Analysis of a pricing method for elastic services with guaranteed GoS

Jou nal o Se ice Science and Managemen , 2012, 5, 386-402 doi:10.4236/jssm.2012.54045 Published Online Decembe 2012 (h p://www.SciRP.o g/jou nal/jssm) Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS Ma cos Pos igo-Boix, José L. Melús-Mo eno Depa men o Telema ics Enginee ing, Uni e si a Poli ècnica de Ca alunya (UPC), Ba celona, Spain. Email: ma cos.p[email p o ec ed], eljmm@en el.upc.edu Recei ed Sep embe 24 h, 2012; e ised Oc obe 26 h, 2012; accep ed No embe 10 h, 2012 ABSTRACT Se ice P o ide s (SPs), which o e se ices based on elas ic ese a ions wi h a gua an eed G ade o Se ice (GoS), should know how o p ice hese se ices and how o quan i y he bene i s in di e en scena ios. This pape analyzes a me hod o e alua ing he p ice o a se ice based on elas ic ese a ions wi h a gua an eed G ade o Se ice. The me hod wo ks as ollows: Fi s , he SP de e mines he equi emen s o he se ice ha wan s o o e ; Second, he SP e alua es he a e age a e o he accep ed elas ic ese a ions o he se ice wi h a gua an eed GoS; Thi d, he SP calcu- la es he p ice ha gua an ees he GoS wi h an agg ega e demand unc ion ha depends on a demand modula ion ac o o he elas ic ese a ions ha is he mean ese ed bandwid h, B es; and Finally, he SP ob ains he op imum alue o he elas ici y o he ese a ions ha gi es he maximum e enue, and he equi ed access bandwid h in his case. The pape no only applies he me hod o a class i o elas ic ese a ions when a linea -based demand and a e enue unc ion a e selec ed, bu i also analyzes he in luence o each one o he conside ed pa ame e s. This me hod could be ex ended o he case o mul iple classes o independen and gua an eed elas ic se ices, applying he me hod o each se ice wi h i s es ima ed demand and e enue unc ions. Keywo ds: Elas ic Rese a ions; S eaming; GoS; Mean Rese ed Bandwid h pe Accep ed Reques ; Agg ega e Demand Func ion; P icing; Re enue 1. In oduc ion Se ice P o ide s (SPs) wan o es ima e he e enue o he se ices ha hey p o ide ha usually depends on he applied p ice o he o e ed se ices. Cu en ly, he se - ices ha he SPs p esen ea o co e a wide spec um o p o iles in he aim o adjus hem o he p e e ences o hei di e en use s. In ha sense he e exis use s ha eques elas ic se ices ha could be deli e ed wi h a iable bandwid h, ha is, hey assume ha no always hey could ecei e he same bandwid h o he eques ed se ice ( he bandwid h ese a ion o he se ice is elas- ic and i luc ua es be ween a minimum and a maximum alues). One example o his ype o elas ic se ice is he deli e y o s eaming ideo lows wi h di e en com- p ession le els. Use s wan o ge high-quali y o hei ese a ions, bu also hey could accep some ole able deg ada ion in he quali y o hei ese a ions i he e- duc ion o he p ice o his se ice is signi ican . Elas ic ese a ions equi e he suppo o new signal- ing mechanisms o he han he mos commonly used o- day, he esou ce ReSe Va ion P o ocol (RSVP) [1]. As an al e na i e, he Nex S eps in Signaling (NSIS) [2] p o ocol amily allows o ese e bandwid h in a speci ic ange. The In e ne Enginee ing Task Fo ce (IETF) c e- a ed he NSIS Wo king G oup in 2001 o sol e new sig- naling needs o ese a ions. Since hen, se e al In e ne RFCs and pape s ha e been published [3,4], including he QoS NSIS Signaling Laye P o ocol (QoS-NSLP) ha desc ibes he p ocedu es o signal QoS ese a ions be ween a Desi ed QoS and a Minimum QoS. In ou sce- na io each one o hem will espec i ely ep esen he bandwid h ha he use wan s o ese e and he mini- mum bandwid h ha he use needs o wo k p ope ly. Figu e 1 shows he p oposed scena io o he ese a- ion o elas ic se ices using he QoS-NSLP-based sig- naling mechanism. Acco ding o Figu e 1, when he use wan s o wa ch a ideo he access o he websi e whe e he SP lis s hei o e ed SLAs. In Figu e 1, he SLA is de ined by he G ade o Se ice (GoS) and o he pa- ame e s such as he Desi ed and he Minimum QoS, which a e espec i ely he highes (H) and lowes (L) bandwid h ese a ions o he se ice, and he elas ici y o he ese a ions (  ). In his pape his pa ame e , o a class i, is de ined acco ding o (1). Thus, i he elas ici y o he ese a ions is 0 he Desi ed and he Mini- mum QoS ha e he same bandwid h and he elas ici y is 1 i Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 387 Figu e 1. Scena io o he ese a ion o elas ic se ices based on he QoS-NSLP signaling mechanism. he Minimum QoS bandwid h is 0. In he scena io o i- deo con en dis ibu ion o Figu e 1 he SP de e mines bo h alues, he highes -quali y (H) and he lowes -qual- i y (L). Thus he elas ici y o he ese a ions o class i would be: 1 ii LH i   (1) In his scena io, ano he impo an pa ame e ha helps use s o quali y and o di e en ia e among SPs is he ese ed bandwid h pe accep ed eques B es,i. I ep esen s he e ec i ely ese ed bandwid h o class i o each use wi hin i s speci ied ange, ha is, be ween he Hi and Li. In addi ion, he me ic , es i B