Cloud Computing Spot Pricing Dynamics: Latency and Limits to Arbitrage

Transcription

1 Cloud Compuing Spo Pricing Dynamics: Laency and Limis o Arbirage by Hsing Kenneh Cheng, Zhi Li, and Andy Naranjo* *Warringon College of Business Adminisraion Hough Graduae School of Business Universiy of Florida Gainesville, Florida kenny.cheng@warringon.ufl.edu; zhi.li@warringon.ufl.edu; andy.naranjo@warringon.ufl.edu Curren Version: Ocober 2013

2 Cloud Compuing Spo Pricing Dynamics: Laency and Limis o Arbirage Absrac This paper examines he influence of laency on cloud compuing pricing dynamics. Using Amazon EC2 eas and wes marke spo insance pricing and laency inra-day daa from April 9, 2010 o May 22, 2011, we find considerable ime variaion in spo insance prices and prices are ofen persisenly greaer in he wes. Bivariae Vecor Auoregressive model resuls show ha wihin-marke auoregressive pricing effecs are larger han acrossmarke effecs. We documen ha a large porion of he relaive price discovery (over 70%) occurs in he eas marke. Our regression resuls furher show ha eas-wes laency differenials have a significanly posiive effec on eas-wes pricing differenials. Laency creaes a dynamic pricing wedge ha widens or narrows condiional on he laency differenials. Using an Error Correcion model, he speed of adjusmen from long-run pricing convergence errors causes he shor-run price differenial o narrow, bu he adjusmen is only parial. Key Words: cloud compuing, spo pricing, pricing dynamics, laency, arbirage 1

3 1. Inroducion Cloud compuing has garnered significan aenion as an increasingly imporan compuing environmen ha will coninue o grow over ime. According o conservaive esimaes by Reid and Kisker (2011), he global cloud compuing marke will grow from $40.7 billion in 2011 o $241 billion in The cloud has various forms, including: SaaS (Sofware as a Service), PaaS (Plaform as a Service), and IaaS (Infrasrucure as a Service). I has succincly been defined as an informaion echnology service model where compuing services (boh hardware and sofware) are delivered on-demand o cusomers over a nework in a self-service fashion, independen of device and locaion (Cheshire 1996). 1 Firms of all sizes have adoped or are considering moving o cloud services. Cloud compuing providers offer basic compuing and sorage resources a relaively low prices. Amazon s Elasic Compue Cloud (Amazon EC2) is he major cloud service provider; in fac, i has been called he Coke of cloud compuing in erms of marke share and here isn ye a Pepsi. 2 The prices of EC2 insances are based on he service cener where he insance is running. Cusomers can purchase EC2 insances hrough on-demand insances, reserved insances, and spo insances. 3 Spo insances are a relaively new mehod as of December 2009 o boh purchase and consume Amazon EC2 insances. They allow cusomers o bid on unused Amazon EC2 capaciy and run hose insances for as long as heir bid exceeds he curren spo price. Cusomers whose bids exceed he curren spo price gain access o he available spo insances. Hisorically, cusomers using spo insances have received significan price discouns beyond on-demand prices for no 1 Similarly, Garner (Plummer e al. 2008) describes he cloud as a syle of compuing where massively scalable IT-relaed capabiliies are provided as a service using inerne echnologies o muliple exernal cusomers. They esimae ha annual global marke for cloud compuing will rise o $150 billion by 2013 (Plummer e al. 2008). 2 In a Wall Sree Journal aricle (Clayon 2011), William Fellows, principal analys of he 451 Group, saes ha in erms of marke share Amazon is Coke and here isn ye a Pepsi. The aricle furher repors ha UBS Invesmen Research esimaed ha Amazon s Web Services revenue for is cloud division reached $500 million in 2010, rising o $750 million in 2011 and could hi $2.5 billion in Indeed, Garner esimaes sugges ha AWS already generaed nearly $3 billion in Jeff Bezos, Amazon s CEO, also old he company s shareholders ha AWS had he poenial o be as big as he firm s reail business, which had oal sales of over $24.5 billion in To iniiae Amazon EC2 cloud insances, here are wo basic seps. Firs, choose he insance ype(s); hen sar, erminae, and monior as many insances as needed using he web service APIs or he variey of managemen ools provided. Second, deermine wheher o run he insance in muliple locaions. There are six main groups of insance ypes: Sandard, Micro, High-Memory, High-CPU, Cluser-Compue and Cluser-GPU. They are divided by differen characerisics for specific work requiremens. 2

4 commimens beyond one hour. The Amazon EC2 spo marke uses he Vickrey aucion syle, where cusomers submi sealed bids and he provider compues a marke clearing price (Mazzucco and Dumas 2011). All winning cusomers pay he same price, which is he value of he lowes winning bid. Research indicaes ha his mechanism is a ruhful aucion given ha he supply level can be adjused ex pos (Zhang e al. 2011). 4 However, a conundrum arises when one examines Amazon EC2 spo prices as a visual inspecion of he spo prices reveals ha Amazon wesern EC2 cener spo prices are consisenly and significanly higher han hose of he easern cener for all of Amazon s compuing plaforms. Since cloud compuing services from he wes and eas ceners for he same compuing plaform are idenical goods, he consisenly posiive price differenials beween he wes and he eas ceners presens a seemingly clear arbirage opporuniy for cloud compuing cusomers and raises a fundamenal quesion abou he marke efficiency of cloud compuing. The consisenly posiive spo price differenials canno be sysemaically aribued o eiher he supply or demand of Amazon EC2 cloud compuing services. Tha is, if he sources for he observed pricing differenials were greaer supply (lower supply) in he easern (wesern) cener or greaer demand (lower demand) in he wesern (easern) cener, Amazon EC2 cusomers could easily aler heir spo bids from a dropdown menu o selec he cener wih he cheaper persisen pricing. Knowing ha he cloud compuing service is cheaper a he Amazon eas cener, all raional cusomers would naurally swich heir bids o he eas cener. This, in urn, would creae more demand a he eas cener, which hen would drive up he spo prices on he eas cener o reach he same level of he wes cener over ime. This equivalen pricing equilibrium, however, has no maerialized as he price differenials are persisen. A fundamenal research quesion concerning cloud compuing marke efficiency is, herefore, wha is he source of he pricing differenials, and does i manifes iself as a pricing wedge ha limis arbirage? Furhermore, given ha Amazon EC2 cusomers only observe spo price informaion and do no know he supply nor he demand of he spo 4 Alhough cloud compuing has dominaed discussions of corporae compuing sraegy, he prior lieraure provides lile guidance on how o opimally price he cloud compuing services o ensure allocaional efficiency and fairness. Das e al (2011) examine he effecs of providing a spo marke wih dynamic prices and forward conracs o hedge agains he risk of demand sochasiciy and unused (and hus wased) capaciy for an Inerne sorage provider. 3

