Probabilistic Coverage and Connectivity in Wireless Sensor Networks

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Probabilistic Coverage and Connectivity in
Wireless Sensor Networks

• Hossein Ahmadi
• hahmadi_at_cs.sfu.ca

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Outline

• Introduction
• Probabilistic Coverage
• Background
• Probabilistic Coverage Protocol
• Evaluation
• Probabilistic Connectivity
• Background
• Probabilistic Connectivity Maintenance Protocol
• Evaluation
• Conclusion and Future Works

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1. Introduction

• Every sensor can detect an event occurring within
  its sensing range, and communicate with sensor
  inside the communication range.
• Objective keep all points in the area covered
  and every pair of sensors connected.

• In many of the previous works, sensing and
  communication ranges are assumed to be uniform
  disks unrealistic

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1. Motivation

• Using disk model may lead to
• Deploying unnecessary sensors -- incurring higher
  cost.
• Activating redundant sensors -- increases
  interference, wastes energy.
• Decreasing the lifetime of the sensor network.
• Furthermore
• Current protocols may not function properly in
  real environments.
• No assessment of the quality of communication
  between nodes.
• Realistic models
• Difficult to analyze.
• More complicated algorithms.

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1. Thesis Contributions

• Distributed probabilistic coverage protocol
• Minimizes the number of activated nodes.
• Consumes much less energy than the others.
• Quantitative measure of communication quality
  between nodes
• Analytically derive this quantity for common node
  deployment schemes.
• Probabilistic connectivity maintenance protocol
• Explicitly accounts for the probabilistic nature
  of communication links.
• Achieves a given target communication quality.
• Integrated coverage and connectivity maintenance
  protocol
• Achieves a given target communication quality
  between nodes while maintaining the area covered.

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2.1 Disk Sensing Model and Coverage

• Using the disk model, the area is covered if any
  arbitrary point in the area has a sensor within
  the sensing range.
• The disk sensing makes coverage maintenance
  protocols less complicated to design and analyze.
  

• Covering an area with disks of same radius can
  optimally be done by placing disks on vertices of
  a triangular lattice.

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2.1 Previous Works

• Several works conduct analytical analysis on
  coverage KLB04, SSS05.
• Several distributed coverage protocols have been
  proposed
• OGDC ZH05
• CCP XWZ05
• PEAS YZC03
• Ottawa TG02
• Several studies have argued that probabilistic
  sensing models are more realistic. AKJ05,
  CYA03, LT04, ZC04, ZC05.

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2.1 Probabilistic Sensing Models

• Probabilistic sensing model has also been studied
  in literature
• Several Models have been proposed AKJ05, CYA03,
  ZC05
• Distributed probabilistic coverage protocol
  CCANS ZC05

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2.2 Probabilistic Coverage

• Definition An area A is probabilistically
  covered with threshold parameter ? if
  for
  every point x.
• pi(x) is the probability that sensor i detects an
  event occurring at x.

• Definition A point x is called the
  least-covered point of A if
  for all y in A.

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2.2 PCP A Probabilistic Coverage Protocol

• We propose Probabilistic Coverage Protocol (PCP)
• Ensure that the least-covered point in the
  monitored area is covered by a probability of at
  least ?.
• Main idea Activate a subset of deployed sensors
  to construct an approximate triangular lattice.
• We divide the area into small triangles
• To implement the idea of the protocol with no
  global knowledge.
• To work optimally under the disk sensing model as
  well as probabilistic models.
• PCP is general and can use any deterministic or
  probabilistic sensing model.

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2.2 PCP A Probabilistic Coverage Protocol

• s is the maximum separation between any two
  active sensors.
• Theorem Under the exponential sensing model we
  have

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2.2 PCP A Probabilistic Coverage Protocol

• We first assume
• Nodes know their location.
• Nodes are time synchronized.
• Single starting node.
• PCP works in rounds of R seconds each.
• In the beginning of each round, all nodes start
  running PCP independent of each other.

