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TotalCostofPreservation(TCP) Page1of20

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TotalCostofPreservation(TCP):

CostModelingforSustainableServices

Rev.0.16–2012‐04‐09

StephenAbrams

PatriciaCruse

JohnKunze

UCCurationCenter,CaliforniaDigitalLibrary 

UniversityofCalifornia,Officeof thePresident

MichaelMundrane

OfficeoftheDeputyCIO

UniversityofCalifornia,Berkeley

1 Introduction

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Informationtechnologyandresourcesarethoroughlyintegratedwith,andindispensableto,

today’sInternetandweb‐basedculture,commerce,science,education,andentertainment.The

digitalassetsunderpinningtheseactivities,however,areinherentlyfragilewithrespecttoever

increasingdisruptivete chnologicalchange.Withouteffective,affordable,andproactivecuration

management,today’sdigitalassets

willnotremainviableandusefulinthefuture.Inorderto

achieveubiquityoflong‐termpreservationeffortsandresults,thefulleconomiccostsof

preservationactivitiesovertime,the“totalcost ofpreservation”(TCP),mustbewellunderstood.

TCPanalysiscanbeappliedusefullyinthedevelopmentof

twospecificpricemodelsfor

preservationservicepricing:

 Pay‐as‐you‐go

 Paid‐up

Thepay‐as‐you‐gomodelisappropriateforsituationswhereareliableandpredictableannual

incomestreamisavailabletotheclientpurchasingpreservationservices.Whenthisisnotthe

case,forexample,

withorganizationsfacingirregularorboom‐or‐bustbudgetarycyclesorfor

grant‐funded,fixedtermresearchprojects,thepaid‐upmodelmaybemoreattractive;indeed,in

manycircumstancesitmaybetheonlyrealisticoption.

2 Totalcostofpreservation

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Long‐termdigitalpreservationisacomplexactivity,involvingsophisticatedtechnical

infrastructureaswellassignificanthumancompetencies,analysis,anddecisionmaking.Given

thedifficultiesinaccounti ngforthemyriadaspectsofpreservationactivity,andofprojectingthe

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costofthoseactivitiesintotheindefinitefuture,any analysisofTCPmustrelyonanumberof

fundamentalassumptions.(SeeAppendixAforasummaryofpriorworkonpreservationcost

analysis.)

2.1 Assumptions

TheTCPanalysisassumesthefollowing:

 Onlythecostspertainingtopreservationserviceprovidersareconsidered.Intermsofthe

OAISreferencemodel[OAIS],thesearethecostsassociatedwithanArchive,“an

organization[ofpeopleandsystems]…thathasacceptedtheresponsibilitytopreserve

information.”Inparticular ,thepreservation

costsassociatedwiththelocalactivitiesof

OAISProducers(e.g.,contentcreationoracquisition, reformatting,packaging,

submission,etc.)areconsideredoutofscope.Ontheotherhand,thecostofsupporting

aProducerinmakinguseofArchivefunctionsisinscope.

 Individualcostcomponentsofthemod elcanbe

categorizedunambiguouslyaseither

fixed,whichareincurredregardlessoflevelofuse,ormarginal,whichscale

proportionallywithuse.

 Individualcostcomponentscanbecategorizedunambiguouslyaseitherone‐timeor

recurring.One‐timecostscanbeannualizedovertheeffectivelifespanoftheactivityor

component.

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 Thevaluesdefinedforindividualcostcomponentsrepresentnominalcosts,thatis,the

costsdefinedforgenericinstancesofactivitiesorsystemcapacities.Thisisreasonable

underafurtherassumptionofapolicyofuniformityofpreservationeffortratherthan

outcome.Forexample,onthebasisofform,structure,

accompanyingmetadata,etc.,

somedigitalcontentmaybemore inhe rentlyamenabletopreservationcareandwill

naturallyreceiveahigherlevelofpreservationserviceandoutcome.

 Actionsperformedonpreservationcontent,e.g.,characterization,fixity,tra nsformation, 

etc.,aresubstantiallyautomated.Thus,themaincostassociatedwithanactionisin

the

acquisition–oranalysis,design,anddevelopment–anddeploymentoftheimplementing

software,whichisindependentofthenumberofobjectsagainstwhichtheactionis

performed.

