maximizing the lifetime of wireless sensor networks through optimal single-session flow routing...

Maximizing the Lifetime of Wireless Sensor Networks through Optimal Single-Session Flow Routing

Y.Thomas Hou, Yi Shi, Jianping Pan, Scott F.MidkiffMobile computing September 2006

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Outline

Introduction Network Reference Model Optimal Single-Session Flow Routing Extension to Variable Bit-Rate Conclusion

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Introduction Consider a two-tier wireless sensor network

and address the network lifetime for upper-tier 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.

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Network model considered here

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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.

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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.

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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.

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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.

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Network Reference Model

Deployed

densely

Within one hop

Constituted by MSN

Energy unconstrained

Aggregation & Relay

Constituted by AFN && BS

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Network Reference Model-power consumption model

When AFN i transmits data to AFN k, the power consumption at transmitter can be modeled as is the power consumption cost of link (

i , k) is the bit-rate of flow sent by AFN i to

AFN k

tik ik ikp c f

ikc

ikf

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Where is a distance-independent term is a coefficient associated with the

distance-dependent term is the distance between these two

nodes n is the path loss exponent and

In this paper we adopt n = 4

nik ikc d

ikd

2 4n

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The power consumption at receiver of AFN j can be modeled as: 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

rj kj

k j

p f

kjf

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Optimal Single-Session Flow Routing-LP method

Variable used introduction Data flow’s bit-rate generated by AFN i is Initial energy at AFN i is The lifetime of AFN is T

We then have the following equations for each AFN i

ig

ie

i mi ik iBm i k i

g f f f

mi ik ik iB iB im i k i

T f T c f T c f e

AFN generated bit + received bit = outgoing bit

The energy required to received and transmit

all these flows, cannot exceed it total energy

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Optimal Single-Session Flow Routing-LP method

We then derive the following LP formulation

Where Our object is to maximizing T

0, (1 )

,(1 )

i mi ik ibm i k i

mi ik ik iB iB im i k i

g T V V V i N

V c V c V e i N

,ik ik iB iBV f T V f T

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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

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Theorem 1 can be proved by constructing a single-session flow routing solution (denoted as ) for a given multi-session flow routing solution , and showing that is equivalent to

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Optimal Single-Session Flow Routing-Numerical Example

Consider the following network

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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

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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 single-session routing schedule. Since and only is unknown, we

obtain = [0,37.79) Similarly, It is easy to verify that the flow balance equation

at each AFN is satisfied throughout[0,302.88).

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1 13

0

( 0)T

g dt f T 13T

14 15, , ...T T etc13T

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Extension to Variable Bit-Rate

We relax the constant bit-rate constraint for at each AFN i

We show that as long as the average bit-rate( denoted by ) for can be estimated, the optimal single-session flow routing solution is also obtainable

ig

ig ( )ig t

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Extension to Variable Bit-Rate- Perfect 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

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We proof theorem 3 by showing that the maximum network lifetime for problem is indeed greater than or equal to maximum network lifetime for problem P.( vice versa )

P

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The significance of theorem 2 and 3 is that they enable us to obtain an optimal single-session 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 Apply algorithm 2 to get an optimal single-

session flow routing solution for p

P

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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 near-optimal single-session flow routing solution.

Conclusion

maximizing the lifetime of wireless sensor networks through optimal single-session flow routing...

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