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2.2 PCP A Probabilistic Coverage Protocol

• One node randomly enters active state.

• The node sends an activation message
• Closest nodes to vertices of the triangular mesh
  are activated.
• Activated nodes send activation messages.

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2.2 PCP A Probabilistic Coverage Protocol

• Every node receiving an activation message
  calculates an activation timer Ta as a function
  of its closeness to the nearest vertex of the
  hexagon

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2.2 PCP A Probabilistic Coverage Protocol

• Definition d-circle is the smallest circle drawn
  anywhere in the monitored area such that there is
  at least one node inside it.
• Optimize the convergence time and saves the
  energy.
• The diameter d is computed for deployment with
• Grid distribution
• Uniform random distribution

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2.2 PCP A Probabilistic Coverage Protocol

• Multiple Starting Nodes
• Faster protocol convergence.
• Number of starting nodes is controlled by setting
  startup timer.
• May increase total number of activated sensors.
• Time Synchronization
• Protocol needs only coarse grained
  synchronization
• Simple synchronization schemes suffice.

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2.3 Analysis 3 Theorems

• Correctness and Convergence Time The PCP
  protocol converges in at most
  time units.
• Convergence time only depends on the size of
  area.
• Shows that PCP can scale.
• Activated Nodes and Message Complexity The
  number of nodes activated by the PCP protocol is
  at most
• The same as the number of exchanged messages in a
  round.
• Very few in comparison with total number of
  deployed sensors.
• Network Connectivity The nodes activated by PCP
  are connected if the communication range of nodes
  rc is greater than or equal to s.
• Holds for most real sensors.

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2.4 Evaluation

• We implemented PCP in NS-2 and in our own packet
  level simulator.
• We deploy 20,000 nodes in a 1km x 1km area.
• We verify correctness of our protocol and show it
  is robust against several parameters.
• We also compare it against state-of-the-art
  protocols
• Probabilistic coverage protocol CCANS
• Deterministic coverage protocols CCP, OGDC
• We repeat each experiment 10 times and report the
  average, and minimum and maximum if they dont
  clutter plots.

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2.4.1 Validation Savings

• Our analytical results are conservative.
• PCP performs better in simulation.
• Significant savings from probabilistic models.

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2.4.2 Robustness of PCP

• PCP is robust against location inaccuracy and
  imperfect time synchronization.

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2.4.3 Comparison versus CCANS

• PCP outperforms CCANS in terms of total energy
  consumed and network lifetime.

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2.4.4 Comparison versus OGDC, CCP

• PCP outperforms both OGDC and CCP protocols in
  terms of energy consumption.

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3. Probabilistic Connectivity

• Another fundamental problem in WSNs.
• A network is connected if every pair of nodes can
  communicate with each other.
• Deterministic Connectivity Many previous works
  represent the network with an undirected
  unweighted graph.
• There is an edge between two nodes if they are
  within the communication range of each other.
• The communication range is typically assumed to
  be a disk.
• Network connectivity is equivalent to graph
  connectivity.

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3.1 Probabilistic Communication Range

• Communication ranges follow probabilistic models
  ABB04, KNE03.
• Two wireless nodes can not said to be connected
  or disconnected.
• It is neither sufficient nor precise to state
  that the network is simply connected.
• A quantitative measure of the quality of
  communications in the network is needed.

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3.2 Connectivity under Probabilistic Model

• Node-to-node packet delivery rate the
  probability that v correctly receives a packet
  transmitted by u, without any retransmission by
  the MAC layer.
• Definition The network delivery rate, a, of a
  sensor network is the minimum packet delivery
  rate between any pair of nodes.

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3.2 Computing Network Delivery Rate

• We derive lower bounds on the network delivery
  rate assuming
• All sensors use the same probabilistic
  communication model.
• Links starting at the same sender node have
  independent delivery rates.
• We only consider the delivery rates between
  immediate neighbors.