5 marke, wha can hey glean from he pricing dynamics of he cloud compuing spo marke, and how migh hey beer reac o ha informaion? We use various economeric modeling approaches o address he aforemenioned fundamenal quesions. We apply vecor auoregressive models (VAR) o documen and measure spo insance pricing dynamics boh wihin and across he Amazon EC2 eas and wes regions. To measure he price discovery for he same good (i.e., Amazon EC2 cloud compuing spo insance) available in wo differen markes (i.e., eas and wes regions), we employ he wo mos widely acceped price discovery measures developed by Hasbrouck (1995) and Gonzalo and Granger (1995) o capure he exen o which pricing relevan informaion on he cloud compuing spo insances raded in differen regions is incorporaed ino he price. For he mos fundamenal quesion on he cloud compuing marke efficiency, we show ha nework laency, defined as he oal elapsed ime from he ime a reques is sen via he Inerne o he ime receiving a response (O3b Neworks 2008), is he key facor conribuing o he persisen posiive spo price differenials beween he Amazon EC2 wes and he eas regions. Our sudy is he firs o provide convincing evidence o explain his inriguing and perplexing cloud compuing marke efficiency issue. Brynjolfsson and Smih (2000) find ha branding, awareness, and rus are imporan sources of heerogeneiy in pricing among inerne reailers, while Brynjolfsson e al. (2009) documen he imporance of geography on he compeiion beween he Inerne channel and local sores. 5 We furher show ha even wih he same cloud compuing provider and compuing plaform (i.e., same provider and same good), price heerogeneiy sill exiss due o laency differenials across markes. Arguably, why should seconds of delay creaed by nework laency maer? In one of he earlies sudies on he response ime effec on user behavior, Miller (1968) showed ha en seconds is he hreshold for user aenion. However, his user aenion hreshold has reduced o wo seconds in oday s e-commerce environmen as consumers have become impaien when web pages ake longer han wo seconds o load (ForreserConsuling 5 Ba, Sallaer, and Zhang (2012) propose a compeiive model o explain he exisence and persisence of price dispersion for idenical producs in online markes. Their game-heoreic analysis suggess ha differences in online reailers service and recogniion levels are associaed wih prices. 4

6 2009). 6 These user aenion hresholds are imporan because a subpar Web experience resuls in los revenue and unfavorable cusomer percepion of he company. For example, an increase of 100ms response ime can resul in a 1% drop of sales a Amazon (Mazzucco 2010), and Google s raffic will drop by 20% for half a second increase in reurning search resuls (Mayer 2009). Laency is a key issue no only for firms offering producs and services o consumers over he Inerne, bu also for corporaions considering he adopion of cloud compuing. In fac, i has been dubbed he Achilles Heel of Cloud Compuing (Minnear 2011). As a furher example of he managemen relevancy and larger conribuion of our sudy, he chief cloud archiec for Neflix, Adrian Cockcrof, recenly saed in an inerview (Babcock 2013), Masering hese business radeoffs of weighing he cos and laency penalies, when hey exis, agains your business goals is one of he fundamenal challenges of cloud compuing. Cockcrof used a rough equaion o formulae he rade-off: How many dollars should you spend o reduce cusomer laencies by 50% if ha increases your conversion rae by 10%? However, here is a scarciy of research examining he impac of laency on various aspecs of cloud compuing implemenaion, including no research ha we are aware of ha examines he effecs of laency on pricing dynamics boh wihin and across markes. We find ha across Operaing Sysem (OS) plaforms and spo insance ypes, here is considerable ime variaion in he pricing dynamics. We also find ha prices in he wes are ofen persisenly greaer han prices in he eas over our sample period. Our bivariae VAR resuls sugges ha here are significan dynamic pricing relaions boh wihin and across he eas and wes markes. The wihin-marke effec is larger han he acrossmarke effec, bu here are also significanly pronounced across-marke pricing effecs. Using boh Hasbrouk s (1995) and Gonzalo and Granger s (1995) price discovery mehodologies, we find ha over 70% of he relaive price discovery occurs in he eas marke. To explain he observed ime varying pricing differenials across he eas and wes markes, we use boh regression procedures and an Error Correcion model (ECM). We find ha boh he eas and wes laency differenials have a significanly posiive effec on he pricing differenial, suggesing ha larger (smaller) laency effecs resul in larger (smaller) pricing differenials. Tha is, laency creaes a dynamic pricing wedge, similar o a varying 6 Cheshire (1996) argues ha 100ms should be he maximum arge response ime for nework ineracions as delays longer han his creae very siled ineracions. 5