de ines he mean ese ed bandwid h pe accep ed eques , which es ablishes he mean size o he ese a ions o class i in he eques ed ange. This me ic ep esen s a demand modula ion ac o o he accep ed ese a ions in he sense ha use s would desi e ha he SP o e ed he alue o his me ic close o Hi. Acco ding o Figu e 1, he SP allows hei clien s o eques elas ic ese a ions wi h he same GoSi in an es- ablished bandwid h ange o each ese a ion o class i. In his pape , some p e ious conside a ions should be done om he scena io desc ibed in Figu e 1: Fi s , he pa ame e s GoS and , es i B a e ela ed o he ese a ions o he class o se ice i. The ese a ions a e ep esen ed by hei leng h and hei ese ed bandwid h o he gene - a ed session. Thus, each es ablished session is cha ac e - ized by he ime since he use asks o he ese a ion un il he session ends up, and does no ake in o accoun he ea u es o he packe s ansmi ed du ing he session; Second, al hough many de ini ions ha e been used o e alua e he GoSi o a class i o se ice, he e alua ion o his pa ame e he e is based on he p obabili y o ob- aining an accep ed ese a ion wi hin he eques ed ange; And hi d, all he ese a ions o class i, ha e he same p io i y. Figu e 2 shows he en i ies in ol ed in he scena io desc ibed in Figu e 1. Thus he SPs, which may also ac as Con en P o ide s (CPs), o e o each class o se ice, class i, a gua an eed GoSi. In ha sense he SPs should es ablish he app op ia ed ag eemen s wi h he Ne wo k P o ide s (NPs) o buy he necessa y access bandwid h ha allow hem o ha e he app op ia ed ac- cess bandwid h (Bi) in o de o gua an ee he o e ed GoSi. The e o e, in his pape , i is p oposed and analyzed a me hod ha e alua es he p ice o a class i o gua an eed elas ic ese a ions ela ed o some o he desc ibed pa- ame e s such as: i s elas ici y, i s gua an eed G ade o Se ice, i s mean ese ed bandwid h and he a ailable access bandwid h o he ese a ions. Quali a i ely speaking i wo ks as ollows: Fi s , he SP es ablish he cha ac e is ics o he se ice ha wan s o o e ; second, he SP ob ains he a e age a e o he accep ed elas ic ese a ions o his class, class i, wi h a gua an eed GoSi; hi d, he SP calcula es he p ice o hese ese a ions ha gua an ee he GoSi wi h a demand unc ion ha also depends on a demand modula ion ac o , , es i B. This las pa ame e could be jus i ied by he desi e o use s o paying mo e o he ese a ion when he alue o , es i B, is close o Hi. And inally, he SP ob ains he alue o he elas ici y o he ese a ions ha gi es he maximum e enue and he op imal bandwid h ha maximizes he e enue o his elas ici y. The p icing me hod o a class o gua an eed elas ic se ice also could be ex ended o he e alua ion o mul iple classes o independen and gua an eed elas ic se ices, applying he ob ained ex- p essions in his pape o each conside ed class. Howe e Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 388 Figu e 2. En i ies conside ed. his me hod is unable o e alua e and o analyze he case o dependen se ices, since o deduce he app op ia e demand unc ions o o es ablish he ela ions be ween he a iables ha a e in ol ed in is e y di icul ask wi h he analy ical ools used he e. I is s aigh o deduce quali a i ely speaking some conclusions, such as, he alue o he es ablished GoS o he ese a ions de e mines he accep ed demand o he eques ed se ices. So, quali a i ely speaking, i he gua an eed GoS is high he accep ed eques s will be less han i he gua an eed GoS is low and consequen ially, he p ice o he se ice would inc ease o he conside ed access bandwid h. Howe e , he SPs no only wan o ge quali a i e esul s, bu hey also need o es ablish p oce- du es o know how o quan i y he p ice o hese se ices and o c ea e he app op ia ed scena io o o e hem. Many ques ions could appea abou he u ili y o his me hod o he SPs. Thus, he i s one could be o hem o y o iden i y he con enience o i s implemen a ion, ha is, when his me hod could be app op ia ed o im- plemen o elas ic se ices? O he , wi hou any speci ic o de , maybe when he SPs don’ ha e enough esou ces (limi ed access bandwid h) and also, hei use s could accep some changes in he ype o se ice hey ha e eques ed. In his case, does he ob ained e enue allow hem o ge wha hey wan ? O e en, will be he ob- ained e enue o he elas ic ese a ions no a away o e en be e han o inelas ic ones? O , he same ques ion could be o mula ed in o he wo ds, wha should be he size o he esou ces (access bandwid h) ha p io i izes he use o he elas ic agains inelas ic ese a ions? How many use s could access o he se ice using elas ic es- e a ions in compa ison o he case o using inelas ic ese a ions? Wha is he alue o he elas ici y o he ese a ions ha ge s he maximum e enue? e c. The me hod mus allow answe ing hese ques ions o he SPs wi h he aim o ge ing he solu ions ha bes i hei equi emen s o p ice elas ic ese a ions. In essence, his pape p esen s ou main con ibu ions:  An e alua ion o he p oposed p icing me hod ha al- lows o assign p ice o mul iple classes o independ- en and gua an eed elas ic s eaming se ices wi h he same p io i y and, acco ding o some pa ame e s such as he elas ici y o hei ese a ions, he a ailable e- sou ces (access bandwid h), as well as, o he pa ame- e s ha de ine and es ablish he o e ed se ices and hei demand unc ions. Each one o he independen classes could be e alua ed ollowing he same p oce- du e as o a class i.  