A Buffer insertion priority mechanism based on the IEEE 802.4 priority scheme

Rochester Institute of Technology

RIT Scholar Works

Theses

Thesis/Dissertation Collections

6-1-1992

A Buffer insertion priority mechanism based on the

IEEE 802.4 priority scheme

Nicholas W. Oddo

Follow this and additional works at:

http://scholarworks.rit.edu/theses

This Thesis is brought to you for free and open access by the Thesis/Dissertation Collections at RIT Scholar Works. It has been accepted for inclusion in Theses by an authorized administrator of RIT Scholar Works. For more information, please [email protected].

Recommended Citation

:{

....

:"..'

...

A Buffer Insertion Priority Mechanism Based

on the IEEE

802.4

Priority Scheme

by

Nicholas W. Oddo

A Thesis Submitted in

Partial Fulfillment of the

Requirements for the Degree of

MASTER OF SCIENCE

in Computer Engineering

Approved by:

Roy S. Czemlkowskl. Ph.D. (Committee Chairman and Department Head) Department of Computer Engineering

JamesE.Hellotls. Ph.D. (Committee Member) Department of Computer Science

Tony Chang. Ph.D. (Committee Member) Department of Computer Engineering

DEPARTMENT OF COMPUTER ENGINEERING COLLEGE OF ENGINEERING

ROCHESTER INSTITUTE OF TECHNOLOGY ROCHESTER. NEW YORK

JUNE 1992

A Buffer Insertion Priority Mechanism Based on the IEEE 802.4 Priority Scheme

I, Nicholas W. Oddo

,

hereby grant permission to the Wallace

Me-morial Library of RIT to reproduce my thesis in whole or in part. Any reproduction will

not

be

for commercial use or profit.

Table

of

Contents

1. Introduction 2

1.1. Goals 2

2. Analysisofthe IEEE 802.4

Priority

Mechanism 5

2.1. Background 5

2.2. Introduction 6

2.3. Functional Description 7

2.3.1.

Priority

Levels 8

2.3.2.AccessClasses 9

2.3.3. Timers 11

2.3.3.1. High

Priority

Token Hold Timer 11

2.3.3.2. Target Rotation Timers 12

2.4.

Meeting

Real-Time Requirements 14

2.4. 1. Alarm Messages 14

2.4.2. Control DataandNetwork Maintenance 15

2.4.3. Routine Data 16

2.4.4. File Transfer 17

2.5.

Analyzing

UtilizationandThroughput 18

2.5.1. General Terms 18

2.5.2. Assumptions 21

2.5.3.Lower

Priority

Levels 22

2.5.3.1.Peak Utilizations 22

2.5.3.2. Actual Utilizations 23

2.5.4. High

Priority

26

2.5.4.1.

Deriving

thePeak Level 6 Utilization 26

2.5.4.2.

Deriving

theGeneral Level6 Utilization 27

2.5.4.2.1. Case 1:

TR(0)

<

TR(2)

<

TR(4)

<CS

₂₈

2.5.4.2.1.1. Case la: 29

2.5.4.2.1.2. Case lb: 30

2.5.4.2.2. Case 2:

TR(0)

<

TR(2)

<

C<TR(4)

₃₀

2.5.4.2.2.1. Case 2a: 31

2.5.4.2.2.2. Case 2b: 32

2.5.4.2.2.3.

Case 2c: 34

2.5.4.2.2.4. Level6 UtilizationModelfor Case 2 34

2.5.4.2.3.

Case 3:

TR(0)<C<TR(2)<TR(4)

36

2.5.4.2.3.1. Case

3a: 37

2.5.4.2.3.2. Case 3b: 37

2.5.4.2.3.3. Case 3c: 39

2.5.4.2.3.4. Case 3d: 40

2.5.4.2.3.5. Case 3e: 41

2.5.4.2.3.6.Level 6 Utilization Model forCase 3 41 2.5.4.2.4. Case 4:

Cs

<

TR(0)

<

TR(2)

<

TR(4)

43

2.5.4.2.4.1. Case4a: 44

2.5.4.2.4.2. Case4b: 45

2.5.4.2.4.3. Case 4c: 45

2.5.4.2.4.4. Case 4d: 46

2.5.4.2.4.5. Case4e: 47

2.5.4.2.4.6. Case4f: 48

2.5.4.2.4.7. Case 4g: 49

2.5.4.2.4.8. Level 6 Utilization Model forCase4 49

2.6.

Analyzing

MediumAccess Delays 51

2.6. 1. WorstCase Level 6 Access

Delay

52

2.6.2. Worst Case Level 4 Access

Delay

53

2.6.3.WorstCase Access

Delay

for Other

Priority

Levels 56

3. Proposed Buffer Insertion

Priority

Mechanism 57

3.1. Introduction 57

3.2. Background 57

3.2.1.

Ring Priority

58

3.2.2. Station

Priority

58

3.2.3. Advantages 59

3.2.3.2. SmallOverhead forMediumAccess 60

3.2.4. Problems AssociatedwithReal-TimeApplications 60

3.2.4.1. Starvation 60

3.2.4.2. Insertion BufferOverflow 61

3.3.FunctionalDescription 61

3.3.1.

Priority

Levels 62

3.3.2.Access Classes 62

3.3.3.High

Priority

Transmissions 63

3.3.3.1. DedicatedInsertion Buffer 64

3.3.3.2.Expedited Propagation 65

3.3.3.3. Algorithm 65

3.3.4. Lower

Priority

Transmissions 67

3.3.4. 1. Partitioned Insertion Buffer 67

3.3.4.2. Starvation Avoidance 68

3.3.4.3. Algorithm 69

3.4.

Analyzing

Medium Access Delays 71

3.5.

Analyzing

Insertion Buffer Delays 73

3.6.

Analyzing

UtilizationandThroughput 74

3.6.1. High

Priority

Transmissions 75

3.6.2. Lower

Priority

Levels 77

4. Conclusion 81

5.

Glossary

86

Abstract

Thefocusofthis thesisistoinvestigatea media access_prioritymechanismfora

buffer insertionnetwork sothatitis bettersuitedforuse inreal-time applications. This

is done

by

_examininga popular_prioritymechanismpresentintheIEEE 802.4tokenbus

standard, andFiberDistributedData Interface

(FDDI)

standard. Mathematicalmodels

forthroughputand

delay

are presentedforthe_{IEEE 802.4 priority}mechanism. These

models arethenusedasabasis for

developing

the_prioritymechanismforthebuffer in

sertionring. Models forthroughputand

delay

arealso presentedforthebuffer insertion

priorityscheme sothat the twomedia accesstechniques_maybecompared.

1.

Introduction

Thereare_manypopular media accesstechniquesfor distributedsystems.

Among

themost popular are

firstcome first_served,

carrier sense multiple access

(CSMA),

token passing,

buffer

insertion,

and slottedrings.

Ofthese,onlyafew havebeen definedorimplementedwitha_prioritymechanismin

mind. This istrue_{for many}reasons. Perhapsthemedia accessprotocoldoesnotlend

itself_easilyto_priority

transmissions,

orperhapstheapplication_runningonthenetwork

isnot_verytimecriticalanddoesnotneedprioritization ofdatatransfers.

Withouta_{prioritymechanism, the}mediaaccessprotocolhasno_wayof_getting

high prioritytransmissions to theirdestinations ina

timely

manner. The framesmust

waitforaccessto themedia

following

the same constraints as_everyotherframe_awaiting

transmission. Thismeansthat_{important data may}havetowaitforaccessto themedia

becauselessimportantdata is

hogging

thebandwidth. One_waytoavoidthisproblemis

by

assigningall_outgoingframesa priority. Basedonthe definitionofthe_priority

mechanism,the_priorityassignedtoaframewill

help

dictatewhenitgains accessto the

medium. Lower priorityframesyieldto thetransmissionofhigher_priorityframes.

1.1. Goals

Thegoals ofthisthesisareto

studya well

designed,

documentedandaccepted_{prioritymechanism,}

and usethisknowledge in

developing

a_prioritymechanismforabuffer

insertionprotocol.

The_prioritymechanismthatwillbe studiedis definedintheIEEE 802.4tokenbusstan

dard. _{This priority}mechanismisalso_verysimilartothatusedintheFiber Distributed

DataInterface

(FDDI)

standard. Section2gives afunctional descriptionofthe_priority

scheme. Itthengoes onto

develop

modelsforthroughputand media accessdelay.

Thesemodelswillaid inboth_{understanding}the_{IEEE 802.4 priority}mechanisms,andin

developing

a similar_prioritymechanismforthebuffer insertionprotocol.