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3.2 Computing Network Delivery Rate

• The network delivery rate, a, is lower bounded
  in
• Triangular mesh with link deliver rate of p by
• Square mesh with link deliver rate of p by
• Uniform random deployment by

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3.3 Probabilistic Connectivity Maintenance
Protocol

• We propose a connectivity maintenance protocol
  (PCMP)
• Explicitly accounts for the probabilistic nature
  of communication.
• Goal To activate a subset of deployed nodes with
  the network deliver rate of at least a.
• PCMP activates nodes to form an approximate
  triangular mesh.
• We choose triangular mesh for two reasons
• Activating nodes on the triangular mesh has been
  shown to be optimal, in case of deterministic
  connectivity.
• Our analysis provide tighter lower bound for
  triangular mesh.

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3.3 Probabilistic Connectivity Maintenance
Protocol

• The spacing between activated nodes should be
  such that we have
• p is the average delivery rate between two nodes
  and is given by (for the log-normal shadowing
  model)
• PCMP works with the same activation mechanism as
  PCP.

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3.4 Integrated Coverage and Connectivity Protocol

• We integrate our connectivity maintenance
  protocol with our coverage protocol.
• d? The spacing required between nodes to
  guarantee ? coverage.
• da The spacing required between nodes to
  guarantee a connectivity.
• To achieve both probabilistic coverage and
  probabilistic connectivity at the same time, we
  activate nodes on an approximate triangular mesh
  with spacing min(da, d?).

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3.5 Evaluation of PCMP

• We use the following experimental setup
• We use NS-2 simulator for all protocols.
• We deploy 1,000 nodes in a 1km x 1km area.
• We use MicaZ radio interface parameters.
• We use Log-normal shadowing propagation model.
• We validate the correctness of PCMP and our
  analysis.
• We compare our PCMP against two state-of-the-art
  connectivity protocols SPAN and GAF.
• Also, we compare it against an integrated
  coverage and connectivity protocol, CCP-SPAN.

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3.5.1 Validation of PCMP

• Our lower bounds on network delivery rate are
  conservative.

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3.5.2 Validation of Integrated Protocol

• Our PCMP protocol can provide both coverage and
  connectivity at the same time.

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3.5.3 Comparison versus SPAN, GAF

• Our protocol outperforms SPAN and GAF in terms of
  total energy consumption and network lifetime.

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3.5.4 Comparison versus CCP-SPAN

• Our integrated protocol outperforms CCP
  integrated with SPAN in terms of number of
  activated nodes and total energy consumption.

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4.1 Conclusions

• Distributed probabilistic coverage protocol (PCP)
  
• Energy efficient.
• Increases the network lifetime.
• Robust against several factors.
• Quantitative measure of the quality of
  communication
• Analysis on different deployment schemes.
• Probabilistic connectivity maintenance protocol
  (PCMP)
• Explicitly accounts for the probabilistic nature
  of communication links.
• Outperforms others in literature.
• Integrated coverage and connectivity maintenance
  protocol
• Achieves a given target communication quality
  while keeping the area covered.
• To the best of our knowledge, this is the only
  protocol that provides probabilistic coverage and
  probabilistic connectivity at the same time.

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4.2 Future Works

• Variable Sensing and Communication Models.
• Adaptive Sensing Models.
• Adaptive Communication Models.
• Network Delivery Rate under Realistic MAC
  Protocols.

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Publications

• M. Hefeeda and H. Ahmadi. A probabilistic
  coverage protocol for wireless sensor networks.
  In Proc. of IEEE International Conference on
  Network Protocols (ICNP'07), Beijing, China,
  October 2007.
• M. Hefeeda and H. Ahmadi. Network connectivity
  under probabilistic communication models in
  sensor networks. In Proc. of IEEE International
  Conference on Mobile Ad-hoc and Sensor Systems
  (MASS'07), Pisa, Italy, October 2007.
• M. Hefeeda and H. Ahmadi. Energy-Efficient
  Protocol for Deterministic and Probabilistic
  Coverage in Sensor Networks. Submitted to
  ACM/IEEE Transactions on Networking.