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Scalable localized routing in wireless sensor networks

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### Scalable localized routing in wireless sensor networks

Tutorial

Ivan Stojmenovic

Ivan@site.uottawa.ca

www.site.uottawa.ca/~ivan

Ivan Stojmenovic

Unit graphs

radius

Sensor networks

Position information

- Routing: source destination

Ivan Stojmenovic

Routing with/out position information ?

- Sensors can function efficiently only with position informationGPS 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

Ivan Stojmenovic

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

Ivan Stojmenovic

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

Ivan Stojmenovic

S

D

S

D

Route discovery by floodingEach 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

Ivan Stojmenovic

- 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

Ivan Stojmenovic

Greedy position based localized routing

A

D

S

B

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

S forwards to neighbor B closest to D

Finn 1987

Ivan Stojmenovic

Greedy: SABCD vs shortest path SECD

S

A

D

B

C

E

Localized vs. globalized protocol

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

Ivan Stojmenovic

An

A1

A2

An-1

D

A3

Assume A1 closest to D

A2 sends to A3 – contradiction, A1is closer

Ivan Stojmenovic

Progress based routing ‘84-86.

A

B

C

A’

D

S

E

F

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

Ivan Stojmenovic

B

A

S

D

A’

B’

may choose different node AD<BD

choice is same most of time!

Similar performance

Ivan Stojmenovic

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

Ko, Vaidya MOBICOM ’98 (LAR)

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

A

D

S

Closest direction

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

location update schemes [BCSW, KV]

Flooding rate (# of messages vs SP) ??

Ivan Stojmenovic

E

H

D

F

G

Transmission radius

Stojmenovic 1998

Greedy and MFR are loop free

Ivan Stojmenovic

- Random unit graphs: Choose n nodes at random in [0,m]x[0,m]
- select average node degreed = 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 disconnected

Success rate = high for high degree, low for low degree

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

floodingrate (#messages vs SP) = close to SP

Independent variable is d, not R !!!

Ivan Stojmenovic

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

Ivan Stojmenovic

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

A

a

r

Stojmenovic IEEE Network 2006

D

S

d

Ivan Stojmenovic

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

Ivan Stojmenovic

Power saving localized routing

A d B

Constant power minimize hop count

power =u(d)= d + c minimize total power

Many 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 cost

Power_reluctance= f(A)u(d)

model by Rodoplu, Meng 1999

Ivan Stojmenovic

s

r

S x A d-x D

D

S

d

Ideal and localized power aware routing- # of hops nd(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

Stojmenovic, Lin 1998

Ivan Stojmenovic

A

a

r

D

S

d

- 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

Ivan Stojmenovic

‘Reluctance’ routing algorithm

a

r

D

d

S

Stojmenovic, Lin 1998

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

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)

Ivan Stojmenovic

A

a

r

D

d

S

Stojmenovic, Lin 1998

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)

Ivan Stojmenovic

a

r

D

d

S

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 …

Ivan Stojmenovic

Lognormal shadowing model

- =4

p(R)=0.5

Packet reception probability

Unit graph model:

Prp(x)=1, xR

Prp(x)=0, x>R

R

Distance between nodes

What is the transmission radius ? Who are neighbors?

Ivan Stojmenovic

- 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

Ivan Stojmenovic

- 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)

Ivan Stojmenovic

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

Ivan Stojmenovic

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

Ivan Stojmenovic

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

Ivan Stojmenovic

Greedy routing is not hop count optimal

x

x

x

x

x

x

1

n

x = d/n

d

- 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

Ivan Stojmenovic

IHC for Different u Values (=2)

Ivan Stojmenovic

Expected progress routing

a

x

A

c

D

Hop by hop ack

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)

Ivan Stojmenovic

- 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

Ivan Stojmenovic

- 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

Ivan Stojmenovic

Loop-free with guaranteed delivery

- Stop if message is to be returned to neighbor it came from = concave node
- MFR, DIR, Greedy
- FloodingGreedy, 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 traffic

Stojmenovic, Lin 1999

Ivan Stojmenovic

1. Constructing planar graph: faces

Bose, Morin, Stojmenovic, Urrutia, 1999

D

A ?

S

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

Ivan Stojmenovic

2. Traverse proper face until recovery

Bose, Morin, Stojmenovic, Urrutia, 1999

D

S ?

B

- Select face containing SD
- Follow that face by left hand or right hand rule
- until recovery (= closer node reached)

C

Ivan Stojmenovic

- 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

Ivan Stojmenovic

P

Q

W

V

U

Gabriel, Sokal 1984

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)

Ivan Stojmenovic

Planar graph = no two edges intersect

Proof by contradiction: Assume

UV, PQ GG(S), UV PQ

P

U

Q

V

PUQ < /2, PVQ < /2,

- UPV < /2, UQV < /2,

Sum of angles in UPVQ < 2

Ivan Stojmenovic

P

Q

W

By contradiction: Assume

PQ MST, PQ GG;

W, PW<PQ, QW<PQ, PWMST

Replace PQ by PW in MST

new MST has smaller sum of edge lengths. contradiction

Gabriel graph connected

Ivan Stojmenovic

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!

Ivan Stojmenovic

Traversal of selected face leads to recovery

D

E

X

S ?

F

B

C

- 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)

Ivan Stojmenovic

X

D

F

Getting closer on the face is guaranteed for GGE

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

Ivan Stojmenovic

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

Ivan Stojmenovic

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 < 1.41 Barriere, 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

Ivan Stojmenovic

Shortcut procedure in FACE mode

Datta, Stojmenovic, Wu 2001

C

E

G

B

F

A

ABCE replaced by AF

2-hop information needed

Ivan Stojmenovic

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

Ivan Stojmenovic

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

Ivan Stojmenovic

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

Ivan Stojmenovic

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

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

A

B

C

Ivan Stojmenovic

- 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

Ivan Stojmenovic

Power/cost aware localized routing with guaranteed delivery

Stojmenovic, Datta 2000

- 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

Ivan Stojmenovic

E

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

Parallel path search = reduced flooding greedy

F

P

A

Q

D

U

B

V

J

W

I

H

G

Lin, Lakhsdisi, Stojmenovic MobiHoc 2001

Routing from A to D: reject nodes

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

Ivan Stojmenovic

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