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 32611 Email: kenny.cheng@warringon.ufl.edu; zhi.li@warringon.ufl.edu; andy.naranjo@warringon.ufl.edu Curren Version: April 2013
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
1. Inroducion Cloud compuing coninues o garner 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 2020. 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 ondemand o cusomers over a nework in a self-service fashion, independen of device and locaion (Marson e al. 2011). 1 Firms of all sizes have adoped or are considering moving o cloud services. In he exuberance over his growing echnological plaform, pricing and qualiy are key issues facing curren and prospecive cusomers. 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. Cloud compuing providers, such as Amazon, offer basic compuing and sorage resources a relaively low prices. Amazon s Elasic Compue Cloud (Amazon EC2) is one of he leading cloud service providers. 2 The prices of EC2 insances are based on he region in which 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 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 (Pring e al. 2010). 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 2014. 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 2009. 3 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
price gain access o he available spo insances. Hisorically, cusomers using spo insances have received significan price discouns beyond on-demand prices for no 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 A fundamenal facor in deermining he pricing dynamics boh wihin and across markes is he role of 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. In fac, i has been dubbed he Achilles Heel of Cloud Compuing (Minnear 2011). 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. 5 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 (Forreser Consuling 2009). 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 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. Bapna e al (2008) are among he firs o develop a marke mechanism ha considers allocaional efficiency, incenive compaibiliy, fairness in allocaion, and compuaional efficiency. A subsequen sudy by Bapna e al (2011) furher exends he analyses from deerminisic demand informaion o a sochasic case where buyers of cloud compuing only know he disribuion of heir demand. 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. 5 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. We furher show ha even wih he same cloud provider and compuing plaform (i.e., same inerne cloud provider and same good), price heerogeneiy may exis due o laency differenials across markes. 3
a Amazon (Mazzucco 2010), and Google s raffic will drop by 20% for half a second increase in reurning search resuls (Mayer 2009). A significan cause of Web applicaion slow response ime is he laency across he Inerne. The one-way laency across he Inerne is measured by he ime from he source sending a packe of informaion o he desinaion receiving i. The primary source of nework laency is he propagaion delay he ime i akes for he packe o ravel in communicaions media from source o desinaion (O3b Neworks 2008). The longer he physical disance of he ransmission pah, he longer he propagaion delay and hus he longer he laency. 6 Undersanding he naure of pricing dynamics boh wihin and across markes is imporan for allocaional and operaional consideraions, among oher consideraions. A key feaure of any well-funcioning marke is he absence or near absence of arbirage opporuniies. Oherwise, individuals would buy in cheap markes and sell in dear markes unil prices equalized. Arbirage is one of he cenral enes of compeiive markes. I helps o enforce he law of one price, hereby helping o keep markes efficien. However, someimes here are imporan impedimens o arbirage ha exis across markes for he same good due o marke fricions and imperfec informaion ha can limi arbirage. These limis o arbirage can creae pricing dynamics and wedges wihin and across markes ha resul in poenially subopimal decisions wih negaive consequences. From a foundaional and raional arbirage perspecive, price differenials should no exis