Anue Systems Inc 1v1.0 - 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: cwebb@anuesystems.com

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-921-B. Packet delay variation and loss are derived for a typical wire rate switch or router..

Telecommunications Industry Association TR-30.3/08-12-023Lake Buena Vista, FL December 8 - 9, 2008

Load, Delay and Packet LossTIA TR 30.3 meetingDecember 8-9, 2008

Orlando, FL

TR 30.3 Meeting 12/8/2008

Goals• Improve TIA-921-A

• Packet based Model• Correctly emulates impairment with different bit rate, packet size and packet

intervals. Can handle mixed traffic.• Contrast with Time based model where the fixed packet size and packet

interval must be specified. Cannot handle mixed traffic.

• Variable bit rate user data (e.g. MPEG4 video)• Results depend on user packet sizes and when they arrive

• Bidirectional network model (asymmetric)• Enforce bandwidth limits• Better correspondence between high latency and lost packets• Fewer “magic” numbers in the model• Fewer test cases

TR 30.3 Meeting 12/8/2008

Goal: Understand this diagram.

Disturbanceload

generator

+Input user

packets

Output userpackets

DisturbancePackets

LinkLatency

TR 30.3 Meeting 12/8/2008

Review of our previous work• Excellent proposal by Alan Clark to create a new model

• The model takes into account traffic characteristics• Models typical TCP flow characteristics.

• We discussed models used for G.8261• Many similarities between TIA-921 and G.8261• But enough differences to warrant a new effort

• We discussed characteristics of disturbance loads• Burstiness definitions• Disturbance load probability density functions

TR 30.3 Meeting 12/8/2008

Modeling strategies• Top down or bottom up

• Many models are hybrids. • Top down models are constructed empirically

• Observe behavior of the system under various conditions• Select parameter values that fits the observations• The parameters may or may not be physical properties of the system

• Bottom up models are constructed analytically• Analyze how an idealized network component should behave• Parameters for these models are usually physical properties of the

system• For example: buffer size in a router or switch

• Test model components individually and compare the idealized results with actual measurements to verify.

• If there’s a discrepancy, the idealized model must be revised

TR 30.3 Meeting 12/8/2008

Modeling Strategies (cont.)• TIA-921 and TIA-921-A

• A hybrid approach• These models are mainly top down models today

• But have some bottom up characteristics

• Some effects (such as serialization delay) derive from actual physical characteristics of the links

• Other effects (such as core network behavior and link impulse probability) are empirically determined.

• Goal for TIA-921-B is to build on previous work• Improved model should have more parts built bottom up.

TR 30.3 Meeting 12/8/2008

The ultimate bottom-up model• We could build a discrete event simulation of every packet

• But it is too computationally intensive. It requires that we simulate both packets of interest (user packets) and disturbance load packets.

• A 24-hour simulation of a 10 hop network built out of GE switches and operating at 50% load with 1400 byte (avg) packets represents about 40 Billion packets.

• That’s half a petabit.• If you watched HDTV for two years straight, without sleeping, it would

use about that many bits.

• Therefore it is not possible to simulate everything. We must make some approximations.

TR 30.3 Meeting 12/8/2008

Strategy for simplification• Create a statistical model of the disturbance load traffic• Derive the delay and loss characteristics for different levels of

disturbance loads.• Fully simulate all of the user packets• Use a statistical approximation of the disturbance load• Alan indicated he had information on characterizing typical TCP flows.

• Last conference call, we talked about load PDFs• Statistical models of the disturbance packets

• Result is a model that only needs to perform calculations when a user packet is received.• Significant increase in performance and accuracy.

TR 30.3 Meeting 12/8/2008

Review: Burstiness• 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 (chosen randomly)

• The time that the generator is off is Tgap

• Choose a linear mapping for burst load• LBmin – Load during burst when Lnom= 0

• LBmax – Load during burst when Lnom= 100%

TR 30.3 Meeting 12/8/2008

Review: Burstiness Equations

minminmax BBBnomburst LLLLL

nom

nomburstburstgap L

LLTT

gapburst

burst

burst

nom

TT

T

L

LDuty

TR 30.3 Meeting 12/8/2008

Review: Burstiness• LBmin= 50%, LBmax= 133%

TR 30.3 Meeting 12/8/2008

Review: Composite Load PDF• Two CBR disturbance load generators• One bursty gamma disturbance load generator

TR 30.3 Meeting 12/8/2008

Idealized wire rate ethernet switch/router

Disturbanceload

generator

+

Input user packets Output

userpackets

DisturbancePackets

LinkLatency

Store &Forward

EnqueueDelay

DequeueDelay

ClockCrossing

Link BitRate R(bits/sec)

FixedLatency

Buffer SizeF(bits)

TR 30.3 Meeting 12/8/2008

Idealized wire rate ethernet switch/router• Delay for idealized switch has several factors

• Fixed latency• constant (approx 500ns)

• Link latency• Time of flight for the signal (photons or electrons)

• Store and Forward delay (serialization delay)• depends on user packet size (receive packet size/receive link rate)

• Random• Clock crossing delay uncertainty (small, dozens of ns)• Enqueue and Dequeue latency (small, hundreds of ns)

• Queuing delay• Load dependent

• This is the hard part

TR 30.3 Meeting 12/8/2008

Our example load PDF

TR 30.3 Meeting 12/8/2008

Delay and loss from disturbance load PDF• Assume that the queue starts out empty

• We’ll revisit this assumption later, don’t worry

• A user packet of size Si arrives at time ti

• Define: • Step 1:

• How much disturbance load arrived between ti-1 and ti?