Thebuffer insertionprotocolischosen as a candidateforthedevelopmentof a

prioritymechanismbecauseofitsuniquenessas a mediaaccess_protocol,andits

inability

tomeetreal-time constraintsunder

heavy loading

conditions. Without anytypeof prior

ity

mechanism,thebuffer insertionprotocoldisplaysa_{steady increase in}media access

delay

asthethroughputofthe systemincreases. Thisisnot_{satisfactory for}real-time_ap

plicationsthatmustguarantee a maximum media access

delay

and

delivery

timefora

certainmessage class. In_{addition, the}buffer insertionprotocol allows forstarvationto

occur. Thiswill occur whena nodeisprohibitedfrom_accessingthenetworkbecauseof

the

heavy

usagefromothernodes. Starvationisalso_{unsatisfactory in}real-timedistrib

uted applications.

A well-designed_prioritymechanismshould allowforgracefuldegradationof

thecommunications system. Thatisto say,whentheofferedloadto thenetwork ex

ceedsitsbandwidthcapabilities,moreimportantmessages(messagesofhigher_priority)

willbethefirstto reachtheirdestinations. Less important datawillbethefirstto suffer

dueto thehigh load. Ifthe loadwastocontinue

increasing,

theperformance ofthenet

work woulddegrade inagraceful way.

Ignoring

thenegative remarks aboutthebuffer insertionprotocol stated_above,it

does have_many

intriguing

featuresthatmakeitanattractive choiceforreal-time sys

tems. This_{is especially}truewithrespectto token_passingprotocols. Theoverheadin

volvedin_{token passing, token regeneration,}andduplicatetoken

detection,

isnolonger

neededinabuffer insertion ring.

Also,

thebufferinsertionalgorithm allows formultiple

transmissions tobe_occurringsimultaneously. Thisiscalledspatial_reuse,and allowsfor

throughput_exceedingthe_capacityofthemedia. Bothcharacteristicsamounttobetter

useofthemediaforalltypesoftransmissions. In other_words,

looking

attotalnetwork

throughputisattractivetoreal-time_{applications,}butthemediaaccessdelaysassociated

withthesehighthroughputsaretheproblem.

Section3gives afunctional descriptionofthe_prioritymechanismproposed for

thebuffer insertionprotocol. Thisis followed

by

thedevelopmentof mathematical mod

elsforthroughputandaccessdelay. The finalsectiondiscussestheresults ofthebuffer

insertion prioritymechanism when comparedto themodelsfortheIEEE 802.4tokenbus

priorityscheme.

2.

Analysis

oftheIEEE 802.4

Priority

Mechanism

2.1. Background

Priority

mechanismsin_{loosely-coupled distributed}systems_playasignificantrole

in howa network will performunderhigh

loading

conditions.

Any

mediaaccessproto

col

(MAC),

even onethatdoesn't incorporatea_{prioritymechanism,} canperformsatisfac

torily

withintheoperational constraintsofthemedia. Whatisconsideredhere ishowa

network willperform whentheofferedtransmissionload beginstoexceedthe available

bandwidth fora giventime. Performanceover a network whose media access protocol

doesnotincorporate_prioritytransmissionswillsuffer. This is becausetheprotocolhas

no_wayof

discerning

important datafromunimportantdata. Data istransmittedina

first-come-first-served fashion. Ifthenetworkis

being

usedinareal-time application

suchasprocess_control,theconsequences couldbe disastrous. Amedia access_priority

mechanism understands which ofthedata queuedfortransmissionisthemosttime criti

cal,andwhichisnot. More importantdatawillbetransmittedsoonerthanlessimportant

data.

The IEEE 802.4standardincorporatesamediaaccesscontrol

(MAC)

protocol

thatusesa_prioritytransmissionmechanism. TheMAC layer isa sub-layerwithinthe

boundsoftheOSIarchitecture'sdatalink layer. A bus

topology

isusuallyassociated

withtheIEEE 802.4_prioritymechanism.

This, however,

does nothavetobethecase.

FDDIalso uses a_prioritymechanismthatis_verysimilarto theIEEE 802.4protocol, and

FDDIisatoken_passing

ring

network. Itis safeto_saythat the_prioritymechanism

being

detailed inthis section couldbeusedin anytoken_passingnetwork. Itisnotdependent

on_{the underlying}physicaltopology. Althoughthetokenbus

topology

is discussed

throughout the

document,

itis importanttorememberthat theprotocolis justas_easily

implemented ina

token-passing

ring

network.

The IEEE 802.4tokenbusexpects stationstobeconfigured_alongalinear

bus,

buttreats thebusas alogical ring. Itisimportantto notethatthephysical_orderingof

thenodes onthebusdoesnot affecttheorder oftokenpassing. Since everystation con

nectedto thebus hears_everytransmission,the tokenis_usuallyaddressedtoa specific

nodethatisthenextlower deviceaddress. Thestationwiththelowestdeviceaddress

obviouslyhastoaddressthetokento thestation withthehighestdevice address. The

specification ofthephysicallayerisnotimportant forourpurposes,butthebus_{is usually}

made_up of75-ohm broadbandcoaxial cable. Transmissionrates of

1,

5,

and 10

Mbits/secare possible.

2.2. Introduction

The IEEE 802.4tokenbusnetworkhasbecomeastandardinthe industrial auto

mationindustry. Thereason for itsacceptance liesinthreemain areas. Theseareas are

stability,

reliability,

and a_prioritymechanism.

The IEEE 802.4 prioritymechanismallows anindustrial networktomeetrigidreal-time

requirements.

Also,

itallows additionalbandwidthtobeusedfortrafficassociated with

applicationsthatare nottime critical, orwhose real-time requirementsarenot as strin

gent. Thisisdone

by

allowingstationsto accessthemedium_{synchronously}andasynch

ronously. Forhigh_{priority transmissions,}eachstationhasa guaranteedamountoftime

foreachtokenrotationinwhichit maytransmit. Thisisguaranteedbandwidthwhatever

the totalcommunicationload. Forlower_priority

transmissions,

each station_mayor_may

notreceive an_opportunityto transmitforeach rotationofthetoken.

Gaining

accessto

themedium_{for lower prioritytransmissionsisbasedupontheoverall communication}

load.

The

following

sections

discuss

theIEEE _{802.4 priority}mechanism. Afunctional

descriptionofthe_prioritymechanismis_given, followed

by

mathematicalmodelsthat

analyzetheeffectsthat the_prioritymechanismhasonthroughputandmediaaccess

delay.

2.3. Functional Description

The IEEE 802.4 prioritymechanismis describedfromafunctionalstandpointin

thissection. Thedescription breaks downthe_prioritymechanismintothree major

groups;

priority

levels,

access_classes,

andtimers.

Eachofthese areasandtheirinterrelationships is discussed.

Acompletedescriptionofthe_prioritymechanismispresentedbelow instructured

English. Thereaderisencouragedtoreferto this top-leveldescriptionwhile_{reading lat}

erthesections_explainingtheusage ofthehigh_prioritytokenholdtime andtargetrota

tiontimers. The IEEE 802.4prioritymechanismisnowpresented.

1. waitfortoken

2. starthigh prioritytokenholdtimer

3. transmitlevel 6 datauntilhigh prioritytokenholdtimerexpires orthereis

no morelevel 6 datatobetransmitted.

4. _{stop high priority}tokenholdtimer

5. passthe token

internally

toaccess class4

6. calculatethelevel 4token

holding

time

by

_storingthe_remainingtime lefton

the level4targetrotationtimer

7. restartthelevel4targetrotationtimer

8. ifthelevel4token

holding

time isgreaterthan0thentransmitlevel 4 data

untilthelevel4token

holding

timeisreached orthere isno morelevel 4 data

tobetransmitted

9. passthe token

internally

toaccess class2

10. calculatethelevel2token

holding

time

by

_storingthe_remainingtimelefton

thelevel2targetrotationtimer

1 1. restartthelevel2targetrotationtimer

12. ifthelevel2token

holding

time isgreaterthan0thentransmitlevel2data

untilthelevel 2token

holding

timeisreached orthereis no morelevel 2 data

tobetransmitted

13. passthe token

internally

toaccess class0

14. calculatethe level 0token

holding

time

by

_storingthe_remainingtime lefton

thelevel 0targetrotationtimer

15. restartthelevel 0targetrotationtimer

16. ifthelevel 0token

holding

timeis greaterthan0then transmitlevel0data

untilthelevel0token

holding

timeisreached orthereisno morelevel0data

tobetransmitted

17. passthetokento thenext stationinthe

ring

18. repeat

2.3.1.