excep for wedges such as poenial ransacion cos differenials. We argue ha laency creaes such pricing wedges across cloud compuing markes. We hypohesize ha laency differenials across markes will significanly influence spo insance pricing dynamics across hese markes. In paricular, we hypohesize ha laency differenials across markes will have a significanly posiive effec on pricing differenials across hese markes. In our paper, we address hree fundamenal quesions. Firs, wha are he sylized pricing dynamics for Amazon EC2 spo insance pricing boh wihin and across U.S. eas 6 Daa e al. (2003) review various caching sraegies o alleviae delay problems caused by nework laency, where a Web cache is a emporary sorage of desired conen beween he original server and end users. They survey he operaions research and managemen science echniques ha can be applied o he Web caching relaed problems. Answering o he call for addiional research in Web caching, Hosanagar e al. (2005) find condiions under which a cache operaor should offer boh a premium service for which he conen publisher pays and a free bes effor service. Consumers are beer off wih more cached conen a a faser delivery speed under such an arrangemen. 4
and wes regions? Second, wha explains he observed pricing dynamics and pricing differenials across he eas and wes markes? Third, wha effec does laency (and oher poenial even indicaors) have on he across-marke pricing differenials? To address hese quesions, we use various economeric modeling approaches and inra-day Amazon EC2 spo insance pricing daa as well as inra-day laency daa from April 9, 2010 o May 22, 2011. 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 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 5
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 2.1.1 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 12Y 2... py p e, (1) 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,)]. 7 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 7 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 non-saionariy problems, we also employ Error Correcion models as discussed in he nex secion. 6
anicipaion effecs (changes in wes pricing following changes in eas pricing and vice versa). 2.1.2 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 (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. 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+ + j1 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 2 11 2 2 1 2 2. 2 1 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 7
second erm on he righ-hand side of (2), k j 1 j j P, describes shor-run deviaions due o imperfec marke condiions. 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), ( 1, 2). Thus, P l e L e, where l (1, 1)'. Hasbrouck defines e as he * ( ) s=1 s 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. 8 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 Ap Ap A p e, (3) 1 1 1 1 1... 20 20 8 Our repored resuls are robus o alernaive inra-day frequencies. 8
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 GG2 1 2 1 2. 2.2 Pricing Differenials 2.2.1 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. 9 In paricular, we employ he following inra-day pricing differenial regression models: PD Eas Wes Cenral DL DL DL, (4) 0 1 2 3 PD PD PD 7 Eas Wes Cenral 0 1 DL 2 DL 3 DL di Di i1 18 DL _ Ciy, 0 i i i1 18 DL _ Ciy 0 i i di i i1 i1 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 9 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 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. 9
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. 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. 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 ix i 1, (9) i1 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. 10
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. 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) plaforms. 10 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. 11 Our resuls are robus o alernaive insance ypes. 12 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. The begin and end daes of our sample period correspond o he availabiliy of he laency daa for our analysis. For our analysis, we also conver he 10 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/. 11 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. 12 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. 11
