Alexander DvinskyTopics in Reliable Distributed Computing (048961)Technion, Jan. 2009

Why ad-hoc wireless networks?Easily and quickly deployedEasily scaledFlexibleLow dependence on infrastructure

Field for applicationsEnvironmental

Glacier and ocean monitoringWild animal observation

MilitaryTracking military vehiclesSelf-healing mine fieldSniper localization

•K. Römer and F. Mattern, “The design space of wireless sensor networks,” IEEE Wireless Communications, vol. 11, no. 6, pp. 54–61, Dec. 2004.•Nitin H. Vaidya, “Tutorial on Mobile Ad Hoc Networks: Routing, MAC and Transport Issues” Infocom 2006•http://www.terranet.se/

Applications cont’dAgriculture

Grape monitoringCattle herding

Civilian environmentsP2P cell-phone networkFire fightingSearch and rescue (avalanche victims)

Personal networking?Do you want your microwave oven to pass

messages from your refrigerator to a TV?What about motion sensor to a lamp?

ChallengesLimitations

RangeBattery lifeComputing powerSizePrice

Transmission errors (interference)Routing complexityInstability

Network partitionsRoute changes

Security issues

RoutingThere’re a lot of (Wikipedia claims “more

than 70”) protocols for wireless routingSome of the things to consider when

choosing areLatency requirementsPower restrictionsStorage restrictions

Reactive routingRoute is discovered when connection is

neededPro

Network is silent until connection is to be established

No need to store routing informationCon

Route requests = floodingHigh latency

Pro-active routingRoutes are discovered and stored for future

usePro

Lower latenciesLower control message flooding

ConExtra storage for routing dataMaintenance of the (potentially unneeded)

routing data

Energy considerationsThe model for signal attenuation is whenThus it is often better to make many small

hops than a single large one

1

d 2

InterferencePrimary interference constraint

Simultaneous send and receiveSimultaneous sendsSimultaneous receives

Hidden node problem

A B C

General interference constraintDotted lines show the nodes that can hear each other

Every link is translatedto a node in theinterference graphEvery interfering pair of links from the original graph are represented by an edge

Primary interference constraint

For example when links are not sufficiently far from each other

Legal schedule is represented by an independent set in the interference graph.

Additional interference

Unfortunately calculating the maximum one is an NP hard problem

Ad-hoc networks in 802.11 - IBSSBasic assumption: everybody hears everyone

– no routingEveryone works on the same channel –

secondary interference constraintThe time is divided to periods (default – 120

ms)During each period there’s a chosen leaderEvery period a beacon is sent

If node does not hear some amount of beacons it assumes it’s disconnected

IBSS – cont’dChoosing the leader

At the beginning of each cycle every node tries to send a beacon. Collisions resolved by exp. back off

The one that succeeds is the leaderLeader answers probe requestsTo announce one’s presence in the network one

must become a leaderLeader is not allowed to sleep during the cycle –

nobody wants to be a leader (except for the new guys)

If two different networks with same name are in range nodes will gradually move to the older one (age data is in the beacon)

I received aresponse. Let’stry to connect …

DemoI hear no one -I must be theonly one aroundBeacon! Beacon!Probe! Probe!Response!I’ll back off 2

I’ll back off 1

*Logical only

Our problemModel

Multi-hop networkStochastic packet arrivalPrimary interference constraintSlotted time. Unit packet lengthNo central authority

TargetMaximize throughputStability

ApproachIteratively find the best solution

Similar problem #1Multi-hop networkStochastic packet arrivalPrimary interference constraintEither central authority is present, or each

node has global topology and queue backlog information

•L. Tassiulas and A. Ephremides. - Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks•L. Tassiulas. Linear complexity algorithms for maximum throughput in radio networks and input queued switches

Solution of problem #1One optimal, stable solution for the problem,

proven by Tassiulas and Ephremides, is the maximum weight matching in the connections graph with queue lengths used as edge weights

A problem with naïve approach is high complexity of calculations required for each slot schedule. That was later fixed by Tassiulas

Reminder:Matching: A set of edges such, that no two touch same nodeMaximal matching: Such a matching, that no more edges can be added to itMaximum matching: A matching with maximal possible weight. If weights are positive, maximum is also a maximal matching

An example

Clearly the above solution contributes the most to stability

Solution of problem #1 cont’dThe state of the network is a set of queue

lengths. This state does not change quicklyInstead of finding a maximum weight

matching for each slot, we’ll converge to itAt each step a (random) matching is chosenIn each iteration: if newly chosen random

matching is “better” than the previous one – use new, otherwise keep the old matching

An example

First solution chosen might be far from optimal, but we’ll inevitably converge to it eventually

6 > 1

7 > 6

6 < 7

10 > 7

Similar problem #2Input-queued switchPackets, arriving stochastically at input ports

are to be scheduled to output portsPorts are locked exclusively by a scheduled

matchCentral authority is available

P. Giaccone, B. Prabhakar, D.Shah. - Randomized scheduling algorithms for high-aggregate bandwidth switches

Scheme of an input-queued switch

Solution of problem #2As before, we’re interested in scheduling as

close to a maximum weight matching as possible

At each iterationconsider k alternativesfor the next step andselect the heaviest one

Can be easilyparallelized in HW

How the alternatives are chosen are chosen semi-randomly. It’s a

union of k-1 “Neighbor” matchings and a next step of “Hamiltonian Walk” over the set of all possible matchings

Both the definition of neighborhood and k can be chosen considering the domain of the solution physical limitations of the HW

1 kS S

Solution of problem #2 cont’dAlternative approach

Find a matching with high potential (heavy matching)

Merge two considered matchings into a third one, better then each of the originals

An improvementConsider the recent arrival

data when generating nextrandom schedule

MIX

Merge example

IdentitiesWhy?