7 ransacion cos, ha widens or narrows condiional on he laency differenials. From he ECM resuls, we also find ha he speed of adjusmen from long-run pricing convergence errors causes he shor-run price differenial o narrow, bu he adjusmen is only parial. The res of he paper is organized as follows. Secion 2 provides our empirical mehodology, while Secion 3 provides informaion on our daa and some descripive saisics. Secion 4 provides he core of our resuls saring wih a VAR model of he dynamic wihin and across marke pricing effecs, o measuring where price discovery is occurring, and ending wih using boh regression procedures and an Error Correcion model o explain pricing differenial effecs. Secion 5 provides some concluding remarks. 2. Empirical Mehodology Our empirical sraegy consiss of wo relaed pars: he firs par documens and measures Amazon EC2 spo insance pricing dynamics and price discovery; he second par ess and measures he exen o which laency and oher facors influence pricing differenials. In he firs par, we use Vecor Auoregressive (VAR) models o measure he dynamics beween eas and wes Amazon EC2 spo pricing. We hen employ Hasbrouck s (1995) and Gonzalo and Granger s (1995) price discovery mehodologies o furher measure he naure of informaion processing across hese markes. In he second par, we use OLS regressions and Error Correcion models o boh es and measure he exen o which laency and oher facors influence he observed pricing differenials across eas and wes Amazon EC2 spo insance markes over ime. 2.1 Pricing Dynamics and Price Discovery Vecor Auoregressive Models To capure he shor-erm pricing dynamics beween eas and wes Amazon EC2 spo insance pricing, we employ Vecor Auoregressive (VAR) models. In is simples form, a VAR model is composed of a sysem of regressions where wo or more dependen variables are expressed as linear funcions of heir own and each oher s lagged values, as well as oher poenial exogenous conrol variables. In more echnical erms, a vecor auoregressive model is he unconsrained reduced form of a dynamic simulaneous equaions model. An unresriced p h -order Gaussian VAR model can be represened as: Y 1Y 1 2Y 2... py p e, (1) 6

8 where Y is a vecor of variables, is a p x 1 vecor of inerceps, 1, 2,, p are p x p marices of parameers wih all eigenvalues of having moduli less han one so ha he VAR is saionary, and e is a vecor of uncorrelaed srucural shocks [ NID(0, )]. A problem arises wih he VAR framework if he variables in he sysem are non-saionary, which we es. To furher capure boh long- and shor-run dynamics and address nonsaionariy problems, we also employ Error Correcion models as discussed in he nex secion. We obain maximum likelihood esimaes of and using ieraed leas squares. The number of lags is chosen based on examinaion of he Akaike Informaion Crieria (AIC), Schwarz Bayesian Informaion Crieria (SBIC), and he likelihood raio selecion crieria for various choices of p. In a wo-equaion framework consising of only eas and wes pricing as endogenous variables, he diagonal coefficiens of represen condiional momenum in eas and wes pricing, while he off-diagonal coefficiens of represen condiional posiive feedback and anicipaion effecs (changes in wes pricing following changes in eas pricing and vice versa) Informaion Shares There are various approaches for measuring price discovery for he same good raded across markes. The fundamenal approaches build on he idea ha prices for he same good converge o a common efficien price in he long-run, bu deviae in he shor-run due o various marke fricions. While Hasbrouck (1995) and Gonzalo and Granger (1995) are he wo mos widely acceped price discovery measures, here is some debae in he lieraure abou how price discovery across markes should be measured and wha procedures should be implemened (Lehmann 2002). Baillie e al. (2002) and De Jong (2002) argue ha boh he Hasbrouck and Gonzalo-Granger definiions of conribuion o price discovery have heir meris. Hasbrouck s approach measures he exen of he common efficien price variaion explained by he price innovaion in each marke. Tha is, i focuses on he proporional conribuion of a marke s price innovaion o he innovaion in he common efficien price. In conras, Gonzalo and Granger s approach decomposes he price ino a long-run permanen price and ransiory componens, wih he price discovery weigh defined as he change in he permanen componen wih respec o he informaion shock. Imporanly, he resuls from using he Gonzalo and Granger approach differ a imes from hose of Hasbrouck s (1995). Therefore, in his paper we apply boh Hasbrouck s 7

9 (1995) and Gonzalo and Granger s (1995) mehodologies o he eas and wes Amazon EC2 spo insance pricing markes o deermine he informaion shares generaed by each marke. In is simples form, one can hink of he informaion shares as capuring he exen o which pricing relevan informaion on a good raded in differen markes is incorporaed ino he price. Tha is, i measures in simple erms he marke where he pricing relevan informaion is being incorporaed, which is subsequenly incorporaed in oher markes for ha same good. The basic idea is ha observed prices impound an efficien implici price ha is common o he markes where he good rades. Sources of variaion in his price can be aribued o differen markes. Therefore, he proporion of he price innovaion ha can be aribued o each marke is ha marke s informaion share -- is conribuion o price discovery. Boh Hasbrouck s informaion share model and Gonzalo and Granger s common facor model are based on he following Vecor Error Correcion (VEC) model: P 'P P e, (2) k 1+ + j 1 j j where is he error correcion erm. The error erm e is a zero-mean vecor of serially uncorrelaed innovaions wih a covariance marix and 2 2 are he variances of e 1 and e 2, is he correlaion coefficien. The firs erm on he righ-hand side of (2), 'P 1, represens he long-run equilibrium of wo price ime series, while he second erm on he righ-hand side of (2), o imperfec marke condiions. k j 1 j j P, describes shor-run deviaions due Hasbrouck convers he VEC model o obain a vecor moving average represenaion, which is P ( L) e and * (1) ( ) s=1 s P e L e. As discussed in Hasbrouck (1995), he long-run impac of a disurbance on each of he prices is inuiively given by (1). The row differences of his coefficien marix are hen checked. If he differences are all less han 0.001, we consider he rows of (1) o be idenical and use only he firs row of he coefficien marix. We use o denoe he firs row vecor in (1), (, ). Thus, 1 2 * ( ) s=1 s, where l (1, 1)' P l e L e. Hasbrouck defines e as he 8