The analysis highligh s he impo ance o he elas ic- i y when he access bandwid h is limi ed, as well as he impo ance o i s app op ia ed dimensioning, in o de o maximize he e enue o he SP.  The analy ical e alua ion o he p ice assigna ion o a single class o elas ic ese a ions, class i, is based on a closed- o m exp ession ha educes he compu- a ional complexi y o he Ma ko models.  The demand unc ion o each se ice will depend no only on i s p ice (€/ ese a ion), pi, as usually is con- side ed, bu also on a demand modula ion ac o , , es i B ha also depends on he access bandwid h. Al- hough he selec ed demand unc ion in he pape is a linea -based unc ion ha depends on he p ice and he access bandwid h, i could be conside ed ano he Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 389 one. In any case, he p ice will be inally ob ained in- e ing his demand unc ion. The emainde o he pape is o ganized as ollows. Sec ion 2 p esen s some esea ch in his ield and i is labeled as ela ed wo k. Sec ion 3 desc ibes he p oposed p icing me hod o se ices based on elas ic ese a ions. Sec ion 4 analyzes and applies he p oposed me hod o e alua e he p ice assigna ion o a single class o elas ic ese a ions, class i, when a linea -based demand unc- ion Di and a e enue unc ion a e selec ed, quan i ying and highligh ing he impo ance o he elas ici y o he ese a ions and he a ailable esou ces (access band- wid h) in he e alua ion o he SPs e enue. Sec ion 5 summa izes he main conclusions. Also his pape in- cludes wo appendices. In Appendix A, he GoSi and he mean ese ed bandwid h pe accep ed eques , es i B a e deduced by means a Ma ko -chain based model (based on quad a ic compu a ional complexi y) and an app oxi- ma e model (based on cons an complexi y). As he ap- p oxima e model is e y close o he Ma ko -chain based, he analysis o he me hod is done based on ha because i allows unde s anding mo e clea ly he ela ions among he pa ame e s ha use his me hod in he p ocess o as- signing p ices in Sec ion 4. In Appendix B, he p ice o a class i o elas ic ese a ions is analy ically deduced, aking in o accoun he selec ed linea -based demand unc ion Di. 2. Rela ed Wo k This pape desc ibes and analyzes a me hod ha helps SPs o p ice elas ic se ices wi h gua an eed GoS, se- lec ing an agg ega e demand unc ion, D, ha es ab- lishes he ela ion be ween he numbe o use s ha a e willing o ge he se ice and he p ice hey pay o i . The p ice o each class o hese se ices is based on: he a e age a e o he accep ed class o elas ic ese a ions wi h gua an eed GoS and hei mean ese ed bandwid h pe accep ed eques , , es i B. In [5] he pa ame e s B es,i and , es i B we e in oduced and was also analyzed how is he in luence o he alue o he GoSi in hei e alua ion In ha sense, he pa ame e , es i Bis conside ed as a de- mand modula ion ac o o he p ice o he elas ic ese - a ions. This pape in oduces he pa ame e , es i B as a new componen in he de e mina ion o he p ice o he elas ic ese a ions and also ca ies ou he analysis and calcula ion o he elas ici y o he ese a ions ha max- imizes a chosen e enue unc ion. Al hough many me h- ods o p ice se ices ha e been p oposed only a ew a e ocused on elas ic ese a ions bu nei he o hem has join ly ackled he issues ea ed in his pape . Fo exam- ple, no pape s assume he GoS as a cons ain ha a ec s he p ice o he se ices based on elas ic ese a ions. Thus, in his sec ion some pape s ha sha e pa o he is- sues ela ed in his pape ha e been e ised. Re e ence [6] analyses he quan i a i e in luence o he gua an eed GoSi in he e alua ion o he mean ese ed bandwid h o each ese a ion , es i B. Addi ionally he pape p oposes a me hod o es ablish he p ices o wo classes o elas ic se ices, bu di e s om he pape p e- sen ed he e since he calcula ed p ice he e didn’ ha e in o accoun he in luence o he use ’s demand, ha is, he p ice o he se ice always depend on he conside ed agg ega e demand unc ion. The p oposal p esen ed in his pape is o ally di e en om he p esen ed he e, since he e he e is selec ed an es ima ed (linea -based) demand unc ion o he se ice ha es ablishes a ela ion wi h he p ice o he se ice and he , es i B. Fu he , is also analyzed how he elas ici y and he bandwid h a ec he SP’s e enue. In [7] he same au ho s o his pape desc ibed a me hod o p ice subs i u e gua an eed se - ices. The e, i was selec ed an exponen ial agg ega e demand unc ion. The p ices we e ound in e ing hei demand unc ions and knowing ha in equilib ium i is accomplished ha he alue o he a e age a e o ac- cep ed