Priority

Levels

The IEEE 802.4 prioritymechanismoffersfour priority levels atwhichdata_may

betransmitted. _{These priority levels}arenamed

0, 2, 4,

and

6,

with 6

being

thehighest

priority. A station connectedtoan802.4tokenbus_maybeconfiguredtouse _anycombi

nation ofthese_priority

levels,

orno_prioritymechanismatall. Astationnotconfigured

tousethe_prioritymechanism_{automatically}

defaults

to

transmitting

its framesat_priority

level 6. Whatevera station's_{configuration,}itcancoexist withotherstations onthebus

usingdifferentprioritylevelconfigurations. Forthepurposes ofthis

discussion,

itisas

sumedthat thestations are configuredtouseallavailable_prioritylevels.

2.3.2. AccessClasses

Access classes aretheentities responsiblefor servicingeach_{priority level}within

a single station. Oneaccessclass existsfor every priority level forwhichthe stationis

configured. For_example,astationconfiguredtouseall four_prioritylevelswillhave

fouraccess classes.

They

arenamedaccessclass

0,

2, 4,

and

6,

afterthe_{priority levels}

that

they

service.

Accessclassescanbethoughtof as virtualsubstations. Eachaccess classpresent

inastationhasitsown queueto store_outgoing

frames,

receivesthetoken,transmits

frames,

andtransmits the token.

However,

forastation configuredtouse allfourprior

ity

levels,

onlyaccess class6receivesthetokenfromphysical_medium,and_onlyaccess

class0transmitsthetokenontothephysical medium. Atall othertimes the tokenis be

ing

passed

internally

withinthe station. Figure 1 showsthisforabustopology.

6 4 2 0 6 4 2 0 6 4 2 0

r -? ->

r

-? n r ? -.

A

?

?

1

? 1 ? T

L

-? - L -?

-i

Figure 1

-Tokenrotationforthe_{IEEE 802.4 priority}schemeisaccomplished_bypass

ingthe token toeachaccess class(orvirtual_sub-station)within anodebe fore_transmittingitacrossthephysicalmediato thenextdevice inthelogical

In Figure

1,

thepathofthe tokenisshown

by

thedotted lineswith arrows. The

large boxesrepresentphysicalstations onthebus. Eachbox is divided into foursmaller

boxestorepresentthevirtualsubstations oraccess classeswithineach station. Eachac

cessclassis labeledwithits priority

directly

above it. Notice howaccess class

6,

the

highest priority access_class,receivesthe tokenfirstwithin eachstation. Itthenpasses

thetoken

internally

toaccess class4. Accessclass4

internally

passesthe token toaccess

class

2,

and so on. Whenthetokenis

finally

transmitted fromaccess class

0,

itisphysi

callysent onthemediato thenext stationinthering.

Whenan accessclassreceivesthe_token,andhasdatato_transmit,itneverpasses

the frame

internally

tothenextlower priorityaccess class. Eachaccess class withina

stationtransmits data

directly

ontothephysicalmedium.

Similarly,

each access class

maintainsits own queuesfor

holding

data pendingarrival ofthe token. Queuesarenot

shared_amongaccess classes.

2.3.3. Timers

Oncethe tokenisreceived, anaccess classuses adedicatedtimerto trackhow

long

data

transmission,

atits_priority

level,

canlast.

Depending

onthe_{priority level}as

sociated withtheaccess_class,theaccess class usesoneoftwo typesof_timers;

ahigh_prioritytoken_{hold timer,}

or atargetrotationtimer.

Theamount oftime thatanaccess classisallowedto transmitis determined

depending

onthe_prioritylevelassociatedwithit. Lower priorityaccessclasses usetargetrotation

timers to

determine

transmission

duration,

while access class6usesthe_{high priority}to

kenholdtimer.

2.3.3.1. High

Priority

Token Hold Timer

Wheneveralevel6access classreceivesthe_token,theamount ofdatathatwillbe

transmittedbeforethetokenispassedisdetermined

by

one oftwo_things;

1. theofferedloadatthatpriority

level,

2. ortheduration ofthehigh_prioritytokenholdtime.

Inotherwords, thehigh prioritytokenholdtimerplaces an upperboundontheamount

ofdatathatalevel 6access class_maytransmitpertokenrotation. Whenthe tokenar

rives,

the_{high priority}tokenholdtimerisstarted, anddatatransmissionbegins. When

the timer expires, thecurrenttransmissioniscompletedandthe token ispassed

internally

to thenextlower priorityaccess_class, ortothenext stationifno other access classesex

ist. Iftheaccess classruns out ofdatatotransmitbeforethehigh prioritytokenhold

timer_expires,the timerisstopped andthe tokenpassed onward. Ifthe timeneededto

transmittheframeonthefrontofthequeueisgreaterthanthe_{high priority}tokenhold

time,onlyoneframewillbetransmittedpertokenrotation.

The_{high priority}tokenholdtimeisa configurable parameterintheIEEE 802.4

standard. It maybeconfigured

differently

_{for every}stationinthenetwork_usingaccess

class

6,

but usuallyall stations_usingaccess class6 are configuredforthesameduration.

Thismeansthat_everynode onthecontrol networkwillhavea reservedbandwidth in

which _{it may}transmitlevel6 frames.

Having

a reservedbandwidthmeansthatwhatever

thecommunications

load,

_everynode cantransmitlevel 6framesuponthearrival ofthe

token. Thiswillbe guaranteed. Theconfigurationofthehigh_prioritytoken_{hold timer,}

forreal-time_networks,isdiscussedinsection2.4.

2.3.3.2. Target Rotation Timers

Theamountoftimethe _{lower priority}accessclasses are allottedfor datatrans

missionarealso governed

by

timers. Thetargetrotationtime isthemaximumtoken

rotationtime thatcan occurinorderfordatatransmissionto takeplacefrom an access

class.Withinastation,these timersareusedinall access classes exceptaccess class

6,

which usesthehigh_prioritytokenholdtimertodeterminetransmissionduration. When

atokenarrives atalower_priorityaccess_{class, the}amountoftimeleftbeforethe target

rotationtimerexpiresisnoted. Thistimeiscalledthe token

holding

time. Afterthe to

ken

holding

timeis saved, thetargetrotationtimerisresetand restarted. Ifthetoken

holding

timewas notedasgreaterthan

0,

the access classisallowedtotransmitdata for

the durationofthetoken

holding

time. Ifthetoken

holding

timeexpiresinthemiddle of

adata

transmission,

thenthattransmissioniscompleted. Iftheaccess classdoesnothave

anymore datato_transmit,but itstoken

holding

timehasnot yet_expired,the tokenis

passed early. Ifthe access class'stoken

holding

timewas

0,

thenitstargetrotationtimer

expired

before

thereturn ofthe

token,

and nodatatransmissionisallowedfromthatac

cess classforthat tokenrotation.

Thetargetrotationtimesfor_prioritylevels

0,

2,

and

4,

are configurable parame

tersintheIEEE 802.4 standard.

They

_{may be}configured

differently

for everystation on

the token

bus,

_{but usually}all stations_usinga particularaccess class are configuredfor

the sameduration.

Also,

thehigher_priorityaccess classes are_normallyconfiguredwith

largertargetrotationtimes. Thismeansthat

they

haveahigher probabilityoftransmit

ting

pertokenrotation.

Itis importantto notethat the targetrotationtimefora particularaccess classde

terminesthemaximum amount ofbandwidthavailabletoallnodes

transmitting

thatlevel

framepertokenrotation. Theactualbandwidthavailablefor_{any priority}level is depen

dentonthenumberof other_{priority frames}thataretransmitted.

Tounderstand_whythisisso,let's firstassumethatnetworktraffic ismade_upof

asingle_{priority level}otherthanlevel 6. Thismeansthatthetargetrotationtimealone

determinesthe totalbandwidthavailableforthis_{priority level}framepertokenrotation.

Ifa singlenodetransmitsforitsmaximumtoken

holding

time,thenno other nodes can

transmitforthattokenrotation.

Every

other nodeonthenetworkwillreceivethetoken

afteritstargetrotationtimerhasexpired.

Now,

let'sadd networktraffic_comprising of

datathatisofhigherpriority,

including

level 6frames. Theavailablebandwidthofour

priority level may

drop

to0ifenoughhigher priority levelframesaretransmitted. Ifthe

prioritylevelinquestionis level

2,

then_prioritylevel6traffic,prioritylevel4traffic,or

a combinationofthe two_mayusetheavailable_{priority level 2}bandwidth. _{If priority}

level4transmissionsare_usingtheentirelevel4targetrotation_time,thennobandwidth

willbe left for level2

transmission,

whateverthelevel 6traffic. Thisisassuming, of

course,thatthetargetrotationtimefor level4is largerthan thatfor level 2.