 Thesizeandscopeofthecontenttobesupportedisknown,andthecostofprovidingfor

itspreservationis

established,atthebeginningofthetimeperiodunderconsideration.

However,underthepay‐as‐you‐gopricemodelthesecostsarebilledforattheendofthe

timeperiodwhileunderthepaid‐upmodeltheyarebilledforatthebeginningofthe

period.

 Thepreservationserviceprovidercancarryforwardbudgetarysurplusesacrossfiscalyear

boundaries.Furthermore,thesesurplusfundscanbeinvestedatmarketrates,withthe

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earnedinterestfurthercontributingtothesurplus.

 Themodelsareultimatelyrevenueneutral,thatis,thereshouldbenosurplus(ordeficit)

fundsremainingattheendoftheperiodunderconsideration.

 Valuescanbedetermined

forvariousannualadjustmentfactors,suchasinflation,

investmentrateofreturn,costoflivingadjustments(COLA),meritpayraises,and

changestotheper‐unitcostofpreservation,which,althoughheldconstantoverthefull

periodofTCPconsideration,areneverthelessreliablypredictiveoflong‐termeconomic,

technological,and

organizationaltrends.

Thelastassumption,althoughthemainstayofthestandardeconomicforecastingtechniqueof

discountedcashflow(DCF)analysis[Damodaran],canbeproblematicoverextendedtime

periods.ConcernsovertheefficacyofDCF‐basedmodelingareaddressedinSection§3.

2.2 TCPanalysis

TheTCPanalysisencompassesthefulleconomiccostsassociatedwiththelong‐term preservation

ofdigitalassets,althoughtheresultingpricemodelscanbeeasilycustomizedtodealonlywith

varioussubsetsofthosecostsasamatteroflocalpolicy.Theindividualcostcomponents

incorporatedintheanalysisarereflective

ofthefollowing11high‐levelcategoriesabstracted

fromtheenvironmentinwhichpreservationactivitiesoccur(seeTable1):

Preservationactivitiesareembodiedinanarchival

 1.

System;composedofvarious

2.

Servicessupportingnecessaryanddesirablefunctions;runningon

 3.

Servers;designed,deployed,maintained,enhanced,andutilizedby

  4.

Staff;insupportofcontent

   5.

Producers;whouse

 6.

Workflowstosubmitinstancesof

 7.

ContentTypes;whichoccupy

  8.

Storage;andaresubjecttoongoing

  9.

Monitoring;andperiodic

  10.

Interventions;allsubjecttoappropriatemanagerial

  11.Oversigh t.

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Table1–Preservationenvironment

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EachoftheprecedingitalicizeditemsisacostcomponentoftheTCPanalysis.Tosimplifythat

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analysis,theSystemcomponentencompassesthebaselinetechnicalinfrastructureand

environmentinwhichpreservationactivitiesareembodied,andinparticular,subsumesthe

ServicesthatsupportnecessarytechnicalfunctionsandtheServersonwhichthoseServicesare

deployed.Similarly,

Staffcostsaresubsumedbytheotherindividualhigh‐levelcostcompon ent

terms.

TheContentTypecomponentencompassesallanalysis,planning,andsoftwareacquisitionor

developmentspecifictosupportinggivenclassofdigitalcontent.

TheMonitoringcomponentencompassestechnologywatchforincipientobsolescenceandother

riskfactorsthatmayimpinge

onlong‐termusability;routinepro‐activemonitoringoftheSystem

(anditsunderlyingServicesandServers)andStorageforavailabilityandresponsivity,ontheother

hand,aresubsumedundertheSystemandStoragecomponentsrespectively.

TheInterventioncomponentencompassesallnon‐periodicorunpredictablepreservation

activitiessuchasformat

migrations,responsestorightschallenges, disasterrecoveryefforts,etc.,

storagemediarefreshandmigrationaresubsumedundertheStoragecomponent.

TheTCPanalysisrepresentsthetotalcostofpreservationtothepreservationserviceprovideras

follows:





 ·  ·ℓ··



··  (1)



TotalcostofpreservationforallProducers.