ese a ions o each class o se ice, ha maxi- mizes he chosen e enue unc ion, is equal o i s agg e- ga e demand unc ion Di. Besides, he conside ed me hod, N classes o subs i u e se ices, was only g aphically analyzed o he case o wo subs i u e se ices, he ac- cess bandwid h and he elas ici y o he ese a ions we e ixed, he de e mina ion o he demand unc ions o he wo subs i u e se ices, each one depending on he p ice o he o he se ice, and he a ainmen o he pai s o he accep ed demand (which we e ob ained by ial and e o un il hey ma ch an exp ession) ha accomplished o bo h se ices he gua an eed GoS and maximized he e- enue. Al hough in his pape he used me hod o deduce he p ice o he elas ic se ices seems o be he p oposed in [7], he e a e many subs an ial di e ences in i s appli- ca ion. Thus, in [7] wasn’ p esen ed any kind o analysis o he ob ained esul s, due o he di icul y o ge ing hem om he use o a Ma ko -chain based model. How- e e , in his pape , he app oxima e analy ical solu ion (closed o m solu ion) allows o es ablish in a clea way he ela ionships be ween he pa ame e s ha in e ene in he me hod in he p ocess o p icing elas ic se ices. This pape di e s om he p esen ed in [7] a leas in h ee aspec s: Fi s , i only ea s wi h one class o se ice, al hough he conside ed dependencies a e mo e complex han he e. In ac , he g aphical esul s depend among o he pa ame e s on he access bandwid h and he elas ic- i y o he ese a ions, wha allows ge ing he elas ici y and he access bandwid h ha op imize he selec ed e enue unc ion. Second, he demand unc ion o he se ices depends no only on he p ice, bu on a demand modula ion ac o , , es i B . Thi d, he u iliza ion o he me hod is based on an app oxima e analy ical model ( e y close o he simula ion model) used in he e alua- Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 390 ion o he GoS and , es i B , and di e en om he model used in [7]. Some pape s p esen di e en me hods o p ice elas ic se ices bu he p oposed solu ions ha a e desc ibed he e a e clea ly sepa a ed o wha is p esen ed in his pape . Thus in [8], he au ho s p esen a combined s udy o p ice compe i ion and a ic con ol in a conges ed ne wo k whe e he SPs se he p ices in he aim o maxi- mize hei p o i s. In [9] he au ho s p esen a S a e Es i- ma ion based In e ne a ic low con ol sys em whe e he objec i e is maximize he agg ega e bandwid h u ili y o ne wo k sou ces o e hei ansmission a es. In [10], he pape ocuses on he p o ide compe i ion aspec , in a game heo e ic se ing, he a ic conside ed is elas ic and he e a e mul iple ypes o i and each ype o a ic is sensi i e o a di e en deg ee o Quali y o Se ice (QoS). In [11] he au ho s design a amewo k ha is composed o eedback signals and he co esponding sou ce adap a ion scheme o p o ide di e en ia ed bandwid h se ice o elas ic and inelas ic applica ions. In [12], au ho s p opose an app op ia e p io i iza ion p icing s uc u e whe e use s a e p o ided wi h incen- i es and a e able o choose be ween wo se ice classes. In [13], au ho s p esen an in eg a ed solu ion (in eg a - ing p icing in o QoS ou ing) o enabling he nex gen- e a ion In e ne o achie e he di e en ia ed se ice and a ailabili y gua an ee. Re e ence [14] desc ibes in a wi eless scena io an admission con ol algo i hm ha op imizes he e enue when he QoS is gua an eed. The p ice depends on he holding p ices (bandwid h ese e), he usage p ice (a e age usage, he elas ici y o he a ic) and he conges ion p ice. Re e ences [15-17] p esen he issue o p icing ela ed o di e en scena ios and u he ea u es o he o e ed se ices. Thus in [15] he au ho s b ie ly e iew he s a e o he a and echnological g ow h o conges ion con ol o in eg a ed se ice ne - wo ks since p icing is a p ope ool o manage conges ion, encou age ne wo k g ow h, and alloca e esou ce o use s in a ai manne . Re e ence [16] is one o he i s books ha ea conjunc ly echnology and p icing and, in e - e ence [17] he au ho s p esen a ecen classi ica ion o he p oposed p icing me hods in wi eless ne wo ks. In e e ences [18-20] di e en me hods a e p esen ed o de e mine he use u iliza ion unc ion. Thus in [18], he au ho s p opose a solu ion o b idging he gap be ween he exis ing heo e ical wo k on op imal p icing and he una ailabili y o p ecise use u ili y in o ma ion in eal ne wo ks. In [19] use s speci y he u ili y o alue hey a ach o di e en quan i ies o esou ce using a u ili y unc ion, so he esou ce alloca o knows he u ili y unc- ion o use s a he ime o esou ce alloca ion and hen alloca es esou ces based on he objec i e o maximizing he agg ega e a e age u ili y ob ained by uni ime. In [20] each use is assumed o ha e a u ili y unc ion which is a conca e inc easing unc ion o he a e a which she sends da a h ough he ne wo k. The p oblem is o ind he ec o o use s’ a es such ha he sum o all use s’ u ili y unc ions is maximized, subjec o esou ce capac- i y cons ain s. O he e e ences e alua e how admission con ol a