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 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 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: 12
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 Wes a ciy i - Average laency o Eas 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 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) 13 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, 2011. P Eas corresponds o he inra-day spo prices a he US eas region, while P Wes 13 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. 13
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. 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 0.132 $ per hour for he Windows plaform and 0.073 $ 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 0.017 versus 0.016. 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 0.056 and 0.010 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. 14 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. 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 14 These resuls are robus across a range of ime pricing inervals, including from 1, 5, 10, and 15 minue ime inervals. 14
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 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. 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 15
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. 4.2 Price Discovery in Eas and Wes Markes using Informaion Shares 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 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. 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 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. 16
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 4.3.1 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). 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 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. 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 17
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. 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. 15 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 significan, he cenral laency differenial has a much more mued effec (less han one-enh 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. 16 15 We also run reverse causaliy regressions and find no evidence consisen wih pricing dynamics influencing laency. 16 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 18
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 wes a ciyi minus he average laency o eas 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 ciy-level laency differenials are used. 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. 4.3.2 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 April 21 s, 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. 19
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. 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 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 -0.544. 5. Conclusion We address hree 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 differenials across he eas and wes markes? Third, wha effec does laency (and oher poenial even indicaors) have on he across-marke pricing differenials? To address hese quesions, we use various economeric modeling approaches and inra-day Amazon EC2 spo insance pricing daa as well as inra-day laency daa over he April 9, 2010 o May 22, 2011 sample period. In addressing he firs quesion, we documen ha across Windows and Linux/Unix OS plaforms as well as spo insance ypes, here is considerable ime variaion in spo prices. We also find ha prices in he wes are ofen persisenly greaer han prices in he 20
