Elham Torabi EECE 565 - Term Paper - April 2006 Department of - - PowerPoint PPT Presentation

• Elham Torabi

EECE 565 - Term Paper - April 2006 Department of Electrical & Computer Engineering The University of British Columbia

Outline

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• 1. Overview and Introduction
• 2. Power Efficient Routing Algorithms
• Minimum Total Transmission Power Routing (MTPR)
• Minimum Battery Cost Routing (MBCR)
• Min-Max Battery Cost Routing (MMBCR)
• Conditional Min-Max Battery Capacity Routing (CMMBCR)
• Max-Min zPmin Routing
• Flow Augmentation (FA) Routing
• 3. Performance Comparison

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 1. Overview and Introduction

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• Ad-hoc wireless sensor networks consist of large numbers of sensor nodes,

which are tiny, low-cost, low-power radio devices dedicated to performing functions such as collecting data, limited data processing, and sending data to infrastructure processing gateways..

• Most nodes operate on their limited battery energy.
• The power consumption is closely coupled with the route selection in these

networks.

• It is important to minimize the power consumption of the entire network, this

implies maximizing the network lifetime.

• Power consumption categorization:
• 1. communication related power used for transmission and reception of mes-

sages.

• 2. non-communication related power used for operations such as sensing and

data processing.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Minimum Total Transmission Power (MTPR)

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• For successful transmissions, the signal-to-noise ratio (SNR) received at node

nj should be greater than a specified threshold ψj, and satisfy the following SNRj = PiGi,j

• k=i PkGk,j + ηj

ψj (BER) , (1) where Pi is the transmission power of host nj, Gi,j = 1/dn

i,j is the path

gain between nodes ni, nj, di,j is distance between two nodes, and n is the propagation exponent. ηj is the thermal noise. The transmission power P(ni, nj) between nodes ni, nj can be used as metric, and the total transmission power for route l, Pl, can be derived from Pl =

D−1

• i=0

P(ni, ni+1) , for all node ni ∈ route, (2) The desired route k can be obtained (using Bellman-Ford algorithm) from Pk = min

l∈A Pl,

(3) where A is the set containing all possible routes.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Minimum Total Transmission Power (MTPR)

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• Modification resulting in fewer hops: Using distributed Bellman-Ford algo-

rithm, at node nj, it computes Ci,j = Ptransmit(ni, nj) + Ptransceiver(nj) + Cost(nj), (4) where ni is a neighboring node of nj, Ptransceiver(nj) is the transceiver power at node nj, and Cost(nj) is the total power cost from the source node to node nj. This value is sent to node ni, where it computes its power cost by using the following equation Cost(ni) = min

j∈NH(i) Ci,j,

(5) where NH(i) = {j; nj is a neighbor node of ni}. The path with min- imum cost from the source node to node ni is selected. This procedure is repeated until the destination node is reached.

• If the minimum total transmission power routes are via specific nodes, the

battery of these nodes will be exhausted quickly and may cause network par- titioning.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Minimum Battery Cost (MBCR)

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• The remaining battery capacity of each node is a more accurate metric to find

the lifetime of each node fi(ct

i) = 1/ct i,

(6) where fi(ct

i) is defined as a battery cost function of node ni, where ct i is the

battery capacity of node ni at time t.

• The battery cost Rj for route i consisting of D nodes is

Rj =

Dj−1

• i=0

fi(ct

i).

(7)

• The route with maximum remaining battery capacity is selected as

Ri = min {Rj|j ∈ A} , (8) where A is the set containing all possible routes.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Minimum Battery Cost (MBCR)

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• This algorithm prevents nodes from being overused.
• Since, only the summation of values of battery cost functions is considered,

a route containing nodes with little residual battery capacity may still be selected.

Figure 1: An illustration of the shortcoming in minimum-hop routing. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Min-Max Battery Cost (MMBCR)

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• The objective function in MBCR can be modified as

Rj = max

i∈routej fi(ct i).

(9) Similarly the desired route i can be obtained as Ri = min {Rj|j ∈ A} (10)

• In this algorithm the battery of each node will be used more fairly than in

previous schemes.

• There is no guarantee that minimum total transmission power paths will be

selected under all circumstances.

• This approach can consume more power to transmit node traffic from a source

to a destination, which will reduce the lifetime of all nodes.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Conditional Min-Max Battery Capacity (CMMBCR)9
• The goal is to maximize the lifetime of each node and use the battery fairly.
• The battery capacity Rc

j for route j at time t is defined as

Rc

j =

min

i∈routej ct i.