ec s he ob ained GoS (conside ed as a echni- cal cons ain ) o he se ices. These pape s analyze no only he case o a class o se ice, bu o mul iple se - ice classes. Thus in [21] au ho s pay hei a en ion o he in e ela ion be ween p icing and admission con ol in QoS-enabled ne wo ks and p opose a a i -based a - chi ec u e amewo k ha lexibly in eg a es p icing and admission con ol o mul i-domain Di se ne wo ks. In [22] a comp ehensi e su ey abou Call admission con- ol in wi eless ne wo ks is shown. In [23] au ho s say ha adi ional CAC schemes mainly ocus on he ade- o s be ween new call blocking p obabili y and hando call blocking p obabili y. The e o e, hey in oduce he p icing as an addi ional dimension o call admission con- ol p ocess in o de o e icien ly and e ec i ely con ol he use o wi eless ne wo k esou ces. In [24] au ho s in es iga e he condi ions whe e bo h BE a ic and a - ic explici ly equi ing QoS (Gua an eed Pe o mance, GP) a e p esen and hey p opose h ee CAC ules o he GP a ic. In [25] au ho s u ilize admission con ol algo- i hms designed o e enue op imiza ion wi h QoS gua- an ees o de i e op imal p icing o mul iple se ice cla- sses in wi eless cellula ne wo ks. O he au ho s analyze p ice assigna ion and p opose solu ions ha wo k in di - e en beha io . Thus in [26], i is desc ibed a scalable connec ion managemen s a egy o QoS-enabled ne - wo ks o ackle he p oblem o app op ia ely p o ision- ing and alloca ing connec ions. In [27] is in oduced a se ice model ha p o ides pe - low bandwid h gua an- ees, whe e use s subsc ibe o a gua an eed a e. In [28] au ho s conside he p oblem o p icing o bandwid h p o isioning o e a single link. The ne wo k adminis a- o con ols he esou ce alloca ion by se ing a p ice a e e y epoch, and each use ’s esponse o he p ice go - e ned by a demand unc ion. In [29] au ho s in es iga e he sensi i i y o esou ce alloca ion and he esul ing QoS o esou ce p ices in a ese a ion-based QoS a chi- ec u e ha p o ides gua an eed bounds on packe loss and end- o-end delay o eal applica ions. In [30] is con- side ed he p icing and alloca ion issues o dis ibu ing digi al con en s ia Web and P2P channels. U ilizing a game heo e ic model, he alloca ion equilib ium wi h espec o a ious business goals is examined. In [31] is es ablished a me hod o assign p ices based on-packe queues sizes in he ne wo ks. 3. A P icing Me hod o Se ices Based on Elas ic Rese a ions This sec ion desc ibes he p icing me hod o mul iple classes o independen and gua an eed elas ic ese a- ions. Howe e , be o e going on wi h he me hod, i is Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 391 con enien o ake in o accoun he di icul y o de e - mining he agg ega e demand unc ion D i, which is a simila p oblem in many p oposals o p icing se ices. The knowledge o his unc ion in ad ance is always, as many esea che s ha e poin ed ou , a e y di icul ask ha he SP needs o sol e. As i is known, he agg ega e demand unc ion usually ep esen s he sum o indi idual demands o each use ha ha e di e en willingness o pay o he se ice. I is ha d o iden i y his beha io and he e o e, he cu e ha shows he desi e o he use s o pay a p ice o he eques ed se ices. Thus, he SP has o es ima e by wha e e means i deems adequa e (analy i- cally, by simula ion, heu is ically, e c.) he demand unc- ion o each se ice. Fo simplici y, his pape assumes ha in he e alua ion o a se ice class o elas ic ese a- ions, class i in Sec ion 4, he chosen agg ega e demand unc ion is linea -based. O cou se, i he demand unc- ion changes, he quan i a i e esul s ha he me hod ob- ains should be di e en . The ou comes o his me hod a e he p ice pi and he alue o he elas ici y o each se ice ξi and he op imal bandwid h ha maximize he SP’s e enue. The me hod consis s o he ollowing s eps: The SP de e mines he se ice equi emen s ha limi i s easibili y. Figu es 1 and 2 illus a e he i s equi e- men : he SP wan s o o e gua an eed and independen se ices based on elas ic ese a ions. This implies ha each se ice has o gua an ee a pa icula GoSi, o he se ice o each elas ic ese a ion wi h elas ici y ξi ha is de e mined by he SP in o de o op imize i s e enue. Also, he se ice equi es a Desi ed QoS equal o Hi Mb/s and he e o e, om (1), he Minimum QoS will be equal o i  1 i H    . O he equi emen could appea om he a ailable esou ces o he SP, ha is, he access bandwid h o each independen se ice (Bi Mb/s). As each se ice alloca es Bi, he sum o he ese a ions o all classes should be below his access bandwid h Bi. Bi may be limi ed due o se e al ci cums ances, such as he ne wo k access echnology used by he SP o o e he se ice. The SP e alua es he maximum demand (in e ms o eques s pe uni ime) ha can be allowed o he se ice in o de o gua an ee he equi emen s o s ep 1, he alue o he GoSi o e e y o e ed class o independen elas ic ese a ions. In his pape , we p esen in Appendix A.2 an analy ical exp ession ha oughly app oxima es he GoSi o he