Online Algorithms for Uploading Deferrable Big Data to The Cloud


 Sabrina Long
 2 years ago
 Views:
Transcription
1 Onlne lgorths for Uploadng Deferrable Bg Data to The Cloud Lnquan Zhang, Zongpeng L, Chuan Wu, Mnghua Chen Unversty of Calgary, The Unversty of Hong Kong, The Chnese Unversty of Hong Kong, bstract Ths work studes how to nze the bandwdth cost for uploadng deferral bg data to a cloud coputng platfor, for processng by a MapReduce fraework, assung the Internet servce provder (ISP) adopts the MX contract prcng schee. We frst analyze the sngle ISP case and then generalze to the MapReduce fraework over a cloud platfor. In the forer, we desgn a Heurstc Soothng algorth whose worstcase copettve rato s proved to fall between /(D+) and ( /e), where D s the axu tolerable delay. In the latter, we eploy the Heurstc Soothng algorth as a buldng block, and desgn an effcent dstrbuted randozed onlne algorth, achevng a constant expected copettve rato. The Heurstc Soothng algorth s shown to outperfor the best known algorth n the lterature through both theoretcal analyss and eprcal studes. The effcacy of the randozed onlne algorth s also verfed through sulaton studes. I. INTRODUCTION Cloud coputng s eergng as a new coputng paradg that enables propt and ondeand access to coputng resources. s exeplfed n azon EC [] and Lnode [], cloud provders nvest substantally nto ther data centre nfrastructure, provdng a vrtually unlted sea of CPU, RM and bandwdth resources to cloud users, often asssted by vrtualzaton technologes. The elastc and ondeand nature of cloud coputng asssts cloud users to eet ther dynac and fluctuatng deands wth nal anageent overhead, whle the cloud ecosyste as a whole acheves econoes of scale through cost aortzaton. Typcal coputng jobs hosted n the cloud nclude large scale web applcatons [3] and bg data analytcs [4]. In such datantensve applcatons, a large volue of nforaton (up to terabytes or even petabytes) s perodcally transtted between the user locaton and the cloud, through the publc Internet. Parallel to utlty bll reducton n data centres (coputaton cost control), bandwdth charge nzaton (councaton cost control) now represents a ajor challenge n the cloud coputng paradg [5], [6], [7], where a sall fracton of proveent n effcency translates nto llons of dollars n annual savngs across the world [8]. Coercal Internet access, partcularly the transfer of bg data, s nowadays routnely prced by the Internet servce Ths work s supported n part by the Natural Scences and Engneerng Research Councl of Canada (NSERC), and grants fro Hong Kong RGC under the contracts HKU 778 and HKU /4/$3. 4 IEEE provders (ISPs) through a percentle charge odel, a draatc departure fro the ore ntutve totalvolue based charge odel as n resdental utlty bllng or the flatrate charge odel as n personal Internet and telephone bllng [5], [9], [7], []. Specfcally, n a θth percentle charge schee, the ISP dvdes the charge perod, e.g., 3 days, nto sall ntervals of equal fxed length, e.g., 5 nutes. Statstcal logs suarze traffc volues wtnessed n dfferent te ntervals, sorted n ascendng order. The traffc volue of the θth percentle nterval s chosen as the charge volue. For exaple, under the 95thpercentle charge schee, the cost s proportonal to the traffc volue sent n the 88 th (95% 3 4 6/5 = 88) nterval n the sorted lst [9], [7], []. The MX contract odel s sply the  th percentle charge schee. Such percentle charge odels are perhaps less surprsng when one consders the fact that nfrastructure provsonng cost s ore closely related to peak nstead of average deand. Due to both ts new algorthc plcatons and ts econoc sgnfcance n practce, ths nterestng percentle charge odel has soon spawned a seres of studes. Most of these endeavours exane cost savng strateges and opportuntes through careful traffc schedulng, ulthong (subscrbng to ultple ISPs), and nterisp traffc shftng. However, they odel the cost nzaton proble wth a crtcal, although soetes plct, assupton that all data generated at the user locaton have to be uploaded to the cloud edately, wthout any delay [9], []. Consequently, the soluton space s restrcted to traffc soothng n the spatal doan only. Realworld bg data applcatons reveal a dfferent pcture, n whch a reasonable aount of uploadng delay (often specfed n servce level agreeent, or SL) s tolerable by the cloud user, provdng a golden te wndow for traffc soothng n the teporal doan, whch can substantally slash peak traffc volues and hence councaton cost. n exaple les n astronocal data fro observatores, whch are perodcally generated at huge volues but requre no urgent attenton. nother wellknown exaple s huan genoe analyses [4], where data are also bg but not tesenstve. The an challenge of effectve teporal doan soothng les n the uncertanly n future data arrvals. Therefore a practcal cost nzaton soluton s nherently an onlne algorth, akng perodcal optzaton decsons based on