10 common facor componen of wo marke prices wih variance '. When e 1 and e 2 are uncorrelaed, he informaion share of he j h marke is IS j 2 2 j j ', j 1, 2. When e 1 and e2 are correlaed, Cholesky facorizaion is used o remove he error caused by he correlaion. In his case, he informaion share of he j h marke is IS j ([ M ] j ) ' 2, where m,, 0 2 1/2. Since he Cholesky facorizaion is sensiive o (1 ) 11 1 M m 12,m 22 2, 2 ordering of he variables, we esimae he upper and lower bounds for each of he markes using boh possible order permuaions of he eas and wes Amazon EC2 prices. We use inra-day five minue inervals o esimae daily informaion shares. Our repored resuls are robus o alernaive inra-day frequencies. For each marke, he average informaion share for he period is calculaed as he mean of is upper and lower bounds. The firs several seps of he Gonzalo-Granger informaion model are similar o Hasbrouck s informaion shares approach. We again use inra-day five minue inervals o esimae daily marke price discovery shares. The eas and wes prices, p1 and p2, are hen shocked wih a uni impulse. We esimae a VEC model using 20 lags: p p A p A p... A p e, (3) where ( 1, 2) is he speed of price correcion when he price in one marke deviaes from ha in he oher marke. The Gonzalo Granger price discovery measures for p 1 and 2 1 p 2 are defined as: GG1, and GG Pricing Differenials OLS Regressions and Error Correcion Models We firs use various OLS regression specificaions o es for he influence of laency and oher facors on he pricing differenials across eas and wes Amazon EC2 spo insance pricing over ime. 7 In paricular, we employ he following inra-day pricing differenial regression models: 7 If he price level series are saionary, he OLS model is appropriae. In general, a series is nonsaionary if is mean, auocovariances, or oher higher momens are ime dependen. For example, if 9

11 PD Eas Wes Cenral DL DL DL, (4) PD PD PD 7 Eas Wes Cenral 0 1 DL 2 DL 3 DL di Di i 1 18 DL _ Ciy, 0 i i i 1 18 DL _ Ciy 0 i i di i i 1 i 1 7 D,, (5) (6) (7) where PD P P is he pricing differenial beween wes and eas Amazon EC2 spo Wes Eas insance pricing a ime, Eas DL, Wes DL,and Cenral DL are corresponding average regional laency differences a ime, DL_Ciyi are corresponding average ciy level laency differences a ime, and Di are various even indicaor variables (i.e., inroducions of new Amazon compuing insances, locaions, and reserved pricing changes). We include all hree regions or all eigheen ciies of he Inerne backbone in our base regression esimaes and herefore suppress he consan, 0, o avoid singulariy problems paricularly hose associaed wih even indicaor variables ha span a large porion of he sample period. We also perform reverse causaliy ess o confirm ha laency is driving he pricing differenial and no vice versa. To capure boh long-run and shor-run Amazon EC2 pricing dynamics, we employ an Error Correcion Model (ECM). The ECM framework allows us o model he eas and wes pricing relaions as an adjusmen process around long-run equilibrium values. Error correcion models are based on he idea ha wo or more ime series exhibi a long-run ime-varying equilibrium o which he sysem ends o converge. This long-erm convergence in pricing is an appealing assumpion given ha long-run pricing in boh he eas and wes should be similar or users would shif heir compuing o he lower priced marke. The long-run influence in he ECM is achieved hrough negaive feedback and error correcion, and his influence measures he degree o which long-run equilibrium forces drive shor-run price dynamics. he mean of a series varies wih respec o ime, i is likely o be non-saionary. The problem is ha if a series is non-saionary, hen simple ime-series echniques can resul in misleading (or spurious) values of inferenial saisics (e.g., -saisics, R 2 and DW) of a ype ha will cause one o erroneously conclude ha a meaningful relaion exiss among he regression variables. Simply saed, he es for a uni roo (non-saionariy) in a ime series is he es ha a regression of a series on iself lagged one period yields a coefficien of one. This es is complicaed by several feaures arising from he non-saionariy of he series under he null hypohesis. 10

12 Following he Engle-Granger wo-sep mehod, a long-run price model is specified in levels. The second-sage, shor-run, adjusmen model is specified in firs differences and includes a long-run error correcion erm from he esimaion of he long-run, equilibrium model. In he firs-sage, heory and economeric evidence are used o deermine if he eas and wes Amazon EC2 spo insance price series conain uni roos and are coinegraed. If he pricing series are coinegraed, a long-run equilibrium relaion (i.e., a coinegraing regression) can be specified in levels as: P Wes Eas P, (8) 0 1 where Eas P and P are he Amazon EC2 spo insance price levels in he wes and eas, Wes respecively. From his regression, we can esimae residuals as he differences beween he acual and esimaed equilibrium values of he price levels. If he residuals from equaion (8) are saionary, hey may be used as an error correcion erm in he shor-run price difference model as follows: PD n 0 i X i 1, (9) i 1 where PD P P is he pricing differenial beween wes and eas Amazon EC2 spo Wes Eas insance pricing in ime, Xi are firs differences of he explanaory variables (i.e., ˆ differences in laency in ime ), 1 is he error correcion erm (i.e., he lagged residuals from he long-run coinegraing regression), and all of he difference erms are saionary. Esimaion of equaion (9) provides evidence on shor-run pricing dynamics relaed o laency differenials (he αi s) and adjusmens o he previous disequilibrium in he longrun relaion, (he speed of adjusmen parameer). 3. Daa and Descripive Saisics 3.1 Amazon EC2 Spo Insance Pricing Daa We use Amazon EC2 eas and wes spo insance inra-day pricing daa over he April 9, 2010 o May 22, 2011 sample period. The begin and end daes of our sample period correspond o he availabiliy of he laency daa for our analysis. We collec hese incurred ransacion inerval pricing daa from Amazon s API, which provides hese daa for five regions, six insance ypes, six compuing capaciies, and wo Operaing Sysem (OS) 11