Similarly,

level 6traffic_mayuse available level2bandwidth _{if many}nodeshave level 6 framesto

transmit.

2.4.

Meeting

Real-Time Requirements

The_prioritymechanisminherent intheIEEE 802.4standard_maybeconfigured

sothatitworks_{efficiently for many different networking}applications. Themain con

cernofthissectionis todetail howthe_{high priority}tokenholdtimeandthe targetrota

tiontimes _maybeconfiguredto meetreal-time requirementsacrossthecontrolnetwork.

Theparticularareaofreal-timecommunicationdiscussed inthissectionisprocess con

trol. The networkdataassociated with process controlisbroken downinto categories.

TheconfigurationoftheIEEE802.4_prioritytimersis discussed foreachcategory.

2.4.1. Alarm Messages

Alarmmessages are_usuallyassociated withmalfunctionsintheprocess control

equipment. Messagessuchasthesearegeneratedfromasingleboardcomputerthat

comprisesasingle station onthecontrol network. Thereare_usuallyno external storage

or

display

peripherals associatedwith it. Inorderforthealarm messagetoreachthe_op

erator, themessagemustbetransmittedontothe controlnetwork. Thealarm messageis

destined foranodeor_groupof nodesthatwill respond

immediately

to themalfunction.

Partofthecontrol network willbeplacedinafail-safe_condition,andplantoperators

willbe informedthroughouttheplant on

display

devices. Ifalarm messagesare

lost,

or

take a

long

time toreachtheir

destinations,

adangeroussituation_mayresult.

Sincealarm messages are soimportantintheprocesscontrol_environment,

they

shouldbetransmittedas_{priority level 6 frames. This}meansthat_everynode onthecon

trolnetworkwillhaveareservedbandwidth inwhichit_maytransmitalarmmessages.

The durationofthe transmissionis determined

by

the_{high priority}tokenholdtime. Ev

erynode cantransmitalarmmessagesuponthe arrivalofthe_token,whatevertheload on

thecommunication network.

2.4.2. Control DataandNetwork Maintenance

Afteralarm_messages, data

directly

relatedto theprocess

being

controlledisthe

nextmostimportant groupof messages onthe controlnetwork. Thisdata_maybetrans

mitted_{synchronously}or_{asynchronously}betweennodesonthe systemtomaintain con

troloftheprocess. Ofequalimportanceis network maintenance. Networkmaintenance

messages consist ofmessagesthatallow nodesthroughoutthenetworktotrackthe acces

sibilityof variousdestinations. If important datamustreach a particular

destination,

but

the destination is downorforanother reasonis

inaccessible,

thenthe source ofthe trans

mission must actappropriately.

Typically,

thismeans _sendingan alarmmessage. Net

work maintenance messages alsohandletheaddition anddeletionof nodesto thelogical

ring

dynamically. Thenetworkdoesnothavetoberebooted_everytimeanode isadded

to the logical

ring,

anddoesnot crash_everytimeanode isremoved. Withoutnetwork

management messages

being

handled

efficiently,the control network_mayfail.

Transmissions containing data importantforthecontrol oftheprocess should also

be highpriority.

Applications

_runninginvarious stationsinthenetwork_maybe_using

control variablesforvarious purposes. Someofthese control variables_maybecollected

outsidethestation

doing

thecalculations andthereforemustbetransmitted acrossthe

control network. Thecontrol variables_maybeupdated_{synchronously}orasynchronous

ly. _{In any}case, thisdata is very important in

keeping

theprocessunder control and must

be delivered ina

timely

fashion.

Priority

level 4 isusedformessages_relatingtocontroldataandnetwork manage

ment. Besidesthealarm messages

being

transmittedatlevel

6,

thecontrol and network

managementtransmissionswillbethe_{highest priority}transmissionsonthecontrolnet

work. This makes_sense,sincethesemessages arethebackboneofthecontrolprocess.

Sincethe number ofalarmmessages

being

transmittedisexpectedtobe_verysmall

(systemmalfunctions shouldbe

infrequent),

controldataandnetwork maintenancewill

usuallybethehighest priority datapresent onthe control network.

2.4.3. Routine Data

Networktraffic categorizedasroutine encompassestransmissionsthatareimpor

tanttothecontrolprocess,butnotastimecriticalascontroldataor network management

data. Anexample ofthiswouldbenetworktraffic associated withconsoledisplays.

Op

erators_mayattemptto

display

various piecesofdataon a

display

device.

Doing

so usu

allymeans_collectingdatafromother stationsinthecontrolnetworkthatare responsible

for maintainingthedisplayedvariables.

Therefore,

thisdatamustbesent acrossthecon

trolnetworkto stations with

display

devices.

Furthermore,

the

display

mustbeupdated

as valuesinthecontrol network change. Thismeansthata periodicflowofdatato the

station

housing

the

display

must occur. Inother_{words, the} dataonthe

display

willbe

updated atsome predetermined periodic rate.

Anotherexample of an applicationthatwould_relyontransmissionsofthisprior

ity

maybeahistorical device. Thiswouldbea station onthecontrol networkresponsi

ble for_{collecting data}onvarious control variablesthroughoutthenetwork. Anoperator

could examinethetrendsinthe

data,

athisconvenience,andfindpossiblefaultsorim

provementsthatcouldbemadeto thecontrol process. Thisinformation isnot criticalto

maintainingthe process,butmust stillbe deliveredcloseto the_samplingrate ofthehis

toricaldevicetomaintain_validityof_anystatistical analysisthat_{may be done.}

Priority

level 2 isusedformessages relatedtoroutinedata. Thisdataisnot as

timecritical aslevel 6and4 transmissions, butshould stillbegiven_priorityoverthe_op

erations described inthenextsection.

2.4.4. File Transfer

The lowest prioritytraffic onthecontrol networkis associatedwithfiletransfer.

Filetransfersoccurwhen a nodeonthecontrol networkis booted.

Many

nodesdonot

contain _anyexternal storagedevicestoloadtheirsoftwareintomemory.

Instead,

they

areinstalledwithboot PROMsthatallowfordownloadacrossthecontrol networkfrom

a servernode_containingallthesoftware. Thistypeoftransferisassociated withlarge

framesoverthetimeittakestocompletethedownload. Atransfersuch asthisat ahigh

priority levelcould endangerthecontrol_process,becausecontroldata_maynotbetrans

mittedbeforetheirhard

deadlines.

Priority

level 0isusedformessages relatedto filetransfer. Theamount oftime it

takes todownloada node overthe control networkisnot asimportantas_maintainingthe

process

being

controlled.

2.5.

Analyzing

UtilizationandThroughput

Theutilization and_queuing

delay

of networktraffic associated withaparticular

prioritylevel is mathematicallymodelledinthissection. Thesemodelswill representthe

functional descriptionsof each_{priority level already}given. Beforethiscanbe

done,

however,

some mathematicalfoundationmustbediscussed. Themodel presentedistak

enfrom [5]. Thismodel willbeusedas abasetobuildother_{models, specifically}the

modelofthebuffer insertionprotocol presentedlater. Thiswill allowthe twoprotocols

tobe_easilycompared.

2.5.1. General Terms

Before explainingthedetailsof_{the model,}somebackground

terminology

must

bepresented.

Utilization, U,

isthe fractionoftimedata frames aretransmittedontothe

control network.

Throughput,

S,

isthetotalnumberofdata bitsreceivedatadestination

persecond expressed asafractionofthebandwidth. Thesetermscanbeusedtodiscuss

network widetrends _concerningall stationsonthecontrol_network,aswell as specific

stations.

Ui

andS.aretheutilization andthroughputof_prioritylevel

i,

where isequalto

0,

2, 4,

or6. _{The relationship between S}and U isgiven

by

St

=_atUi

where

a,= Tt

{Ti

+

Toh)

Ts

isthemeanframe lengthof_prioritylevelitransmissions. Iftransmission time

ismeasuredin bit times, ortheamount oftime ittakes totransmitone

bit,

then T.isalso

the transmission timeof_priorityleveliframes. Forexample,a 5byte framewilltake40

bittimes to transmit. Themeanlengthof aframe doesnotinclude_{any header}ortrailer

information.

Toh

isthenumber of overheadbits inaframe. Thisvalue isthesamefor

all_priority levels. It isalso the timeittakesto transmittheoverhead portionof_any

frame. Figure2portrays atypicalframe

format,

_showingthe

header,

_trailer,anddata

portions oftheframe.

