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Empirical tests Numerical evaluations Theoretical proofs for stationary settings Looking for a MAC protocol μ -MAC AI-LMAC B-MAC BitMAC BMA CC-MAC CMAC CSMA-MPS ARC DMACE 2 -MAC EMACs f-MAC FLAMA G-MAC HMAC LMAC LPL MFP MMACMR-MAC O-MAC PACT PCM PicoRadio PMAC

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Relocation Analysis of Stabilizing MAC Algorithms for Large-Scale Mobile Ad Hoc Networks Pierre Leone, Geneva (Switzerland) Marina Papatriantafilou, Chalmers (Sweden) Elad Michael Schiller, Chalmers (Sweden)

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Challenges Collisions When neighboring nodes simultaneously broadcast Collision

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Challenges Collisions Mobile nodes Random moves

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Challenges Collisions Mobile nodes Random moves Possibly adversarial

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Challenges Collisions Mobile nodes Transient faults Modeling the location of mobile nodes Arbitrary violations of the assumptions that model the locations Short-lived malfunctions hardware/software

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Opportunities Synchronization Clock synchronization algorithms and/or GPS

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Opportunities Synchronization Wireless broadcast A powerful primitive ensuring that: Nodes reach nearby nodes and receive the same messages

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Our approach Stabilization Assume that after the last transient fault the system state is random Steady state behaviors do not depend on that random state Natural self-stabilizing extensions arbitrary starting state guaranteed system recovery using periodic restarts Our negative results hold for self- stabilizing systems

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Outline 3 Bounded Relocation Rate 2 Negative Results 1 Relocation Analysis

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Random moves Each mobile node randomly moves in the Euclidian plane Two mobile nodes can directly communicate if their distance is less than a threshold

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In the short run G t, G t+1 G Many mobile nodes have similar neighborhoods in G t and G t+1 e.g., large communication radius In the long run this similarity disappears There are independent random relocations of the mobile nodes e.g., G t,G t+x are independent when x Relocation Analysis Random moves Evolving graphs Ferreira04, Avin et al.08 G =(G 1, G 2, …) In time t, graph G t G models the communications and interferences

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Relocation Analysis Between G t, G t+1 G, α|V| nodes relocate to new neighborhoods –α in [0, 1] is the relocation rate Relocating nodes and their new neighborhoods are chosen randomly Random moves Evolving graphs Relocation rate

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Relocation Analysis Between G t, G t+1 G, α|V| nodes relocate to new neighborhoods –α in [0, 1] is the relocation rate Relocating nodes and their new neighborhoods are chosen randomly Random moves Evolving graphs Relocation rate Our assumptions are different from: Random walks do not consider short-term (independent) random relocations Population protocols do not consider long-term neighborhood similarity

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Relocation Analysis Between G t, G t+1 G, α|V| nodes relocate to new neighborhoods –α in [0, 1] is the relocation rate Relocating nodes and their new neighborhoods are chosen randomly Low rate = less collisions Random moves Evolving graphs Relocation rate

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Relocation Analysis Between G t, G t+1 G, α|V| nodes relocate to new neighborhoods –α in [0, 1] is the relocation rate Relocating nodes and their new neighborhoods are chosen randomly Random moves Evolving graphs Relocation rate High rate=more collisions

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Relocation Analysis Between G t, G t+1 G, α|V| nodes relocate to new neighborhoods –α in [0, 1] is the relocation rate Relocating nodes and their new neighborhoods are chosen randomly Useful in analyzing MAC algorithms Random relocation causes unexpected interferences Expressiveness A single parameter defines the rate of unexpected interferences Simpler proofs than Kinetic models Random moves Evolving graphs Relocation rate

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Outline 3 Bounded Relocation Rate 1 Relocation Analysis 2 Negative Results

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Impossibility Result Collision Claim 1: There is no efficient and deterministic MAC algorithm

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Impossibility Result Claim 1: For arbitrary relocation rate, there is no efficient and deterministic MAC algorithm Collision Focus on randomized MAC algorithms

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Lower Bound Claim 2: For arbitrary relocation rate, oblivious strategies are the best that you can hope for … Oblivious strategies ignore the broadcast history Consider random relocation of all nodes after every algorithm step Learning the history is of no use Focus on bounded relocation rate

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Outline 1 Relocation Analysis 2 Negative Results 3 Bounded Relocation Rate

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Throughput Related Trade-off Oblivious Ignores the history of broadcasts

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Throughput Related Trade-off Oblivious Non-oblivious P = E.g., based on vertex-coloring – Luby '93

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Throughput Related Trade-off P = Can I use ? Great! I will keep I will pick another one Collision I will pick another one Oblivious Non-oblivious E.g., based on vertex-coloring – Luby '93 – Color uniqueness: A node has a color different than its neighbors, i.e., no collisions

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Throughput Related Trade-off E.g., based on vertex-coloring – Luby '93 – Color uniqueness: A node has a color different than its neighbors, i.e., no collisions P = Next round Oblivious Non-oblivious

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Throughput Related Trade-off Oblivious Non-oblivious Trade-off Critical-threshold relocation rate Above which oblivious is better Below which non-oblivious is better Simplifying assumptions 1. No dependencies among neighbors 2. A ll relocations occur once in every round 3. Collision detection is easy B roadcasts can inform about color choices Later today: Remove these assumptions