13 plaforms. 8 In our primary analysis, we use sandard m1.xlarge spo insance prices across he eas and wes U.S. regions for boh Windows and Linux/Unix operaing plaforms. 9 Our resuls are robus o alernaive insance ypes. 10 The eas and wes U.S. regions are chosen o keep he pricing analysis wihin one counry, and he ime-samped price daa across he wo regions are synchronized o a unified GMT. For our analysis, we also conver he incurred ransacion inerval daa (boh price and laency) o an hourly frequency by inerpolaing hem in beween incurred ransacion prices wih he mos recen incurred ransacion price. This allows us o ime mach boh our price series as well as our laency ime series. Our resuls are robus o alernaive iming frequencies. 3.2 Laency Daa The laency daa measured in seconds are colleced from CloudSleuh.com over he April 9, 2010 o May 22, 2011 sample period. CloudSleuh records and compares he performance of PaaS and IaaS providers from around he world. They use he Gomez Performance Nework (GPN) o measure he performance of an idenical sample applicaion running on several popular cloud service providers, which is how well he sample 8 The Amazon EC2 spo price insance regions are he U.S. Eas (Virginia, 08/2006), U.S. Wes (N. California, 12/2009), Europe (Ireland, 12/2008), Asia Pacific (Singapore, 04/2010) and Asia Pacific (Tokyo, 03/2011). The insance ypes are Sandard, Micro, High-memory, High-CPU, Cluser Compue, Cluser GPU, while he compuing capaciies are small, medium, large, xlarge, 2xlarge, 4xlarge. The OS plaforms are Windows, Linux/Unix. See hp://aws.amazon.com/ec2/insance-ypes/. 9 Each insance has a ype describing is compuaional resources as follows: m1.small, m1.large and m1.xlarge, respecively denoe small, large, and exra-large sandard insances; m2.xlarge, m2.2xlarge, and m2.4xlarge respecively denoe exra-large, double exra-large, and quadruple exra-large high memory insances; and c1.medium and c1.xlarge respecively denoe medium and exra-large high CPU insances. For each progression, he compuaional resources are scaled up by a facor of 2. For example, he sandard xlarge insance (API name: m1.xlarge) feaures are: 15 GB memory, 8 EC2 Compue Unis (4 virual cores wih 2 EC2 Compue Unis each), 1,690 GB insance sorage, 64-bi plaform, I/O Performance: High, EBS-Opimized Available: 1000 Mbps. These compuaional resources are wice as large as he m1.large insance. An insance is purchased wihin a geographical region. We use daa from Amazon s wo U.S. EC2 regions: US-eas and USwes, which correspond o Amazon s daa ceners in Virginia and California. 10 Sandard insances are well suied for mos applicaions. Micro insances (1.micro) provide a small amoun of consisen CPU resources and are well suied for lower hroughpu applicaions and web sies ha require addiional compue cycles periodically. High-Memory insances offer large memory sizes for high hroughpu applicaions, including daabase and memory caching applicaions. High-CPU insances have proporionally more CPU resources han memory (RAM) and are well suied for compue-inensive applicaions. Cluser Compue insances provide proporionally high CPU resources wih increased nework performance and are well suied for High Performance Compue (HPC) applicaions and oher demanding nework-bound applicaions. Cluser GPU insances provide general-purpose graphics processing unis (GPUs) wih proporionally high CPU and increased nework performance for applicaions benefiing from highly parallelized processing. 12

14 applicaion performs over ime from Inerne backbone locaions around he globe. Throughou each day a approximaely hiry minue o one hour inervals and from many backbone nodes, CloudSleuh moniors he response ime he oal ime elapsed while downloading boh web pages in he muli-sep es ransacion. The laency daa ha we obain correspond o he measured laency beween 18 backbone nodes from ciies hroughou he US o Amazon EC2 US-wes and US-eas. Similar o he spo pricing daa, he ime-samped laency daa are synchronized o a unified GMT, and we also conver he measured laency inerval daa o an hourly frequency by inerpolaing he in-beween laency measures wih he mos recen measured laency. This again enables us o ime mach boh our price series as well as our laency ime series. In our analysis, we use ciy-level (i.e., 18 nodes) laency daa. We also aggregae he ciy-level laency daa ino hree regions as follows: Eas = average (Newark + Alana + Boson +NY + Philadelphia + DC + Reson) Wes = average (San Jose + Mesa + Denver + LA +San Diego + Seale) Cenral = average (Dallas + Houson +Kansas Ciy + S. Louis + Chicago) Since he spo insance pricing differenials across he eas and wes markes should be relaed o laency differenials across hese markes, we creae he following laency difference variables: Laency Difference Variable DL_Ciyi L EasToEas L EasToWes L WesToEas L WesToWes L CenralToEas L CenralToWes DL Eas DL Wes DL Cenral Definiion (a each ime ) Average laency o Amazon Wes EC2 cener a ciy i Average laency o Amazon Eas EC2 cener a ciy i Average laency from Eas region backbone nodes o Amazon Eas EC2 cener Average laency from Eas region backbone nodes o Amazon Wes EC2 cener Average laency from Wes region backbone nodes o Amazon Eas EC2 cener Average laency from Wes region backbone nodes o Amazon Wes EC2 cener Average laency from Cenral region backbone nodes o Amazon Eas EC2 cener Average laency from Cenral region backbone nodes o Amazon Wes EC2 cener L EasToWes L EasToEas L WesToEas L WesToWes L CenralToWes L CenralToEas 13

