Maximizing the Lifetime of Wireless
Sensor Networks through Optimal
Single-Session Flow Routing
Y.Thomas Hou, Yi Shi, Jianping Pan,
Scott F.Midkiff
Mobile computing September 2006
Outline





Introduction
Network Reference Model
Optimal Single-Session Flow Routing
Extension to Variable Bit-Rate
Conclusion
2
Introduction
 Consider a two-tier wireless sensor network
and address the network lifetime for uppertier aggregation and forwarding node.
 Existing flow routing solutions proposed for
maximizing network lifetime require AFNs
to split flows to different path during
transmission, which we called multi-session
flow routing.
3
Network model considered here
4
Introduction
 Owing to the transmission bottleneck of
AFN, the lifetime of whole sensor network
here is the lifetime of AFN.
 The majority of power consumption at an
AFN is due to its radio communication , it is
essential to devise strategies that can
minimize radio-related power consumption
at AFN.
 One promising approach to maximizing
network lifetime is to dynamically control
the output power level of radio transmitters.
5
Introduction
 Existing solutions to this problem,
obtained under linear programming,
require each AFN to split data flows to
multiple path during transmission,
which we call multi-session flow
routing solutions.
6
Introduction
 Multi-session flow routing solutions
has some problems here:
 Necessary for the AFN to perform power
control at packet-level to conserve
energy.
 To guarantee packet-level power control
between a transmitter and a receiver, the
synchronization requirement is stringent
and will bring in considerable overhead.
7
Introduction
 Our goal is to develop single-session
flow routing solutions, where routing
topologies are relatively static and
are adjusted (via power control) on
large timescale.
 To achieve this objective, we first
show that an optimal multi-session
can be transformed into an equivalent
single-session flow routing solution.
8
Network Reference Model
Energy
unconstrained
Aggregation & Relay
Constituted by
AFN && BS
Within one hop
Deployed
densely
Constituted by
MSN
9
Network Reference Modelpower consumption model
 When AFN i transmits data to AFN k,
the power consumption at transmitter
t
p
can be modeled as ik  cik  fik

cik is the power consumption cost of link
( i , k)
 fik is the bit-rate of flow sent by AFN i to
AFN k
10
Network Reference Modelpower consumption model
 Where cik      d
  is a distance-independent term
n
ik
  is a coefficient associated with the
distance-dependent term
 dik is the distance between these two
nodes
 n is the path loss exponent and
2n4
 In this paper we adopt n = 4
11
Network Reference Modelpower consumption model
 The power consumption at receiver of
r
p
AFN j can be modeled as: j    f kj
k j
 f kj is the incoming bit-rate of composite
flow received by AFN j from AFN k
  is the coefficient of receiver, there is a
detailed discussed in other paper
12
Optimal Single-Session Flow
Routing-LP method
 Variable used introduction
 Data flow’s bit-rate generated by AFN i is gi
 Initial energy at AFN i is ei
 The lifetime of AFN is T
 We then have the following equations
for each AFN i
 gi   f mi   fik  fiB
m i
k i
AFN generated bit +
received bit = outgoing bit
 T    f mi  T   cik fik  T  ciB fiB  ei
m i
k i
The energy required to
received and transmit
all these flows, cannot
exceed it total energy
13
Optimal Single-Session Flow
Routing-LP method
 We then derive the following LP
formulation
 giT  Vmi  Vik  Vib  0, (1  i  N )
m i
  V
m i
mi
k i
  cikVik  ciBViB  ei ,(1  i  N )
k i
 Where Vik  fik  T ,ViB  fiB  T
 Our object is to maximizing T
14
Optimal Single-Session Flow
Routing-Single flow method
 Advantages of single flow routing
 Power control and topology change are
only done on a much larger time scale
instead of on the per-packet basis
 Synchronization requirement compared
to multi-session is quite low and its
overhead is negligible when compared to
multi-session flow routing
15
Optimal Single-Session Flow
Routing-Single flow method

 Theorem 1 can be proved by
constructing a single-session flow
routing solution (denoted as ˆ ) for a
given multi-session flow routing
solution  , and showing that ˆ is
equivalent to 
16
Optimal Single-Session Flow
Routing-Single flow method
17
Optimal Single-Session Flow
Routing-Single flow method
18
Optimal Single-Session Flow
Routing-Single flow method
19
Optimal Single-Session Flow
Routing-Single flow method
20
Optimal Single-Session Flow
Routing-Single flow method
21
Optimal Single-Session Flow
Routing-Single flow method
22
Optimal Single-Session Flow
Routing-Numerical Example
 Consider the following network
23
Optimal Single-Session Flow
Routing-Numerical Example
 With the LP approach, we obtain a
static multi-session flow routing
solution.
 For given initial energy at each AFN,
the maximum network lifetime
obtained by solving the corresponding
LP problem is T = 302.88 days
24
Optimal Single-Session Flow
Routing-Numerical Example
 According to algorithm 1, since nodes 2, 4,
5 are already in single-session mode, there
is no need to perform transformation on
them.( except the flow rate of 4 and 5 need
to be recomputed )
 We then transform AFN 1 to a singlesession routing schedule.
 Since  ( g  0)dt  f  T and only T13 is unknown, we
T13
1
13
obtain T13 = [0,37.79)
 Similarly, T14 , T15 , etc...
 It is easy to verify that the flow balance
equation at each AFN is satisfied
throughout[0,302.88).
0
25
Optimal Single-Session Flow
Routing-Numerical Example
26
Optimal Single-Session Flow
Routing-Numerical Example
27
Extension to Variable Bit-Rate
 We relax the constant bit-rate
constraint for gi at each AFN i
 We show that as long as the average
bit-rate( denoted by gi ) for gi (t ) can
be estimated, the optimal singlesession flow routing solution is also
obtainable
28
Extension to Variable Bit-RatePerfect knowledge of average bit-rate

 As above, this theorem can be proved
by constructing a single session flow
routing solution for P with the same
network lifetime as that obtained for P
29
Extension to Variable Bit-RatePerfect knowledge of average bit-rate
30
Extension to Variable Bit-RatePerfect knowledge of average bit-rate
31
Extension to Variable Bit-RatePerfect knowledge of average bit-rate

 We proof theorem 3 by showing that the
maximum network lifetime for problem P
is indeed greater than or equal to
maximum network lifetime for problem
P.( vice versa )
32
Extension to Variable Bit-RatePerfect knowledge of average bit-rate
 The significance of theorem 2 and 3 is that
they enable us to obtain an optimal singlesession flow routing solution for a general
sensor network of variable bit-rate AFNs.
 In a nutshell, this approach takes the
following two steps
 Find an optimal multi-session flow routing
solution  for P
 Apply algorithm 2 to get an optimal singlesession flow routing solution  for p
36
Conclusion
 For a node with single transceiver, this would require
a packet-level power control to conserve energy,
which calls for considerable overhead in
synchronization among the AFNs.
 We show that the packet-level power control is not
necessary.
 Instead, it is possible to achieve the same maximum
network lifetime by employing power control in a
much larger timescale with so-called single-session
flow routing method.
 In practice, the estimated average bit-rate for g could
deviate from actual value.
 As long as this discrepancy is not substantial, the
procedure developed previously can still yield nearoptimal single-session flow routing solution.
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