Ivan Stojmenovic 1

Scalable localized routing in wireless sensor networks

Ivan Stojmenovic

Ivan@site.uottawa.ca

www.site.uottawa.ca/~ivan

Tutorial

Ivan Stojmenovic 2

Sensors route reports to a fixed sink …

Sink

End user

humidityInternet

Ivan Stojmenovic 3

Multi-hop networks: Routing

Unit graphsradius

Sensor networksPosition information

•Routing: source destination

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Routing with/out position information ?• Sensors can function efficiently only with position information

GPS and location estimation advanced rapidly(cubic cm sensor with 7mm x 7mm x 2mm GPS)

• Sink can flood network with/out its own position

• Routes can be learn while flooding, or

• Only position of sink is learned and used

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Proactive routing: ad hoc networks• Routing table contains the first hop/neighbor toward

each destination

• Bellman-Ford: Each node exchanges its routing tables with all its neighbors, and

• Best neighbors N for route from S to D is one that minimizes: cost of link S to N + cost N to D (from routing table in N)

• OLSR (Optimized Link State Routing): link changes are flooded + Dijkstra’s shortest path

• MPR (MultiPoint Relay) to reduce flooding

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Reactive routing: ad hoc networks• Source floods route discovery (short) message

• Destination node replies back to source upon receiving discovery message(s) using memorized hops (AODV) or paths (DSR)

• Source sends full message using recorded path

• Multi-paths for QoS

• Route discovery message may contain accumulated delay, congestion, power, cost etc. along paths;

best path selected at destination

• Local route maintenance; expanding ring search

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Route discovery by flooding

S D

S DEach sensor retransmits once

Problem: sink stable but sensors may sleep

DSR, AODV in ad hoc networks, position info not needed =‘directed diffusion’ for sensors Intanagonwiawat, Govindan, Estrin 2000

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Directed diffusion• Monitoring center

broadcasts packet to all sensors in a region

• Sensors create links for reporting along reverse broadcast tree

• Link is toward sensor from which the first copy of packet is received

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Greedy position based localized routing

SDA

B

Localized protocol: S knows only position of itself, its neighbors and destination D

S forwards to neighbor B closest to D

Finn 1987

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Greedy: SABCD vs shortest path SECD

S A

E C

D

Localized vs. globalized protocol

SP Overhead: messages to maintain global information at each node following mobility and/or sleep/active periods changes

B

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Greedy is loop-free

Assume A1 closest to D

A2 sends to A3 – contradiction, A1 is closer

D

An

An-1

A3

A2

A1

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Progress based routing ‘84-86.

Random progress (Nelson, Kleinrock): A, C or FNFP- nearest forward progress (Hou, Li): C

MFR - most forward within radius(Takagi, Kleinrock): A

AB C

D

E FS

MFR: Choose closest projection on SD; minimize SA.SD

A’

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MFR is loop-free

DAn.DA1 > DA2

.DA1

DAn.DA1>DA1

.DA2>DA2.DA3>…>

DAn-1.DAn > DAn

.DA1

A1 A2

D

An

An-1

A3

A2

A1

Proof by Stojmenovic, Lin 1998

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Greedy vs. MFR

D

B

A’

A

S

B’

may choose different node AD<BD

choice is same most of time!

Similar performance

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DIRectional routing methods

SDA

Basagni, Chlamtac, Syrotiuk, Woodward MOBICOM’98 (DREAM)

Ko, Vaidya MOBICOM ’98 (LAR)

Kranakis, Singh, Urrutia CCCG’99 (compass routing)

Send to all neighbors within angular range from direction [BCSW,KV]

location update schemes [BCSW, KV]

Closest direction

Flooding rate (# of messages vs SP) ??

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DIR is not loop-free !

Transmission radius

D

H

G

F

E

Stojmenovic 1998Greedy and MFR are loop free

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Performance evaluation

• Random unit graphs: Choose n nodes at random in [0,m]x[0,m]

• select average node degree d = 2,3,4,5,…

• sort all (n-1)n/2 edges in increasing order

• Radius R= nd/2-th edge in sorted order!

• Reject graph if disconnectedSuccess rate = high for high degree, low for low degree

hop count = successful Greedy/MFR close to SP, DIR >

flooding rate (#messages vs SP) = close to SP

Independent variable is d, not R !!!

