Performance Comparison of Existing Leader Election
Algorithms for Dynamic Networks
Plamen Ivanov Faculty Mentor: Jennifer Walter
Department of Computer Science, Vassar College
Mobile Ad Hoc (Dynamic) Networks:
Collection of potentially mobile computing devices.
Communication through wireless medium.
Typically no fixed infrastructure.
When nodes move, communication topology can change.
Leader Election:
Goal is to select a unique processor among many in a distributed system. Used as a primitive in other distributed
algorithms. Some applications include:
- primary-backup approach to replication-based fault-tolerance.
- group communication systems.
- video conferencing.
- multi-player games.
Leader Oriented Directed Acyclic
Graph (DAG):
Graphs use heights to orient links.
Heights are parameters determined by the leader
election algorithm.
DAG is used as a representation of the topology of a
network.
Project Goals:
Expand the simulator to better model the system assumptions.
Establish performance parameters and compare the two algorithms based on those parameters.
Experimentally validate the claims made by Derhab and Badache for their algorithm.
Existing Algorithms:
Use heights ( n-tuples ) associated to each node to maintain the leader oriented DAG and guarantee that each connected component of the
graph has a leader. Links between nodes are oriented from higher to lower heights. Heights are compared lexicographically. The algorithms use
link reversal as a response to changes in the topology and the heights of the nodes.
Algorithm Presented by Derhab and Badache
Algorithm Presented by Ingram et al.
- A DAG converges to a state with just one leader
within a finite amount of time even if topological
changes occur during the convergence time.
- Handles multiple concurrent topology changes.
- Uses 5 types of messages.
- Based on a time-interval computation.
- Uses a 9-tuple as height:
(Certain, Ts, Lid, Tb, Te, Oid, Refl, Delta, ID).
Certain
Ts
Lid
Tb
Te
Oid
Refl
Delta
ID
–
–
–
–
–
–
–
–
–
1 if node has a path to leader, 0 otherwise.
time at which the leader has started the creation of its DAG.
the identifier of the node considered to be the leader.
beginning of the Reference Level Interval.
end of the Reference Level Interval.
0 or the ID of the node that started this reference level.
0 for initiated, 1 for reflected reference level.
distance from leader.
the identifier of a node.
- Guarantees that after topology changes cease, all DAGs
will have a unique leader within a finite amount of time.
- Works for arbitrarily changing network topologies.
- Handles multiple concurrent topology changes.
- Works with asynchronous message delays.
- Uses one type of message.
- Uses a 7-tuple as height:
(Tau, Oid, Refl, Delta, Lts, Lid, ID).
Tau
Oid
Refl
Delta
Lts
Lid
ID
–
–
–
–
–
–
–
0 or the time when this reference level was initiated.
0 or the id of the node that started this reference level
0 for initiated, 1 for reflected reference level.
distance from leader.
the negative of the time when the current leader was elected.
the identifier of the node considered to be the leader.
the identifier of a node.
Future Work:
System Assumptions:
- There are N nodes.
- Nodes have perfect clocks.
- Nodes communicate through message passing.
- Messages are only lost if they are in transit on a link that goes down.
- Messages are delivered in sending order over each link.
- Message delays are asynchronous or synchronous.
- Nodes move at a random constant speed in random directions.
- All movement stops at some point in time.
Simulator:
A discrete event simulator written in java.
Simulator models node mobility,
dynamic topology and synchronous or
asynchronous message delays.
Displays the topology.
Records topology changes and can replay
same topology record with different
leader election algorithms.
Completed Work:
Established performance parameters:
- number of messages generated.
- number of leaders elected.
- time for stabilizing after last link change.
Improved Simulator Functionality:
- added additional GUI elements.
- improved visual output of the simulator.
- extended support for more versatile system model.
- created a recording system to store and replay
topological changes.
Checked the correctness of implementation of Ingram’s algorithm.
Tentative Conclusions:
We have a hypothesis that the algorithm by Derhab and Badache
cannot tolerate variable message delays.
Complexity for that algorithm appears to be overwhelming when
number of nodes is high or the network is very dense.
Implementing correctly the algorithm presented by Derhab and
Badache.
Generate topology records with different network configurations:
- different number of nodes;
- different communication delays;
- different node maximum speeds.
Run both algorithms on same topology records to compare their
performance.
Draw conclusions about the functionality and correctness of the
two algorithms.
References:
An Asynchronous Leader Election Algorithm for Dynamic Networks
by Ingram et al.
A self-Stabilizing Leader Election Algorithm in Highly Dynamic Ad
Hoc Mobile Networks by Derhab and Badache.
This material is based upon work
supported by the National Science
Foundation under Grant No. 0712911.