 Definition of energy minimizing localized routing metrics?

Data Communication

Localized Routing Metrics

Energy Efficiency

 Energy is a very limited resource in WSNs

 Energy efficiency is often a primary optimization goal

 How to make data communication energy efficient?

• Apply data communication on an energy efficient topology;

example:

• Run MECN topology control first

• Apply greedy routing over MECN links only

• Incorporate energy efficiency in the protocol directly; example:

• Elaborate an energy aware greedy routing weight

• Apply greedy routing using this weight

 Definition of energy minimizing localized routing metrics?

Using the Path Loss Formula

 Remember: channel model for RF communication

 Energy required to send a message from S to T amounts u(d) = d^a + c, while d = |ST|

 Observation

• Assume an arbitrary number n of equidistant intermediate forwarding nodes can be placed between S and T

• Power required to send a message from S to T amounts: n * (d/n)^a + c) = n*(d/n)^a + n*c

• Define f(x)=x*(d/x)^a + x*c

• Is there an optimal x minimizing f(x)?

• If x0 or x ∞ then f(x)∞

• There exists one solution x₀ which satisfies f’(x)=0

S T

d

Using the Path Loss Formula

 n = floor(x

) can be expressed in a closed form

• We can compute constant c1

• Which depends on a and c only and

• Which satisfies n = c1 * |ST|

 Power consumption v(|ST|) in this case can be expressed in a closed form as well

• We can compute constant c2

• Which depends on a and c only and

• Which satisfies v(|ST|) = c2 * |ST|

 How can we use this result to express a

localized routing metric?

Using the Path Loss Formula

 Estimate on total power consumption when selecting next hop node A: u(|SA|) + v(|AD|)

 Greedy routing: select the node in forward direction which minimizes the expression u(|SA|) + v(|AD|)

 Result directly related to path loss formula d^a + c

 What if other models are used?

• New theoretical analysis to compute u(.) and v(.) are necessary

• Problem if the model function can not be derived

• Problem if the power metric is given by empirical values

 Other localized metric approaches A

S D

Assume minimal power consumption v(|AD|) on remaining path from A to D Assume power

consumption u(|SA|) to send a message

from S to A

The Cost over Progress Framework

 Progress achieved by selecting node A: d-t

 Assume each node provides same progress

 Number of routing steps: d / (d-t)

 Assume each routing step consumes energy u(s)

 Approximation of total energy consumption: u(s) * (d / (d-t))

 Greedy routing: select neighbor A which minimizes u(s) / (d-t)

 Observe: any cost function can be plugged into this expression

S D

A t

d s

Increasing Network Lifetime

 Define: network lifetime – time it takes until first node dies

 Are energy optimized paths increasing network lifetime?

 Observation

• Selecting minimum energy consuming path p(S,D) will only use nodes on this path

• If p(S,D) is used continuously, nodes along this path will die first

 This motivates the use of cost metric c(v)

• The cost to use node amounts c(v) = 1/g(v)

• g(v) reflects v’s remaining power in [0,max_power]

 Try to find a path p=v₁… v_n which reduces total cost

 Local approximation: node s selects node v which minimizes c(v) / (|sd| -

|vd|)

) ( / 1 )

,

( v w g w

f ^{( p ) }   ^{f ( v}

^{, v}

⁾

c

Addressing Lifetime and Energy Consumption

 Problem

• Addressing network lifetime only might produce very energy consuming paths

• Total energy consumption will affect network lifetime as well

 Solution: combine cost c(w) metric and energy metric u(v,w) in one

 Example: pc(v,w) = c(w) * u(v,w)

• If u(v,w) is high and another node x with about same or better c(w) exists it is unlikely that w is selected

• If c(w) is high and another node x with with about same or better u(v,w) exists it is unlikely that w is selected

V

W

X u(v,w)

u(v,x)

c(w)

c(x)

u(v,x) * c(x) u(v,w) * c(w)