PREAMBLE SD FC DA SA DATA FCS ED

Figure2-Theframe format_oftheIEEE802.4MAC_sublayeris_made

upof12 to 14bytesof overhead. Thisis dueto thepreamblewhichcanbe 1,2,or3by

tes_dependingonthe_capacityofthebus. Thedatafield_maycontain_any wherefrom 0to 1014 bytesofinformation.

The frameoverhead consists ofthe preamble,startdelimiter

(SD),

framecontrol

(FC),

destinationaddress

(DA),

source address

(SA),

frame check sequence

(FCS),

and endde

limiter(ED). Thestart

delimiter,

framecontrol, andenddelimiterareonebyte fields.

The destinationaddressandsource addressaretwobyte fields. Theframe checkse

quenceis athreebyte field. Thepreambleis

1, 2,

or3 bytes

depending

on whetherthe

capacityofthebus is

1,

5or 10Mbits/secrespectively. Thespecific_meaningof each

field isnotimportant forthisanalysis. Itis just importanttonotethatthesefieldsare

whatmake_upthevariable Toh. Thedata fieldinFigure2changessize

depending

onhow

muchinformationanapplicationhasto transmit. _{It may}be0to 1014bytes insize.

a,

isa factor_relatingthedataportion of aframeto theoverall sizeofthe

frame,

including

the

headers

andtrailers. Fromthe earlier_{equation, the}difference between

throughputand utilizationisevident. Utilizationisa measureofthe totalframestrans

mitted. Throughput isameasure ofthedatareceived,excludingoverhead.

Anothermetricthatisusedtoevaluatethestate ofanetworkistheoffered load.

The offered

load,

G,

isthenumberofdata bitsgenerated

by

allactive stations persecond

expressed asafractionofthechannelbandwidth. More _simply,it istheamount ofdata

generated,

by

all_nodes, for_{transmission,}overagiventime. Ifthenetworkcanhandle

theamountofdata

being

generatedfor_{transmission,}then the offeredloadwillequalthe

utilization. Ifthenetworkcannothandletheamountofdata

being

generatedfortrans

mission,thentheofferedloadwillbegreaterthantheutilization. Likeutilizationand

throughput,

Gt

representstheoffered load for priority levelitransmissions.

G/

istheof

fered loadof_prioritylevel iwhenthe offeredload isconsideredtobeall ofthebits gen

eratedperunit_time, notjustthedata bits. Inother_words,

Ui

isto

G/

asS. isto

Gr

T,

representsthemeantoken_passingtimebetweentwo stations onthelogical

ring. Thistime includesthestation

delay,

thehead-end

delay,

the transmitterand receiv

ermodem

delays,

the token transmissiontime,andthepropagationdelay.

If,

forexam

ple, thereareAfstations on_{the ring, then}

NT,

wouldbethe minimum amount oftime

neededforthe token tocirculatetheentire network. Thisminimumtokenrotationtime

occursifno station onthe

ring

transmits_anydata. Theminimumtokenrotationtime is

represented

by

C0. C representsthemeantokenrotationtime. Thisisthemeantime

betweenthe token_arrivingat a particular access_class,and_returningtothesameclass.

Timevalues associatedwiththe_{high priority}tokenholdtimeare represented

by

thesymbol Tt.

Similarly,

thetargetrotationtimesforaccess classes

4, 2,

and0are repre

sented

by

thevariables

TR,(4), 1^(2),

and

TR(0)

respectively.

Lastly,

TJi)

representsthe

amount oftimeaccess classiholdsthetokenafteritshigh prioritytokenholdtimeror '

targetrotationtimerhasexpired. Rememberthatas

long

as atransmissionbeginsbefore

the timer_expires, itwillalways complete. Forexample,thevalueof

TJ6)

rangesfrom 0

tothetransmission timeofthemaximum sized

frame,

depending

on whenthehighprior

ity

tokenholdtimerexpires.

2.5.2. Assumptions

Aswith_anymathematical_model,certain_simplifyingassumptions needtobe

madeto

keep

themodeltractable. The

following

are assumptionsmadeforthemodel

being

presented.

errorfreeoperation ofthenetwork

noadditions ordeletionsofnodesfroma_runningsystem

alargenumberofnodes

the targetrotationtimesare greaterthan theminimumtokenrotationtime

thetargetrotationtimesarewellseparated anddecreasewith

decreasing

priority.

Theseassumptions willbecomeclearerasthemodelispresented. A largenum

berof nodesmustbeusedbecausethemodel

being

presentedis baseduponthemean

kenrotationtimeofthenetwork. Forthemodeltobeprecise, theactualtokenrotation

timemustremain_verycloseto themeantokenrotationtime. This isaccomplishedwhen

alargenumberofnodes existinthe system.

Targetrotationtimesmustbeseparated

by

_{many bit}timessothattheutilization

andthroughputgiven

by

themodelisclearfora particular_{priority level. Target}rotation

times tooclose willresultinutilizationsthatare a combination oftwo ormore_priority

levels.

2.5.3. Lower

Priority

Levels

Theutilization models ofthe_{lower priority levels}arediscussed first. Thesemod

els representtheutilizationsoflevel

4,

level

2,

andlevel 0transmissions. These are pres

entedfirstsince

they

are moreintuitiveandthereforeeasiertounderstandthan themodel

representingtheutilization characteristicsofaccess class6.

Normally

the targetrotationtimersof each access classareconfigured sothat

TR(0)

<

TR(2)

< TR(4).

This, however,

doesnothavetobethecase. Thetimers_{may be}

configuredsothat_anyaccess classisgreater orlessthan_anyother. The only criteriabe

ing

that

they

arewell separated. Forthe

following

discussion,

we willassumethat

TR(0)

<

TR(2)

< TR(4).

2.5.3.1. PeakUtilizations

Examining

each_{priority level}separately, itiseasytoseethattheutilization ofa

particular_{priority level increases}astheofferedloadofthat_{priority level}increases. This

will occur untilthemeantokenrotationtimeexceedsthe targetrotationtime forthatac

cess class.

Assuming,

foramoment,thatall networktraffic iscomprised of a single

priority

level,

i,

andthat the tokenrotationtimeisequalto thetargetrotationtime for

that_priority

level,

then theutilizationisatitsmaximum andisgiven

by

7XQ

-C,

whereirepresentsthe_prioritylevelof

4, 2,

or

0,

again where

Ce

istheminimumtoken

rotation_timer, andPrepresentsthepeak utilizationof_{priority level i.}

Any

wastedband

widthisbecauseoftheoverheadinvolvedwith_passingthe_{token,otherwise,}all ofthe

bandwidthavailableto_{priority level}iis

being

used.

Continuing

the assumptionthatall networktraffic is

being

made_upof a single

lower_priority

level,

the

following

statementabout utilization_maybemade. Theutiliza

tionofa_prioritylevelmustbethe minimum oftheofferedloadofthat_priority

level,

and

thepeak utilization ofthat_{priority level. In}otherwords,

U,=MIN(G,i,

Pt)

ifnetworktrafficismade_upof_onlyaccessclassitransmissions.

2.5.3.2. Actual Utilizations

Theprevious section explained whathappenstotheutilizations ofthelower

priorityaccess classes whenallnetworktrafficbelongstoa single_prioritylevel. Howev

er, thenetwork_usuallyhasamixtureof_{many differentpriority}levels

being

transmitted

ina singletokenrotation. Networktrafficofahigher priority levelwill usebandwidth

thatwouldotherwisebeavailableto_{lower priority}transmissions. For_example,when

themeantokenrotationtimeincreasesabovethelevel 4targetrotation_time,the level4

utilizationbecomes dependentontheutilizationofthe_{higher priority level (level}

6)

and

thetokenrotationtime ofanidle bus.

Therefore,

whenthe tokenrotationtimereaches

the targetrotationtimeof a particular_priority

level,

theutilization forthat_{priority level}

willhavereached alocalmaximumforthatparticularcombinationof offeredloads.

Only

when networktraffic consists ofthe_prioritylevelinquestioniswhentheutilization

ofthe_prioritylevelreachesitspeak

described

intheprevioussection.

Therefore,

theuti

lizationwhenthemeantokenrotationtimeequalsthetargetrotationtimeof aparticular

prioritylevelwill alwaysbetheminimumoftheofferedloadofthat_{priority level}and

thepeakutilization ofthat_prioritylevelminusthecombinedutilizations ofthehigher

prioritylevels. Notethattheutilizationat_{any priority}levelcan neverbecome lessthan

zero. Iftheutilizationfromahigher_priorityleveluses all ofa particular_prioritylevel's

bandwidththen theutilizationforthat_{priority level} remains zero anddoesnot gonega

tive. Itshould alsobe notedherethatnetworktraffic ofalower priority levelcannot re

ducetheutilizationofahigher priority level. The lower priority levels havesmaller

targetrotationtimesandcannotdrivethemeantokenrotationtime abovethetargetrota

tiontime ofthe_{priority level in}question.