2 htherto nput. It s agan, surprsng, to dscover that the onlne cost nzaton for deferrable upload under percentle chargng, even when defned over a sngle lnk fro one source to one recever only, s stll hghly nontrval, exhbtng a rch cobnatoral structure, yet never studed before n the lterature of ether coputer networkng or theoretcal coputer scence (wth an only excepton below) [5]. The only study of the onlne cost nzaton proble under percentle charges that we are aware of s a recent work of Golubchk et al. [5], whch focuses exclusvely on the sngle ponttopont lnk case. The onlne algorth they present, referred to as Sple Soothng here, s extreely sple, and nvolves evenly soothng every nput across ts wndow of tolerable delay for upload. Nonetheless, ths seengly straghtforward algorth s proven to approach the offlne optu wthn a sall constant under the MX odel. In ths work, we frst desgn our own onlne algorth for a sngle lnk, also adoptng the MX odel, n preparaton for the MapReduce data processng case. Based on the nsght that Sple Soothng gnores valuable nforaton ncludng the axu volue recorded so far and the current aount of backlogged data and ther deadlnes, we talor a ore sophstcated soluton, whch ncorporates a few heurstc soothng deas and s hence referred to as Heurstc Soothng. We prove that Heurstc Soothng always guarantees a copettve rato no worse than that of Sple Soothng, under any possble data arrval pattern. Theoretcal analyss shows that Heurstc Soothng can acheve a worstcase copettve rato between D+ and ( e ), where D s the tolerable delay. We further extend the sngle lnk case to a cloud scenaro where ultple ISPs are eployed to transfer bg data dynacally for processng usng a MapReducelke fraework. Data are routed fro the cloud user to appers and then reducers, both resdng n potentally dfferent data centres of the cloud [6]. We apply Heurstc Soothng as a plugn odule for desgnng a dstrbuted and randozed onlne algorth wth very low coputatonal coplexty. The copettve rato guaranteed by the randozed onlne algorth ncreases fro that of Heurstc Soothng by a sall constant factor. Extensve evaluatons are conducted to nvestgate the perforance of the proposed onlne algorths. The results show that Heurstc Soothng perfors uch better than Iedate Transfer (IT), a straghtforward algorth that gnores teporal soothng. Meanwhle Heurstc Soothng also acheves saller copettve ratos than Sple Soothng does. In ost cases tested, the observed copettve rato of Heurstc Soothng s saller than.5, better than the theoretcal upper bound, and relatvely close to the offlne optu. Such superor perforance s attrbuted to less abrupt responses to hghly volatle traffc deand. Eprcal studes for the cloud scenaro further verfy the effcacy of the randozed cost reducton algorth, n ters of both scalablty and copettve rato. In the rest of ths paper, we dscuss related work n Sec. II, and ntroduce the syste odel n Sec. III. Heurstc Soothng and the randozed algorth for the cloud scenaro are desgned and analyzed n Sec. IV and Sec. V, respectvely. Evaluaton results are n Sec. VI. Sec. VII concludes the paper. II. RELTED WORK Slar to deferrng data upload to nze the peak bandwdth deand, there have been studes on schedulng CPU tasks to nze the axu CPU speed, that s closely related to the power consupton. Yao et al. [] ntally provde an optal offlne algorth, the YDS algorth, to optally nze power consupton by scalng CPU speed under the assupton that the forer s a convex functon of the latter. Bansal et al. [] further propose the BKP algorth wth a copettve rato of e, for nzng the axu speed when facng arbtrary nputs wth dfferent delay requreents, and arbtrary workload patterns. Towards new challenges brought by the prolferaton of ultcore processors, lbers et al. [3] desgn an onlne algorth for ultprocessor job schedulng wthout nterprocess job graton. Bngha et al. [4] and ngel et al. [5] further propose polynoalte offlne optal algorths, wth graton of jobs consdered. Grener et al. [6] generalze a ccopettve onlne algorth for a sngle processor nto a randozed cb α copettve onlne algorth for ultple processors, where B α s the αth Bell nuber. Dfferent fro the MX traffc charge odel n ths work, they focus on the total volue based energy charges coputed by ntegratng nstantaneous power consupton over te. In recent years, data centre workload schedulng wth deadlne constrants has been extensvely studed n the cloud coputng lterature. Gupta et al. [7] analyze the energy nzaton proble n a data center when avalable deadlne nforaton of the workload ay be used to defer job executon for reduced energy consupton. Yao et al. [8] tackle the power reducton proble wth deferrable workloads n date centers usng the Lyapunov optzaton approach, for approxate te averaged optzaton. few studes exst on the transfer of bg data to the cloud. Cho et al. [9] desgn a statc costaware plannng syste for