Department of Information Engineering University of Padova, ITALY Performance Analysis of...

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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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


What and Why…

Motivations & Motivations & PurposesPurposes


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


Aim of the study

Providing an approximate performance

analysis in case of

Use of multi-slot packets

Asymmetric and unbalanced traffic matrix


What the standard says…

Bluetooth basicBluetooth basic


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


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


Mathematical Model

System Model for System Model for Ideal ChannelsIdeal Channels


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


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


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


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


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)


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


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


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


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…


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


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


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


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


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


That’s all!

Thanks for

your attention!

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