Ingegneria%20dell'Informazione

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Department of Information EngineeringUniversity
of Padova, ITALY
Performance Analysis of Limited1 Polling in a
Bluetooth Piconet
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Department of Information EngineeringUniversity
of Padova, ITALY
Special Interest Group on NEtworking
Telecommunications
Performance Analysis of Limited1 Polling in a
Bluetooth Piconet
Daniele Miorandi, Andrea Zanella
daniele.miorandi, andrea.zanella_at_dei.unipd.it
CITSA05, Orlando, 14-17 July 2005
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Outline of the contents

• Motivations Purposes
• Bluetooth Basic
• System Model
• Performance Analysis
• Concluding Remarks

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What and Why

• Motivations Purposes

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Motivations

• Analytical models for Bluetooth systems permit
• Performance estimation (packet delay statistics)?
• Buffer dimensioning (queue length statistics)?
• Segmentation and reassembly strategy (packet type
  selection)?
• Recently, some models have been proposed for
  simple scenarios with multi-slot packets
  Bruno,Misic
• Approximate delay estimation using M/G/1 queues
  with vacations
• Exact analysis for symmetric systems (equally
  loaded nodes) only
• Literature still lacks a mathematical model that
  takes into consideration multislot packets and
  asymmetric traffic load among nodes

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Aim of the study

• Providing an approximate performance analysis in
  case of
• Use of multi-slot packets
• Asymmetric and unbalanced traffic matrix

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What the standard says

• Bluetooth basic

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Bluetooth piconet

• Two up to eight Bluetooth units sharing the same
  channel form a piconet
• In each piconet, a unit acts as master, the
  others act as slaves
• Channel access is based on a centralized polling
  scheme
• Full-duplex is supported by Time-division-duplex
  (TDD), with time slots of T0.625 ms

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Multi-slot packets

• Data packets can be
• 1, 3, or 5 slot long
• Unprotected or 2/3 FEC protected
• Unprotected packet formats (DH)
• higher data capacity
• more subject to errors
• Protected packet formats (DM)
• medium data capacity
• higher protection against errors

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Mathematical Model

• System Model for Ideal Channels

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System Model

• Number of units
• N-1 slaves and 1 master
• System model
• 2N-2 interacting queues
• Traffic model
• Packets arrive at link i,j as a marked Poisson
  process of rate ?i,j and weights ?ij(l), l1,3,5
• Only single-hop communications
• Pure Round Robin (PRR)?
• One packet per queue is served per polling cycle
• Polling cycle has a random duration depending on
  the size of the packets found waiting at each
  queue-head

Downlink master queues (one per slave)?
N-1
Uplink slaves queues
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Cycle Time
Queue service time (B0,1)?
Queue service time (B1,0)?
Bi,j part of the cycle time spent in serving
queue (i,j)?
Cycle Time (TC)?
TC time required to complete a polling cycle
Pi,j(0) probability of empty (i,j) queue
?i,j load factor of (i,j) queue
Littles law
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Cycle Time Statistics

• According to the head of the queue packet type we
  have
• Empty queue Bij 1 slot (POLL or NULL packet)?
• DH1 or DM1 Bij 1 slot
• DH3 or DM3 Bij 3 slots
• DH5 or DM5 Bij 5 slots
• Taking expectations we get
• Average service time for (i,j) queue bijEBij
• Average cycle time
• Putting pieces together, we get a system of 2N-2
  equations

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Average cycle time

• Solving the system we easily get

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Delay time
Slave 1
Slave 1
Queue delay (Qij)?
Vacancy delay (Vi,j)?
Cycle Time (TC)?
Slave 2
Slave 2
Slave k
Slave k
Slave 1
Transmission time (Zi,j)?
Slave 2
Slave k
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Packet Delay

• Let Wij be the access delay for link (i,j), i.e.,
  the time spent in the queue before entering the
  service
• The access delay Wij can be expressed as
  where
• Vi,j vacancy time
• time between the packet arrival and the instant
  the queue gets the service
• Qi,j queue delay
• time for getting rid of all the packets found in
  the queue
• Hence, the packet delay Dij for link (i,j) will
  be given by

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Queue Delay

• The queue delay Qij can be expressed as follows
• where
• Li,j number of queued packets at the packet
  arrival epoch
• Uij(k) inter-visit time for the k-th queued
  packet at (i,j) queue
• time for getting rid of all the packets found in
  the queue
• NOTE Uij(k) is a special polling cycle, since it
  refers to the specific case in which at least a
  packet is waiting in the (i,j) queue
• Assuming Uij(k) to be independent of packet index
  k we get

Queue service time obtained with
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Equivalent load factor

• Once again we get a system of equations
• that solves for

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Laplace-Stieltjes Transform (LST)?

• Applying LST assuming delay components to be
  independent we get
• Packet service time
• Number of queued packets
• Queue delay
• Queue service time
• Inter-visit time
• Access delay

The LST of the vacancy time is still missing
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Vacancy Time

• The LST of the vacancy time, Vi,j(s) can be
• either derived extending the method proposed by
  IbeCheng COMM89
• or approximated by applying the random look
  theory (much easier!)?
• This approximation allows to get a closed form
  expression of the average packet delay

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Results (1)?

• We checked the accuracy of our approximated model
  for balanced scenarios, for which exact solution
  is known
• N4, ??(1)?(3)1/9, ?(5)7/9
• Queues are equally loaded
• Symmetric Traffic
• Remark the proposed model closely approximates
  the exact result also for high traffic loads

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Results (2)?

• Balanced asymmetric scenarios
• N4, ??(1)?(3)1/9, ?(5)7/9
• Queues are equally loaded
• Download Traffic only
• Remark the accuracy of the proposed model is
  even more clear for asymmetric scenarios

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Results (3)?

• Unbalanced scenarios
• N4, ??(1)?(3)?(5)1/3
• ?0,1 ?1,0 ?0,2 ?2,00.3
• ?0,3 ?3,0 0.9

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Conclusions Future work

• Summary
• Simple mathematical model for ideal Bluetooth
  links with unbalanced load has been presented
• Average packet delay estimations given by the
  model closely approximates the exact results in
  balanced scenario, largely improving the models
  previously presented in the literature
• The model seems to offer rather good performance
  estimation also in unbalanced scenarios

• Next steps
• Model can be extended to error-prone links
• A fading channel model might be considered
• Remark this might exacerbate the interdependency
  among the queues, making the model less accurate

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Thats all!

• Thanks for
• your attention!