15 3.3 Conrol Indicaor Variables As addiional conrol variables, we creae a series of indicaor variables corresponding o a series of Amazon EC2 evens ha migh influence he spo insance pricing dynamics. In paricular, we creae he following indicaor variables ha ake on a value of one a heir begin even daes and zero oherwise: Micro: Micro insances announced (Sepember 9, 2010) Singapore: Asia Pacific Region (Singapore) announced (April 29, 2010) 11 CC: Cluser Compue insances (Linux Only) announced (July 13, 2010) Free: AWS Free Usage Tier inroduced (Ocober 21, 2010) CG: Cluser GPU insances announced (November 15, 2010) Reduced: m2.2xlarge and m2.4xlarge on-demand reserved price reduced (Sepember 1, 2010) Tokyo: Asia Pacific Region (Tokyo) announced (March 2, 2011) 3.4 Descripive Saisics Table 1 provides summary saisics for he Amazon EC2 sandard xlarge inra-day spo insance price daa on Windows and Linux/Unix plaforms from April 9, 2010 o May 22, P Eas corresponds o he inra-day spo prices a he US eas region, while P Wes corresponds o he spo prices a he US wes region. Boh are measured in $ per hour. The mean, median, sandard deviaion, max, min, and correlaion marix are given for each series. Panel A provides descripive saisics on he prices a heir incurred ransacions, while Panel B provides descripive saisics on spo prices a 60 minue inervals. --- Inser Table 1 abou here --- Looking a he resuls in Panel A of Table 1, we find ha he average and median prices a heir incurred ransacion inervals across boh he Windows and Linux/Unix plaforms are higher in he wes relaive o he eas over our sample period. The average price differences are $ per hour for he Windows plaform and $ per hour for he Linux/Unix plaform. Looking across he OS plaforms, we also find ha he Linux/Unix prices are lower han he Windows plaform prices. For he Windows plaform, he sandard deviaion is higher for he wes relaive o he eas a versus Noe ha he Singapore indicaor variable spans a large porion of he sample period, bu is inclusion is no problemaic as he consan is suppressed o avoid singulariy problems. In effec, he Singapore indicaor is a consan. 14

16 However, here is subsanially more price variaion using he Linux/Unix plaform, and especially so for eas prices where we documen a sandard deviaion of and for he eas and wes, respecively. In Panel B of Table 1 we repor he spo insance prices for sandard X-Large a 60 minue inervals. The mean, median, and sandard deviaions of he 60 minue inerval prices are nearly idenical o he incurred level prices, indicaing ha he disribuion of he incurred and 60 minue inerval prices are very similar. The 60 minue inerval prices also allow us o examine he correlaion of he aligned prices. Ineresingly, he conemporaneous inra-day eas and wes price correlaions across boh OS plaforms are no differen from zero. 12 Our documened eas and wes pricing differences coupled wih heir insignifican correlaions provides some preliminary uncondiional evidence suggesing ha here may be some persisence in he pricing differenials across hese markes. --- Inser Figure 1 abou here --- To examine he ime varying characerisics of he pricing differenials, we provide a ime series plos of he wes minus eas pricing differenials for he Windows plaform in Panel A of Figure 1 and for he Linux/Unix plaform in Panel B. Given he high frequency of he daa, we plo he pricing differenials a he average weekly level (using daily averages based on he inra-day 60 minue inerval prices) for depicion purposes. In boh panels of Figure 1, we can see ha here is indeed a persisence in he pricing differenial whereby wes price are consisenly higher han eas prices over ime across boh OS plaforms. Furhermore, he plos show ha here is significan ime variaion in he pricing differenials. These resuls sugges ha here is a dynamic relaion in he pricing differenials, which we address in our condiional analysis. 4. Resuls 4.1 The Dynamic Relaions beween Eas and Wes Prices using a Bivariae VAR Model The descripive saisics and price differenial figures sugges ha eas and wes prices vary over ime. To examine hese pricing dynamics, we use a bivariae VAR model o es he price relaions wihin and across he eas and wes markes. Table 2 provides 12 These resuls are robus across a range of ime pricing inervals, including from 1, 5, 10, and 15 minue ime inervals. 15

17 resuls from he esimaion of he bivariae VAR model using he 60 minue inerval daa and five lags as suggesed by he Akaike Informaion Crieria (AIC), Schwarz Bayesian Informaion Crieria (SBIC), and he likelihood raio selecion crieria for various lag choices. --- Inser Table 2 abou here --- The resuls in Table 2 show ha he auoregressive componen wihin each marke is highly significan, bu he cross marke effecs are largely mued. These resuls are consisen wih our repored low conemporaneous correlaions of he eas and wes prices. In paricular, looking a he Windows plaform resuls, we find ha prices in he eas are significanly relaed o prior eas prices a a largely decreasing rae for up o four hours. A he same ime, he eas prices are weakly relaed o wes prices excep a he five hour lag where we find a significan effec a he 3% level. Turning o he wes prices wih he Windows plaform, we again find a significan diminishing auoregressive effec of lagged wes prices influencing curren wes prices. However, we do no find evidence of a significan relaion beween lagged eas prices influencing wes prices using he Windows plaform. In he righ panel of Table 2, we repor he bivariae VAR resuls beween eas and wes prices using he Linux/Unix OS plaform. We again find a significan relaion beween curren and lagged eas prices for up o four hours a a largely diminishing rae over ime. However, unlike he Windows plaform resuls, we find ha lagged wes prices have a significan influence on eas prices wihin one hour and also a higher level lags. Similarly, for he wes prices under he Linux/Unix plaform, we find a significan effec of lagged wes prices on curren wes prices. However, here again in conras o he Windows plaform resuls, we find ha lagged eas prices have a significan influence on wes prices as shown by he wo hour lag effec of eas prices on curren wes prices. The fi of he wes price marke as measured by he adjused R 2 is also significanly higher relaive o he oher price fis. Taken ogeher, our bivariae VAR resuls sugges ha here are significan dynamic pricing relaions boh wihin and across he eas and wes markes. The wihinmarke effec is larger han he across-marke effec, bu here are also significanly pronounced across-marke pricing effecs. 16

