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06/12/22 Anue Systems, Inc. www.anuesystems.com 1 v1.0 - 20050426 D ocum entCoverSheet ProjectN um ber PN -3-0062-RV 2 (TIA -921-B) D ocum entTitle Furtherdetailsregarding a new network model Source A nue System s C ontact Name: Chip W ebb Com plete A ddress: 9111 Jollyville Rd Austin, TX 78759 Phone:512-527-0453x102 Fax: Email: [email protected] D istribution TR-30.3 ForIncorporation Into TIA Publication x ForInformation Intended Purpose ofD ocum ent (Selectone) Other(describe)- The docum entto which this coverstatem entis attached is subm itted to a Form ulating G roup or sub-elem entthereofofthe Telecom m unications Industry A ssociation (TIA )in accordance with the provisionsofSections6.4.1–6.4.6 inclusive ofthe TIA EngineeringM anualdated M arch 2005,all of which provisionsare hereby incorporated by reference. A bstract An introduction to a delay and packetlossmodel based on disturbance load probability which isextensible forTIA-921B.Burstinessisdefined and examplesare provided.Then based on the burstinessdefinition variousexample load probabilitiesare derived.A subsequentcontribution will show how to derive packet delay variation and packetlossprobability using the load probability. Telecommunications Industry Association TR-30.3/08-12-022 Lake Buena Vista, FL December 8 - 9, 2008
description
Telecommunications Industry AssociationTR-30.3/08-12-022 Lake Buena Vista, FL December 8 - 9, 2008. v1.0 - 20050426. Overview. Recap last meeting Define a Burstiness Model Define the disturbance Load PDF Simple generators (CBR, Gamma) Bursty case Composite case - PowerPoint PPT Presentation
Transcript of v1.0 - 20050426
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v1.0 - 20050426
Document Cover Sheet
Project Number PN-3-0062-RV2 (TIA-921-B)
Document Title Further details regarding a new network model
Source Anue Systems
Contact Name: Chip Webb Complete Address: 9111 Jollyville Rd Austin, TX 78759
Phone: 512-527-0453x102 Fax:
Email: [email protected]
Distribution TR-30.3
For Incorporation Into TIA Publication x For Information
Intended Purpose of Document (Select one) Other (describe) -
The document to which this cover statement is attached is submitted to a Formulating Group or sub-element thereof of the Telecommunications Industry Association (TIA) in accordance with the provisions of Sections 6.4.1–6.4.6 inclusive of the TIA Engineering Manual dated March 2005, all of which provisions are hereby incorporated by reference.
Abstract
An introduction to a delay and packet loss model based on disturbance load probability which is extensible for TIA-921B. Burstiness is defined and examples are provided. Then based on the burstiness definition various example load probabilities are derived. A subsequent contribution will show how to derive packet delay variation and packet loss probability using the load probability.
Telecommunications Industry Association TR-30.3/08-12-022Lake Buena Vista, FL December 8 - 9, 2008
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Overview
Recap last meeting Define a Burstiness Model Define the disturbance Load PDF
Simple generators (CBR, Gamma) Bursty case Composite case
Next presentation: Putting it all together The Relationship between load and
delay/loss one node multiple cascaded nodes
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Recap: G.8261 Network model
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Recap: Node model
10 cascaded instances of this basic element
Disturbanceload
generator
+Input
packets
Output packets
DisturbancePackets
LinkLatency
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Recap: Test casesScenario Note
G.8261 MEF18
Test Case TM DS1 E1 DS3 E3
Static Load 1 TM2
Step Changes2 TM1
2 TM2 6.1a 6.1b 6.1c 6.1d
Slow Ramp 24 hr3 TM1
3 TM2 6.2a 6.2b 6.2c 6.2d
Network Outage
10 sec4 TM1
4 TM2 6.3a 6.3b 6.3c 6.3d
100 sec4 TM1
4 TM2 6.4a 6.4b 6.4c 6.4d
Congestion
10 sec5 TM1
5 TM2 6.5a 6.5b 6.5c 6.5d
100 sec5 TM1
5 TM2 6.6a 6.6b 6.6c 6.6d
Route Change
1 hop6 TM1
6 TM2 6.7a 6.7b 6.7c 6.7d
5 hops6 TM1
6 TM2 6.8a 6.8b 6.8c 6.8d
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TM1 and TM2 TM1 is composed of packets carrying voice and SMS
messages and is specified as 80% minimum size packets (64 bytes) 5% medium size packets (576 bytes) 15 % maximum size packets (1518 bytes)
TM2 is composed of larger packets representative of a more data-centric network. It is specified as 30% minimum size packets (64 bytes) 10% medium size packets (576 bytes) 60 % maximum size packets (1518 bytes)
The maximum size packets for both TM1 and TM2 occur in bursts lasting between 0.1s and 3 s.
The minimum size packets for TM1 are constant bit rate (CBR).
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A fly in the ointment
Definitions of TM1 and TM2 in G.8261 are incomplete Burstiness is critical and not defined I’ll define one view of burstiness later
And only max-len pkt generators are bursty. Others need to be specified as well.
Assume CBR for simplicity, but there is no loss of generality in the subsequent analysis.
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Burstiness: Definitions
Define as an off and on process Disturbance load generator is off or on
Definitions: Nominal generator load is Lnom
While the generator is on, it creates a burst load Lburst While the generator is off, it generates load of 0% The time that the generator is on is Tburst
The time that the generator is off is Tgap
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Burstiness: Some math Require: Average load over a burst and immediately
following gap must equal Lnom. Therefore:
To complete the burstiness definition Must define either Lburst or Tgap.