Wheneverthemeantokenrotationtimeis smallerthan thetargetrotationtimefor

aparticular_priority

level,

there is bandwidthavailabletohandletheofferedloadofthat

priority level. More

formally,

U4

=

\

G4,

C<TR(4)

MAX(0,

P4-U6),

C>TR{4)

and

U2

=

G2,

C<TR(2)

MAX

(0,

P2-U6-Ua),

C>

7>(2)

U0

=

\

MAX(0,

P0-U6-Ua-U2),

C<TR(0)

C>TR.(0)

Calculating

these threeutilizations still requiresthatthemeantokenrotationtime

be known. At leastwhenrepresentedinthisform it does. It_mayalsobeexpressedin

the

following

notation.

Ua

=MAX(MIN

(G4,

Pa

-U6), 0)

U2

=_MAX(MIN

(G2,

Pa-U6-Ua), 0)

U0

=MAX(MIN

(Go,

Pa~U6-Ua-

U2),

0).

Noticethateachofthe_{lower priority level}utilizations_maynowbecalculated if

theoffered

load,

targetrotation_time,minimumtokenrotation_time,andhigh priorityuti

lizationis known. Allofthese factors have_already

been

expressedexcept_{one, the}level

6utilization. Without

it,

none oftheotherutilizations_maybecomputed. Thenextsec

tion is dedicatedto_explainingthemathematical modelassociatedwith_computingthe

level6utilization.

2.5.4. High

Priority

Expressing

thelevel6utilization_{mathematically is}moredifficultthan_expressing

theutilizations ofthelower_prioritylevels. _{This is mainly}dueto the factthatthehigh

prioritytokenholdtimerisused

differently

than the targetrotationtimersofthelower

prioritylevels. Thetargetrotationtimers

indicated

themaximumamountoftimeaccess

classes of a particular_prioritylevel_maytransmitina singletokenrotation. Thehigh

prioritytokenholdtimerdoesn'tgivethemaximumtokenrotationtimeif_{only level 6}

framesare

being

transmitted.

Instead,

itgivestheamountoftimeeach station onthe net

work_maytransmitlevel 6 data. Thissectionexplainshowthelevel 6utilizationcanbe

expressedintermsoftargetrotation_times, offered

loads,

_etc., sothat_{it may be}usedto

solvetheequations oflower priorityutilization. Notethatitmakesno sensetomodelthe

level 6utilization intermsofthelevel

4, 2,

or0utilizationssincethe goalistousethe

resultheretoresolvethe finalvariableinthoseequations.

2.5.4.1.

Deriving

the Peak Level 6 Utilization

Asstated above, thehighprioritytokenholdtimerdoesnotexpressthemaximum

tokenrotationtimefor

transmitting

_onlylevel6dataasdoesthe targetrotationtimers.

However,

themaximumtokenrotation_time, ifnetworktrafficis_onlymade_up oflevel 6

data,

canbeexpressedintermsofthe_{high priority}tokenholdtimeas

follows;

CS

=

(TS

₊

Tm(6)

+T,)N.

whereNisthenumber ofstationson_{the network,}

Ts

isthehigh_prioritytoken

hold time,

TJ6)

isthemaximum overshootfora_prioritylevel 6access_class,and

T,

isthe token

passingtimebetweentwoadjacentstations.

Toachieve maximumlevel_{6 utilization,} each oftheNstations onthenetwork

musttransmitfortheirentirehigh_prioritytoken_{hold time,}plus some additionaltrans

missiontimetofinish_uponcethetimerexpires. Eachstation mustalso passthetoken to

the nextdevice.

Again,

assumingthatnetworktrafficismade_upof_{only level} 6 transmissions,the

peak utilization of_prioritylevel6 isgiven

by

P6

= ^S ^O

Since itis knownthat

C0=NTP

theexpressionisequivalentto

[r,+rw(6);pv-P6=

c,

2.5.4.2.

Deriving

theGeneral Level 6 Utilization

Depending

onhowthevalue ofthemaximumlevel 6tokenrotation_time,

Cs,

comparesto the targetrotation_times,theactual level 6utilization_{may be}simple or_very

difficulttomodel. Unlikethe targetrotationtimersofthe_{lower priority}

levels,

Cs

de

pends uponthenumber of stations inthenetwork. Italso dependsuponthemean sizeof

level 6transmissions,buttoamuchlesserextent. Itispossiblethatthemaximumlevel

6tokenrotation_time,

C

fallanywhereintherange oftargetrotationtimers

depending

onthevalue ofthe high_prioritytokenholdtimeandthenumber ofstationsinthenet

work. For anytimer configuration,one ofthe

following

conditionswill exist

1.

7^(0)

<

7^2)

<

7^4)

<C,

2.

TR(0)

<

TR(2)

<CS<

TR(4)

3.

TR(0)

<

C,

<

TR(2)

<

TR(4)

4.

C,

<

TR(0)

<

TR(2)

< _TR(4).

Thelevel 6utilizationforeach ofthesecasesis different. Eachcaseistreated_separately

inoneofthenextfoursections.

Before proceeding,some general conclusions aboutlevel 6utilization willbe

drawn,

as wasdone forthelower levelutilizationsinthe_preceding sections. Thiswillbe

used as abasisforthelevel 6utilization models.

Theequationforthelevel 6peak utilization_onlyapplieswhenthenetworktraffic

consists of_{strictly level 6}transmissions. The factthat thelevel 6utilizationfallsbe

tweentheoffered loadandthepeak utilization underthese same constraintshasalsobeen

discussed. Thesemodels weredeveloped basedonthepremisethatthemeantokenrota

tion timedidnot exceedCs.

However,

ifnetworktraffic consists oftransmissionsfrom

many priority

levels,

the meantokenrotationtime_mayexceed

Cs

inthreeout ofthe four

caseslistedabove.

Therefore,

the level6utilizationundermixednetworktraffic should

notbedependentuponthevalueof

Cs,

butrather onthe meantokenrotationtime. It

maybestatedthat

Ingeneral,thelevel 6utilization willbetheminimum ofthelevel 6offeredloadandthe

maximumlevel 6transmission timedivided

by

meantokenrotationtime.

2.5.4.2.1. Casel:

TR(0)

<

TR(2)

<

TR(4)

<

Cs

Thecase when allofthetargetrotationtimesaresmallerthan

C,

isthe easiestto

model. To

fully

analyzethelevel 6utilizationwhen

Cs

is greaterthanall ofthetarget

rotationtimes themodel mustbebrokenintotwosub-cases. Thesesub-cases are

1.

C=CS,

themeantokenrotationtimeisequalto the level6tokenrotation

time.

2. C<

Cr,

themeantokenrotationtime is lessthan thelevel 6tokenrotation

time.

2.5.4.2.1.1. Case la:

C=CS

Whenthemeantokenrotation reaches

C,

,theutilizationof alllower priority lev

elswillbe drivento 0. Inother_words,level 6trafficiscapableof

increasing

themean

tokenrotationtimesothatnoother_priorityleveltransmission takesplace. Thismeans

thatthelower_prioritylevelscannothaveanaffectontheutilizationof_{priority level}

6,

andthatthemaximumlevel 6utilizationis_actuallythepeaklevel 6_utilization,P6.

Amoreformalproof ofthisderivation follows.

Theorem: ifC=

Cs

_and

TR(0)

<

TR(2)

<

TR(4)

<

Cs

then

U6

=

P6

Proof:

1. U6=MIN

(g'6,

[r'+7f(<5)]*

)

definitionof

U6

2

p6

=

It,+t(6)-]n

definitionof

P6

w

3.

P6

= =

4. ifC=CsthenG'6>^Zf^

from(l)

5 u6=

[r'+6)>r

from (1

)

and

(4)

6.

U6=P6

from

(3)

and

(5)

2.5.4.2.1.2. Case lb:

C<CS

Whenthemeantokenrotationtime_{is less}than thelevel 6tokenrotation_time,

bandwidth

still exists formorelevel6transmissionstotakeplaceinasingletokenrota

tion.

Therefore,

thelevel 6utilization mustbeequaltothe level 6offeredload.

Theorem: ifC<

Cs

and

TR(0)

<

TR(2)

<

TR(4)

<

Cs

then

U6

=

G'6

Proof:

1.

U6

=MIN

[g'6,

[r'+rg(6)]")

definitionof

U6

2. ifC<CsthenG'6<lT'+Tf)lN

3.