Traffic Balance by Randomization

 Requires criteria which selects some nodes in forward direction

• Example 1: All nodes closer to destination

• Example 2: All nodes lying a threshold closer to the destination

• Example 3: All nodes in forward direction but not exceeding a certain delay threshold

 Randomly select a node out of this set

• Example 1: uniformly distributed

• Example 2: weighted distribution with highest weight on best node

 Effect: traffic balance in a large relay area

• Reduced congestion

Data Communication

Beacon-less Routing

Beacon-less Routing (1)

 Traditional greedy routing need information about all one- hop neighbors

• Periodic hello messages

• Transmitted with maximum signal strength

• Independently of current data traffic

• Problem of directional connections

 Heissenbüttel, Brown: Beacon-less routing (BLR)

• Node is unaware of its neighbors

• Just broadcast a message to all unknown neighbors

• Receiving node introduces a small timeout before forwarding

• Node located at the “best” position introduces the smallest delay

• Nodes hearing of retransmission cancel the scheduled packet

Beacon-less Routing (2)

 Problem: Message duplicates

• E and F are in backward direction

• E.g.: B introduces smallest delay

• A removes scheduled packet

• C does not hear transmission from B and forwards the packet too

 Avoiding message duplicates

• Only nodes in a certain forwarding area allowed as candidate nodes

• Nodes in forwarding area are able to overhear retransmission of each other node in that area

 Active selection method: control Message instead of full packet

• Forwarding node sends unicast to “winning”

node

• Large packet can be sent with reduced transmission power

S

D

A B

C

E F

Beacon-less Routing (3)

 Possible delay functions (r=radius, p=progress, d=

distance)

• Basically MFR:

Max_delay(r-p)/r

• Slightly modified NFP:

Max_delay(p/r)

• An advanced delay function

 Possible forwarding areas

• Circle: good forwarding area regarding progress and

successful hops

Data Communication

The Greedy Routing Failure

Greedy Routing Failure

 Choosing node in backward direction may lead to packet loops

 Nevertheless, there may exist a path from S to D (S may also be an intermediate node)

 Loop-freedom and delivery rate are conflicting goals

 Solutions?

Improved Single-Path Strategies

 Improvements trying to reduce package drop probability

 Example: GEDIR – Allow message to travel one hop in backward direction, i.e. packet dropped only if it would be sent back to the previous node

 However, fact: greedy heuristic can not guarantee delivery

 Additional requirements to provide delivery guarantees

• Network with specific properties supporting greedy routing

• Recovery strategies for greedy routing failures

Data Communication

Guaranteed Delivery Based on Memorization

Motivation

 Many greedy routing schemes perform well in dense networks

 Greedy routing has a small communication overhead

 Desirable to run Greedy routing as long as possible

 However, greedy routing might fail in sparse networks

 Guaranteed delivery is desirable property as well

 On the following slides: in case of failure  run a recovery mechanism which requires memorizing past routing information

• In the message

• In the visited node

Recovery by Flooding

 Stojmenovic, Lin: Partial flooding to guarantee delivery (f- GEDIR, f-MFR, f-DIR)

• Intermediate nodes handle packet according to GEDIR, MFR, …

• Concave node broadcasts packet to all neighbors

• To avoid message loops: concave node rejects further copies of the message, concave nodes are removed from the list of candidate nodes

 Example: Message from S to D

S C

E

F

A

B G

H

D

unicast broadcast

Recovery by Flooding

 When there is a path from source to destination then one of the neighbors lies on the path → guaranteed delivery

 Observation: flooding produces many redundant message transmissions

 Improvement: Component routing

• Connected components in node v – partitions in the one-hop neighborhood graph N(v) when removing v

• Algorithm

• Concave node determines connected components

• Forward message to only the best neighbor in each component

• Number of message transmissions reduced significantly

e.g. concave node has at most four connected components in the unit disk graph model

DFS-Based Routing

 Jain et al.: Geographic Routing Algorithm (GRA)

• Intermediate node handles message greedily

• Concave node maintains route to destination node

• Start route discovery for outdated routing tables

• Stuck packet is routed to destination after successful route discovery

 How to perform route discovery?