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How many nodes no longer have unique colors after a round? Collision Uniform distribution of colors Assume uniformity in the starting configuration Show uniformity in every configuration that follows At most ~α|V| nodes are expected to no longer have unique colors after a round From Stationary to Non-stationary Simplifying assumptions 1. No dependencies among neighbors 2. A ll relocations occur once in every round 3. Collision detection is easy B roadcasts can inform about color choices Later today: Remove these assumptions

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How many nodes start having unique colors after a round? From Stationary to Non-stationary Using the vertex-coloring algorithm (1- β) 1/e Let y be the number of nodes with conflicting colors Let (1- β)y be the expected number of nodes whose colors become unique within a broadcasting round

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Conflicting Unique From Stationary to Non-stationary When the recovery is slower than the relocation (1 - β) < α Convergence Recovery Relocation

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Conflicting Unique From Stationary to Non-stationary When the recovery is slower than the relocation (1 - β) < α When the relocation is slower than the recovery (1 - β) > α Convergence Recovery Relocation

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Throughput 80% 60% 40% 20% 0.20.40.60.8 Oblivious strategy non-oblivious strategy 0.20.40.60.8 Too good to be true!We discover a critical-threshold relocation rate Guaranteed throughput of non-oblivious strategies Eventual Throughput Simplifying assumptions 1. No dependencies among neighbors 2. A ll relocations occur once in every round 3. Collision detection is easy B roadcasts can inform about color choices Later today: Remove these assumptions We remove the simplifying assumptions and bound the recovery ratio (1- β) [σ(1- α),1/e], where σ=(5+3/e)/32 Relocation Rate α

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CSMA/CA Existing Approaches Such as Herman Tixeuil 04 Divided ratio time –Overhead –TDMA time slots CSMA/CA in overhead part for Local leader election Vertex coloring When nodes relocate in every broadcasting round No guarantees for leader election Overhead

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RTS Existing Approaches CSMA/CA RTS/CTS dialog Request to Send / Clear to Send Facilitates short exposure time –period during which a transmitted packet might be intercepted –shorter than a time slot Defer

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CTS Existing Approaches CSMA/CA RTS/CTS dialog Request to Send / Clear to Send Facilitates short exposure time –period during which a transmitted packet might be intercepted –shorter than a time slot RTS Defer

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ACK Data Existing Approaches CSMA/CA RTS/CTS dialog Request to Send / Clear to Send Facilitates short exposure time –period during which a transmitted packet might be intercepted –shorter than a time slot Defer

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Our Approach Divided time slots Competition part –MaxRnd rounds DATA part Competition rounds DATA packet Competition rounds DATA packet Competition rounds DATA packet Competition rounds slot 1slot 2slot 3slot 4 round 1 round 2 round 3 round 4 Max competition rounds, e.g., MaxRnd = 4

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Our Approach Divided time slots Round based competition Time slot Data partCompetition part Recovery is facilitated because of: 1. Simple winner and losers 2.Unlucky winners and lucky losers Neighbors may choose the same slot On the k competition round, competitors send RTS with probability 2 (k-MaxRnd )

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Our Approach Divided time slots Round based competition Neighbors may choose the same slot On the k competition round, competitors send RTS with probability 2 (k-MaxRnd ) Time slot Data partCompetition part RTC CTS DATA Simple winner and losersThe simple winner chooses the slot as its permanent one The simple losers are aware of the winners broadcast and continue to look for other broadcasting slots

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Neighbors may choose the same slot On the k competition round, competitors send RTS with probability 2 (k-MaxRnd ) Our Approach Divided time slots Round based competition Time slot Data partCompetition part CTS Unlucky winners and lucky losers RTC DATA Collision Unlucky winners are not aware of their coalitions and continue to compete for this slot on the next round Lucky losers are aware of the winners collisions and stop competing for this slot on the next round

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Neighbors may choose the same slot On the k competition round, competitors send RTS with probability 2 (k-MaxRnd ) Our Approach Divided time slots Round based competition Time slot Data partCompetition part Simple winner and losers + Unlucky winners + Lucky losers = Recovery rate of (5+3/e)/8 Simplifying assumptions 1. No dependencies among neighbors 2. A ll relocations occur once in every round 3. Collision detection is easy B roadcasts can inform about color choices Later today: Remove these assumptions Recovery rate of (5+3/e)/8 Recovery rate of (1- α) (5+3/e)/8 Recovery rate of (1- α) (5+3/e)/32

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Looking for a MAC protocol Confused?! μ -MAC AI-LMAC B-MAC BitMAC BMA CC-MAC CMAC CSMA-MPS ARC DMACE 2 -MAC EMACs f-MAC FLAMA G-MAC HMAC LMAC LPL MFP MMACMR-MAC O-MAC PACT PCM PicoRadio PMAC Let us help you! Consider your favorite decentralized vertex-coloring algorithm The good news: the algorithm possibly can migrate from stationary settings to non-stationary ones

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Conclusions Novel throughput-related trade-off –between oblivious and non-oblivious strategies –depends on the relocation rate of mobile nodes Circumventing the difficulties of –collision detection –modeling the locations of mobile nodes A study of a fault-tolerant and stateful algorithm –Extendable to consider self-stabilization

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Algosensors09: 5th International Workshop on Algorithmic Aspects of Wireless Sensor Networks July 10-11, 2009

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Thank you for your attention Contact info. elad@chalmers.se TR-2008:23, Department of Computer Science and Engineering, Chalmers University of Technology

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