1 iii tt

ti-1 ti

Si

TR 30.3 Meeting 12/8/2008

Disturbance Load CDF• CDF is cumulative distribution function for PDF• Is piecewise continuous, monotonically increasing and invertible

TR 30.3 Meeting 12/8/2008

Inverse CDF function (CDF-1)• The inverse CDF function can help

• It is a mapping from uniform random numbers (easy to make) to random numbers of any distribution (hard to make)

• This mapping can be pre-computed and saved in memory (very fast!)UniformRandomNumber

TR 30.3 Meeting 12/8/2008

Delay and loss from disturbance load PDF• A user packet of size Si arrives at time ti

• Step 1: • How much disturbance load arrived between ti-1 and ti?

• Generate by mapping a uniform random number through CDF-1

• Get a load percentage for ti: Li

ti-1 ti

Si

TR 30.3 Meeting 12/8/2008

Divide into three simpler sub-problems• Non-congested

• Load is between 0 and LCONGEST (100%)

• Congested• Load is between LCONGEST (100%) and LDROP

• Overloaded• Load is more than LDROP

• We’ll define LDROP in a moment

TR 30.3 Meeting 12/8/2008

Three simpler sub-problems

TR 30.3 Meeting 12/8/2008

Simplest sub-problem: Overload• Easiest sub-problem: the user packet gets dropped

• This happens if the disturbance load percentage is so high that the queue is completely full when the user packet arrives.

• Define LDROP as the load threshold above which a drop must occur.

• If Li >= LDROP then the user packet is dropped

• If F=16k bytes, R=100Mbit/second, and =1ms, then LDROP=231%

RF

LDROP %100

TR 30.3 Meeting 12/8/2008

Next simplest problem: non-congested• If 0 < Li < 100% then the queue will contain at most one disturbance

load packet when the user packet arrives. The user packet is not dropped in this case.

• Therefore it will be serviced immediately after any in-progress packet• Delay depends on the size of the disturbance packet (known), and

when the user packet arrives relative to the disturbance packet (random). Assume arrival times are uncorrelated -> uniform RV.

• Assume that the disturbance packets are E bits, which means that the maximum amount of time it has to wait (δ) is

• So for this case, the delay is a uniform random value: [0.. δ]

RE

TR 30.3 Meeting 12/8/2008

Non-congested case: Example

δ=110.4us

TR 30.3 Meeting 12/8/2008

Non-Congested case: 50% TM2• TM2 has 30%-64Byte, 10%-576Byte, 60%-1518Byte

• So a 50% TM2 load is 15%,5%,30%. • This PDV histogram is often said to resemble a church or cathedral

TR 30.3 Meeting 12/8/2008

Non-Congested case: Lab measurements• See the characteristic “cathedral”

shape of the PDV?Typical measured PDV

TR 30.3 Meeting 12/8/2008

Congested case• Disturbance load 100% < Li < LDROP

• Seems hard (but actually turns out to be simple)• We assumed that the buffer started out empty

• (remember, we’ll fix this in a few more slides)

• Conservation:• Bits added to queue during i: Li * i * R

• Bits removed from queue during i: i * R

• The difference is the buffer fullness (G)

• And the delay is Gi/R

iiiiii RLRRLG )1(

iii LD )1(

TR 30.3 Meeting 12/8/2008

Adding memory• We assumed that the queue always started out empty

• This essentially means that the time intervals () are independent• It is a reasonable approximation when the buffer size is much smaller

than the number of bits serviced by the queue during . • It’s usually a good approximation for high speed links• But not for low speed links like TIA-921 Access links

• So, to fix that, save the queue state as a variable Gi

• Need an equation to calculate Gi+1

• Change the threshold levels for LCONGEST and LDROP

TR 30.3 Meeting 12/8/2008

Add memory• Adjust the thresholds LCONGEST and LDROP

• Update equation for Gi

(after calculation, Gi+1 is limited to be less than or equal to F)

)%100(i

iCONGEST R

GL

iCONGESTDROP R

FLL

iiiii SLRGG )1(1

TR 30.3 Meeting 12/8/2008

Conclusion

• Statistically modeling the disturbance load allows moreaccurate implementation of TIA-921-B

• Supports• Variable bit rate user data (e.g. MPEG4 video)

• Results depend on user packet sizes when they arrive

• Bidirectional network model (assymetric)• Enforces bandwidth limits• Better correspondence between high latency and lost packets• Fewer “magic” numbers in the model

TR 30.3 Meeting 12/8/2008

Next Steps• TBD