eas over our sample period. Resuls from using a bivariae VAR model of eas and wes spo insance prices suggess ha here are significan dynamic pricing relaions boh wihin and across he eas and wes markes. We find ha he wihin-marke auoregressive pricing effec is larger han he across-marke 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 also find ha a large porion of he relaive price discovery (over 70%) occurs in he eas marke relaive o he wes marke. To explain he observed ime varying pricing differenials across he eas and wes markes (i.e., addressing our second and hird quesions), 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 differenials. These resuls sugges ha larger (smaller) laency effecs resul in larger (smaller) pricing differenials. Similar o a ime varying ransacion cos band, laency creaes a dynamic pricing wedge 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 resuls from our paper can be viewed in a broader conex and also provide a framework for some addiional follow-on research quesions. From a broader conex, our research provides some furher evidence and insighs ino marke-based pricing dynamics and marke efficiency issues in a burgeoning new marke wih unique characerisics, including laency effecs. Alhough markes have become increasingly inegraed due o echnological innovaions and reducions in barriers across markes, several sudies show ha geographical disance sill maers in behavioral, economic, and financial oucomes. These sudies esablish he relevance of geographical proximiy o consumer s coss of acquiring informaion, which in urn influences he behavior of boh consumers and firms. The effecs of disance manifes hemselves hrough higher search coss ofen relaed o informaion acquisiion problems (e.g., degree of informaion asymmery and uncerainy as well as oher informaion and marke impedimens) and behavioral biases (e.g., anchoring and loss aversion). Boh higher search coss and behavioral biases may lead o he paymen of higher prices for a given good. In his regard, our research on laency effecs provides some evidence consisen wih he role of marke impedimens playing a fundamenal role in he cloud pricing dynamics. A he same ime, consumers may suffer 21
from behavioral biases which may cause hem o anchor heir expecaions on local or personal circumsances and prior decisions. Furher research on undersanding he naure of hese poenial facors in he pricing dynamics of cloud compuing could yield some addiional ineresing insighs. 22
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Zhang, Q., Q. Zhu, R. Bouaba. 2011. Dynamic resource allocaion for spo markes in cloud compuing environmens. 2011 Fourh IEEE Inernaional Conference on Uiliy and Cloud Compuing (UCC), 178-185. 24
Table 1 Summary Saisics This able provides summary saisics for he Amazon EC2 M1 (sandard) X-Large inra-day spo insance price daa on Windows and Linux/Unix plaforms from April 9, 2010 o May 22, 2011. 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 price series 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. Panel A: Spo prices: M1 X-Large a Incurred Transacion Inerval Windows Linux/Unix P Eas P Wes P Eas P Wes Obs 6407 5440 6384 5343 Mean 0.400 0.532 0.246 0.319 Median 0.402 0.529 0.242 0.318 Sd dev 0.016 0.017 0.056 0.010 Max 0.960 0.560 1.000 0.336 Min 0.380 0.506 0.228 0.304 Panel B: Spo Prices for M1 X-Large a 60 minue inervals Windows Linux/Unix P Eas P Wes P Eas P Wes Obs 9816 9816 9816 9816 Mean 0.400 0.532 0.245 0.320 Median 0.401 0.530 0.241 0.319 Sd. dev. 0.014 0.016 0.045 0.010 Max 0.960 0.560 1.000 0.336 Min 0.380 0.506 0.228 0.304 Correlaion (P Eas ) 1.00000 0.00279 (0.7826) 1.00000-0.00492 (0.6263) Correlaion (P Wes ) 0.00279 (0.7826) 1.00000-0.00492 (0.6263) 1.00000 25
Table 2 The Dynamic Relaions beween Eas and Wes Prices using a Bivariae VAR Model This able presens resuls obained from esimaing unresriced VAR models using Amazon EC2 M1 X-Large spo prices a 60 minue inervals over he April 9, 2010 o May 22, 2011 sample period (N = 9,816). An unresriced p h -order Gaussian VAR model can be represened as: Y 1Y 1 2Y 2... py p e, We esimae a bivariae model where he lag-lengh of he VAR is chosen by he AIC, SBIC, and he likelihood raio crierion for various choices of p. We find ha five periodic 60 minue lags provide he bes fi. P-values are repored in parenheses. Windows Linux/Unix P Eas P Wes P Eas P Wes Consan 0.319 0.358 0.027 0.211 (0.0001) (0.0001) (0.1093) (0.0001) P Eas -1 0.110-0.004 0.471-0.003 (0.0001) (0.7354) (0.0001) (0.264) P