elas ic se ices ha a e o e ed using an access bandwid h Bi. This exp ession has been alida ed by simula ion and using he loss sys em model also in- cluded in Appendix A.2. The SP ob ains he p ice o he se ice i ha gua an- ees he GoSi. In o de o ob ain he p ice o he se ice, he SP needs o es ima e he demand unc ion Di by wha e e means i deems adequa e. This pape assumes a linea -based demand unc ion, explained in Appendix B, ha depends on he p ice and he mean ese ed band- wid h , es i B, (a demand modula ion ac o ha is calcu- la ed in Appendix A.3). Since , es i B is also dependen on Bi, he demand unc ion is also de ined in e ms o he p ice o he se ice and Bi. The SP e alua es he e enue Ri using he ob ained p ice in s ep 3 and inds ou he elas ici y o he ese a- ions ha maximizes he e enue. In addi ion, i band- wid h was no limi ed, he SP could ob ain he bandwid h ha op imally de e mines he se ice access bandwid h Bi. The e enue unc ion, used in his pape , assumes o simplici y ha only depends on he p ice, he a e o ac- cep ed eques s and he cos o he access bandwid h. Howe e , i is well known ha mo e complex exp es- sions, which may exp ess pa o he SP’s business model, could also be used. 4. Analysis o he Me hod: The Impo ance o he Elas ici y o he Rese a ions and he Bandwid h on he SP’s Re enue In his sec ion we apply he p icing me hod, desc ibed in Sec ion 3, o analyze quan i a i ely how he p ice o a class i o elas ic ese a ions and he e enue change depending on he elas ici y o he ese a ions and he access bandwid h o he se ice. 4.1. S ep 1: De e mining he Requi emen s o he Se ice Be o e he SP applies his me hod, i should de ine he sui able pa ame e s o each class o elas ic se ice. Thus, in his pape i is assumed a gua an eed GoSi = gi, o all ese a ions, he same elas ici y, and he highes band- wid h o he eques ed ese a ion ange is Hi ha is equal o he maximum equi ed bandwid h o deli e he con en (B op,i). Speci ically, i is supposed a gua an eed GoSi o 0.95, Hi = 1 Mb/s, and 3 minu es o he mean ese a ion holding ime. Also, o he pa ame e s o he linea -based demand unc ion as i is p esen ed in Ap- pendix B a e: Dmax,i = 120 ese a ions/minu e, B op,i = Hi = 1 Mb/s and Pmax,i = 10€ . S ep 2: E alua ing he maximum demand ha gua an- ees he GoS. The SP calcula es he a e age a e o he accep ed es- e a ions,  i, ha gua an ees he GoSi. Using he ap- p oxima ion (12) in Appendix A.2, he exp ession o he maximum accep ed demand (2) is ob ained.   1 GoS 11 ii iiii g i BH g   i        (2) Figu e 3 shows g aphically how he maximum ac- cep ed demand ha gua an ees a GoSi = 0.95 changes o di e en alues o elas ici y and bandwid h. I he elas- Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS Copy igh © 2012 SciRes. JSSM 392 ici y ends o 1, he demand ends o +∞, since he es- e a ion eques s always a e accep ed. On he o he hand, i he elas ici y is ze o, he demand ends o a minimum alue i bandwid h is ixed, since a ese a ion wi h elas- ici y 0 equi es no less han Hi Mb/s. Fo he es o combina ions o bandwid h and elas ici y,  i inc eases sligh ly o low-medium elas ici y alues and o high elas ici y alues  i inc eases sha ply app oaching o a e ical asymp o e o +∞ o elas ici y equal o 1. As Bi inc eases, he maximum accep ed demand also inc eases in a linea way wi h a highe slope as elas ici y ap- p oaches o 1. Also i is wo h o men ion ha he alues o he gua an eed GoSi, Hi and he holding ime 1 i  ha e an impac on he maximum accep ed demand. Thus, he lowe hey a e, he highe can be he maximum ac- cep ed demand. wi h he maximum accep ed demand. Rega ding he gua an eed GoSi and acco ding o (3) he p ice ends o be 0 as lowe is gi. This is because he SP can gua an ee a GoSi ha ends o 0, e en i he maximum accep ed de- mand is conside ed. The Desi ed QoS,Hi, and he mean holding ime o he ese a ions, 1 i  , make he p ice o inc ease i bandwid h is limi ed, since he equi ed esou ces (bandwid h) also inc eases. Finally, he in- c easing o he maximum accep ed demand Dmax,i, im- plies ha he p ice augmen s in he aim ogua an ee he GoSi and he e o e, he a e age a e o accep ed ese a- ions dec eases. On he o he hand, an augmen o he maximum p ice Pmax,i implies ha he p ice inc eases since he willingness o pay o use s also inc eases. 