http://parasol.tamu.edu
Regional Consecutive Leader ElectionIn Mobile Ad-Hoc Networks
Hyun Chul Chung*, Peter Robinson**, Jennifer L. Welch* * Texas A&M University
** Vienna University of Technology
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Motivation (1)• Recent oil spill in the Gulf of Mexico :
• Deploying seaswarm robots for clean up.
• By having a leader robot, non-conflicting decisions/instructions can be made (guide robots to areas where oil spill is concentrated, etc).
• Since robots may become damaged, the process of electing a leader should be consecutive.
Source : www.free-download-blog.com Seaswarm robot prototypeSource : www.computerworld.com (Courtesy of MIT)
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Motivation (2)• Leader election.
• Mobile ad-hoc networks.
• Region (w/ bounded communication diameter)
• “Regional Consecutive Leader Election” (RCLE) problem.
• Other applications : Deploying search and rescue robots at disaster sites.
leader
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System Model (1)
• Mobile nodes communicating via wireless broadcast.
• Leader election in a single fixed geographical region.
• Exact time and location information (e.g. GPS).
InOut 87321
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System Model (2)• Nodes execute in synchronous rounds of communication and computation.
• Such rounds can be guaranteed by having bounded 1-hop message delay and exact time information which can be provided by, for instance, the Abstract MAC Layer [Kuhn et al. 2009] and the GPS clock.
• Each round begins by broadcasts by nodes.
• Continues with nodes receiving certain broadcasts.
• At the end of each round, each node uses its current state and the set of messages received during the round to change its state and decide what to broadcast at the beginning of the next round.
r r+1 r+2
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System Model (3)• Nodes have a (common) communication radius.
• Just-In-Time (JIT) path starting at round r from nodes v0 to vk of length k:
• A sequence of nodes v0, v1, ... , vk such that for all i : 0 ≤ i ≤ k-1
• vi and vi+1 are live and within communication radius of each other throughout round r+i.
• vi is in the region at the beginning of r+i.
• vi+1 is in the region throughout round r+i.
round r
v1 is in the region and within comm. radius of v0 throughout round r : v1 receives v0’s message
v2 is in the region and within comm. radius of v1 throughout round r+1 : v2 receives v1’s message
vk is in the region and within comm. radius of vk-1 throughout round r+(k-1) : vk receives vk-1’s message
v0
v1
v2
vk-1
round r+1round r+(k-1)
vk
…
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System Model (4)• We assume D-connectedness:
• For any pair of nodes p and q, and every round r:
• If p is in the region at the beginning of r and live throughout r, and
• If q is live and in the region throughout [r, r+D-1], then
• There exists a JIT path starting at r from p to q of length at most D.
• We further assume that D is known to all
nodes in the system.
p
q
≤ D
D rounds
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The RCLE Problem (1)
• Goal : Electing a leader within a region.
• Mobility and failures require consecutive leader election:
• Leader could exit the region.
• Any node (including the leader) might crash.
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6
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The RCLE Problem (2)
• An algorithm solves the RCLE problem if...
• (Agreement) : All nodes in the region that elect a leader elect the same leader.
• (Validity) : If some live node p in the region considers some node q as a leader, then node q must have been in the region recently.
• (Termination) : If some live node remains in the region for a sufficiently long period of time, then it must elect a leader.
• (Stability) : Decision is irrevocable unless leader crashes or leaves the region.
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The RCLE Algorithm (1)
• Once a leader is elected...
• The leader generates a “leader” message every D rounds
• Message propagation is ensured by the “relaying” message communication pattern employed
• Every node sends the contents of its message buffer at every round.
p
q r
s
LM
LM
LM
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The RCLE Algorithm (2)
• Two situations in which a node p should elect (or re-elect) a leader:
• p has chosen a leader but fails to receive a leader message in a timely fashion.
• leader must have left the region or crashed.
• p enters the region.
p
q r
s
LM
leader = r
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The RCLE Algorithm (3)• In order to elect (or re-elect) a leader
• p generates an “instance” message.