U6

=

G'6

from

(1)

and

(2)

2.5.4.2.1.3. Level 6 Utilization Model for Case 1

Theentire level6utilization model whenthelevel 6maximumtokenrotation

timeisgreaterthanallofthetargetrotationtimes canbestated as

follows,

ifC=

Cs

then U6=MIN

[g'6,

pA

else

U6

=G6.

Thisreducesto

u6=min(g'6,

p6]

sincetheelseconditionis_alreadyasubset ofthefirstcondition.

2.5.4.2.2. Case 2:

TR(0)

<

TR(2)

<

C,

<

TR(4)

Thissectiondevelopsa modelfor level 6utilizationwhenthemaximumtoken

rotationtimefor level 6traffic is lessthanthetargetrotationtime of_prioritylevel 4.

Cs

isnolongerthemaximumtokenrotationtimeoftheentire network.

Instead,

thevalue

ofthelevel4targetrotationtimeisthemaximumtokenrotationtimepossible. This

meansthatbandwidthwill stillbeavailableforlevel4transmissionsafterlevel 6traffic

hasreacheditspeak. Additional level4trafficwilldecreasetheutilizationof_priority

level 6. Inother_words,oncethemeantokenrotationtime grows greaterthan

Cs,

the

maximumlevel 6utilizationbecomesdependentuponthetargetrotationtimeof_priority

level4. Astheadditionallevel4trafficpushesthemeantokenrotation greaterthan

Cs,

the level 6utilizationdecreases. Ifthemeantokenrotationtime is lessthan

Cs

thenlevel

4traffic hasno effectonlevel 6utilization.

Toexaminethelevel 6utilization, themodelmustbe broken intothreecases.

1.

C=TR(4),

themeantokenrotationtimeis equaltothelevel 4targetrotation

time.

2.

CS<C<TR(4),

themeantokenrotationtimeislessthan the targetrotation

timeand greaterthanor equaltothe level 6tokenrotationtime.

3.

C<CS,

themeantokenrotationtime is lessthenthelevel 6tokenrotation

time.

2.5.4.2.2.1. Case 2a:

C=TR(4)

Whenthemeantokenrotationtime equalsthelevel 4targetrotation_time,the

meantokenrotationtimehasreacheditsmaximumvalue. The level 6utilization,under

these circumstances, is dependentuponthelevel 4targetrotationtime. Themaximum

level 6utilizationwill still occur when allTVstations onthecontrol networkaretransmit

ting

level6 data forthereentirehigh prioritytokenholdtimes,butthemeantokenrota

tion timewillbegreaterthanCs.

Mathematically

stated,

[Ts

+Tm(6)]N H4"

TR(4)

'

where

H4

isthemaximumlevel 6utilization possiblewhenthemeantokenrotation is

equalto thelevel 4targetrotation_time,andbothare greaterthan Cs.

Ifthemaximumamount oflevel 6 data hasnotbeen transmitted,thenthelevel 6

utilizationisequalto the offeredloadof_{priority level} 6. The level6utilizationcan now

bestated as

follows,

U6=MIn(g'6,

H^.

A formalprooffollows.

Theorem:

ifC=

TR(4)

and

7>(0)

<

7>(2)

<

Cs

<

TR(4)

then

U6

=MIN

[g'6,

Ha

J

Proof:

1.

C=r*(4)

given

2.

U6

=_MIN

[g'6,

[rj+7g(6)]Af

)

definitionof

U6

3

if(J,6

< [r,+7,(6)> ^

^

= G/

from

(2)

4. l/G/>lZ>^^nrj6=

lZl^

from

(2)

5

f76

= [r^r-(6)^ substitute

(1)

into

(4)

6.

#4

=

U6

7.

C/6

=MIN

[g'6,

Ha

]

from

(3), (5),

and

(6)

2.5.4.2.2.2. Case 2b:

C,<C<r*(4)

Whenthemeantokenrotationtimefalls betweenthelevel 4targetrotationtime

andthelevel 6tokenrotation_time,the totalutilizationofthesystemcannolonger be

represented

by

PA

eventhoughitstill consists of_{only level 4} andlevel 6traffic. The

maximumlevel 6utilizationmust stillberepresentedintermsofthelevel4trafficload.

Inother_{words, the} level 6utilizationisthe fractionofthepeakutilizationthatisnotdi

minished

by

level4traffic. Sincenetworktrafficismade_upof_{only level 4}andlevel6

transmissions, 1

-G'A

representsthefractionofutilizationthatisnotmade_upoflevel 4

traffic.

Therefore,

u6=min[g'6,p6(\-g'S]

representsthelevel6utilization forthis specificcircumstance.

A formalproof ofthelevel 6utilizationfollows.

Theorem:

if

CS<C<

TR(4)

and

TR(0)

<

TR(2)

<CS<

TR(4)

then

u6=min[g'6,

P6(\-G'S]

Proof

1. ifC<TR(4)thenUA=

G'4

2.

U6=MIn(g'6,

lT'+Tf)lN)

definitionof

U6

3 < It1+tW fhen

Us

= G/

from

(1)

4 >

Iz+T^

then

Ue

=

rr^r^

from(1)

5. U=

Ua

+

U6

6 u=Gi

+

ILH^n

substitute

(1)

and

(4)

into

(5)

n jj z definitionofutilization

c

8.

definitionof minimum

tokenrotationtime j_

Qi

_

c^Tt+rm(6)lN

substitute

(6)

into

(7)

9. C0=NT,

10.

l-G'4=lTs+Tm-)+T'lN substitute

(9)

into

(8)

Nicholas W. Oddo

c

11.

CS

=

(TS

₊

Tm(6)

+T,)N definitionof

C,

12. 1

-G'4

=

-|-substitute(1

1)

into

(10)

13.

P&

=

'n

definitionof

P.

₆

14-

P6

=

^3:

substitute

(12)

into

(13)

C(l_G^) '

15.

P6(\-G'A)

=

^-simplify

(14)

16.

P6(l-Gf4)

=

U6

_from

(4), (9), (11),

and

(14)

17.

U6=MIN\G'6,

P6(l-G4'))

from

(3)

and

(16)

2.5.4.2.2.3. Case2c:

C<CS

Wheneverthemeantokenrotationtimeis lessthanthe level6maximumtoken

rotation_time,theentirelevel6 offeredload_maybe handled.

Therefore,

U6

=G'6.

2.5.4.2.2.4. Level6 Utilization Model for Case 2

Theentirelevel6utilizationmodelwhenthe level6maximumtokenrotation

timeisthan thelevel 0andlevel 2targetrotation_times,andlessthanthelevel 4target

rotation_time,cannowbe stated completely.

ifC=

TR(4)

then

U6

=MIN

(g'6,

Ha]

else ifCs

<C<TR(4)

then

U6

=MIN

(g'6,

P6(\~

G'6)\

elseifC<

Cs

then

U6

=

G'6

Thethreeconditionsfor level 6utilization_mayalsobeexpressedintermsof uti

lizations,

insteadoftokenrotationtimes. Thisis done foreach ofthe threeconditionals

andtherevisedmodelispresentedbelow.

Whenthemeantokenrotationtimeequalsthelevel4targetrotation_time,theof

fered loadoflevel 4mustbe greaterthan theutilization oflevel 4.

Also,

thetotalutiliza

tionofthesystem mustbeequaltoP4. Thisis notto _saythat theentire utilizationis

made_upoflevel4traffic. Infact it isnot,itismade_upoflevel 4andlevel6traffic

only. Theutilizations of_{priority level 0}andlevel2are0becausethemeantokenrota

tion timeisgreaterthan thererespectivetargetrotationtimes.

Therefore,

sayingthatthe

level4offeredloadandthelevel6utilizationis greaterthan thelevel 4peak utilization

isequivalentto _statingthat themeantokenrotationtimeequalsthatlevel 4targetrota

tiontime.

\g'4

+MIN

[g'6,

H^PA~\=

\Cs

=_Cand

TR(0)

<

TR(2)

<CS<

TR(4)~]

Ifthelevel 4offeredloadandlevel 6utilizationarenotgreat enoughtoexceed

thepeak_{utilization, then}perhapsthelevel 4andlevel 6trafficaregreaterthanthelevel

6maximumtokenrotationtime. Thiswould meanthat thelevel 4 andlevel 6offered

loadsexceededthelevel 6peak utilization. More

formally

stated,

\_G'4

+

G'6

P<~]

=

[CS<C< TR(4)

and

TR(0)

<

TR(2)

<CS<7^(4)].