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Is hop count the best metric ?• Power consumption

• Reluctance (avoiding nodes with low energy)

• Power_reluctance

• Delay

• Expected hop count (realistic physical layer)

• COST - selected metric

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Cost to progress ratio framework• Progress: measures advance toward destination• Progress = |SD|-|AD|=d-a• Select neighbor A that minimizes

cost(SA)/progress(A)• Hop count: cost=1 Maximize advance

S D

A

d

r aStojmenovic IEEE Network 2006

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Parameterless behavior• Cost-to-progress ratio framework has no added

parameters such as thresholds

• Threshold based approach: eliminate ‘bad’ links, drop packet if there is no ‘good’ neighbor

• What if a solid path has just one weak ‘bridge’?• Experiments so far indicate that threshold based approaches are

inferior for all threshold values - either high failure rate or suboptimal since there is no notion of ‘best’ neighbor

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Constant power minimize hop countpower =u(d)= d + c minimize total powerMany articles assume c=0; in practice c>0 since power is needed to run hardware at each node, and correct reception requires minimal transmission power (no energy free transmission at zero distance)

reluctance f(A) to forward packets ==1/g(A) g(A) in [0,1] lifetime minimize total costPower_reluctance = f(A)u(d)

A d B

Power saving localized routing

model by Rodoplu, Meng 1999

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Ideal and localized power aware routing

• # of hops n d(a( -1)/c)1/

• minimal power: v(d)= dc(a(-1)/c)1/ + da(a( -1)/c)(1-)/ = O(d)

• A = minimizes u(r)+ v(s) among neighbors of S

S x A d-x D

Stojmenovic, Lin 1998S D

A

dr s

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Localized power aware routing

• Kuruvila, Nayak, Stojmenovic 2004

• Power progress: minimize (r+c)/(d-a)

• Iterative power progress: select B if power(SB)+power(BA) < power(SA)

• (Iterative) Projection power progress

S D

A

dr a

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‘Reluctance’ routing algorithmA

S Ddr a

f(A)= reluctance =1/g(A) g(A) in [0,1] lifetime

A = neighbors of S that minimizes f(A) + f’(S)*s/R( cost of A + average cost around S * ideal number of hops from A to D)

If D is neighbor of S then deliver to D else forward to A

Reluctance/progress: minimize f(A)/(|SD|-|SA|)

Kuruvila, Nayak, Stojmenovic 2004 (no added parameters)

Stojmenovic, Lin 1998

Rediscovered by: Yu, Govindan, Estrin: GEAR, TR-01-0023, Aug. 2001.

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Power_reluctance routing

S D

A

dr a

A = neighbors of S that minimizes u(r) + v(s)

If D is neighbor of S and u(d) < min [u(r) + v(s)]

then deliver to D else {A = neighbor of S that minimizes f(A)u(r) + v(s)f’(S); forward to A }

Power*reluctance/progress: minimize f(A)power(SA)/(|SD|-|SA|)

Kuruvila, Nayak, Stojmenovic 2004 (no added parameters)

Stojmenovic, Lin 1998

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Physical layer impact• Expected hop count (counting all transmissions and

possibly acknowledgements)

• F(SA)= expected hop count from S to A

• Minimize F(SA)/(d-a)• Kuruvila, Nayak, Stojmenovic 2004

• Delay …

• QoS routing …

• Bitrate …

S D

A

dr a

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Physical layer impact

=4

p(R)=0.5

Pac

ket r

ecep

tion

pro

babi

lity

R

Unit graph model:

Prp(x)=1, xR

Prp(x)=0, x>R

Lognormal shadowing model

Distance between nodes

What is the transmission radius ? Who are neighbors?

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Simulation dilemma• Home-made simulator or one used by others (NS-2,

Qualnet, J-sim,…)?• Greedy routing uses hop count as measure• NS-2 applies realistic physical layer, which mostly

penalizes long hops • Why to use simulator that defeats the model, hides physical

models and parameters which impact the data, impact comparison, and provide no explanation?

• Solution: build protocols and simulators in parallel, so that results can be explained and protocols improved

• Network layer protocol need to be designed with more realistic physical layer, not with unit disk graph model

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How to simulate ?• Study one variable at a time, explain it fully

• Ideal MAC, no congestion, for initial studies

• If one routing A is on average better than one routing B, it should cause less congestion, thus show even more advantage at the transport layer

• Simulation to match ‘ideal’ assumptions• Stable graphs first; localized design takes care of dynamics

• Independent variable is one that matters e.g. density (average number of neighbors per node), not transmission radius

• Compare against the best (e.g. shortest path), not against worst (e.g. flooding)

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Approximate packet reception probability

p(x) 1-(x/R)q/2 for x < R

(2-x/R)q/2 for 2R x R

q depends on L, packet length, 2 6• Signal strength is a random variable, and deviation cannot be predicted in advance (but some articles use it to select best neighbors)

• Transmission power is assumed fixed and same • q=1 for L=1; q2 for L=120.• Exact formula complex, time consuming and unreliable• each bit is received or not independently (no coding) packet received correctly iff all bits received