FixedcostofthebaselinearchivalSystem.

NumberofcontentProducers.

UnitcostofsupportingaProducer.

NumberofsubmissionWorkflows.

UnitcostofsupportingaWorkflow.

ℓ

NumberofContentTypes.

UnitcostofsupportingaContentType.

NumberofunitsofpreservationStorage.

UnitcostofStorage.

NumberofpreservationMonitoring activities.

UnitcostofaMonitoring activity.

Numberofpreservation Interventions.

UnitcostofanIntervention.

FixedcostofadministrativeandmanagerialOversight.

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Table2–TCPnotation

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ThebaselinearchivalSystemandadministrative/managerialOversightareconsideredfixedcosts,

thereforetheyarerepresentedinEquation(1)bysingleterms,

and

, respectively.Allother

componentsaremarginalcosts,eachre presentingbytwoterms:aunitcostandthenumberof

unitsallocatedorconsumed.

TheTCPanalysiscanbeusedasthebasisforpartialcost‐recoverybyremovingorzeroing‐out

particularcostcomponentsthataresubsidizedasamatter

oflocalpolicy.Thespecificpay‐as‐

you‐goandpaid‐uppricemodelsarebasedonaderivationofthepreservationcostsattributable

toagivencontentProducer.

2.3 Pay‐as‐you‐gopricemodel

Thepay‐as‐you‐gopricemodelisbasedonanannualbillingcycle,

 0,1,2,….Certaincost

components–System,Workflow,ContentType,Monitoring,Intervention,andOversight–are

considered“commongoods”;thatis,theyareapplicableandbeneficialtoallPr oducersequally,

andassuch,areproperlyapportionedacrossallProducers.ThenumberofunitsofStorage,on

theotherhand,

isspecifictoasingleProducer.Theannualpay‐as‐you‐gopriceforagiven

Produceris:





 ·  ℓ· 



··







·

(2)



Pay‐as‐you‐goprice.

NumberofunitsofpreservationStorage attributabletoagivenProducer.



Table3–Pay‐as‐you‐gopricemodelnotation

Theoperationofthepay‐as‐you‐gomodelisillustratedinthecashflowdiagram[Neftci]inFigure

1.(Valuesabovethehorizontaltimeaxisrepresentincomeorprice;thosebelowtheaxis

representexpensesorcosts.)Aseries

ofequalcosts

areincurredattheendofeachservice

year.Toachieverevenueneutralitythesearematchedwithcorrespondingprices.

Income

  

  t=0 1 2 3

  

Expense



Figure1–Pay‐as‐you‐gopricemodelcashflowdiagram



Thelong‐termcosttoaProducerunderthepay‐as‐you‐gomodelisfoundbysummingtogether

theannualpayments

overaperiodof

years.

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







 (3)









· (4)







Cumulativepay‐as‐you‐gopriceover

years.

Annualpay‐as‐you‐goprice.

Fixedtermof

years.

Table4–Pay‐as‐you‐gopricemodelnotation

Unfortunately,thiscumulativepriceincreaseslinearlyasafunctionoftimeand,mostalarmingly,

as

approaches“forever”(

 ),thetotalpricealsoapproaches infinity.

∞∞ (5)

However,recallingtheassumptionofanannualdecreaseintheaggregatecostofproviding

preservationservice,

,theseriesofannualcostsandpricesdecreasesuniformly,asillustra tedin

Figure2.

Income



1   ·  1  



·

   

  t=0 1 2 3

   

Expense



 1   ·  1  



·

Figure2–Discountedpay‐as‐you‐gopricemodelcashflowdiagram

Thesizeoftheannualdecreaseisproportionalto1–

,whichcompoundsovertime.Again,the

long‐termcostofisfoundbysummingtogethertheannualpaymentsover

years.





,



   ·



1



·1



·1





(6)





,



·

11







(7)

∞,







(8)







Cumulativediscountedpay‐as‐you‐gopriceover

years.

Annualpercentagerateofdecrease inaggregatepreservationservicecost

(asadecimal,forexample,0.1fora10%annualdecrease).