• If, during the next 2D rounds, p does not receive a leader message or an instance message from a node that entered the region earlier than p did
• p elects itself as the leader.p
q r
s
IM
IM
IM
wait 2D rounds
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The RCLE Algorithm (4)• In order to elect (or re-elect) a leader
(continued)
• If p receives a leader message before 2D rounds elapse
• p adopts the generator of the leader message as its leader
p
q r
s
waiting 2D rounds
LM
leader = r
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The RCLE Algorithm (5)• In order to elect (or re-elect) a leader
(continued)
• If, during those 2D rounds, p receives one or more instance messages that were generated by nodes that entered the region earlier than p did
• p sets the generator that entered the earliest as its “candidate leader”
• p then waits for a leader message from the candidate leader
• If p receives the leader message from the candidate leader in a timely fashion, then p elects that node as its leader
• Otherwise, p initiates a new instance message
p
q r
s
q:IM
r:IM
s:IM
entered regionthe earliest
candidate leader = r
waiting 2D rounds
LM
leader = r
p:IM
p:IM
p:IM
wait for r’s leader msg
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The RCLE Algorithm (6)
• The algorithm...
• Does not rely on...
• Knowledge of the number of nodes in the system.
• Common start up time.
• Relies on the knowledge of the bounded communication diameter of the region.
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Bounds• Each node has a leader variable (node p’s leader variable : leaderp).
• Nodes elect the leader by setting the leader variable.
• (Termination)
• If some node p stays in the region for (6D-2)Ne + D rounds it will elect itself as the leader assuming that no other node elected itself as the leader during this period (Ne : number of nodes in the region when p entered the region)
• (Validity)• If leaderp = q at round r, then there exists a round in [r-2D+1,r] where
node q is live and in the region.
• (Stability)
• If leaderp = q at round r1 and leaderp ≠ q at round r2 where r1 < r2, then there exists a round in [r1-2D+1, r2] where node q has either crashed or left the region.
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A Condition on Mobility
δ : minimum progressC : communication radius
S (v0)
δ
C
F
v1
S (v0)
δ
C
F
v1
region
S (v0)
δ
C F
v1
region
v2
• We restrict the nodes to follow a condition on
mobility:
• Assume for any node (S) and any position (F) in the region
• there exists a sequence of nodes S = v0, v1, ... , vk
such that for all i : 0 ≤ i ≤ k-1
• vi broadcasts at round r+i,• vi and vi+1 are within communication
radius of each other throughout r+i and when vi+1 broadcasts it lies within the shaded area of the figure,
• Position F is within the communication radius of vk
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Calculation of D (1)• Considering information propagation from S to F
• the worst case position of v1 when it broadcasts will be either point A or B
• The distance between F and A (resp. B)
is
• less than the distance between S and F.
• can be calculated with the distance between S and F.
δ : minimum progressC : communication radius
S (v0)
δ
CF
A
B
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Calculation of D (2)• Recursive !
• Consider our single fixed region to be a rectangle where the worst case distance between any source and destination pair is L:
• We obtain D by recursively applying the above method until the information gets close enough (within communication radius) to the destination.
• D : depth of recursion
δ : minimum progressC : communication radius
S (v0)
δ
CF
B
S (v0) F
BP
C
δ
δ : minimum progressC : communication radius
G HC
δ
G
δ
C
HL
regionG
H
L
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Related Work (1)• Leader election in mobile ad-hoc environments
• Using geographical information
• [Kuhn et al. 2009] :• Entire geographical space is divided into single-hop regions where
leader is elected for each region and these leaders form a leader backbone.
• We consider a single fixed region with multi-hop communication.
• [Hatzis et al. 1999] :• Elects leader by node encountering each other.• Entire space is divided into subspaces where nodes encounter each
other by falling into the same subspace.• Probabilistic analysis considering movement of nodes as random
walks.• We provide a condition on mobility that gives a deterministic bound
on message propagation.
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Related Work (2)• Not using geographical information
• [Boukerche & Abrougui 2006], [Malpani et al. 2000], [Ingram et al. 2009], [Masum et al. 2006], [Parvathipuram et al. 2004], [Vasudevan et al. 2004] :
• All consider networks that can have an arbitrarily large communication diameter.
• Our approach considers leader election in a region with bounded communication diameter which is a better fit for situations when leader election is needed only among nearby nodes.
• [Brunekreef et al. 1996] : • Considers leader election in a 1-hop network in which messages are
received instantaneously. • Our approach considers multi-hop networks.
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Summary and Future Work• Introduced the Regional Consecutive Leader Election (RCLE) problem.
• Provided an algorithm that solves the RCLE problem when D-connectedness holds.
• Gave a condition on mobility that ensures D-connectedness.
• Future Work
• Improved algorithm : better time and message complexity.
• better than O(nD) time (from initiating an instance message to electing a leader) where n is the total number of nodes in the system.
• better than O(nD) messages per node per round.
• Weaker mobility conditions that guarantee D-connectedness.
• Lower bounds for the RCLE problem.
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Have a nice flight back home !
