Ingegneria dell'Informazione

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Department of Information EngineeringUniversity
of Padova, ITALY
On Efficient topologies for Bluetooth Scatternets
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Department of Information EngineeringUniversity
of Padova, ITALY
Special Interest Group on NEtworking
Telecommunications
On Efficient topologies for Bluetooth Scatternets
Daniele Miorandi, Arianna Trainito, Andrea Zanella
miornadi, trainito, zanella_at_dei.unipd.it
PWC2003 Venice 23-25 September 2003
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Outline of the contents

• Motivations and Related works
• Bluetooth Basic
• System model
• Network Capacity and Transport Capacity
• Limiting Performance
• Efficient Topologies
• Stability constraints
• Performance evaluation for uniform traffic
• Platonic solids as efficient topologies
• Final Remarks
• (A glance to the next steps)?

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Motivations

• Expected low cost and wide diffusion of Bluetooth
  devices have excited researchers imagination
• Ad-hoc multihop networks
• Sensor networks
• Hybrid systems
• Much attention has been devoted to scatternet
  formation and management issues
• Law, Zaruba, Basagni, Petrioli, Baatz, Kalia,
• However, literature still lacks in thorough
  investigation of the optimal scatternet
  topologies!

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Goals

• Aim
• provide a mathematical insight into the relation
  between scatternet topology and performance
• Expected Results
• Optimality criteria for scatternet topology
  design
• Performance characterization of scatternet
  topologies
• Obtained Results
• Basic optimality criteria
• Performance characterization of some planar and
  solid topologies
• In other words
• The work is far to be complete, but something is
  better than nothing!

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What the standard says

• Bluetooth basic

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Piconet architecture

• Basic brick for networking
• Two up to eight units share a FH channel
• A unit acts as master, the others act as slaves
• Channel access is based on a mater-driven polling
  scheme
• Time Division Duplex (TDD) provides full duplex
  communication

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Scatternet architecture

• Piconets overlapping in space do not interfere
  much each other
• Piconets can be interconnected by Inter-piconet
  Units that may act as Gateways (GWs), forwarding
  traffic among adjacent piconets
• GWs must time-division their presence among the
  piconets
• Time division can be realized by using SNIFF mode

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Scatternet Configuration

• Scatternet topology is defined by
• Nodes partition into piconets
• Assignment of master role in each piconet
• Miorandi Zanella, MedHocNet02
• Identification of the shared units for each
  piconet

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Assumptions, Notation, Metric
System Model
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Assumptions

• Assumptions on the piconet
• Pure Round Robin (PRR) polling strategy
• Single-slot packets (DH1) only
• Assumptions on the scatternet
• All nodes in range
• Negligible GW switchover time
• GWs equally shared among piconets
• Equal number of nodes for any piconet
• Balanced routing

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Definitions Notation

• N total number of nodes in the network
• M total number of resulting piconets
• ?i,j average end-to-end traffic offered by node
  i to node j
• ??i,j end-to-end traffic matrix
• ?i,j average effective traffic flowing in the
  physical link between node i to node j
• i and j must be master and slave nodes of a same
  piconet
• ??i,j effective traffic matrix
• Note the effective traffic matrix does depend on
  
• End-to-end traffic matrix
• scatternet topology
• routing algorithm

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Network capacity

• Network capacity C
• maximum aggregate offered traffic that preserve
  stability
• where ? denotes the set of stable ? matrixes for
  a given topology

• Transport capacity T
• maximum aggregate effective traffic that preserve
  stability
• where ? denotes the set of stable ? matrixes
  for a given topology

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Some preliminary results (1)?

• The network capacity C equals the transport
  capacity T
• Capacity is attained for very local traffic only
• The capacity of M isolated piconets is CM
  pck/slot
• A scatternet of M piconets may achieve an
  aggregated throughput of at most M pck/slot
• Shared units are slaves in all the piconets they
  belong to
• Masters must never be left alone in their
  piconets

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Some preliminary results (2)?

• A scatternet of N interconnected nodes may
  achieve an aggregated throughput of at most ?N/2?
  pck/slot
• The closed-loop topology achieves maximum
  capacity for any N
• It is an asymptotically optimal topology!

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Getting closer to real world

• In realistic scenarios we have that
• traffic is generally not localized
• overlapping piconets do interfere
• How do efficient topologies perform in such
  scenarios?
• Let Uui,j be a uniform end-to-end traffic
  matrix
• each node offers an equal average traffic to
  every node in the scatternet ui,j u for each
  link i,j
• Let Ps(M) be probability of successful packet
  transmission with M overlapping piconets
• El-Hoyd, Comm.Lett,. Jun01

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A step further
Analysis of efficient topologies
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Efficient configurations

• Efficient topologies ought to
• Support maximum traffic capacity
• Provide fairness
• Scale with the number of nodes
• Examples are
• Planar topologies
• Close-loop
• Start-shaped
• Solid topologies
• Platonic solids

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Stability under PRR regime

• Isolated piconet
• For each link (i,j) (either i or j is the master)
  it must hold
• nij number of nodes in the piconet i and j
  belong to
• Connected piconet
• GWs are active only for a fraction of the time
• For regular structures, GWs presence follows a
  periodic pattern
• Averaging over a GWs cycle period we get

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Uniform Capacity definition

• Expressing the stability condition in terms of
  end-to-end uniform traffic u we end up with a
  condition of the form
• where ? depends on the scatternet topology!
• The uniform capacity is the defined as
• Finally, considering interference we get

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Uniform Capacity evaluation
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Small number of nodes
3 nodes per piconet
Uniform Capacity (pck/slot)?
8 nodes per piconet
Number of nodes
Number of nodes
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High number of nodes
3 nodes per piconet
Uniform Capacity (pck/slot)?
8 nodes per piconet
Number of nodes
Number of nodes
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Optimal setting
Optimal Number of piconets
Number of piconets
Optimal Uniform Capacity (pck/slot)?
Number of nodes
Number of nodes
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Conclusions

• Intrinsic capacity limit can be achieved with
  local traffic only
• Uniform traffic matrix generally determines
  drastic reduction on aggregated network
  throughput
• Performance strongly depends on the number of
  nodes in each piconet
• With few nodes Slim configurations outperform
  Fat ones
• With many nodes (n gt 100) inter-piconet
  interference becomes relevant and minimization of
  number of piconets becomes advantageous
• Uniform capacity rapidly decreases as the number
  of nodes increases

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Watching behind the corner

• What happens with sparse traffic matrices?
• Find communicating clusters (graph theoretical
  approach

Kernighan-Lin
Offered Traffic pck/sec
Offered Traffic pck/sec
nodes
nodes
nodes
nodes
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Once clustered
Average inter-piconet traffic pck(s
Matrix density
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Re-Concluding

• We have just moved the first steps but the
  study is still far to be complete!

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Department of Information EngineeringUniversity
of Padova, ITALY
Special Interest Group on NEtworking
Telecommunications
On Efficient topologies for Bluetooth Scatternets
Daniele Miorandi, Arianna Trainito, Andrea Zanella
miornadi, trainito, zanella_at_dei.unipd.it
PWC2003 Venice 23-25 September 2003