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Reactive routing with physical layer• In route discovery phase, forward the sum of

Expected Hop Counts along partial route, or

• Wait retransmission proportional to EHC on link

• Problems:

• A single retransmission by a given node may not reach the best forwarding neighbor; tradeoff # of retransmissions and gains made

• Real traffic may not use routes created by control traffic – different packet lengths, or low packet reception probability

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Hello messages with physical layer• ‘fixed hello protocol’

• Send hello messages fixed number of times, to increase the probability of reception by neighbors

• ‘variable hello protocol’• Send hello packets until sufficient number of such

packets from neighbors received (learn enough neighbors for desired density)

• Goel, Kalaichelvan, Nayak, Stojmenovic, Villanueva-Pena 2006

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Greedy routing is not hop count optimal

• Ideal routing

– Place additional nodes between Source and Destination as required. – Ideal Hop count computed for different u and values– Each received packet is acknowledged u times

• Low values for 0.6Rx 0.9R u=1• 50% higher at x=R, very high x>R or x<0.1R

•Kuruvila, Nayak, Stojmenovic 2004

x = d/nx xxxxx

n1d

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IHC for Different u Values (=2)

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Expected progress routing

C D

Axa

c

Progress: c-a

Expected hop count for u=1: f(x,1) = 1/p2(x)+1/p(x)

Best value of u: u1/p(x)

Forward to neighbor (closer to destination) that maximizes

(c-a)/f(x,1) (EPR-1) or (c-a)/f(x,u) (EPR-u)

Hop by hop ack

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tR Greedy Algorithm

• The redefined notion of greedy routing. • Current node S selects neighbor closest to D

among all neighbors that are closer to D than itself, and which are at distance at most tR from S, for forwarding the message.

• Experiments for t = 1, 1.25 and 1.4377• Threshold based greedy routing

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Performance summary

• Good performance for localized parameterless algorithms

• low hop counts for dense networks and 100% success rates

• tR-greedy are significantly inferior: a choice of ‘long’ edge is quite likely on a

route which then contributes to very high expected hop count measure, or– ‘optimistic’ parameter choice fails traffic unnecessarily

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Loop-free with guaranteed delivery

• Stop if message is to be returned to neighbor it came from = concave node

• MFR, DIR, Greedy• Flooding Greedy, Flooding MFR:• Concave nodes flood message to all

neighbors and then reject further copies of the same message

• Loop-free methods that guarantee delivery, reasonable flooding rate

• But nodes memorize past trafficStojmenovic, Lin 1999

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Routing around void areas ?

S

A ?

Recovery, perimeter, face mode

D

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1. Constructing planar graph: faces

S

Some planar graphs (Gabriel graph) can be constructed without message exchange!

Bose, Morin, Stojmenovic, Urrutia, 1999

A ?D

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2. Traverse proper face until recovery

-Select face containing SD

- Follow that face by left hand or right hand rule

until recovery (= closer node reached)

Bose, Morin, Stojmenovic, Urrutia, 1999

S ?D

B

C

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GFG= Greedy-FACE-Greedy• run Greedy until delivery or a failure node A, |AD|=d, • run FACE until delivery or B reached, |BD|<d, • run Greedy …• paths close to SP for higher degrees, • <3.5 times longer than SP for low degrees• No traffic memorization, localized, close to SP

scalable !!• Karp and Kung MOBICOM 2000 duplicated (with citation)

GPSR= GFG (added MAC, mobile nodes)Bose, Morin, Stojmenovic, Urrutia, 1999

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Gabriel graph

U V

P QW

Gabriel graph GG(S) contains an edge (U,V) iff the disk with diameter (U,V) contains no other point from S

= distance from other points to center of UV is > |UV|/2

= Acute angles for all joint neighbors in GG

GG(S) is planar and connected (contains MST)

Gabriel, Sokal 1984

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Gabriel graph is planar

Planar graph = no two edges intersect

U

VQ

P Proof by contradiction: Assume

UV, PQ GG(S), UV PQ

PUQ < /2, PVQ < /2,

UPV < /2, UQV < /2,

Sum of angles in UPVQ < 2

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Gabriel graph contains MST

P Q

WBy contradiction: Assume

PQ MST, PQ GG;

W, PW<PQ, QW<PQ, PW MST

Replace PQ by PW in MST

new MST has smaller sum of edge lengths. contradiction

Gabriel graph connected

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Unit (connected) graph contains MST

Kruskal’s algorithm to construct MST:

Sort all edges by their length, from shortest to longest.

Consider each edge in that order for inclusion in MST:

Include it in MST if its addition does not create a cycle.

Unit graph edges considered before any other edge. After their consideration, MST is already connected, and no more edges can be added.

GG(S) U(S) planar and connected!

