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Department of Information Engineering
University of Padova, ITALYPerformance Analysis of Limited–1 Polling in Performance Analysis of Limited–1 Polling in
a Bluetooth Piconeta Bluetooth Piconet
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are adapted from (or perhaps identical to) our slides, and put a link to the authors webpage:
www.dei.unipd.it/~zanella
Thanks and enjoy!
A note on the use of these ppt slides:We’re making these slides freely available to all, hoping they might be of use for
researchers and/or students. They’re in PowerPoint form so you can add, modify, and delete slides (including this one) and slide content to suit your needs. In return for use, we
only ask the following:If you use these slides (e.g., in a class, presentations, talks and so on) in substantially
unaltered form, that you mention their source.If you post any slides in substantially unaltered form on a www site, that you note that they
are adapted from (or perhaps identical to) our slides, and put a link to the authors webpage:
www.dei.unipd.it/~zanella
Thanks and enjoy!
Department of Information EngineeringUniversity of Padova, ITALY
Performance Analysis of Limited–1 Polling in Performance Analysis of Limited–1 Polling in
a Bluetooth Piconeta Bluetooth Piconet
{daniele.miorandi, andrea.zanella}@dei.unipd.it
Daniele Miorandi, Andrea Zanella
CITSA’05, Orlando, 14-17 July 2005
Special Interest Group on NEtworking & Telecommunications
CITSA05, Orlando (Florida), 14-17 July, 2005
Outline of the contents
Motivations & Purposes
Bluetooth Basic
System Model
Performance Analysis
Concluding Remarks
CITSA05, Orlando (Florida), 14-17 July, 2005
What and Why…
Motivations & Motivations & PurposesPurposes
CITSA05, Orlando (Florida), 14-17 July, 2005
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
CITSA05, Orlando (Florida), 14-17 July, 2005
Aim of the study
Providing an approximate performance
analysis in case of
Use of multi-slot packets
Asymmetric and unbalanced traffic matrix
CITSA05, Orlando (Florida), 14-17 July, 2005
Bluetooth piconet Two up to eight Bluetooth units sharing the
same channel form a piconetpiconet
In each piconet, a unit acts as master, the
others act as slaves
Channel access is based on a centralized centralized
polling schemepolling scheme
Full-duplex is supported by Time-division-Time-division-
duplexduplex (TDD), with time slots of T=0.625 ms
active slavemaster
parked slavestandby
slave1
slave2
slave3
master
CITSA05, Orlando (Florida), 14-17 July, 2005
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
0
50
100
150
200
250
300
350
Byt
es1 slot 3 slots 5 slots
Paylod Capacity
Medium rate High rate
CITSA05, Orlando (Florida), 14-17 July, 2005
Mathematical Model
System Model for System Model for Ideal ChannelsIdeal Channels
CITSA05, Orlando (Florida), 14-17 July, 2005
Downlink master queues(one per slave)
Uplink slaves queues
System Model Number of units
N-1 slaves and 1 master
System model 2N-2 interacting queues2N-2 interacting queues
Traffic model Packets arrive at link i,j as a marked
Poisson process of rate λi,j and weights
ij(l), l=1,3,5
Only single-hop communications
Pure Round Robin (PRR) One packet One packet per queue is served per
polling cyclepolling cycle Polling cycle has a random duration random duration
depending on the size of the packets found waiting at each queue-head
N-1
CITSA05, Orlando (Florida), 14-17 July, 2005
Cycle Time