18 4.2 Price Discovery in Eas and Wes Markes using Informaion Shares Consumers of he Amazon EC2 cloud compuing spo insances are ineresed in he dynamics of how he prices of he same spo insance are discovered (i.e., deermined) in wo differen markes (i.e., he Amazon eas and wes service ceners). To beer undersand he dynamic naure of price discovery across he eas and wes markes, we use boh Hasbrouck s (1995) and Gonzalo and Granger s (1995) mehodologies o esimae he relaive informaion shares across hese wo markes. In is simples form, he informaion shares capure he exen o which relevan informaion on he same good raded in differen markes is incorporaed ino he price. As an illusraing example, a Canadian sock may be cross-lised a boh he Torono Sock Exchange (TSE) and he New York Sock Exchange (NYSE). The new earning informaion of he sock may affec he sock price a he domesic marke (TSE) more han he foreign marke (NYSE), while he greaer compeiion a he NYSE may lead o a greaer conribuion of NYSE o he price discovery. The informaion shares provide a useful summary measure of each marke s conribuion of o he price discovery of he same good raded a differen markes. In Table 3, we provide descripive saisics on he relaive price discovery across he eas and wes markes for boh OS plaforms. Panel A provides he means, medians, and sandard deviaions of daily Hasbrouck informaion shares over our sample period, while Panel B provides he same descripive saisics for our esimaed daily Gonzalo-Granger informaion shares. --- Inser Table 3 abou here --- Looking firs a he Hasbrouck informaion share resuls in Panel A of Table 3, we find ha a large porion of he relaive price discovery occurs in he eas marke relaive o he wes marke. The average daily informaion shares using he Windows plaform prices are 78.8% in he eas and 21.2% in he wes. In comparison, he Linux/Unix plaform resuls in he righ panel also indicae ha a large porion of he informaion processing occurs in he eas marke a an average of 72.3% and 27.7% for he wes marke. The median resuls furher confirm ha a large porion of he relaive price discovery occurs in he eas marke relaive o he wes. In Panel B of Table 3, we provide descripive saisics on he daily informaion shares using he Gonzalo-Granger mehodology. Consisen wih he Hasbrouck 17

19 informaion share resuls, we again find ha he eas marke has greaer price informaion processing relaive o he wes. The average daily price informaion shares are 70.9% in he eas and 29.1% in he wes for he Windows OS, and 78.9% and 21.1% for he eas and wes price informaion shares, respecively, using he Linux/Unix OS. The median price informaion share resuls also sugges ha he eas price informaion processing is larger han he wes across boh OS plaforms. Overall, he informaion share resuls using boh Hasbrouk s and Gonzalo-Granger and across boh OS plaforms sugges ha a large porion of he relaive price discovery occurs in he eas marke, which also has persisenly lower price han he wes marke. 4.3 Laency and Eas versus Wes Price Differences Price Difference Regressions The earlier repored descripive saisics and price differenial figures sugges ha eas and wes prices vary over ime, while our VAR model resuls sugges ha here are significan wihin and across marke pricing dynamics. The informaion shares furher sugges ha a larger porion of price discovery occurs in he eas marke relaive o he wes marke. We argue ha a key deerminan of he pricing differenials over ime is laency differences. To es his hypohesis, we use regression procedures whereby we regress laency differences and various even indicaors on he differences in prices beween he wes and eas markes. In paricular, we esimae four differen regression models as represened by equaions (4)-(7). --- Inser Tables 4 and 5 abou here --- Table 4 provides a descripion of he variables ha we use in he regression analysis. We use boh ciy level laency differenial measures and regional laency differenial measures derived from he ciy measures. We also use a series of Amazon even indicaor explanaory variables. The inraday summary saisics associaed wih he regional laency differenial variables are shown in Table 5 a 60 minue inervals. We find ha he eas laency differenial is on average smaller han he wes laency differenial. The median resuls furher confirm ha he eas laency differenials are smaller han he wes laency differenials. Boh he sandard deviaions and range sugges ha here is some subsanial variabiliy in he laency differenials over ime. The cenral laency differenials are he smalles of he regional laency differenials by design in ha hey are 18

20 more cenrally locaed beween he eas and wes markes and hence he laency differenial resuls in a smaller laency difference. Also as expeced, here is a negaive correlaion beween he eas and wes laency differenials. --- Inser Figure 2 abou here --- As addiional moivaion, in Figure 2 Panels A and B we plo he pricing differenials along wih he eas and wes laency differenials aggregaed a he weekly level for graphical purposes. In Panel A, we repor he Windows plaform pricing differenials, while in Panel B we repor he Linux/Unix plaform pricing differenials. From boh panels in Figure 2, we see ha here is significan ime variaion in he laency differenials and ha he paern of he laency differenials and pricing differenials is similar over ime. In many cases, he pricing differenials are also bounded by he laency differenials. To furher examine and es he relaion beween he pricing and laency differenials, we use regression procedures wih various model specificaions. --- Inser Table 6 abou here --- Table 6 provides he resuls from esimaing our four differen regression specificaions across he Windows and Linux/Unix plaforms. These wo panels show he resuls of regressing he price differenials on laency differenials and various even indicaor variables. The lef panel of he able conains he regression resuls using he Windows plaform, while he righ panel conains he resuls using he Linux/Unix plaform. For Model 1, we include he regional laency differenials in he regression specificaion, while for Model 2 we augmen he regional laency differenials wih he even indicaor variables. Model 3 uses ciy-level laency differenials, while Model 4 augmens he ciy-level laency differenials wih he even indicaor variables. The resuls in Table 6 show ha laency differenials have a significan effec on he pricing differenial. We also run reverse causaliy regressions and find no evidence of simulaneiy issue of pricing dynamics influencing laency. For Model 1, we find ha boh he eas and wes laency differenials have a significanly posiive effec on he pricing differenial, suggesing ha larger (smaller) laency effecs resul in larger (smaller) pricing differenials. Tha is, laency creaes a dynamic pricing wedge, similar o a varying ransacion cos, ha widens or narrows condiional on he laency differenials. While 19