transferrng large aounts of data to the cloud provder va both the Internet and courer servces. Consderng a dynac transfer schee where data s produced dynacally, Zhang et al. [6] propose two onlne algorths to nze the total transfer cost. Dfferent fro ths work, they assue andatory edate data upload, and adopt a total volue based charge odel nstead of the percentle charge odel. Goldenberg et al. [9] study the ulthong proble under 95percentle traffc charges. Grothey et al. [] nvestgate a slar proble through a stochastc dynac prograng approach. They both leverage ISP subscrpton swtchng for traffc engneerng, so that the charge volue s nzed. However, data traffc n ther studes cannot be deferred. dler et al. [] focus on careful routng of data traffc between two types of ISPs (verage contract, Maxu contract) to pursue the optal onlne soluton, leadng to an onlne optzaton proble slar to the classc skrental proble. Golubchk
3 et al. [5] study the nzaton of transsson cost by explotng a sall tolerable delay when ISPs adopt a 95 percentle or MX charge odel, focusng on a sngle lnk only, and proposng the Sple Soothng algorth. between DC and DC, and ISP B for councatng between DC and DC3. If two nterdc connectons are covered by the sae ISP, t can be equvalently vewed as two ISPs wth dentcal traffc charge odels. III. SYSTEM MODEL We consder a cloud user who generates large aounts of data dynacally over te, requred for transfer nto a cloud or a federaton of clouds for processng usng a MapReducelke fraework. The appers and reducers ay resde n geographcally dspersed data centres. The bg data n queston can tolerate bounded upload delays specfed n ther SL. User Locaton DC DC DC ' DC '. The MapReduce Fraework MapReduce, ntally unveled by Dean and Gheawat [], s a prograng odel targetng at effcently processng large datasets n parallel. typcal MapReduce applcaton ncludes two functons ap and reduce, both wrtten by the users. Map processes nput key/value pars, and produces a set of nteredate key/value pars. The MapReduce lbrary cobnes all nteredate values assocated wth the sae nteredate key I and then passes the to the reduce functon. Reduce then erges these values assocated wth the nteredate key I to produce saller sets of values. There are four stages n the MapReduce fraework: pushng, appng, shufflng, and reducng. The user transfers workloads to the appers durng the pushng stage. The appers process the durng the appng stage, and delver the processed data to the reducers durng the shufflng stage. Fnally the reducers produce the results n the reducng stage. In a dstrbuted syste, appng and reducng stages can happen at dfferent locatons. The syste wll delver all nteredate data fro appers to reducers durng the shufflng stage, and the cloud provders ay charge for nterdatacentre traffc durng the shufflng stage. Recent studes [], [3] suggest that the relaton between nteredate data sze and orgnal data sze depends closely on the specfc applcaton. For applcatons such as ngra odels, nteredate data sze s uch bgger, and the bandwdth cost charged by the cloud provder cannot be neglected. We use β to denote the rato of orgnal data sze to nteredate data sze. B. Cost Mnzaton for MapReduce pplcatons We odel a cloud user producng a large volue of data every hour, as exeplfed by astronocal observatores [6]. s shown n Fg., the data locaton s ulthoed wth ultple ISPs, for councatng wth data centers. Through the nfrastructure provded by ISP, data can be uploaded to a correspondng data centre DC. Each ISP has ts own traffc charge odel and prcng functon. fter arrval at the data centers, the uploaded data wll be processed usng a MapReducelke fraework. Interedate data need to be transferred aong data centers n the shufflng stage. Towards a general odel, we agan assue that ultple ISPs are eployed by the cloud to councate aong ts dstrbuted data centers, e.g., ISP for councatng DC 3 DC 3' Data Sources Mappers Reducers Fg.. n llustraton of the network for deferrable data upload under the MapReduce fraework. The syste runs n a teslotted fashon. Each te slot s 5 nutes. The charge perod s a onth (3 days). M and R denote the set of appers and the set of reducers, respectvely. Snce each apper s assocated wth a unque ISP n the frst stage, we eploy M to represent the ISP used to connect the user to apper. ll appers use the sae hash functon to ap the nteredate keys to reducers [3]. The upload delay s defned as the duraton between when data are generated to when they are transtted to the appers. We focus on unfor delays,.e., all jobs have the sae axu tolerable delay D, whch s reasonable assung data generated at the sae user locaton are of slar nature and portance. We use W t to represent each workload released at the user locaton n te slot t. Let x d,t be a decson varable ndcatng the porton of W t assgned to apper at te slot t+d. The cost of ISP s ndcated by f (V ), where V s the axu traffc that goes through ISP at te slot t. To ensure all workload s uploaded nto the cloud, we have: x d,t, M. () D x d,t =, t. () Gven the axu tolerable uploadng delay D, the traffc V t between the user and apper s: D V t = W t d x d,t d, M. (3) Let V be the axu traffc volue of ISP, whch wll be used n the calculaton of bandwdth cost. V satsfes: V V t, t. (4) We assue that ISPs n the frst stage, connectng user to appers, eploy the sae chargng functon f ; and ISPs n the second stage fro appers to reducers use the sae chargng functon f,r. Both chargng functons f and f,r are nondecreasng and convex. We further assue that the frst stage s nonsplttable,.e., each workload s uploaded