DFS-Based Routing

 Depth first search from concave node S

• Yields an acyclic path from S to D

• Node X puts its address on route discovery packet p

• Forward to neighbor who has not seen p before

• Select neighbor Y which minimizes |XY|+|YD|

• If no possible neighbor exists, remove address from p and send it back to the node from which p was originally received

 Alternative implementation: memorize DFS data in nodes

 Other metrics may be applied on next neighbor selection

• Quality-of-service paths (delay and bandwidth criteria, connection time, …)

X W

1 2 3

Y1

Y2 root Y3

t1, t6: path = …W

t2: path = …W X

t3: path = …W X Y1

t4: path = …W X Y2 t5: path = …W X Y3

MEMORYLESS MESSAGE DELIVERY WITH

GUARANTEED DELIVERY?

67

68 Geographic Greedy Routing

T S

A

(a)

F B

D C

E

Strategy: select from nodes closer to the destination the one which minimizes a local cost metric

B

E T S

(b)

?

A

C

D F

G

Problem: greedy routing failure

69 Recovery based on Planar-Graph Routing

source node

destination node

70 Planar Graph Routing Example

T S

P

F

71 Planar Graph Routing Example

T S

Q

F

P

72 Planar Graph Routing Example

T S

F

P

73 Planar Graph Routing Example

T S

P

F

Übersicht

 Untersuchte Netzstruktur und Problemstellungen

 Topologie-basierte Routingprotokolle

 Geographische Routingprotokolle

• Greedy-Routing und Planar-Graph-Routing

• Konstruktion von planaren Graphen

• Lokales Multicasting

• Beispiel MSTEAM

74

75 We need a Planar Graph

U V U V

Gabriel Graph (GG) Relative Neighborhood Graph (RNG)

W

U

V

Delaunay

Triangulation (DT)

76 We need a UDG or QUDG

 UDG: Localized GG and RNG versions based on 1-hop neighbors

 UDG: Localized DT version based on 2-hop neighbors (and less)

 QUDG: Sort of localized GG (possibly the same for RNG)

Quasi unit disk graph (QUDG)

U V

Unit disk graph (UDG)

r_min r_max

U

77 Problems and Limitations

 Locally constructing a planar graph in arbitrary networks is impossible

 Even worse: localized unicast routing is impossible in arbitrary graphs

 Localized single path algorithms deviation from shortest paths

• Let k be the hop/Euclidean length of the shortest path connecting s and t

• Localized single path algorithms may produce paths of length O(k²)

• Some even worse but some exist which are upper bounded by O(k²) u

x v

y

t s

78 Localized Unicast Routing in Practice!

 Wireless network graph has structure!

 Aim at localized unicast approaches with high delivery rate

 Method of choice: sorts of clustering

arbitrary graph wireless network graph

79 Geographic Clustering

80 Geographic Clustering

81 Geographic Clustering

82 Geographic Clustering

83 K-Hop Clustering

84 K-Hop Clustering

85 K-Hop Clustering

86 K-Hop Clustering

Übersicht

 Untersuchte Netzstruktur und Problemstellungen

 Topologie-basierte Routingprotokolle

 Geographische Routingprotokolle

• Greedy-Routing und Planar-Graph-Routing

• Konstruktion von planaren Graphen

• Lokales Multicasting

• Beispiel MSTEAM

87

88 Localized Multicast Forwarding Problem

Assumptions:

 Location system

 Nodes know position of

• Themselves

• Their neighbors

• The destinations source node

destination node destination node

destination node

destination node

89

Building Blocks

T1

T3

T2 S

B A

D C

90

Building Blocks – Message Split

T1

T3

T2 S

B A

D C

91

Building Blocks – Next Hop Selection

T1

T3

T2 S

B A

D C

?