One way: Define Lburst as a function of Lnom.
Where LBmin and LBmax represent the minimum and maximum burst load values
Thus there is a linear relation between burst & nominal load
burstburstgapburstnom TLTTL
minminmax BBBnomburst LLLLL
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Burstiness: more math
The only remaining item is Tgap:
Can calculate burst duty cycle as well:
nom
nomburstburstgap L
LLTT
gapburst
burst
burst
nom
TT
T
L
LDuty
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Burstiness Example #1
LBmin=0, LBmax=200%, then: Lburst= 2 x Lnom
Duty is always 50%.
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Burstiness Example #2
LBmin= LBmax= 100%, then: Burst load is constant at 100% Duty decreases as Lnom increases.
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Burstiness Example #3
LBmin= 50%, LBmax= 133%
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Question
What happens if we take LBmin= 0%, LBmax= 100%
??
Burstiness disappears entirely.
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Burstiness:
So: Is this a good way to define burstiness? Yes. It is a good way to set up a model. It is flexible to model a wide variety of
network conditions, while still being mathematically tractable.
We gave three examples (+1) of how the mathematical model can be used.
This shows its flexibility.
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Load Probability Density Function (PDF)
The Load PDF represents the fraction of time that a given disturbance load generator is generating a given short-term load level.
We analyze two fairly simple cases here CBR generator Gamma generator
Then generalize to bursty sources using the foregoing burstiness model
And further generalize to sums of disturbance loads.
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CBR generator
A CBR packet generator always generates the same percentage load, so it has a load PDF consisting of an impulse at the generator’s percentage load.
)();( LxLxfCBR
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Gamma generator
A Gamma packet generator has a load PDF that is based on the Gamma probability density function.
The gamma distribution has two parameters The shape of the distribution The horizontal scale.
We choose k=2 and then substitute =/k=/2 so that the PDF is parameterized by its mean value .
2
2/1 4
);(thus2
let)(
),;(
x
k
xk xexf
k
k
k
exkxf
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Gamma Generator (cont.)
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Load PDF for bursty generators
The PDF of a bursty generator has two parts: An impulse at zero load, which represents the
proportion of time that the generator is off. A scaled copy of the load generator’s PDF which
represents the time that the generator is on. The relative weights of these two parts are
given by the duty cycle of the bursts which we calculated earlier
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Bursty CBR PDF: Example #1
Take a bursty CBR generator at Lnom=50% LBmin = 50% and LBmax= 133%
Calculate that Lburst=92% and Duty=55%.
)92.0(55.0)(45.0
)()()1(
);()()1(),;(_
xx
LxDutyxDuty
LxfDutyxDutyDutyLxf
Burst
BurstCBRBurstBurstyCBR
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Bursty CBR PDF: Example #1 (cont.)
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Bursty Gamma PDF: Example #2
Take a bursty Gamma generator at Lnom=50% LBmin = 50% and LBmax= 133%
Burstiness same as before Lburst=92% and Duty=55%.
x
xBurstBurstBursty
exx
xeDutyxDuty
LxfDutyxDutyDutyLxf
17.2
2
2_
60.2)(45.0
4)()1(
);()()1(),;(
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Bursty Gamma PDF: Example #2 (cont.)
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Composite Disturbance Load PDFs
A composite disturbance load is just a sum of two or more underlying disturbance loads.
Want to calculate the load PDF for such a source (e.g. TM1)
For TM1, the traffic mix is 80%/5%/15%, so a 50% nominal load has 40% load of CBR 64 byte packets 2.5% load of CBR 576 byte packets 7.5% Bursty load of 1518 byte packets
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Composite Disturbance Load PDFs
For max size (1518 byte) bursty generator, we use the same burst parameters as before, LBmin = 50% and LBmax= 133%, which gives Lburst=56% and Duty=13%.
40% CBR64-byte
2.5% CBR576-byte
7.5% Bursty1518-byte
50% TM1CBR Bursty
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Composite Disturbance Load PDFs
We know the load PDF for the two CBR generators
We do not know the load PDF underlying the bursty generator. It is not specified.
Therefore, analyze for both the CBR and Gamma cases TM1 Bursty CBR TM1 Bursty Gamma
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Load PDF: TM1 Bursty CBR
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Load PDF: TM1 Bursty CBR
To calculate the overall PDF, weeed to calculate the PDF of a sum of random variables.
This can be accomplished by convolution.
Use the symbol to represent convolution
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Load PDF: TM1 Bursty CBR
)15.0;(
)05.0;(
)8.0;();(
_
__1
BurstBurstyCBR
nomCBR
nomCBRnomBurstyCBRTM
Lxf
Lxf
LxfLxf
)99.0(13.0)425.0(87.0%)50;(__1 xxxf BurstyCBRTM
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Load PDF: TM1 Bursty CBR
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Load PDF: TM1 Bursty Gamma
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Load PDF: TM1 Bursty Gamma
)15.0;(
)05.0;(
)8.0;();(
_
__1
BurstBurstyGamma
nomCBR
nomCBRnomBurstyGammaTM
Lxf
Lxf
LxfLxf
)5.42(57.3__1 )5.42(66.1)425.0(87.0%)50;( xBurstyGammaTM exxxf
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Load PDF: TM1 Bursty Gamma
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Next steps
Analytical Show how the disturbance load PDF is related
to packet latency and loss at one node Show how this can be generalized to two or
more cascaded nodes Show how Packet Delay Variation PDV can be
predicted using an analytical model Discuss how to modify the disturbance
load model to better suit the needs of next version of TIA-921B.