If you already broadcast out loud, at least say whom to

Protocols are easier that wayWhy not?

Nodes are produced identicalRandomly generated identities are possible,

but duplicates are to be managed somehow

Example: Initially Partitioned Network

D’s packets for address a routed to A

•Nitin H. Vaidya, “Tutorial on Mobile Ad Hoc Networks: Routing, MAC and Transport Issues” Infocom 2006

Duplicate address detection (DAD) important To avoid misrouting

Merged Network

•Nitin H. Vaidya, “Tutorial on Mobile Ad Hoc Networks: Routing, MAC and Transport Issues” Infocom 2006

DecentralizationThe problems presented above are almost

identical to ours, except for the centralization aspect

All we need is a decentralized match and a decentralized mix algorithms

Decentralized match

R

L

R L

LL

R

R

Decentralized match cont’dThe match above works, but how well?Weights are at all not considered when

generating a matchWe could spend multiple iterations before

finding a match, that at least resembles maximum

Alternative decentralized matchNext algorithm approximates maximum

matching by a factor of 2GreedyBuilt for undirected graphs, but can be

extended

Distributed weighted matching protocol by node v

•Jaap-Henk Hoepman - Simple Distributed Weighted Matchings - eprint cs. DC/0410047, October 2004.

Set of nodes that haverequested to connectto our

Our neighborsInform c, that we’d liketo connect to it

If someone has requested toconnect to us – write it down

If someone has requested todisconnect from us – removehim from working neighbor set

If our candidate hasdropped – recalculatethe candidate

If we’ve chosen c andc has chosen usDisconnect from allthe neighbors

We’re left with the heaviest unmatchededge – add it to the matching

Candidate is the nodethat we have the heaviestedge to among all our neighbors

Examplec=null

c=C

c=B

c=F

c=B

c=null

c=FR={C,F}

R={B, G}

R={C}

c=D R={D}

Result12 instead of optimal 15

But hey, it could bemuch worse!

Decentralized mixCombination of two matches forms a set of circles and

paths (as each node can be touched at most by two edges)

Summation mechanismA message is sent by each node (in a match) along the path

or cycle, calculating weight differences between the matchings

D(A)=0

D(A)=3

D(A)=-1

D(A)=4

D(A)=1

D(A)=3

D(A)=-3

Mix by gossipBoth of the gossip algorithms in the paper

were presented last week by Ittay. Only minor details vary

Gosp-Algo 1Instead of subtracting sums, subtract averagesEach node randomly averages values with

randomly chosen neighborAfter enough ( ) iterations, each

node has a good approximation of the path/circle average it resides in

Verify, that every node in the component has the same sign of the result

If yes – act accordinglyif no – retain previous schedule

logO Ln n

Gosp-Algo 2Utilize the property of independent

exponential random variablesIf then Each node draws a value of rate equal to its

weight and sends it to neighborsWhen all values are collected, minimum can

indicate the approximation of the sum of ratesTo raise confidence, k values and not one are

drawn by each node and the average of minimums is used

1 1~ exp ,..., ~ expL Lx r x r 11

,..., ~ expL

L ii

Min x x r

Discussion pointsIdentities - is that really so hard to justify a

gossip-based mix algorithm? Running an complex algorithm to find

optimal schedule. How stable must the network be to make it worth it? When plain exponential back off is not enough?

When does ad-hoc worth the hassle? How hard is it to put some kind of coordinator in the middle?

2O n

References Eytan Modiano, Devavrat Shah, Gil Zussman - Maximizing Throughput in Wireless

Networks via Gossiping. SIG Metrics/Performance 2006.

P. Giaccone, B. Prabhakar, D.Shah. - Randomized scheduling algorithms for high-aggregate bandwidth switches. IEEE J. Sel. Areas Commun.,21(4):546-559, May 2003

L. Tassiulas and A. Ephremides. - Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Autom. Control, 37(12):1936-1948, December 1992.

L. Tassiulas. Linear complexity algorithms for maximum throughput in radio networks and input queued switches. In Proc. IEEE INFOCOM’98, April 1998.

• Nitin H. Vaidya, “Tutorial on Mobile Ad Hoc Networks: Routing, MAC and Transport Issues” Infocom 2006

• K. Römer and F. Mattern, “The design space of wireless sensor networks,” IEEE Wireless Communications, vol. 11, no. 6, pp. 54–61, Dec. 2004.

• http://www.terranet.se/• Jaap-Henk Hoepman - Simple Distributed Weighted Matchings - eprint cs.

DC/0410047, October 2004.