Eas -2 0.030 0.004 0.085-0.006 (0.0028) (0.7025) (0.0001) (0.0787) P Eas -3 0.071 0.008 0.180 0.004 (0.0001) (0.4685) (0.0001) (0.2776) P Eas -4-0.023-0.010 0.107 0.005 (0.0229) (0.3879) (0.0001) (0.1288) P Eas -5-0.002-0.007 0.016 0.001 (0.8383) (0.5178) (0.1195) (0.6477) P Wes -1 0.001 0.305-0.088 0.329 (0.9339) (0.0001) (0.0072) (0.0001) P Wes -2 0.015-0.002 0.036-0.009 (0.1254) (0.8861) (0.2966) (0.4184) P Wes -3-0.013 0.042-0.044 0.032 (0.1868) (0.0001) (0.2011) (0.0024) P Wes -4-0.012-0.028 0.082-0.014 (0.2161) (0.0073) (0.0177) (0.1836) P Wes -5 0.020 0.015 0.036 0.000 (0.0265) (0.1349) (0.2725) (0.9695) Adj R 2 0.020 0.096 0.109 0.581 Obs 9816 9816 9816 9816 26
Table 3 Price Discovery in Eas and Wes Markes using Informaion Shares This able provides descripive saisics for daily informaion shares using inra-day 5 minue pricing ime inervals. Panel A provides he means, medians, and sandard deviaions of Hasbrouck s daily informaion shares: 2 2 j j IS j ', when e and e 1 2 are correlaed. 2 ([ M ] j ) IS j, when e 1 and e2 are uncorrelaed and where ' m 11, 1, 0 M m 2 1/2. 12,m 22 2, 2(1 ) Since he Cholesky facorizaion is sensiive o 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. For each marke, he average informaion share for he period is calculaed as he mean of is upper and lower bounds. Panel B provides he means, medians, and sandard deviaions of he daily informaion shares using he Gonzalo-Granger model: 2 1 GG1 and GG2. 1 2 1 2 For each region, we repor he saisics for informaion shares. P Eas corresponds o he informaion share for he region of US Eas, whereas P Wes corresponds o he informaion share for he region of US Wes. The sample period is from April 9, 2010 o May 22, 2011. Panel A. Hasbrouck s Informaion Shares Windows Linux/Unix P Eas P Wes P Eas P Wes Obs 409 409 409 409 Mean 0.788 0.212 0.723 0.277 Median 0.866 0.134 0.838 0.162 Sd. dev. 0.222 0.222 0.298 0.298 Panel B. Gonzalo-Granger s Informaion Shares Windows Linux/Unix P Eas P Wes P Eas P Wes Obs 409 409 409 409 Mean 0.709 0.291 0.789 0.211 Median 0.597 0.403 0.576 0.424 Sd. dev. 2.901 2.901 4.341 4.341 27
Table 4 Descripion of Regression Variables used o explain he Price Differenial This able provides a descripion of he variables used in he regressions wih price differenial as he dependen variable. PD P Wes P Eas DL_Ciyi Average laency o wes a ciy i - Average laency o eas a ciy i L EasToEas Average laency from Eas region backbone nodes o Amazon Eas EC2 cener L EasToWes Average laency from Eas region backbone nodes o Amazon Wes EC2 cener L WesToEas Average laency from Wes region backbone nodes o Amazon Eas EC2 cener L WesToWes Average laency from Wes region backbone nodes o Amazon Wes EC2 cener L CenralToEas Average laency from Cenral region backbone nodes o Amazon Eas EC2 cener L CenralToWes Average laency from Cenral region backbone nodes o Amazon Wes EC2 cener DL Eas L EasToWes - L EasToEas DL Wes L WesToEas - L WesToWes DL Cenral L CenralToWes - L CenralToEas Micro Micro insances announced (Sepember 9, 2010) Singapore Asia Pacific Region (Singapore) announced (April 29, 2010) CC Cluser Compue insances (Linux/Unix 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) 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) 28
Table 5 Laency Summary Saisics DL Eas DL Wes DL Cenral Obs 9816 9816 9816 Mean 4.908 6.082 0.765 Median 4.796 5.925 0.445 Sd. dev. 2.286 2.675 2.970 Max 94.739 47.773 118.104 Min -21.664-66.279-23.651 Correlaion (DL Eas ) Correlaion (DL Wes ) Correlaion (DL Cenral ) 1.000-0.512 (<.0001) -0.512 (<.0001) 0.586 (<.0001) 0.586 (<.0001) 1.000-0.457 (0.6263) -0.457 (<.0001) Inraday laency daa measured a 60 minue inervals. 1.000 29