Table5–Pay‐as‐you‐gopricemodelnotation(continued)



Mathematically,Equations(7)and(8)arethesolutionsoffiniteandinfinitepowerseries

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respectively,whicharesolvableonlywhentherateofdecreaseinaggregatepreservationservice

cost,1–

,islessthan1.Fordetailsofthederivationoftheseequations,seeAppendicesBandC.

Forthederivationofthevalueof

seeAppendixD.

2.3 Paid‐uppricemodel

Thepaid‐uppricemodelisbasedonaone‐timeprice, paidatthebeginningoftheperiodunder

consideration,thatissufficienttofinanceallsubsequentpreservationactivitiesoverthatperiod.

Thisperiodcanbeeitherafixedterm

or“forever,”thatis,for

 .Intherelevantcashflow

diagraminFigure3,theone‐timepaymentFispaidbytheProduceratthebeginningofyear1(

 0).Thesubsequentincometermsaretheresultoftheinvestmentreturn

appliedtoeach

year’ssurplusfunds.Notethat

isthenominalannualpercentagerate(APR)ofinvestment

return.Theeffectiveannualrate,

,incorporatingtheeffectofmonthlycompounding,is

[Tucker]:







1







1

(9)



Thepay‐as‐you‐gocost

isscaledbyafactorof

toaccountforthefactthattheservice

providerincurscoststhroughouttheserv iceyearbutthesearenotbilledandpaidforuntilthe

endoftheyear.

Income

·

·



1



·







1



·

·



1





1



·























  

  t=0 1 2 3

  

Expense



 1   · 



1





·

Figure3–Paid‐uppricemodelcashflowdiagram

Thepaid‐upprice

isderivedinAppendixE.





,,



·





1

 ·







1





1





·







1







1





 

·





1  



1  





(10)





,,



·







1









1







1





·



(11)

∞,,  ·









(12)



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





Paid‐uppricefor

years.

Thenominalannualpercentagerate(APR)ofinvestmentreturn(asa

decimal,forexample,0.02for2%.

Theeffectiveannualpercentagerateofinvestmentreturn(asadecimal).



Table6–Paid‐uppricemodelnotation



Equations(11)and(12)arealsopowerseriesandaresolvableonlywhenthediscountfactoris

lessthantheeffectiveinvestmentretur n,1–

 1

.Fordetailsofthederivationofthese

equations,seeAppendixE.

ItisdesirableforaProducertobeabletoswitcheasilybetweenapay‐as‐you‐goandpaid‐up

basis.Therelevantfactorinthistransitionisthe“coefficientofpermanence,”thatis,theone‐

timepremium,

ormultiplier,oftheannualpay‐as‐you‐goprice,

,thatonemustincurinorderto

achievepaid‐uppermanence.





·



(13)



φ

Coefficientofpermanence;theone‐timemultiplierofthepay‐as‐you‐goprice

necessarytoachievepaid‐uppermanence.



Table7–Paid‐upmodelnotation(continued)



Thus,aProducercurrentlypaying

onanannualbasiscan“tradeup”toservicepermanencewith

aone‐timepaymentof

·

·

.

Thepaid‐upmodelisdesignedtobeultimately revenueneutral,thatis,withnosurplus(or

deficit)fundsremainingattheendoftheterm.Thiscanbeillustratedinthefollowingexample

foratenyearterm(

=10),apay‐as‐you‐goprice

of$650(for1TBofstorage),anominal

annualinvestmentrateofreturnof2%(

=0.02),andanannualdecreaseintheaggregatecost

ofpreservationserviceof10%(

=0.1).FromEquation(11),thisleadstoapaid‐upprice

of

$4,764.14.Incomeinyears1,2,3,...istheresultoftheinvestmentreturnonthesurplus

remainingattheendoftheprioryear.