(11) A is a set containing all possible routes between any two nodes at time t and satisfying the following equation Rc

j ≥ γ. for any route j ∈ A,

(12) where γ is a threshold between 0 and 100. Let Q denote the set containing all possible paths between the specified source and destination nodes at time t, then – If A ∩ Q = ∅, that implies all nodes at some paths have remaining battery capacity higher than γ, choose a path in A ∩ Q by applying the MTPR scheme. – Otherwise, choose route i with the maximum battery capacity: Rc

i =

max

• Rc

j|j ∈ Q

• .

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Conditional Min-Max Battery Capacity (CMMBCR)

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• γ can be considered as a protection margin.
• The performance of CMMBCR depends on the value of γ.

The normalized

Figure 2: Normalized network lifetime of CMMBCR versus its parameter γ.

network lifetime RX denotes the ratio between the network (system) lifetime

• f the algorithm and the optimal solution obtained by solving the linear pro-

gramming problem.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Max-Min zPmin

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• This is an online power-aware routing algorithm in a sense that it does not

know ahead of time the sequence of messages that has to be routed over the network.

• Maximizing the lifetime of the network is modeled as the time to the earliest

time a message can not be sent.

• The maximal number of messages sustained by a network from the source

node to the sink node can be formulated as a linear programming problem, and goal is to maximize the number of messages in the network Maximize

• j

nsj s.t.

• j

nij · eij ≤ Pi,

• j

nij =

• j

nji (for i = s, t), (13)

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Max-Min zPmin

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where the total number of messages from node vi to node vj is denoted by nij, and eij represents the power cost to send a message from node vi to node vj, and s and t denote the source and the sink in the network. Pi denotes the power of node i.

• It’s desired to route messages along the path with the maximal minimal frac-

tion of remaining power after the message is transmitted, called the max-min path, but the performance of max-min path can be very bad as seen below

Figure 3: The performance of max-min path can be very bad.

• Going through the nodes with high residual power may be expensive as com-

pared to the path with the minimal power consumption, where too much power consumption decreases the overall power level of the network, and thus decreases its lifetime.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Max-Min zPmin

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• Therefore, a trade-off between minimizing the total power consumption and

maximizing the minimal residual power of the network should be considered.

• Enhancing a max-min path by limiting its total power consumption will be the

goal.

• The two extreme solutions to power-aware routing for one message are:
• 1. compute a path with minimal power consumption Pmin
• 2. compute a path that maximizes the minimal residual power in the network.

This algorithm optimizes both criteria.

• The minimal power consumption for the message is relaxed to be zPmin with

parameter z ≥ 1 to restrict the power consumption for sending one message to zPmin.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Max-Min zPmin

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• 1. Find the path with the least power consumption, Pmin by using the Dijkstra

algorithm.

• 2. Find the path with the least power consumption in the graph.

If the power consumption > zPmin or no path is found, then the previous shortest path is the solution, stop.

• 3. Find the minimal utij on that path, let it be umin.
• 4. Find all the edges whose residual power fraction utij ≤ umin, remove them

from the graph.

• 5. Goto 2.

P(vi) denotes the initial power level of node vi, eij the weight of the edge between vi and vj, and Pt(vi) be the power of node vi at time t. Then, the residual power fraction after sending a message from vi to vj is defined as utij =

Pt(vi)−eij P(vi) .

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Max-Min zPmin

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• The parameter z is an important factor in the max-min zPmin algorithm,

which measures the trade-off between the max min path and the minimal power path.

• Note that max-min zPmin is an on-line approximation algorithm, which gives

a lower performance bound and has no constant competitive ratio to the

• ptimal off-line algorithm, but shows good empirical competitive ratio close

to the optimal solution.

• It is important to investigate an adaptive way of computing z > 1 such that

max-min zPmin will lead to a longer lifetime for the network than each of the max-min and minimal power algorithms.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Max-Min zPmin

16 Figure 4: Normalized network lifetime of max-min zPmin versus its parameter z. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Max-Min zPmin

17 Figure 5: The top graph compares the performance of max-min zPmin to the optimal solution, where the weight formula is eij = 0.0001 ∗ d3

ij . The bottom graph shows the histogram that compares max-min zPmin to optimal, where eij = 0.001 ∗ d3 ij.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

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• The goal of this algorithm is maximizing the lifetime of the network, which is

equivalent to maximizing the time to network partition.

• In this approach, maximizing the network lifetime is modeled as a linear pro-

gramming problem for two separate scenarios: fixed information-generation rate, and arbitrary information-generation processes.