4 through one ISP only. The user decdes to delver the workload to apper n te slot t. ssue t takes a unt te to transt data va denote the total data sze at apper n te slot t +. M t+ can be calculated as the suaton of all transtted workloads at te slot t: D M t+ = W t d x d,t d, M. ISPs. Let M t+ ssue the appers take te slot to process a receved workload. Therefore the appers wll transfer data to the reducer n te slot t+. Let T,r t+ be the traffc fro apper to reducer r s n te slot t + : V t+,r = βm t+ y t+,r, M, r R. (5) The axu traffc volue of the ISP (, r), V,r, satsfes: V,r V t+,r, t. (6) Notce that the MapReduce fraework parttons the output pars (key/value) of appers to reducers usng hash functons. ll values for the sae key are always reduced at the sae reducer no atter whch apper t coes fro. Furtherore, we assue that data generated n the data locatons are unforly xed, therefore we have: y t+,r = z r, M, r R. (7) Ths equaton also ples that the superscrpt of y,r t+ can be gnored. Now we can forulate the overall traffc cost nzaton proble for the cloud user, under the MX contract charge odel: nze f (V ) + f,r(v,r) (8),r subject to: V V t, t, (8a) V,r V,r t, t,, r (8b) D x d,t = n, t, (8c) n =, (8d) x d,t, n {, }, (8e). where V t and V t,r are defned n Eqn. (3) and Eqn. (5), respectvely. n s a bnary varable ndcatng whether ISP s eployed or not. For ease of reference, notatons are suarzed l n Tab. I. IV. THE SINGLE ISP CSE We frst nvestgate the basc case that ncludes one apper and one reducer only, colocated n the sae data center, wth no bandwdth cost between the pars. Gven a MX charge odel at the ISP, the algorth tres to explot the allowable delay by schedulng the traffc to the best te slot wthn the allowed te wndow, for reducng the charge volue. Ths can be llustrated through a toy exaple: n t =, a Sybol Defnton TBLE I NOTTION D the axu delay fro the te data s generated to the te the data locaton begns to transt t to the appers. M the set of appers. R the set of reducers. Soe apper and reducer ay be n the sae locaton,.e., M R. W t the workload released n user locaton at te slot t. x d,t the porton of the workload W t that s assgned to apper at te slot t + d. β the rato of the sze of output of a apper to the sze of ts nput. y,r t the porton of the output of apper that s transtted to reducer r at te slot t. z r the porton of the key space apped nto reducer r. V t the total traffc that goes through ISP at te slot t. f (y) the cost of ISP for the nput y. job (MB, ax delay = 9 te slots) s released; n the followng te slots, no jobs are released. If the algorth sooths the traffc across the te slots, the charge volue can be reduced to M B/5n, fro M B/5n f edate transsson s adopted.. The Pral & Dual Cost Mnzaton LPs We can drop the locaton ndex (, r) n ths basc scenaro of one apper and one reducer locatng n the sae data centre. Note that the chargng functon f s a nondecreasng functon of the axu traffc volue. Mnzng the axu traffc volue therefore ples nzng the bandwdth cost. Consequently, the cost nzaton proble n our basc sngle ISP scenaro can be forulated nto the followng (pral) lnear progra (LP): subject to: n{d,t } nze V (9) W t d x d,t d V, t T (9a) D x d,t =, t T D (9b) x d,t, V, d D, t T D, (9c) where T = [, T ], T D = [, T D], D = [, D] and x d,t =, t > T D, d D Introducng dual varable y and z to constrants (9a) and (9b) respectvely, we forulate the correspondng dual LP: subject to: axze T y t t= T D t= z t () (a) z t W ty t+d, t T D, d D (b) y t, t T (c) z t unconstranted, t T D (d)