Year(T) Income Expense Surplus

0 $4,764.14  $0.00  $4,764.14 

1 $96.16  $655.99  $4,204.31 

2 $84.86  $623.19  $3,665.98 

3 $73.00  $592.03  $3,147.94 

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4 $

63.54  $562.43  $2,649.05 

5 $53.47  $534.31  $2,168.21 

6 $43.76  $507.59  $1,704.38 

7 $34.40  $482.21  $1,256.57 

8 $25.36  $458.10  $823.83 

9 $16.63  $435.20  $405.26 

10 $8.18  $ 413.44  $0.00 



Table8–10yeartermpaid‐uppricemodelexample



Therelationshipbetweenthepay‐as‐you‐goandpaid‐upmodels isillustratedinFigure4.The

cumulativeanddiscountedpay‐as‐you‐gopricesandthepaid‐upprice,



,



,



,

areshownasthered,orange,andgreencurves,

respectively.Thecum ulativepay‐as‐you‐goand

paid‐uppricesfor“forever,”

,



and

,

,areshowninmagentaandblue,

respectively.



Figure4–Relationshipbetweenpay‐as‐you‐goandpaid‐uppricemodels

Thedifferencebetweenthecumulative(red)anddiscounted(orange)pay‐as‐you‐gopricesis 

accountedforbythediscountingfactor

,theassumedannualdecreaseinthecostofproviding

preservationservice.Thedifferencebetweenthefixedtermpay‐as‐you‐go(orange)andpaid‐up

(green)prices,aswellasthe“forever”prices(magentaandblue),isaccountedforby

,the

assumedannualinvestmentrateofreturn.

Thecurveforthefixedtermpaid‐uppricecharacteristicallyapproachestheforeverprice

asymptoticallysolongastheinvestmentrateofreturnandannualdecreaseinaggregate

2000

4000

6000

8000

10000

12000

14000

16000

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30

Cost($)

Year(T)

Cumulativepay‐as‐you‐go

price,G(T)

Discountedpay‐as‐you‐go‐

price,G(T,d)

Discountedpay‐as‐you‐go

price,G(,d)

Pai

‐upprice,F(T,d,r)

Pai

‐upprice,F(,d,r)



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preservationservicecostaregreaterthan0(

 0 and

 0,oriftheaggregatecostincreases

(i.e.,

 0),whentheinvestmentgainisgreaterthantheservicecostincrease(

 |

|).

2.4 Rateofchangeofpreservationservice cost

Thevariable

inEquations(7),(8),(11),and(12)isacompositevalueorfunctionthatsumsthe

individualcomponent‐specificchangesinquantityandunitcost,weightedbythecomponent’s

proportionatecontributiontotheoverallcost(seeAppendixE).

3 Predicativereliability

ManyoftheassumptionsbuiltintotheTCPmodelmaybeproble maticoversignificanttime

spans,particularlytheassumptionthatthevariousannualadjustmentfactors–investmentrate,

rateofdecreaseofunitcost,inflation,COLA, etc.–areconstantovertime[Rosenthal].

Severalavenuesareavailabletoamelioratethesedifficulties.



3.1 Modeltherisk

Thevaluesforranddcanberoundedup(ordown)asappropriatetorepresentafixedrisk

“premium”forthefutureuncertaintyoffinancialandtechnologicaltrends.Abetterapproachis

toaddanadditionalriskcomponentRtothepay‐as‐you‐goEquation(2).







 ·  ℓ· 



··







· 

(14)



R Riskcostposedbyuncertaintyoverthefuturevaluesofrandd.



Table9–Risknotation

ThegrowinginfluenceofRovertime,reflectiveofincreasinguncertainty,canbecontrolledby

settingtheappropriatevaluefor

and

,theweightingfactorandexpectedannualrateof

changeinriskusedinEquation(14)for

,therateofchangefortheaggregatecostof

preservationinEquations(7),(8),(11),and(12).

Insurersprotectthemselvesfromtrulyunexpectedlylargepayoutsbypurchasingreinsurance:in

essence,insuranceagainstexcessiveclaims[Reinsurance].Theadditionalcostintroducedinto

thepricingequations throughtheriskfactorRcanbe

seenasrepresentingareinsurance

“premium”thataccumulatesovertimeinanticipationofmeetingsomefutureunexpectedneed.

Thisisalsosimilartotheideaofa“rainydayfund”thatgovernmentsfundduringperiodsof

budgetarysurplusinanticipationoffutureshortfalls [Rainy].

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3.2 Recalibration

Ratherthankeepingkeymodelvariables,

,

,and

,constantovertime,theycanbe

recalibratedperiodicallyonthebasisofcumulativeexperienceandcurrentknowledge.