Lastly,

if bothoftheprevious conditions cannotbe satisfied,thenthemeantoken

rotationtimemustbelessthanCs. Theentiremodel_maynowberestated as follows.

if\Gf4

+MIN

[g'6,

H4

)

/%

]

then

u6=min[g'6,Ha^

else

if

\_G'4

+

G'6>P6']

then

u6=min(g'6,p6(i-g4)}

else

U6

=

G'6

2.5.4.2.3. Case3:

TR(0)

<

Cs

<

TR(2)

<

TR(4)

This sectiondiscussesthecharacteristicsoflevel 6utilization when

Cs

islessthan

thetargetrotationtimeforlevel

2,

and greaterthan the targetrotationtimeoflevel 0.

Theargument usedinthe_{precedingsection,}when

Cs

fellbetweenthetargetrotation

timesoflevel 4 andlevel 2 , canbeextendedforthissituation.

Inthe_{precedingsection, to}

fully

analyzethelevel6utilization, theproblemhad

tobe broken down intothree caseswith respectto themeantokenrotationtime. This

approachcanbe followedwhen

Cs

falls betweenthe targetrotationtimesoflevel 2and

level0 as well. Theequationsfor level6utilizationderivedforthepreviouscasewill

also_apply

here,

since a portion ofthisderivationoverlapsthepreviousderivation.

Whenthe level 6tokenrotationtimefallsbetweenthelevel 2andlevel 0target

rotation_times,thederivations forthelevel 6utilization model_{may be}brokeninto five

distinctcasesbasedonthemeantokenrotationtime. Thesecasesare

1. C=

TR(4)

_,themeantokenrotationtimeequalsthe level 4targetrotation

time.

2.

7^(2)

<C<

77?(4),

themeantokenrotationtimeis lessthanthe level 4

targetrotationtimeand greaterthanthe level 2targetrotationtime.

3. C=

TR(2)

,themeantokenrotationtime equalsthelevel 2targetrotation time.

4. CS<C<

TR(2)

,themeantokenrotationtimeis lessthanthe level 2target

rotationtimeand greaterthanor equalto the level 6tokenrotationtime.

5. C<

Cs

,themeantokenrotationtimeislessthanthe level6targetrotation

time.

Noticethatcase 1 andcase5 forthislevel 6utilizationanalysis areidenticalto

the level 6utilization analysiswhenthe level 6tokenrotationtime fell betweenthe level

4andlevel2targetrotation_{times. This}meansthattwoofthe fivecases outlined above

have_alreadybeensolved. Themodelsforthese twocaseswillberepeatedforcomplete

ness.

However,

forafull_{understanding}ofthe derivationtheprevious sections shouldbe

examined.

2.5.4.2.3.1. Case3a:

C=TR(4)

Thelevel 6utilization underthesecircumstancesis equivalentto thederivation

done insection 1.5.4.2.2.1. Thiscanbe statedsincethe

following

threecriteria arethe

samefor bothcases.

1. Themeantokenrotationtime isequaltothe level4targetrotationtime.

2. Themeantokenrotationtimeisgreaterthan Cs.

3. The level 4targetrotationtime isgreaterthanthelevel0andlevel 2target

rotationtimes.

Itis irrelevantthat thelevel 6maximumtokenrotationtime falls betweenthelevel 0and

level 2targetrotation_times,insteadof the level 2andlevel 4targetrotationtimes. The

resultispresentedhereforcompleteness.

U6=MIN(G/6,

774)

2.5.4.2.3.2. Case 3b:

TR(2)

<C<

TR(4)

Whenthemeantokenrotationtime isgreaterthan thelevel 2andlevel 0target

rotation_times,theutilization forthese_prioritylevelswillbe 0.

Therefore,

themeanto

kenrotationtimeis caused

by

networktraffic fromthe level4andlevel6 prioritylevels only. Notethatthenetworktrafficmust consist oftransmissionsfromboth_priority

classes,orjust from level 4. _{Level 6trafficalone cannotincreasethemeantokenrota}

tiontimeabovethelevel2targetrotationtime.

Whentheofferedloadof_{priority level6 islessthanthe}maximumallowable

bandwidth,

then the level 6utilizationisequalto thelevel 6offeredload.

However,

whenlevel 6 transmissionsreachtheir_maximum,thatistosay,whenallstationsonthe

network are

transmitting

fortheirfull high_prioritytokenhold_time,the level 6utilization

maydwindle duetoan

increasing

loadoflevel 4transmissions.

Therefore,

itcanbe said

thatthelevel 6utilization underthesecircumstancesisafractionofthelevel6peak uti

lization.

More _{specifically,}

U6

=P6(l-G'4).

Noticethatasthelevel4offeredloadreachesthepoint whereit becomesthe total

utilizationofthenetwork,the level 6utilizationdropsto 0. Thishastobethecase since

level 6transmissionsareguaranteed at eachnodeforthe_{high priority}tokenholdtime.

Alsonotethat asthelevel 4offeredload dropsto

0,

the level 6utilizationapproachesthe

peak utilization. The level6utilizationwillnever reachitspeak_value,

however,

since a

level 4offered loadmustbepresenttoincreasethemeantokenrotationtimeabovethe

level 2targetrotationtime.

The level 6utilizationcan nowbepresentedas

follows,

u6=min(g/6,

/>6(1-C?i)).

Noticethatthisexpressionfor level 6utilizationis identicaltotheexpressionfor level 6

utilizationderivedinsection 1.5.4.2.2.2. Forthat

derivation,

themeantokenrotation

timewas greaterthanor equalto

Cs,

andlessthan thelevel 4targetrotationtime. The

sameistrueforthis

derivation,

exceptthatthemeantokenrotationtime can never equal

C,. The factthat

C,

was greaterthan thelevel2targetrotationforthe derivation insec

tion

1.5.4.2.2.2,

andlessthan the level2targetrotationtime forthisderivationis irrele

vant. The

derivation

is

done

onthe

foundation

that themeantokenrotationtimeis less

than thelevel4targetrotation

time,

and greaterthanCs. Theprooffromsection

1.5.4.2.2.2 isthereforeidentical forthisderivationand isnot repeated.

2.5.4.2.3.3. Case 3c:

C=TR(2)

Thederivationofthelevel6utilizationwhenthemeantokenrotationtimeequals

the level 2targetrotationtime_{is very}similartothederivationoflevel 6utilization when

themeantokenrotationtimeequaledthelevel 4targetrotationtime. This derivationwas

done insection 1.5.4.2.2.1.

Whenthemeantokenrotationtimeequalsthe level 2targetrotation_time,the

meantokenrotationtimehasreacheditsmaximum value. Thelevel6utilization,under

these circumstances, isdependentuponthe level 2targetrotationtime. Themaximum

level 6utilization will stilloccurwhenallNstationsonthe control networkaretransmit

ting

level 6 data forthereentirehigh prioritytoken_{hold times,}butthemeantokenrota

tion timewillbegreaterthanC3.

Mathematically

stated,

lTs

+Tm(6)^N 2"

TR(2)

'

where

H2

isthemaximumlevel 6utilization possible whenthemeantokenrotationis

equaltothe level 2targetrotation_time, andbotharegreaterthanCs.

Ifthemaximum amountoflevel 6 data hasnotbeen_transmitted,then thelevel 6

utilizationisequalto theofferedloadof_{priority level 6. The}level 6utilization can now

be stated as

follows,

u6=min(g'6,h2]

Theproofforthisexpression oflevel 6utilization isidenticalto theproofforthecaseof

themeantokenrotationtime_equalingthe level4targetrotationtime. _{The only differ}

ence isthat thelevel2targetrotation_time,

TR(2),

shouldbesubstitutedforthelevel 4

targetrotation

time,

TR(4),

throughout theproof.

2.5.4.2.3.4. Case 3d: CS<C<

TR(2)

Whenthemeantokenrotationtimefalls betweenthelevel 2targetrotationtime

andthelevel6tokenrotation_time,thetotalutilization ofthesystem canno longer be

represented

by

P2. Forthis case,thelevel 6 utilizationisthefractionofthelevel 6peak

utilizationthat isnotdiminished

by

level 4 andlevel 2traffic. Sincenetworktrafficis

made_{up level}

2,

level 4andlevel 6 _{transmissions,} 7*6(1

G2

G4)

representsthe frac

tionoflevel6utilizationthatisnotmade_upoflevel 2 orlevel4traffic.

Therefore,

U6

=MIN

[g'6,

P6(\

-G'2-G'4)j

representsthelevel 6utilizationforthisspecificcircumstance.

Theproofforthisexpressionoflevel 6utilizationisidenticalto theproofinsec

tion _{1.5.4.2.2.2. The only difference}isthatthetotalutilizationisequaltoth