5 The nput begns wth W and ends wth W T D, and W T D+ =,..., W T = s padded to the tal of the nput. We use P and D to denote feasble solutons to the pral and dual LPs, respectvely. The optzaton n (9) s a standard lnear progra. For an offlne optal soluton, one can sply solve (9) usng a standard LP soluton algorth such as the splex ethod or the nterorpont ethod. B. Onlne algorths The splest onlne soluton n the basc one ISP scenaro s the edate transfer algorth (IT). Once a new job arrves, IT transfers t to appers edately wthout any delay. Next we analyze the copettve rato of IT, as copared to the offlne optu. Theore. IT s (D + )copettve. Proof: Consder the followng nput: (W,,,,,...). IT wll process t edately wth bandwdth cost: W. However the offlne optal algorth wll dvde the workload nto sall peces: W/(D+), W/(D+),...W/(D+),,,,...), feasble wthn the deadlne D, wth axu traffc volue W/(D + ). W Copettve rato λ W/(D + ) = D + We hence obtan a lower bound on the copettve rato of IT, D +. Next we prove D + s also an upperbound. Wthout explotng any delays, IT provdes a feasble soluton to the pral proble, whch s denoted as P IT. P IT = ax W t t Now we desgn a feasble soluton to the dual proble as follows (assue τ = arg ax t W t ): { /(D + ) f t = τ,..., τ + D y t = otherwse { /(D + )Wt f t = τ z t = otherwse D = D + Wτ So the copettve rato s: Copettve rato λ = PIT OP T PIT D = D + Rearks: f D =,.e. jobs are not deferrable, the offlne optal algorth degrades nto IT, agreeng wth the theore, whch clas IT s copettve (D + = ). IT s apparently not deal, and ay lead to hgh peak traffc and hgh bandwdth cost as copared wth the offlne optu. Golubchk et al. [5] desgn a costaware algorth that strkes to spread out bandwdth deand by utlzng all possble delays, referred to as the Sple Soothng lgorth. Upon recevng a new workload, Sple Soothng evenly dvdes t nto D + parts, and processes the one by one n the current te slot and the followng D te slots, as shown n lgorth. lgorth The Sple Soothng lgorth [5] : for τ = to T D do : for d = to D do 3: x d,τ = /(D + ) 4: end for 5: end for Theore. [5] The copettve rato of Sple Soothng s D+. Theore can be proven through weak LP dualty,.e., usng a feasble dual as the lower bound of the offlne optal. Sple Soothng s very sple, but guarantees a worst case copettve rato saller than. Nonetheless, there s stll roo for further proveents, snce Sple Soothng gnores avalable nforaton such as the htherto axu traffc volue transtted, and the current pressure fro backlogged traffc and ther deadlnes. Such an observaton otvated our desgn of the ore sophstcated Heurstc Soothng algorth for the case D, as shown n lgorth. Here T s the charge perod, τ s the current te slot, and H d s the total volue of data that have been buffered for d te slots. lgorth The Heurstc Soothng lgorth : V ax = : W τ =, τ = T D +,..., T ; 3: H d =, d =,..., D; 4: for τ = to T do { 5: V τ = n } D d= H d D } W τ + D d= H d, ax{v ax, Wτ D+ + 6: f V ax < V τ then 7: V ax = V τ ; 8: end f 9: Transfer the traffc followng Earlest Deadlne Frst (EDF) strategy; : Update H d, d =,..., D; : end for Theore 3. The copettve rato of Heurstc Soothng s lower bounded by ( e ). Proof: Consder the followng nput: (W, W,...W,,..., ) whose frst D + te slots are W. The traffc deand V ncreases untl te slot D +. V D+ = W D + + W (D )W + D + (D + )D (D )D W (D + )D D = W D + ( + D( ( D )D )) We can fnd a feasble pral soluton whch yelds the charge volue D+ D+W. Ths pral soluton s an upper bound of the offlne optu. Therefore the lower bound D+ of the copettve rato λ V D+ (D+) = D+ (D+) ( + D( ( D )D )) ( e ) as D +. Notce that
6 D+ (D+) ( + D( ( D )D )) s a decreasng functon for D [, + ), we further have λ ( e ). Theore 4. The copettve rato of Heurstc Soothng s upperbounded by D+. Proof: We take the Sple Soothng algorth (lgorth. ) as a benchark, and we prove that P sooth P heurstc, where P heurstc s the charged volue produced by lgorth 3. lgorth 3 wll only ncrease the traffc deand when W τ D+ + D d= H d/d exceeds V ax. Therefore, we rearrange H d to copute the axu traffc deand. Let V t+d = ( W t+d D + + Wt+D D + (D )Wt+D (D )D W t ) (D + )D (D + )D D Then P heurstc = ax t V t+d. Let τ = arg ax t V t+d, and we have t+d W t P sooth = ax t D + =t τ+d =τ W τ D + Wτ+D D + + Wτ+D D + + (D )Wτ+D (D + )D (D )D W τ (D + )D D = P heurstc Snce the sple soothng algorth s D+ copettve, the copettve rato of lgorth 3 cannot be worse than D+. Fro the proof above, we have followng corollary. Corollary. For any gven nput, the charge volue resultng fro Heurstc Soothng s always equal to or saller than that of Sple Soothng. lgorth Coplexty. ll three onlne algorths dscussed have oderate te coplexty, akng the lghtweght for practcal applcatons. More specfcally, IT, Sple Soothng and Heurstc Soothng have a te coplexty of O(T D), O((T D)D), and O(T D), respectvely. V. CLOUD SCENRIO In ths secton, we apply the algorths desgned for the sngle ISP case to the cloud scenaro, whch utlzes a MapReducelke fraework for processng bg data. Defne Cost = f(v), Cost =,r f,r(v,r), and adopt power charge functons by lettng f (x) = f,r (x) = x α, α >.. lgorth Desgn The twophase MapReduce cost optzaton proble s defned n (8), and s a dscrete optzaton wth nteger varables. Consequently, an offlne soluton that solves such an nteger progra has a hgh coputatonal coplexty, further otvatng the desgn of an effcent onlne soluton. natve onlne algorth selects a fxed apper and schedules the traffc on the correspondng ISP usng the Sple Soothng lgorth. Theore 5. The copettve rato of the natve onlne