RecalibratedpriceswouldapplyforprospectiveProducersonly;retrospectiveProducerswould

remain“lockedin”atthepriceinforceatthetimetheyestablishedtheirrelationshipwiththe

serviceprovider.

3.3 Hybridpricing

Thehybridapproachtopricingdistinguishesbetweenthosecostcomponentsthatareconsidered

easytoquantifyandforecast,andthosethataren’t.Paid‐uppricingisappliedonlytotheformer;

activitiesassociatedwiththelatterareperformed,ifitall,onapay‐as‐you‐gobasis.

Forexamplepreservation

Interventions,futureactionstakeninresponsetofuture,possibly

unanticipated,conditions,maybeconsideredtofallintothedifficult‐to‐quantifycategory.The

paid‐uppricewouldthereforeonlyincorporatethecostsforpreservationactivitiesthatcanbe

performedatthetimeofcontentingestviaWorkflowsastheresult

ofContentTypeanalysis,such

asthecreationofnormalizedordesiccated[WAS,Desiccation]derivativeformsofthe

contributedcontent.

Inamoreextremecase,thebaselinepaid‐uppreservationfunctioncouldberestrictedtobit‐level

preservationonly.Thisservicemoderequiresonlythreecostcomponents:theSystem,Storage

,

andProducer;supportforWorkflowisnotnecessaryasthesinglerequiredworkflowisassumed

tobesubsumedundertheSystem,whileContentTyp es,Monitoring,andInterventionsarenot

necessarysinceonlybit‐levelactivitiesareencompassedatthisservicelevel.

3.4 Shortentheterm

Uncertaintyinthepredictivereliabilityofthevalueschosenforranddisproportiontothelength

oftimeunderconsideration;thelongertheterm,thegreatertheuncertainty.Withthisinmind,

itmaybeprudenttoshortenthetermtoonemoreamenabletoreliableforecasting,withthe



possibilityforsubsequent“renewal”ofpreservationservice.Forsomebodiesofcontentafixed

term–10year?20years?–mayinfactbeanappropriateinitialterm.Shorttomid‐term

preservationprovidesanopportunityfo rthecontenttoproveitsvalue,asevidencedbythe

commitmentof

acuratorialadvocatetopayforitssubsequen tpreservation.

3.5 Stochasticmodeling

RosenthalsuggestsusingmoresophisticatedeconomictechniquesbasedonMonteCarlo

simulationtomodelpotentialfuturescenariosstochastically[Rosenthal].

 

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AppendixA Priorwork

Anumberofinternationaleffortshaves tudiedthequestionoflong‐termpreservationcosts;most

notably,theNationaalArchiefoftheNetherlandsin2005[Archi ef];theLIFE

project(LifeCycle

InformationforE‐Literature)workonaGenericPreservationModel(GPM)in2008[Ayris,Hole,

LIFE];theKRDSproject(KeepingResearchDataSafe)in2010[Beagrie,KRDS];thePrinceton

DataSpaceinitiativein2010[Goldstein];andtheDanishNationalArchivesandRoyalLibrary

CMDP(CostModelforDigital

Preservation)in2011[Kejser,CMDP].(See[Zell er]forasummaryof

theseandotherrelevantactivities.)

Allofthesemodelsanalyzepreservationcoststhroughoutthefulllifecycleofpreservedassets.

BoththeNationaalArchiefandLIFEprojectworkemployveryfine‐grainedanalysisofcost

componentsandarebasedonrepresentative

actualcostsratherthanthenominalcosts

employedbyTCP.TheLIFEmodelincludescostcomponentsforcontentcreationandacqui sition,

whichareconsideredoutofscopeintheTCPanalysis.Furthermore,LIFEscalespreservation

actioncostsbythenumberofexpectedobjects.TCPassumesthatthereisnoper‐

objectmarginal

cost;instead,marginalcostsareassociatedonlywiththevariousContentTypesofwhichobjects

aremembers.TheKRDSmodelis specifictotheresearchdatalifecycle,butitsfindingsappearto

beapplicabletoothercontexts.UnlikethetheNationaalArchiefandLIFEmodels,KRDSassumes

adiscounting

functionthatannuallydecreasestheaggregatecostofpreservationservice.The

DataSpacemodelisalsobasedonadiscountingfunction,butitsanalysiscoversonlythecosts

associatedwithpreservationstorage,whicharedefinedonapayonce,storeforever(POSF)basis.