Queue service time (B0,1)
Queue service time (B1,0)
Cycle Time (TC)
,
,C i j
i j
T B
Bi,j: part of the cycle time spent in serving queue (i,j)
TC: time required to complete a polling
cycle
0 1ij ijP
Pi,j(0): probability of empty (i,j) queue
i,j: load factor of (i,j) queue
Eij ij C ij CT t
Little’s law
, ,
, ,
EC i j i ji j i j
t B b
CITSA05, Orlando (Florida), 14-17 July, 2005
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: bij=E[Bij]
Average cycle time
Putting pieces together, we get a system of 2N-2 equations
, 4 5 2 3 1i j ij ij ijb
Cycle Time Statistics
, ,
, ,
4 5 2 3 1C i j i j ij iji j i j
t b
,,
,,
4 5 2 3 1i ji j ij ij
i ji j
,
1 1 , 1;
Pr , 3,5;
0
ij ij ij
i j ij ij
k
B k k k
otherwise
CITSA05, Orlando (Florida), 14-17 July, 2005
Average cycle time
Solving the system we easily get
,,
,
2
1 4 5 2 3ij
i jl m lm lm
l m
N
,
, ,,
2
1 4 5 2 3i j
Ci j l m lm lm
l m
Nt
,
,,
,
2 4 5 2 34 5 2 3 1 1
1 4 5 2 3i j ij ij
i j ij ij ijl m lm lm
l m
Nb
CITSA05, Orlando (Florida), 14-17 July, 2005
Delay time
Slave 1
Slave 2Slave k
Vacancy delay (Vi,j)
Slave 1
Slave 2Slave k
Queue delay (Qij)
Slave 1
Slave 2Slave k
Transmission time (Zi,j)
Cycle Time(TC)
CITSA05, Orlando (Florida), 14-17 July, 2005
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
Packet Delay
, , ,i j i j i jW V Q
, , ,i j i j i jD W Z
CITSA05, Orlando (Florida), 14-17 July, 2005
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 Delay
,
, ,1
i jL
i j i jk
Q U k
, , , , ,
, ,i j i j l m i j
l m i j
U Z B
Queue service time obtained with
, , , , , , ,El m i j l m i j l m i jU u
CITSA05, Orlando (Florida), 14-17 July, 2005
Equivalent load factor
Once again we get a system of equations
that solves for
, , ,, , , ,
, ,,
4 5 2 3 1l m i ji j h k i j hk hk
h k i jl m
z
, ,
, , ,
, , ,, ,
2 1
1 4 5 2 3l m i j
l m i j
h k h k h kh k i j
z N
, , , ,,
, , , ,, ,
2 1
1 4 5 2 3l m i j i j
i jl m h k h k h k
h k i j
z Nu
CITSA05, Orlando (Florida), 14-17 July, 2005
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
,
*,
1,3,5i j
sli j
l
Z s l e
, ,
* *, ,i j i j i j i jL z W z
, ,
* * *, ,i j i j i j i j ijQ s W U s
, ,
* * *, , ,
, ,i j i j l m i j
h k i j
U s Z s B s
*, , , , , , , , , ,
1,3,5
1s sll m i j l m i j l m i j l m
l
B s e l e
, , ,
* * * *, ,i j i j i j i j i j ijW s V s W U s
The LST of the vacancy time is still missing…
CITSA05, Orlando (Florida), 14-17 July, 2005
Vacancy Time
The LST of the vacancy time, V*i,j(s) can be
either derived extending the method proposed by Ibe&Cheng [COMM89]…
or approximated by applying the random look theoryrandom look theory (much easier!)
This approximation allows to get a closed form expression of the average
packet delay
*
*,
1
EC
i jC
T sV s
s T
2
,
, , , , , , , ,, ,
2 1 2 4 5 2 3 4 5 2 3
Ci j
C i j i j i j h k i j h k h kh k i j
tw
t N
CITSA05, Orlando (Florida), 14-17 July, 2005
Results (1)
We checked the accuracy of our
approximated model for balanced
scenarios, for which exact solution
is known
N=4, (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
CITSA05, Orlando (Florida), 14-17 July, 2005
Results (2)
Balanced asymmetric scenarios
N=4, (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
CITSA05, Orlando (Florida), 14-17 July, 2005
Results (3)
Unbalanced scenarios
N=4, (1)=(3)=(5)=1/3
0,1 = 1,0 =0,2 =2,0=0.3
0,3 = 3,0 =0.9
CITSA05, Orlando (Florida), 14-17 July, 2005
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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