• Analyzing a wireless sensor network G(N, A) with fixed information-generation

rate:

• Information is generated at origin node i with rate Q(c)

i , i.e.,

O(c) =

• i|Q(c)

i

> 0, i ∈ N

• ,

(14)

• The transmission rate of commodity from node i to node j is denoted by q(c)

ij

and to be assigned by the routing algorithm.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

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• The lifetime of node under a given flow q =
• qc

ij

• is given by

Ti(q) = Ei

• j∈Si et

ij

• c∈C q(c)

ij + j:i∈Sj er ji

• c∈C q(c)

ji

. (15)

• N is the set of all nodes. A is the set of all directed links (i, j), and link (i, j)

exists if and only if j ∈ Si. Si is the set of all nodes that can be directly reached by node i with a certain transmit power level in its dynamic range.

• Ei is the initial battery energy of each node i.
• et

ij denotes the transmission energy consumed at node i to transmit a data

unit to its neighboring node j, and er

ij denotes the energy consumed by the

receiver node j.

• Multiple commodities are assumed, where a commodity is defined by a set of

source nodes and destination nodes.

• Each commodity c ∈ C, is given a set of origin nodes O(c), and a set of

destination nodes D(c).

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

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• the network lifetime under flow q as the minimum lifetime over all nodes, is

defined as Tsys(q) = min

i∈N Ti(q)

(16)

• The goal is to find the flow that maximizes the network lifetime under the

flow conservation condition. Maximize T s.t. ˆ q(c)

ij ≥ 0, ∀i ∈ N, ∀j ∈ Si, ∀c ∈ C,

• j∈Si

et

ij

• c∈C

ˆ q(c)

ij +

• j:i∈Sj

er

ji

• c∈C

ˆ q(c)

ji ≤ Ei, ∀i ∈ N,

• j:i∈Sj

ˆ q(c)

ji + TQ(c) i

=

• j∈Si

ˆ q(c)

ij , ∀i ∈ N − D(c), ∀c ∈ C.

(17)

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

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where ˆ q(c)

ij = Tq(c) ij is the amount of information of commodity c transmitted

from node i to node j until time T.

Figure 6: Conservation of flow condition at node i for each commodity c requires that the sum of information-generation rate and the total incoming flow must be equal to the total outgoing flow. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

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• Implementation of flow augmentation (FA) algorithm for fixed information-

generation rates, using distributed Bellman-Ford algorithm:

• 1. At each iteration, each origin node o ∈ O(c) of commodity calculates the

shortest cost path to its destination nodes in D(c).

• 2. The flow is augmented by an amount of λQ(c)

i

• n the shortest cost path,

where λ is the augmentation step size, which is equivalent to the amount

• f information routed between routing information updates.
• 3. Residual energy at each node is updated just before each routing informa-

tion update, which will change link costs.

• 4. With the updated link costs, the shortest cost paths are recalculated and

the procedures are repeated until any node i ∈ N runs out of its initial total energy Ei.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

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• The link cost costij is defined as

costij = (et

ij)x1E−x2 i

Ex3

i + (er ij)x1E−x2 j

Ex3

j .

(18) where the energy expenditures for unit data transmission over the links, are et

ij and er ij, Ei and Ej are the initial energies. Ei and Ej are the residual

energies, and et

ij = eT + ǫampd4 ij,

(19) and er

ij = eR.

(20) where eT, and eR are the energy consumed in the transceiver circuitry at the transmitter and the receiver respectively, and ǫamp is the energy consumed at the output transmitter antenna for transmitting one meter. x1, x2, and x3 are non-negative weighting factors for each item.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

24 Figure 7: Performance of FA(1, x, x) is compared with FA(1, x, 0). Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

25 Figure 8: Performance of FA(1, x, x) is compared with FA(0, x, x). Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

26 Figure 9: The average performance of FA(1, x, x) for various values of λ. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 2. Power Efficient Routing Algorithms: Flow Augmentation (FA)

27 Figure 10: Normalized network lifetime of FA(1, x, x) versus its parameter x. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 3. Performance Comparison

28 Figure 11: Comparison of average and the worst case performances of algorithms are made in a single commodity. Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

• 3. Performance Comparison

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• Both CMMBCR and max-min zPmin have much better performance than

MTPR, but they were not quite as good as FA.

• Max-min zPmin and FA algorithm can achieve network lifetime that is very

close to the optimal network lifetime obtained by solving the linear program- ming problems.

• CMMBCR and max-min zPmin algorithms require some type of centralized

coordination, while FA algorithm does not. The lower level of complexity of FA algorithm makes it a good candidate for low-cost wireless sensor network devices.

• Due to the inherent non scalability of table-driven routing approach in FA,

this algorithm is not scalable, and therefore not suitable for large networks at this point.

• The performance of FA significantly depends on its parameter x, however, no

exact method has been proposed to calculate the optimal parameter x.

Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks

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• Elham Torabi : Maximum Lifetime Routing Algorithms for Wireless Sensor Networks