TheOAISactivity‐basedCMDPworkconcentrateson

postfactomeasuringofpreservationcosts,

ratherthanonforecasting,althoughitispossibleusingtheframework.WhileDataSpaceis

explicitlyconcernedwith“forever”pricing,neitheritnoranyoftheothermodelsassumethe

benefitofanannualinvestmentreturninoffsettingaportionofongoingcosts.Most,ifnot

all,of

theindividualcostcomponentsofthesemodelscanbemappedtoOAISenvironmentaland

functionalentities[OAIS]orTRACcriteria[TRAC],facilitatingcommonpointsofreferenceand

comparison.

Anumberofinstitutions,bothcommercialandnon‐profit/academic,nowofferlong‐term

preservationservices.(Oratleastpersistentstorage;

theimportantdistinctionbetweenthetwo

isnotalwaysapparentfromthedescriptionoftheseserviceofferings.)Carboniteis

representativeofcommercialpreservationserviceofferings[Carbonite].Itscostis$599/yearfor

upto500GB,withfurtherincrementsof100GBavailablefor$89/year.TheLifeTimeLibraryat

theUniversityof

NorthCarolinaoffersstudentspermanentstorage“andassociatedservices”for

250GB,apparentlywithnoassociatedfees[UNC].TheUSCDigitalRepositoryoffersapaidup

licensefor20yearsofpreservationservicefor$1000/TB[USC].Ingeneral,however,little

informationisavailableexplainingthebasisoftheirbusinessmodels.



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AppendixB Powerseries

Thesolutionforageneralpowerseries,









∑

·







,canbederivedasfollows:









   ·  ·



·





(15)



Equation(15)canbescaledbyafactorofx:

·







 ·  ·



  ·



·





(16)



SubtractingEquation(16)from(15)yields:









·







  



··



·



·



  ·





(17)









·







   ·





(18)











1



· 1  





(19)



Thus,dividingEquation(19)by1–

:









 ·

1



1



where

 1



(20)



Theequationfor



asaninfiniteseriesisderivedbyobservingthat

inEquation(20)

approaches0as

approaches,solongas0≤

 1.

lim













0

1



 (21)

lim















1



where0 

 1



(22)



VariousotherequationsintheTCPmodelsarederivedbysubstitutingtheappropriatetermsfora

and

inEquations(20)and(22).



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AppendixC Pay‐as‐you‐gopricemodel

Thecumulativediscounte dpay‐as‐you‐gopriceover

yearsisbasedonthesumofa

geometricallydecreasingseriesofpayments,eachproportionallydiscountedfromGbyafactorof

1–

(seeFigure2):





,



   ·



1



·1



·1



(23)



ThesolutionforEquation(23)issimplythegeneralsolutionforafinitepowerseriesgivenby

Equation(20)with

substitutedfor

and1–

for

.

,·

1



1



where



and

 1

 (24)



Substitutingfor

and

andsimplifyingproducesthecumulativediscountedpay‐as‐you‐goprice

over

years.

,·

11







where

 0



(25)



Likewise,thefinitepowerseriesalsohasasolutionforthecasewheretimeisarbitrarilylargeas

longasitsatisfiestheconvergencecriterion, 0 

 1.





∞,







1



wherea=Gandx=1−d

(26)

Substitutinginfor

and

andsimplifyingproducesthecumulativediscountedpay‐as‐you‐go

pricefor“forever.”





,







where0  1–

1



(27)





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AppendixD Discountfactor

Thevariable

inEquations(7),(8),(11),and(12)isacompositevalueorfunctionthatsumsthe

individualcomponent‐specificchangesinquantityandunitcost,weightedbythecomponent’s

proportionatecontributiontotheoverallcost(seeAppendixE).