4.3. S ep 4: Es ablishing he Elas ici y o Rese a ions and he Bandwid h in O de o Maximize he Re enue 4.2. S ep 3: Calcula ing he P ice Appendix B desc ibes he demand unc ion o he ana- lyzed se ice ha depends on he use s’ willingness o pay and a demand modula ion ac o (i.e., he mean e- se ed bandwid h pe accep ed eques ha is desc ibed in Appendix A). In his s ep, he SP ob ains he p ice o he accep ed elas ic ese a ions ha gua an ee a GoSi = gi. This p ice can be ob ained using exp essions (2) and (19) when B op,I = Hi. The SP calcula es he e enue om he deduced p ice o he se ice ha gua an ees he GoS o his class o se - ice, class i. In his pape , an in ui i e e enue unc ion Ri(4) is conside ed ha ha e h ee e ms: he accep ed se ice’s demand DiGoSi, he p ice paid o he se ice pi and he cos o he alloca ed esou ces, which is sup- posed p opo ional o he access bandwid h. Al e na i ely, o he mo e complex e enue unc ions [32] could be ap- plied in o de o include o he special cha ac e is ics o each SP. Figu e 4 shows g aphically how he p ice pi changes o di e en alues o elas ici y and bandwid h. The p ice dec eases o 0€ when he elas ici y i  app oaches o   GoS Cos λGoS € minu e ii ii i iiiii RD p B pB      (4)  max, 1 1 342 Mb/s ii i i i BDHg B  , o simila ly, when Bi app oaches o The SP e alua es he e enue subs i u ing in exp es- sion (4) he alue o he p ice ha gua an ees he GoSi (3), he alue o  i o , op i i B   22 max, 113421 ii i i i i DH g    Mb/s . H(32), and he alue o he GoSi (12), as i is shown in exp ession (5). A p ice o 0€ means ha he GoSi is gua an eed e en    2 max, max, 2 max, GoS 2 max, 1 1 11 11 1 01 ii i ii ii ii g i iiii i B PBD g HD p BDH g                    iiii i Hg  (3)     2 max, max, 2 max, 2 max, 1 1 11 11 11 11 ii iiii i ii i i i ii ii i i i i i BB PBBD g HHD R BBD                   iii Hg Hg   (5) Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 393 0 200 400 0 0.5 1 0 1000 2000 3000  i B i (Mb/s)  i ( eq/min) Figu e 3. Maximum demand o a gua an eed GoSi = 0.95 and Hi = 1 Mb/s. 0 200 400 0 0.5 1 0 5 10  i B i (Mb/s) p i (€) Figu e 4. P ice o a Gua an eed GoSi = 0.95 and Hi = 1 Mb/s. In he case ha he SP has a limi ed bandwid h he elas ici y o he ese a ions ha maximizes he e e- nue, * i  is: max, max, max, 31 13 1 03 ii ii ii i i ii i BBDH HD g R BDH           i i g g  (6) Figu e 5 shows g aphically how he e enue Ri(5) changes o di e en alues o elas ici y and bandwid h and Figu e 6 shows how he elas ici y ha maximizes he e enue o a Gua an eed GoSi depends on bandwid h. Analyzing exp essions (5) and (6), i can be deduced ha he e enue inc eases un il he alue o elas ici y gi en by 1114 Mb ii B   0 200 400 0 0.5 1 0 100 200 300  i B i (Mb/s) R i (€/min) Figu e 5. Re enue o a Gua an eed GoSi = 0.95 and Hi = 1 Mb/s. 0100 200 300 400 0 0.2 0.4 0.6 0.8 1 B i (Mb/s)  i * Figu e 6. Values o he elas ici y o he ese a ions ha maximize he e enue o a Gua an eed GoSi = 0.95 and Hi = 1 Mb/s. demand Dmax,i, makes he e enue and he elas ici y ha maximize he e enue o inc ease and an inc emen o he maximum p ice Pmax,i, o ces he e enue o inc ease, since he willingness o pay o he use s also inc eases, bu his e ec has no impac on he op imum elas ici y. The e enue o he op imum elas ici y o he ese a- ions is he ollowing: max, max, max, max, max, max, max, max, 3 2 9 1 when 3 1 1 11 11 when 3 1 when . 3 ii ii ii ii iiiii i iii i ii ii ii ii ii i ii ii iii iii i B RP DgB H BDHg BB RP g HHD DHgB DHg RB BDHg                              s, i 114 Mb s i B. I band- wid h is highe han his alue, he elas ici y o he ese - a ions will no p o ide any signi ican bene i in compa i- son wi h an inelas ic ese a ion. The op imum alue o he elas ici y is di e en o each conside ed Bi and dec eases as Bi inc eases. This beha io is due o he ac ha an inc e- men o Bi implies mo e esou ces ha allow accep ing mo e use s wi h less elas ici y in hei ese a ions. On he o he hand, i he SP is o ced o use a p e-es ablished p ice, he use o a lowe gi can inc ease i s e enue. The inc ease o Hi, and 1i  implies ha he op imum elas ici y aug- men s. Finally, an inc ease o he maximum accep ed ii B  (7) In he case ha he SP has no limi ed bandwid h he alue o he bandwid h ha gi es he bes e enue, when Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 394 is applied he elas ici y o he ese a ions ha maxi- mizes he e enue. I u he allows an op imal dimen- sioning o he access bandwid h Bi, is * i B and is ex- p essed acco ding o (8). * max, 2 max, max, max, * 2 max, max, max, 0 13 27 11 2 ii ii i i ii i ii i i ii ii ii i iiii P H PDg P BH H P H Dg PH    3 i i i                        (8) Figu e 7 shows how he e enue * ii i R    (7) changes o di e en alues o bandwid h. As i can be seen, he e enue has a maximum equal o 268.16€/min o i= 165.87 Mb/s ha co esponds o B0 i    . The alue o he op imum bandwid h i dec eases wi h he inc emen o he p ice o he access bandwid h ( B i  ). 