Impact of Mobile Relay Nodes
on Static Ad Hoc Network
Zhenqi Lu
Shanghai Jiaotong University
June 17, 2010
Outline
Introduction
 Model and Assumptions
 Throughput Per Node in Ad Hoc Network
with Infinite Mobile Relays
 Throughput Per Node in Ad Hoc Network
with Finite Mobile Relays
 Conclusion

Introduction

Gupta and Kumar’s Result:

static ad hoc network


1
 n   
 n log n 




converges to zero when
n 
Grossglauser and Tse’s Result:

mobile ad hoc network
  n    1
Model I/IV

The Protocol Model
 The
distance between sender and receiver is no
more than r .
Xi  X j  r
 Cochannel
sender must be 1    r far from
receiver.
X k  X j  1    r
Model II/IV

The Physical Model
 SIR
at receiver must be greater than a certain
gate value 
P

Xi  X j
P
N 
k 
k i
 where
Xk  X j


 is the pass loss exponent.
Model III/IV

Throughput Capacity
 Time
average of the number of bits transmitted
to destination per node
Model IV/IV
static nodes deployed on a planar disk of
unit area (of radius 1 )
n
 randomly
located, i.e., independently and
uniformly distributed
m
mobile relay nodes
function Yi  t  stationary and
ergodic, with stationary uniform distribution
 location-time
Routing Scheme I/II

Multi-hop Routing
a
straight line from source X i to destination X d i 
– Proved to have some rather powerful uniformity
properties
 Each
hop intersects the straight line to
approximate the straight-line segments.

Two-hop Routing
 only
transmission from static node to mobile
relay and mobile relay to static node permitted
Routing Scheme II/II

During multi-hop routing, packets are
permitted to be transmitted to mobile relays.
Source
Destination
Source
Destination
Source
Destination
Source
Destination
Source
Destination
Source
Destination
Source
Destination
Source
Destination
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Destination
Source
Destination
Source
Destination
Source
Destination
Source
Destination
Source
Destination
Impact on Simultaneous S-R
Pairs

Upper Bound Increased
NS R
 intuitive
nm

2
explanation for capacity increase
Ad Hoc Network with Infinite
Mobile Relays I/III

Fixed Node-to-Relay Ratio 
n

m
 Numbers of mobile relay and static nodes are of
same order.

Multi-hop Transmission Not Permitted
 Two-hop
transmission can provide high
throughput.
Ad Hoc Network with Infinite
Mobile Relays II/III

Number of Feasible S-R Pairs N
lim
E  N 
n 

n

Throughput Per Node
 n 
E  N 
n

  1
n 
Ad Hoc Network with Infinite
Mobile Relays III/III

Optimistic Result
 approaching
the upper bound for ad hoc
network

Assumption Too Strong
 impossible
of users
to equip mobile relays of same order
Ad Hoc Network with Finite
Mobile Relays I/III

Variable Node-to-Relay Ratio   n 


m
n
  n    1,  
m
far smaller than n
Multi-hop Transmission Permitted
 acting
as major method of transmission
Ad Hoc Network with Finite
Mobile Relays II/III
Scheduling Scheme
Fixing One Constant Sender Density 
 Transmitting to the Nearest Node Each
Time Slot

 transmission
to mobile relay during multi-hop
transmission permitted

Transmitting with Unit Power  Pi  1
 on

accordance to the random model
Transmitting One Packet to Receiver Each
Time Slot
Ad Hoc Network with Finite
Mobile Relays III/III


Probability of Transmitting to Mobile Relay
m
Prob  mobile     
n
Throughput Per Node
m

1
m
1
 n    


n
n
n log n
n log n 

 1

1
1
1
 



  n
n log n   n  n log n 

Discussions

Throughput Per Node
 1

1
1
1
  n   



  n

n
  n log n 
n log n

 Converges


1

to  
 n log n 
if m
n (Gupta &
Kumar’s result)
 Converges to  1 if m   n where  is a
constant between 0 and 1 (Grossglauser &
Tse’s result)
Conclusion
Mobile relay increases throughput per node
in static ad hoc network.
 It is not a optimistic result, because it
requires the number of mobile relays to be
of same order with static nodes.
 It still converges to zero when n   .

Thank You!