92

Building Blocks – Recovery

T1

T3

T2 S

B A

D C

?

?

Übersicht

 Untersuchte Netzstruktur und Problemstellungen

 Topologie-basierte Routingprotokolle

 Geographische Routingprotokolle

• Greedy-Routing und Planar-Graph-Routing

• Konstruktion von planaren Graphen

• Lokales Multicasting

• Beispiel MSTEAM

93

94 EMST Backbone Assisted Localized Routing

T9

T7

T6

T4

T1

T3 S

T8

T5

T2 T1,…,T9

95 EMST Backbone Assisted Localized Routing

T8 T9

T7

T6

T5

T4

T1

T2

T3 S

EMST(S,T1,…,T9)

96 EMST Backbone Assisted Localized Routing

T8 T9

T7

T6

T5

T4

T1

T2

T3

D1

D2 D3

S

97 EMST Backbone Assisted Localized Routing

T8 T9

T7

T6

T5

T4

T1

T2

T3 A

B

C

S

T7,T8,T9

T1,T2,T3 T4,T5,T6

98 The Cost over Progress Framework

T3

T1

W V

T2 S

Which one is the better next hop node?

T1,T2,T3

99 The Cost over Progress Framework

 Approximate expected number of hops H(S,V)

 H(S,V)  |EMST(S,T1,T2,T3)| / (|EMST(S,T1,T2,T3)| - |EMST(V,T1,T2,T3)|)

 Approximate expected cost C(S,V) = cost(S,V) * H(S,V)

 Select node X which provides progress and minimizes C(S,X) T3

T1

W V

T2 S

100

MSTEAM & MFACE

S T6

T5

T4

T3

T1

T2

F1

F2

101

MSTEAM & MFACE

S T6

T5

T4

T3

T1

T2

F1

F2

102

MSTEAM & MFACE

S

U

V W

F1 F2

F3

T1

T2 T3

103

MSTEAM & MFACE

S

U

V W

F1 F2

F3

T1

T2 T3

104

MSTEAM & MFACE

S

U

V W

F1 F2

F3

T1

T2 T3

105

MSTEAM & MFACE

S

U

V W

F1 F2

F3

T1

T2 T3 p

106

MSTEAM & MFACE

S

U

V W

F1 F2

F3

T1

T2

107

MSTEAM & MFACE

S

U

V W

F1 F2

F3

T2

Zusammenfassung

 Untersuchte Netzstruktur und Problemstellungen

 Topologie-basierte Routingprotokolle

 Geographische Routingprotokolle

108

Zusammenfassung

 Wir betrachteten hier: drahtlose Vernetzung ohne aufwendige (und ggf.

kostenpflichtige) Infrastruktur

 Abdeckung größerer Gebiete trotz limitierter Kommunikationsreichweite  Multihop-Kommunikation

 Wir haben es hier somit hauptsächlich mit einem Netzwerkproblem zu tun

 Wesentliche Probleme: Routing und Topologiekontrolle

 Anpassung traditioneller Routing-Verfahren: Topologie-basiertes Routing

 Neuer Routing-Ansatz auf der Basis von Knotenkoordinaten

 Dieser Ansatz erlaubt ganz neue Formen der Datenkommunikation und generell ganz neue Formen von Netzorganisation

 Generelles Paradigma, um mit der Dynamik solcher infrastrukturlosen Multihop- Netze umzugehen: lokale Algorithmen/Verfahren

 Dieses Paradigma ist auch zur Beherrschung von komplexen und dynamischen Internet-Overlay-Topologien anwendbar

 Mit den hier behandelten lokalen Verfahren wurde nur ein kleiner Ausschnitt eines interessanten Forschungsfeldes betrachtet

 Mehr in der Vorlesung „Lokale Netzstrukturen“

109