algorth s lower bounded by M α, where M s the nuber of appers. Proof: Consder the nput (W,, W,,, ) whose frst D + tes are W. We can verfy that the charge volue s D+. The correspondng cost s ( D+ )α + r (βz r D+ )α. Next we consder a ore ntellgent algorth that assgns the jth workload to the apper (j od M ). Ths algorth acts as the upper bound of the offlne optu. Its charge volue s (D+) M. The correspondng cost s M ( (D+) M )α + M r (βz r (D+) M )α. Therefore, Copettve rato ( D+ )α + r (βz r D+ )α M ( (D+) M )α + M r (βz r = M α (D+) M )α We next present a dstrbuted randozed onlne algorth for (8). For each workload, the user chooses ISPs unforly at rando to transfer the data to a randoly selected apper. Forally, let W be the randozed workload assgnent allocatng each workload to appers. For each selected ISP, the user runs Heurstc Soothng to gude onestage traffc deferral and transsson, as shown n lgorth 3. lgorth 3 Randozed Uploadng Schee : Generate a randozed workload assgnent W whch allocates each workload to a randoly selected apper. : For each ISP, apply the sngle ISP algorth, e.g., lgorth to schedule the traffc. We analyze lgorth 3 by buldng a connecton between the uploadng schee π and the randozed workload assgnent W. We cobne π and W to a new uploadng schee π W. Let t = < t < t e = T. Durng each nterval [t, t + ), each ISP s eployed to transfer at ost one workload n the uploadng schee π. If a workload s processed n [t, t + ), then t cannot be fnshed before t +. Due to the MX charge odel, the transfer speed for workload w n [t, t + ) s a sngle speed, say v,w. If workload w s not processed n [t, t + ), we set v,w =. Therefore, for any gven, there are at ost M values of v,w. ssue there are n workloads, forng a set W. Let Ω = {w all workloads assgned to ISP } W. In schee π W, the user transfers data at speed of w Ω v,w n te nterval [t, t + ). Let φ n (Ω ) be the probablty that exactly the workloads Ω are allocated to ISP. φ n(ω ) = ( M ) Ω ( M )n Ω
7 We next defne functon Λ n(x) where x R n \ {}: Λ n(x) = M φ n n(ω )( x w) α / x α w w Ω w= Ω W Lea. Gven any uploadng schee π and a randozed workload assgnent W, we have a randozed uploadng schee π W, whch satsfes: E(Cost (π W ) + Cost (π W )) ax Λ M (x)(cost x (π) + Cost (π)) Proof: Snce the traffc pattern n ISP (, r), r s exactly the sae as ISP, we only consder one stage. Let us consder schee π frst. In the frst stage, the cost s: Cost (π) = ax,w (v,w) α ax M Σ M (v α,w) where v,w ndcates the transfer speed n ISP durng [t, t + ) for workload w. Σ M (vα,w ) s the su of the largest M values of v,w α when gven. The nequalty holds because there are at ost M nonzero speeds for any gven duraton [t, t + ). We next have the cost of the second stage: Cost (π) = ax,w (βzrv,w) α r = β α zr α ax,w (v,w) α r β α zr α ax Σ M (v,w) α r The cost of the frst stage n π W s: E(Cost (π W )) = φ n(ω W ) ax( M Ω W W = M ax )( φ n(ω W Ω W W w Ω W w Ω W v,w) α v,w) α The second equalty above holds because the assgnent s unforly rando. Slarly, The cost of the second stage n π W s: E(Cost (π W )) = M Ω W = M β α r φ n(ω W P z α r ax ) r ax(z r φ n(ω W Ω W W w Ω W )( w Ω W βv,w) α v,w) α gan because for any [t, t + ), there are at ost M values of v,w. We have M Ω W = M Ω W W φ n(ω W Σ M (vα,w ) = Λ n (v) = Λ M (v ) )( w Ω W v,w) α W φ n(ω W )( w Ω v W,w ) α n w= (vα,w ) where v s an M densonal subvector of v R n \ {}, whch contans all nonzero transfer speeds n [t, t + ). Therefore, the rato for the frst stage s: E(Cost (π W )) Cost (π) M Ω W W φ(ωw ) ax ( w Ω W ax Σ M (vα,w ) M Ω W W φ(ωw )( w Ω W Σ M (vα,w ) ax Λ M (x) x v,w) α v,w)α where = arg ax ( w Ω v,w) α. Slarly, the rato W for the second stage s also bounded by ax x Λ M (x),.e., E(Cost (π W )) Cost (π) ax x Λ M (x). Ths proves Lea. Let S(α, j) be the jth Strlng nuber for α eleents, defned as the nuber of parttons of a set of sze α nto j subsets [4]. Let B α be the αth Bell nuber, defned as the nuber of parttons of a set of sze α [4]. The Bell nuber s relatvely sall when α s sall: B =, B =, B 3 = 5, B 4 = 5. The defntons also ply: α S(α, j) = B α j The followng lea s proven by Grener et al. [6]. Lea. [6] α N and α M, ax x Λ M (x) = M! S(α, j) α j= M j ( M j)!. Theore 6. Gven a λcopettve algorth wth respect to cost for the sngle ISP case, then the randozed onlne algorth s λb α copettve n expectaton. Proof: Let π be the optal uploadng schee, the correspondng randozed uploadng schee s πw. The algorth we use s π W. Snce the workloads n πw and π W are the sae, we have: E(Cost (π W )) λe(cost (π W )) () snce the algorth s λcopettve. Slarly, E(Cost (π W )) λe(cost (π W )) () snce the traffc pattern n ISP (, r), r s exactly the sae as n ISP. Lea ples: E(Cost (π W ) + Cost (π W )) ax x Λ M (x)(cost (π ) + Cost (π )) (3) Snce Λ M (x) s a onotoncally ncreasng functon of α, we use α as an upper bound of α >, obtanng a correspondng upper bound of Λ M (x). Cobnng Eqn. () () and (3) as well as Lea, we have the followng expected cost of the randozed onlne algorth:
8 E(Cost (π W ) + Cost (π W )) λe(cost (π W ) + Cost (π W )) λ ax x Λ M (x)(cost (π ) + Cost (π )) α M! = λ S( α, j) M j ( M j)! (Cost(π ) + Cost (π )) j= α λ S( α, j)(cost (π ) + Cost (π )) j= λb α OP T Reark: For a sngle lnk, we can eploy Heurstc Soothng, whose copettve rato s saller than wth respect to axu traffc volue. Then the copettve rato of lgorth s α n cost. Thus lgorth 3 s α B α  copettve n expectaton. When α =, the copettve rato s 8, a constant regardless of the nuber of appers. VI. PERFORMNCE EVLUTION We have pleented Sple Soothng, Heurstc Soothng, as well as the randozed onlne algorth, for perforance evaluaton through sulaton studes. The default nput W t s generated unforly at rando, as shown n Fg., where all data are noralzed,.e., scaled down by ax t W t. We assue there are 5 appers at dfferent locatons, and 5 reducers at dfferent locatons. We choose α =, thus the charge functon f (x) = f,r (x) = x.. The Sngle ISP Case Frst we copare Heurstc Soothng wth Sple Soothng. The two algorths are executed under a delay requreent D = 5. Fg. 3 llustrates the traffc volue scheduled at each te slot. Copared wth Sple Soothng, Heurstc Soothng results n a axu traffc volue ths s about 8% saller. Heurstc Soothng tres to explot the avalable delay to average the traffc and s less senstve to the fluctuaton of traffc deand, as copared wth Sple Soothng. For exaple, at around t =, the traffc of Sple Soothng ncreases abruptly due to hgh traffc deand n the nput; around t = 4, t goes down due to low traffc deand. In coparson, Heurstc Soothng results n ore even traffc dstrbutons around t = and t = 4. Next we exane how the tolerable delay affects the perforance of the proposed onlne algorths. We execute Sple Soothng, Heurstc Soothng and IT aganst a varety of delays rangng fro D = to D = 4. We also copute the offlne optu as a benchark. The observed copettve ratos are shown n Fg. 4. The results suggest that both Sple Soothng and Heurstc Soothng perfor uch better than IT. Heurstc Soothng also beats Sple Soothng, by a saller argn. Heurstc Soothng approaches the offlne optu rather closely; the observed copettve ratos are always below.5 and usually around., uch better than the theoretcally proven upper bound n Theore 4. Heurstc Soothng s further evaluated under other rando nputs, ncludng Posson dstrbuton n Fg. 5, Gaussan dstrbuton n Fg. 6 and a specfcally desgned rando nput n Fg. 7. ll results verfy that Heurstc Soothng works best aong the three onlne cost nzaton algorths. B. The Cloud Scenaro We pleented the randozed algorth n lgorth 3 and the natve algorth n Sec. V. They are evaluated under three types of nputs: unfor dstrbuton, Posson dstrbuton and Gaussan dstrbuton. We copare the costs of the two algorths usng these nputs, as shown n Fg. 8, Fg. 9 and Fg., respectvely. We observe that the randozed algorth acheves uch lower cost than the natve algorth, n partcular wth longer tolerable delays. For exaple, Fg. 8 shows that the randozed algorth saves approxately 45% cost as copared wth the natve algorth when D = 5, and t saves ore than 68% when D =. Ths suggests that longer tolerable delays provde the randozed algorth ore space of aneuver, leadng to ore evdent cost reduce. We further nvestgate the nfluence of β, the rato of orgnal data sze to the nteredate data sze. Results are shown n Fg.. When D s sall, a large β causes a rather hgh cost. However when a large D s used, e.g., D = 4, even a large β only produces a relatvely sall cost. Noralze Cost β Fg.. Relatonshp between traffc cost and paraeters D, β. VII. CONCLUSION ISPs now charge bg data applcatons wth a new, nterestng percentle based odel, leadng to new onlne algorth desgn probles for nzng the traffc cost pad for uploadng bg data to the cloud. We studed two scenaros for such onlne algorth desgn n ths work. Heurstc Soothng algorth s proposed n the sngle lnk case, wth proven better perforance than the best alternatve n the lterature, and a saller copettve rato below. randozed onlne algorth s desgned for the MapReduce fraework, achevng a constant copettve rato by eployng Heurstc Soothng as a buldng odule. We have focused on MX charge rules, and leave slar onlne algorth desgn for 95percentle charge rules as future work. REFERENCES [] azon Elastc Copute Cloud, [] Lnode, https://www.lnode.co/speedtest/. [3] azon EC Casestudes,