Table 6 Price Differenial Regressions This able provides regression resuls of he price differenials (P Wes P Eas ) on he laency differenials and various even indicaor variables. The variable definiions are provided in Table 4. The regressions use inraday daa measured a 60 minue inervals, and he sample period runs from is from April 9, 2010 o May 22, 2011. All esimaes are muliplied by 1000. Windows Linux/Unix Model 1 Model 2 Model 3 Model 4 Model 1 Model 2 Model 3 Model 4 DL Eas 12.770 6.420 7.480 4.000 (0.0001) (0.0001) (0.0001) (0.0001) DL Wes 10.400 5.550 5.780 3.310 (0.0001) (0.0001) (0.0001) (0.0001) DL Cenral -0.841-0.273-1.120-0.227 (0.0001) (0.0639) (0.0001) (0.0639) Eas: DL_Alana 0.356 0.038-0.520-0.623 (0.0001) (0.7153) (0.0001) (0.7153) DL_Boson 0.799 0.466 0.775 0.515 (0.0001) (0.0001) (0.0001) (0.0001) DL_DC 1.250 0.586 0.687 0.355 (0.0001) (0.0001) (0.0001) (0.0001) DL_Newark 2.590 1.580 1.930 1.450 (0.0001) (0.0001) (0.0001) (0.0001) DL_NY 0.744 0.379 0.434 0.238 (0.0001) (0.0001) (0.0001) (0.0001) DL_Philly 2.830 1.710 1.660 1.150 (0.0001) (0.0001) (0.0001) (0.0001) DL_Reson 3.040 2.060 1.830 1.290 (0.0001) (0.0001) (0.0001) (0.0001) Wes: DL_Denver -0.372-0.222-0.192-0.134 (0.0001) (0.0001) (0.0001) (0.0001) DL_LA -1.910-1.460-0.933-0.642 (0.0001) (0.0001) (0.0001) (0.0001) DL_Mesa -1.300-0.713-0.869-0.603 (0.0001) (0.0001) (0.0001) (0.0001) DL_SD -3.650-2.160-1.980-1.260 (0.0001) (0.0001) (0.0001) (0.0001) DL_SJ -1.660-0.878-1.060-0.684 (0.0001) (0.0001) (0.0001) (0.0001) DL_Seale -1.670-0.924-0.878-0.508 (0.0001) (0.0001) (0.0001) (0.0001) Cenral: DL_Chicago 0.509 0.545 0.063 0.361 (0.0001) (0.0001) (0.0001) (0.0001) DL_Dallas -0.017-0.080 0.037-0.012 (0.82) (0.3015) (0.82) (0.3015) DL_Houson 0.064-0.069-0.287-0.164 (0.194) (0.1836) (0.194) (0.1836) DL_KC -0.155-0.255 0.108-0.092 (0.0132) (0.0001) (0.0132) (0.0001) DL_SLouis 0.623 0.441 0.366 0.447 (0.0001) (0.0001) (0.0001) (0.0001) Indicaors: Micro 0.777 0.892 9.030 8.320 (0.7351) (0.6664) (0.7351) (0.6664) Singapore 70.560 54.840 26.610 15.910 (0.0001) (0.0001) (0.0001) (0.0001) 30
CC -1.450 0.304 7.680 8.020 (0.2108) (0.7488) (0.2108) (0.7488) Free -0.789-0.315-0.578-0.251 (0.604) (0.8126) (0.604) (0.8126) CG 2.060 0.260-1.830-3.050 (0.7726) (0.3071) (0.7726) (0.3071) Reduced -4.820-2.670-4.280-1.830 (0.0373) (0.2151) (0.0373) (0.2151) Tokyo -3.840-3.390-0.813-0.566 (0.0001) (0.0001) (0.5688) (0.6886) Adj R 2 0.928 0.950 0.946 0.957 0.692 0.706 0.707 0.714 Obs 9816 9816 9816 9816 9816 9816 9816 9816 31
Table 7 Shor and Long Run Price Differenial Dynamics using an Error Correcion Model This able provides ECM esimaes using he Windows plaform prices. Uni roo ess sugges ha he Windows eas and wes prices are non-saionary a he 10% significance level and are coinegraed. 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. The variable definiions are provided in Table 4. Xi are firs differences of he explanaory variables (i.e., differences in laency in ime ), ˆ 1 is he error correcion erm (i.e., he lagged residuals from he long-run coinegraing regression, lagres), and all of he difference erms are saionary. The regressions use inraday daa measured a 60 minue inervals, and he sample period runs from is from April 9, 2010 o May 22, 2011. Price and laency differenial esimaed coefficiens are muliplied by 1000. Panel A: Sage 1, Variable P Wes Parameer Esimae Eas 0 1P Pr > Inercep 0.531 <.0001 P Eas 3.200 0.7826 Panel B: Sage 2, PD X 1, Variable n 0 i i i1 Parameer Esimae Pr > lagpd 0.849 <.0001 DL Eas 1.590 <.0001 DL Wes 1.860 <.0001 DL Cenral -0.085 0.3901 lagres -0.544 <.0001 32
Panel A 0.138 0.136 Figure 1 Weekly price differenial of m1.xlarge.windows PD=P Wes P Eas 0.134 0.132 0.13 0.128 0.126 0.124 04/09/10 05/14/10 06/18/10 07/23/10 08/27/10 10/01/10 11/05/10 12/10/10 01/14/11 02/18/11 03/25/11 04/29/11 Panel B 0.09 Weekly price differenial of m1.xlarge.unix PD=P Wes P Eas 0.085 0.08 0.075 0.07 0.065 0.06 0.055 0.05 0.045 4/9/2010 5/14/2010 6/18/2010 7/23/2010 8/27/2010 10/1/2010 11/5/2010 12/10/2010 1/14/2011 2/18/2011 3/25/2011 4/29/2011 33
Figure 2 Panel A Weekly price differenial of m1.xlarge.windows and laency differenial pd_m1xlarge_windows ld_wes 0.138 0.136 0.134 0.132 0.13 0.128 0.126 ld_eas 7.5 7 6.5 6 5.5 5 4.5 4 0.124 4/9/2010 5/14/2010 6/18/2010 7/23/2010 8/27/2010 10/1/2010 11/5/2010 12/10/2010 1/14/2011 2/18/2011 3/25/2011 4/29/2011 3.5 Panel B 0.085 0.08 0.075 0.07 0.065 0.06 0.055 Weekly price differenial of m1.xlarge.linuxunix and laency differenial pd_m1xlarge_linuxunix ld_wes ld_eas 7.5 7 6.5 6 5.5 5 4.5 4 0.05 4/9/10 5/14/10 6/18/10 7/23/10 8/27/10 10/1/10 11/5/10 12/10/10 1/14/11 2/18/11 3/25/11 4/29/11 3.5 34