·



 



·



·











ℓ

·









·



·









·



·



  









·









·





(28)

where









·



(29)







·

·



(30)







ℓ·

·



(31)









·

·



(32)







·

·



(33)







·





(34)









·



(35)



Annualpercentagerateofchangeinaggregatepreservationservicecost.



WeightingfactorfortheSystem component.

AnnualpercentagerateofchangeinfixedcostofthearchivalSystem.



WeightingfactorfortheWorkflow component.

AnnualpercentagerateofchangeinthenumberofsupportedWorkflows.

AnnualpercentagerateofchangeinthenominalunitcostofaWorkflow.



WeightingfactorfortheContentType component.

ℓ

AnnualpercentagerateofchangeinthenumberofsupportedContentTypes.

AnnualpercentagerateofchangeinthenominalunitcostofaContentType.



WeightingfactorfortheMonitoring component.

AnnualpercentagerateofchangeinthenumberofsupportedMonitoring

activities.

AnnualpercentagerateofchangeinthenominalunitcostofaMonitoring

activity.



WeightingfactorfortheInte rvention component.

UCCurationCenter

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TotalCostofPreservation(TCP)  Page16of20

AnnualpercentagerateofchangeinthenumberofsupportedInterventions.

AnnualpercentagerateofchangeinthenominalunitcostofanIntervention.



WeightingfactorfortheStorage component.

AnnualpercentagerateofchangeinthenumberofStorage unitsconsumed.

AnnualpercentagerateofchangeinthenominalcostofaunitofStorage.



WeightingfactorfortheOversight component.

AnnualpercentagerateofchangeinthenumbercostofaunitofOversight.



Table11–Changeinpreservationservicecostnotation

SincetheSystemandOversightarefixedcosts,thenumeratorsofEquations(29)and(35)only

havetheunitcostterm;allotherweightingfactorshavebothnumberofunitsandunitcost

terms.SincethecostsforSystem,Workflows,

ContentTypes,Monitoring,Interventions, and

Oversightarecommongoods,theyareapportionedacrossallnProducers,asreflectedinthe

denominatorsofEquations(29)–(33)and(35);StorageisalwaysspecifictoagivenProducer,so

thereisnonterminEquation(34).

Notethatallof

thediscountfactorsarerealratesofchange,incorporatingtheeffects,ifany,of

inflation.



UCCurationCenter



TotalCostofPreservation(TCP)  Page17of20

AppendixE Paid‐uppricemodel

Likethepay‐as‐you‐goprice,thepaid‐uppriceover

yearsisbasedonthesumofageometrically

decreasingseriesofpayments(seeFigure3).Thepresentvalue

ofthefutureseriesof

paymentsusingthebasecostGdecliningannuallyby1–d,andanominalinvestmentreturn



compoundedmonthlyis:





,,



·





1

 ·





1



1





·







1







1





… 

·







1







1







(36)



Theeffectiveinvestmentreturne,incorporatingtheeffectofmonthlycompounding,is[Tucker]:

1



1









(37)



Eachdecliningterm,·



1





,representingafuturepaymentisconvertedtoitspresentvalue

byadjustingforthemonthly‐compoundedtimevalueofmoney,thatis,scalingby







1





,

andtheresultsaresummedtoproducethetotalpresentvalue.Rearrangingthetermsof

Equation(36)gives:

,,



1





·1 

1

1





1







1





…



1







1







(38)

ThesolutiontoEquation(38),issimplythegeneralsolutiontothepowerseriesgivenbyEquation

(20)whereais









andxis





.

,, ·

1



1



where  



1





and 

1

1



(39)

Substitutingfor

and

andsimplifyingproducesthepaid‐uppricefor

years.

,, ·







1









1







1





·





(40)

Likewise,thefinitepowerseriesalsohasasolutionforthecasewheretimeislargeaslongasit

satisfiestheconvergencecriterion,0 

 1.





∞,,







1



where



1





and 

1

1



(41)

Substitutingfor

and

andsimplifyingproducesthepaid‐uppricefor“forever.”

UCCurationCenter

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TotalCostofPreservation(TCP)  Page18of20





∞,,















where0

1

1

1



(42)

UCCurationCenter



TotalCostofPreservation(TCP)  Page19of20

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>,

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