 Lemma 6.5: Under the cluster dense regime, the delay for a
particular bit b of Part I and its scheduling parameters comply the
following inequality
 where c1d is a positive constant and variable Xbd denote the
variable X under cluster dense regime for a particular bit b.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Basic tradeoff for radio resource of Part I
 Lemma 6.6: Under cluster dense regime and concerning radio
resource, the following inequality holds
 where c2d is a positive number, h1bd is the number of transmission
hops after message being captured by the node in Cd,and rbh is
the transmission range of each hop.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Basic tradeoff for half duplex of Part I
Basic tradeoff for multihop of Part I
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Detailed Upper bound of Part I
 Theorem 6.1: Under cluster sparse regime, let D1d denote the
mean delay averaged over all bits and let λ1d be the throughput of
each source-destination pair. Assume all the key parameters are
same for all bits. In Part I, the following upper bound holds,
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Basic tradeoff for delay of Part II
 Lemma 6.8: Under the cluster dense regime, the delay for a
particular bit b of Part II and its scheduling parameters comply the
following inequality
 where c1d is a positive constant and variable Xbd denote the
variable X under cluster dense regime for a particular bit b.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Basic tradeoff for radio resource of Part II
 Lemma 6.9: Under cluster dense regime and concerning radio
resource, the following inequality holds
 where c4d is a positive number, h2bd is the number of transmission
hops after message being captured by destination and rbh is the
transmission range of each hop.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Basic tradeoff for half duplex of Part II
Basic tradeoff for multihop of Part II
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Detailed Upper bound of Part II
 Theorem 6.2: Under cluster sparse regime, let D2d denote the
mean delay averaged over all bits and let λ2d be the throughput of
each source-destination pair. Assume all the key parameters are
same for all bits. In Part II, the following upper bound holds,
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
Overall detailed Upper bound
 Theorem 6.2: Under cluster sparse regime, let Dd denote the mean
delay averaged over all bits and let λd be the throughput of each
source-destination pair. Assume all the key parameters are same
for all bits. In Part II, the following upper bound holds,
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Detailed upper bound of cluster dense regime
 Blue line is tradeoff of Part I
 Red line is tradeoff of PartII
 Green line is tradeoff of Xiaojun Lin
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
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
41
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.
Correlated mobility can increase the tradeoff for
both cluster sparse regime and cluster dense
regime.
Heterogeneous can increase the delaythroughput tradeoff, if we designe the
heterogeneous specifically.
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks
Thank you for listening.
Any question?
Delay-Throughput Tradeoff with Correlated Mobility in Ad-Hoc Networks