5. Conclusions This pape p oposes a p icing me hod ha helps SPs o assign sui able p ices o mul iple classes o independen s eaming elas ic se ices wi h gua an eed GoS. The pa- pe de e mines he p ice o one class i o elas ic s eam- ing se ices aking in o accoun he accep ed a e age a e o ese a ions λi, wi h a gua an eed GoSi and, assuming a linea -based unc ion as agg ega e demand unc ion Di. The SPs ha wan o o e elas ic se ices should ha e o calcula e hei p ices. In his p ocess his me hod could help hem in calcula ing hem by means o de ining o es ima ing in ad ance o hese se ices some o he pa- ame e s ha bes could ma ch hei needs o he a ail- able esou ces. Some o hem a e: he alue o he o e ed elas ici y o he ese a ions ξi (i could be wha o e s he maximum e enue), he highes alue o he ese a- 0100 200 300 400 -100 0 100 200 300 B i (Mb/s) R i   i =  i * (€/min) Figu e 7. Op imum bandwid h o he elas ici y o he es- e a ions ha maximizes he e enue o a Gua an eed GoSi = 0.95 and Hi = 1 Mb/s. ion Hi, his pa ame e is ela ed o he maximum quali y o he deli e ed con en ha he SP expec s o gi e hei use s, he alue o he gua an eed GoSi ( his alue could be se acco ding o he alue o e ed by o he SPs o o- ally di e en ) and he a ailable esou ces (i.e., he ac- cess bandwid h, Bi). On he o he hand an issue ha could be di icul o de e mine is he agg ega e demand unc ion. Howe e , i is known ha he SPs ha e he app op ia e ools o ap- p oxima ely es ima e his unc ion and o o e come his si ua ion. The accu acy o his es ima ion is c ucial o e alua e he p ice using his me hod. Cu en ly we a e de eloping simula ion ools o es i- ma ing and es ablishing he p o ile o he use s ha could access o his ype o se ices wha would make possible o deduce app op ia ed agg ega e demand unc ions in scena ios whe e he SPs could o e hese elas ic se ices. Also, we a e also wo king on ex ending his me hod o he case o subs i u e se ices and o include di e en p io i ies o he ese a ions based on hei elas ici y. Finally i is ou challenge o analyze he case o mul iple classes o elas ic se ices ha a e no independen , in his sense simula ion ools a e unde in es iga ion since ana- ly ic models o deduce he de i ed agg ega ed demand unc ions in his case and he ela ions be ween he pa- ame e s ha in e ene a e eally ha d o ind ou . Fu u e wo k should also include a deep e ision and p oposal o new e enue unc ions and consequen ly in he hei e a- lua ion, he alue o he elas ici y ha maximizes hei e enues and wha should be he ela ion in each case among he elas ici y, he access bandwid h and o he pa- ame e s in ol ed in he aim o ge he maximum e e- nue. 6. Acknowledgemen s This wo k was suppo ed by he Spanish Resea ch Coun- cil unde p ojec s TEC2009-14598-C02-02, and he con- solida ed esea ch g oup 2009 SGR 1242 unded by he Gene ali a de Ca alunya. REFERENCES [1] B. B aden, e al., “Resou ce ReSe Va ion P o ocol (RSVP), Ve sion 1, Func ional Speci ica ion,” RFC 2205, 1997. h p://www. c-edi o .o g/ c/pd c/ c2205. x .pd [2] R. Hancock, G. Ka agiannis, J. Loughney and S. Van den Bosch, “Nex S eps in Signaling (NSIS): F amewo k,” RFC 4080, 2005. h p://www. c-edi o .o g/ c/pd c/ c4080. x .pd [3] J. Manne , G. Ka agiannis and A. MacDonald, “NSIS Signaling Laye P o ocol (NLSP) o Quali y-o -Se ice Signaling,” RFC 5974, 2010. h p://www. c-edi o .o g/ c/pd c/ c5974. x .pd [4] J. Ash, A. Bade and C. Kapple , “QoS-NSLP QSPEC Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS 401 0 5 10 0200 400 0 50 100 B i (Mb/s) p i (€)  i ( eq/min) Figu e 16. Pa icula ized demand unc ion o i  = 0, Dmax = 120 eques s/minu e, Pmax = 10 € and B op = 1 Mb/s. 0 5 10 0200 400 0 50 100 B i (Mb/s) p i (€)  i ( eq/min) Figu e 17. Pa icula ized demand unc ion o i  = 0.8, Dmax = 120 eques s/minu e, Pmax = 10€ and B op = 1 Mb/s.      max, ,max, 2 max, 2 max, ,max, max, ,max, max, 2 max, 2 ,max, ,11 1 when , 1 1 , ,1 when , 11 ii iiii i i op i i ii iii ii i opi i ii iii ii op i i ii ii iii i opi i Dp DpB H BP Dp pP B H BP Dp DpB B BP pP DpHB BP                           max, , max, 1, ii op i ii DpB P        max, max, max, max, , max, max, ,1 1 when , 1 , ,0 when . i iii i i i iii i o ii iii ii p DpB D P p pP B D B P DpB pP             I : , op i i BH      max, ,max, 2 max, 2 max, ,max, max, ,max, max, 2 max, 2 ,max, ,11 1 when , 1 1 , ,1 when , 11 ii iiii i i op i i ii iii ii i opi i ii iii ii op i i ii ii iii i opi i Dp DpB H BP Dp pP B H BP Dp DpB B BP pP DpHB BP                             max, 2 max, max, ,max, max, 2 max, ,max, max, 1, ,1 1 when , 1 , ,0 when . ii i ii ii iii i op i i ii iii i i opi i iii ii Dp H P Dp DpB H BP Dp pP B H BP DpB pP                  (32) Also, we can exp ess he alue o p ice as ollowing. I   ,1 op i i i BH  :  max, max, max, max, 1 , 0 i ii i iii ii PD D pB D            i (33) I   , 1 ii opii H BH   :        max, , max, max, , 2 , max, max, max, , , max, max ,1 1 when 1, 1, 1 ,1 when , 1 , ,1 i iii i opi ii i ii iiiiii op i i op i i iii i iii iii iiiiii op i i i i iii i pBP B DH DHBH B B pBP DB DBH B B B pBP D                            opi   , max, , when , , ,0 o he wise. i i iii opi i iii DB B pB         (34) pi (31) I : , op i i BH Copy igh © 2012 SciRes. JSSM Analysis o a P icing Me hod o Elas ic Se ices wi h Gua an eed GoS Copy igh © 2012 SciRes. JSSM 402        max, , max, max, , 2 , max, max, max, , max, max, ,1 1 when 1, 1, 1 ,1 when , 1 , ,1 i iii i opi ii i ii iiiiii op i i op i i iii i iii iii iiiiii op i i i i iii i i pBP B DH DHBH B B pBP DB DBH B H B B pBP D                            i   , max, , when , , ,0o he wise. op i i ii iiii op i i iii H DHB H B pB         (35)