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Traversal of selected face leads to recovery

-Line SD intersects the face in X on an edge EF

- E or F is closer to D than A (if nothing else found before)

B

S ?D

XE

F

C

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Getting closer on the face is guaranteed for GG

E

F

DS X

S < /2, D< /2 since EF is in GG E > /2 or F > /2

F > /2 |SD| > |FD| F is closer to D than S

Frey, Stojmenovic MOBICOM 2006

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Conclusions

• Imprecise location information is challenge for georouting with guaranteed delivery

• Georouting in 3D has no guaranteed delivery• Unit disk graph is required• For planar graphs GFG still always works,

but GPSR by Karp and Kung does not

• For other metrics, there is still no alternative to GG based face routing for recovery mode, which prefers close neighbors (except shortcuts, dominating sets..)

Frey, Stojmenovic 2006

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Greedy, GFG (greedy-face-greedy)

W

U

I

A

G

V

D

J

KL

CE

F

H

B

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Robustness of GFG

• GFG requires unit graph = equal transmission radius, no obstacles, nodes in plane

• Extension for fuzzy unit graphs = connected if distance < r, nor connected if distance >R, may or may not be connected otherwise, R/r < 1.41Barriere, Fraigniaud, Narajanan, and Opatrny 2001

• Loop-free for static nodes; loops can be created by mobile nodes but exit can be found by adding timestamp of the last intersection with imaginary line SD and ignoring links created afterwards

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Shortcut procedure in FACE mode

AF

EC

B G

ABCE replaced by AF

2-hop information needed

Datta, Stojmenovic, Wu 2001

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Restricting FACE to a dominating set

• Paths in FACE mode may be quite long

• Reduce paths by restricting routes to a connected dominating set (CDS)

• Each node is either in CDS or neighbor of a node from CDS

• Localized maintenance of CDS preferred

• Dominating set status to be communicated, or 2-hop information needed

Datta, Stojmenovic, Wu 2001

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Beaconless greedy routing• Füßler, Widmer, Käsemann, Mauve, Hartenstein 2003• Heissenbüttel Braun 2003

• No ‘hello’ messages• S transmits packet containing position of destination• Each receiving node sets timeout based on its distance to destination• If a packet from a neighbor received while waiting, cancel

retransmission• Otherwise retransmit at end of timeout• Details for reducing the # of paths searched, e.g.• Sender asks for help, and sends full message only to neighbor that

responded first

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Beaconless routing with guaranteed delivery

• In face mode, nodes respond to S based on distance to S, not distance to D

• Closer neighbors respond sooner

• In basic variant, all neighbors respond (optimizations possible)

• ‘Witness’ node B for a non-GG edge SA responds before A since |SB|<|SA|, and that message is received by A

• Neighbors that discover ‘witness’ cancel their Gabriel edge

• After learning Gabriel edges, apply face mode routing

• Chawla, Goel, Kalaichelvan, Nayak, Stojmenovic 2006

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QoS routing• Find a route which satisfies delay, bandwidth etc. QoS

criteria• Huang, Dai, Wu 2004• Localized routing, maximizes progress/cost• Progress =advance on the projection to destination • Cost from QoS criterion used• Backward checking = iterative improvement

A B

C

Instead of routing to B, route to C if cost(AC)+cost(CB) < cost (AB)

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QoS DFS routing

• Depth First Search with Greedy to sort neighbors, and O(1) memory in each node, guarantee delivery

• bandwidth criterion = edge elimination

• delay criterion = hop count + more bandwidth

• new connection time criterion • Jain, Puri and Sengupta; Stojmenovic, Russell, Vukojevic 1999

• Power and cost addition: Vukojevic, Stojmenovic 2005

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Power/cost aware localized routing with guaranteed delivery

PFP= power-face-power

• run Power-aware until delivery or a failure node A, |AD|=d,

• run FACE until delivery or B reached, |BD|<d,

• run Power-aware …

• CFC = Cost-FACE-Cost

• PcFPc = PowerCost-FACE-PowerCost• Competitive with respect to globalized solutions

Stojmenovic, Datta 2000

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Component routing

DU

FE

B

A

W

V

GHI

J

QP

Routing from A to D: reject nodes

B forwards to E,W from two neighbors connected components; E fails, W delivers

Concave nodes send packet to one neighbor in each connected component of subgraph of neighbors:

Parallel path search = reduced flooding greedy

Lin, Lakhsdisi, Stojmenovic MobiHoc 2001

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Assisted routing

AP1

AP2

S

D

A B

C

Figure 4: the operation of AGPF

AP1

AP2

S

D

A B

C

AP1

AP2

S

D

A B

C

Figure 4: the operation of AGPF

Blazevic, Giordano, Le Boudec 2000