21 significan, he cenral laency differenial has a much more mued effec (less han oneenh he size) on he pricing differenial as expeced given he relaive disances and consequen laencies, hough i has an unexpeced negaive effec. In Model 2 under he Windows plaform where we now include he even indicaor variables, we again find ha he eas and wes laency differenials have a significanly posiive effec on he pricing differenial. The cenral laency differenial is again also much more mued in is impac, bu i is now only marginally significan a he 10% level. Ineresingly, he inroducion of a reducion in he m2 2x and 4x large on demand reserved prices has a negaive effec on he pricing differenials as does he laer inroducion of he Tokyo Asia Pacific region. In conras, he earlier inroducion of he Singapore Asia Pacific region has a posiive effec on he pricing differenial. As addiional robusness checks, we include various addiional variables in our specificaions. Our resuls are robus o heir inclusion. In paricular, including Amazon EC2 Eas cener s failure on April 21s, 2011 does no aler our resuls -- he even is no saisically significan in our esimaes. If we include a lagged dependen variable in our specificaions, we again obain similar resuls. Models (3) and (4) provide he resuls using he ciy-level laency differenials and augmened model wih even indicaor variables. Recall ha he ciy-level laency differenials are measured as he average laency o Amazon wes EC2 cener a ciyi minus he average laency o Amazon eas cener a ciyi. As expeced, across boh models (3) and (4) we find ha he ciy-level laency differenials have a significan effec on he pricing differenials. The posiive signs on he easern ciy differenials are as expeced as are he negaive signs on he wesern ciy differenials given how we define he ciy-level laency differenials. Tha is, he wesern ciies will have lower laencies o he wes by design given heir locaion, resuling in a negaive laency differenial given he larger laency o he eas. The inerpreaion of he negaive laency differenial on he price differenial defined as P Wes -P Eas in his case would resul in an inverse relaion. As expeced, several of he cenral ciy laency differenials do no have a significan effec on he pricing differenial given ha heir laencies are ofen similar o he wes and eas markes. In Model (4) augmened wih he even indicaor variables, we again find ha he inroducion of Tokyo and Singapore resuls in negaive and posiive price differenial effecs, respecively. However, he reduced indicaor even is no longer significan when he ciylevel laency differenials are used. 20

22 The Linux/Unix plaform resuls are repored in he righ side panel of Table 6. Similar o he Windows plaform resuls, we again find ha laency differenials have a significan effec on he pricing differenials for boh he differenial laencies measured a he regional or ciy-level. The indicaor even effecs are also very similar o hose discussed for he Windows plaform resuls, wih he only excepion ha he Tokyo inroducion does no have a significan effec across any of our model specificaions wih he Linux/Unix plaform Shor and Long Run Price Differenial Dynamics: Error Correcion Models To capure boh long-run and shor-run pricing dynamics, we also employ an Error Correcion Model (ECM). The ECM model is appropriae if he series are non-saionary and coinegraed. Uni roo ess sugges ha he Windows eas and wes prices are nonsaionary a he 10% significance level and are coinegraed. The ECM framework allows us o model he eas and wes pricing relaions as an adjusmen process around heir longrun equilibrium price convergence. Error correcion models are based on he idea ha wo or more ime series exhibi a long-run ime-varying equilibrium o which he sysem ends o converge. This long-erm convergence in pricing is an appealing assumpion given ha long-run pricing in boh he eas and wes should be similar or users would shif heir compuing o he lower priced marke hrough negaive feedback and error correcion, wih he laency differenial playing an imporan role in he poenial pricing convergence. Following he Engle-Granger wo-sep mehod, we specify a long-run price model in levels. In he shor-run second sage adjusmen model, he variables are specified as firs differences and include he residuals from he firs sage model as an error correcion erm. Consisen wih our prior empirical specificaions, he variable of ineres is he crossmarke price dynamic. We chose o be more conservaive in our approach by using boh price difference regressions and a modified ECM model o furher show he robusness of our resuls if one was concerned wih poenial non-saionariy problems. However, our fundamenal resuls in he paper do no hinge on he ECM model resuls, and he ECM model resuls are robus o alernaive ECM model specificaions. --- Inser Table 7 abou here --- Table 7 repors he resuls from esimaing he ECM model using he Windows plaform insance prices. In Panel A, we find ha eas prices have a posiive long-run 21

23 relaion on wes prices, hough he sandard errors of he equilibrium esimae are large. In Panel B, we find ha lagged price differenials have a posiive and significan influence on curren price differenials, suggesing some persisence in he pricing differenials. We also find ha he eas and wes laency differenials coninue o have a posiive and significan influence on he pricing differenials. This suggess ha laency plays an imporan role in he shor-run pricing dynamics across he eas and wes markes. Looking a he error correcion erm, lagres, we find ha he speed of adjusmen parameer is boh significan and negaive, suggesing ha a wider disequilibrium (i.e., larger errors) from he long-run price convergence cause he shor-run price differenial o narrow, bu he adjusmen is only parial a Conclusion Conribuion o Lieraure Our sudy addresses an inriguing and perplexing issue regarding he spo marke for cloud compuing, where Amazon wes EC2 cener spo prices are consisenly and significanly higher han hose a he eas cener for all compuing plaforms. Such persisen posiive price differenials presen a clear arbirage choice for cloud compuing cusomers and raises a fundamenal quesion abou he marke efficiency of cloud compuing. In he exuberance over his growing echnological plaform, pricing and qualiy are key issues facing curren and prospecive cusomers considering moving o cloud services. In his paper, we focus on hese fundamenal issues by examining cloud compuing spo pricing dynamics and he role ha laency plays in he pricing dynamics across cloud compuing markes. We show ha a fundamenal facor in deermining he pricing dynamics boh wihin and across markes is laency. Laency is a key issue no only for firms offering producs and services o consumers over he Inerne, bu also for corporaions considering he adopion of cloud compuing. Our research is he firs ha examines he effecs of laency on pricing dynamics boh wihin and across differen spo markes and provides convincing evidence o ha even wih he same cloud compuing provider and compuing plaform, price heerogeneiy sill exiss due o laency differenials across markes. We furher address oher key quesions in his paper. Firs, wha are he sylized pricing dynamics for Amazon EC2 spo insance pricing boh wihin and across eas and wes marke regions? Second, wha explains he observed pricing dynamics and pricing 22