9 Noralzed Data Traffc.6.4 Unfor Input Te Noralzed Scheduled Traffc.6.4 Sple Soothng Heurstc Soothng Te Copettve Rato IT Sple Soothng Heurstc Soothng Copettve Rato.5.5 Fg.. Unforly Rando Input. IT Sple Soothng Heurstc Soothng Fg. 5. Copettve rato over varous delay wndow szes under nput of Posson dstrbuton. Fg. 3. Sple Soothng vs. Heurstc Soothng, D = Copettve Rato IT Sple Soothng Heurstc Soothng Fg. 6. Copettve rato over varous delay wndow szes under nput of Gaussan dstrbuton. Fg. 4. Copettve rato over varous delay wndow szes under nput of unfor dstrbuton. Copettve Rato IT Sple Soothng Heurstc Soothng Fg. 7. Copettve rato over varous delay wndow szes under a specfcally desgned nput. Randozed lgorth Natve lgorth Randozed lgorth Natve lgorth Randozed lgorth Natve lgorth Noralze Cost.6.4 Noralze Cost.6.4 Noralze Cost Fg. 8. Coparson between the proposed randozed algorth and the natve algorth under nput of unfor dstrbuton and β =. Fg. 9. Coparson between the proposed randozed algorth and the natve algorth under nput of Posson dstrbuton and β =. Fg.. Coparson between the proposed randozed algorth and the natve algorth under nput of Gaussan dstrbuton and β =. [4] E. E. Schadt, M. D. Lnderan, J. Sorenson, L. Lee, and G. P. Nolan, Coputatonal Solutons to Largescale Data Manageent and nalyss, Nat Rev Genet, vol., no. 9, pp , Sep.. [5] L. Golubchk, S. Khuller, K. Mukherjee, and Y. Yao, To Send or not to Send: Reducng the Cost of Data Transsson, n Proc. of IEEE INFOCOM, 3. [6] L. Zhang, C. Wu, Z. L, C. Guo, M. Chen, and F. Lau, Movng Bg Data to The Cloud: n Onlne CostMnzng pproach, IEEE Journal on Selected reas n Councatons, vol. 3, no., pp. 7 7, 3. [7] H. Wang, H. Xe, L. Qu,. Slberschatz, and Y. Yang, Optal ISP Subscrpton for Internet Multhong: lgorth Desgn and Iplcaton nalyss, n Proc. of IEEE INFOCOM, 5. [8] S. Peak, Beyond Bandwdth: The Busness Case For Data cceleraton, Whte Paper, 3. [9] D. K. Goldenberg, L. Quy, H. Xe, Y. R. Yang, and Y. Zhang, Optzng Cost and Perforance for Multhong, n Proc. of CM SIGCOMM, 4. []. Grothey and X. Yang, Toppercentle Traffc Routng Proble by Dynac Prograng, Optzaton and Engneerng, vol., pp ,. [] F. Yao,. Deers, and S. Shenker, Schedulng Model for Reduced CPU Energy, n Proc. of IEEE FOCS, 995. [] N. Bansal, T. Kbrel, and K. Pruhs, Speed Scalng to Manage Energy and Teperature, J. CM, vol. 54, no., pp. 3: 3:39, Mar. 7. [3] S. lbers, F. Müller, and S. Schelzer, Speed Scalng on Parallel Processors, n Proc. of CM SP, 7. [4] B. Bngha and M. Greenstreet, Energy Optal Schedulng on Multprocessors wth Mgraton, n Proc. of IEEE ISP, 8. [5] E. ngel, E. Baps, F. Kace, and D. Letsos, Speed Scalng on Parallel Processors wth Mgraton, n EuroPar Parallel Processng, ser. Lecture Notes n Coputer Scence, C. Kaklaans, T. Papatheodorou, and P. Spraks, Eds. Sprnger Berln Hedelberg,, vol. 7484, pp [6] G. Grener, T. Nonner, and. Souza, The Bell s Rngng n Speedscaled Multprocessor Schedulng, n Proc. of CM SP, 9. [7] M.. dnan, Y. Ma, R. Sughara, and R. Gupta, Dynac Deferral of Workload for Capacty Provsonng n Data Centers, [8] Y. Yao, L. Huang,. Shara, L. Golubchk, and M. Neely, Data Centers Power Reducton: Two Te Scale pproach for Delay Tolerant Workloads, n Proc. of IEEE INFOCOM,. [9] B. Cho and I. Gupta, New lgorths for Plannng Bulk Transfer va Internet and Shppng Networks, n Proc. of IEEE ICDCS,. [] M. dler, R. K. Staraan, and H. Venkataraan, lgorths for Optzng the Bandwdth Cost of Content Delvery, Coput. Netw., vol. 55, no. 8, pp. 47 4, Dec.. [] J. Dean and S. Gheawat, MapReduce: Splfed Data Processng on Large Clusters, Coun. CM, vol. 5, no., pp. 7 3, Jan. 8. [] S. Rao, R. Raakrshnan,. Slbersten, M. Ovsannkov, and D. Reeves, Salfsh: Fraework for Large Scale Data Processng, Yahoo!Labs, Tech. Rep.,. [3] B. Hentz,. Chandra, and R. K. Staraan, Optzng MapReduce for Hghly Dstrbuted Envronents, Departent of Coputer Scence and Engneerng, Unversty of Mnnesota, Tech. Rep.,. [4] H. Becker and J. Rordan, The rthetc of Bell and Strlng nubers, ercan journal of Matheatcs, vol. 7, no., pp , 948.
Stochastic Models of Load Balancing and Scheduling in Cloud Computing Clusters
Stochastc Models of Load Balancng and Schedulng n Cloud Coputng Clusters Sva Theja Magulur and R. Srkant Departent of ECE and CSL Unversty of Illnos at UrbanaChapagn sva.theja@gal.co; rsrkant@llnos.edu
More informationStochastic Models of Load Balancing and Scheduling in Cloud Computing Clusters
Stochastc Models of Load Balancng and Schedulng n Cloud Coputng Clusters Sva Theja Magulur and R. Srkant Departent of ECE and CSL Unversty of Illnos at UrbanaChapagn sva.theja@gal.co; rsrkant@llnos.edu
More informationStochastic Models of Load Balancing and Scheduling in Cloud Computing Clusters
01 Proceedngs IEEE INFOCOM Stochastc Models of Load Balancng and Schedulng n Cloud Coputng Clusters Sva heja Magulur and R. Srkant Departent of ECE and CSL Unversty of Illnos at UrbanaChapagn sva.theja@gal.co;
More informationAn Electricity Trade Model for Microgrid Communities in Smart Grid
An Electrcty Trade Model for Mcrogrd Countes n Sart Grd Tansong Cu, Yanzh Wang, Shahn Nazaran and Massoud Pedra Unversty of Southern Calforna Departent of Electrcal Engneerng Los Angeles, CA, USA {tcu,
More informationBasic Queueing Theory M/M/* Queues. Introduction
Basc Queueng Theory M/M/* Queues These sldes are created by Dr. Yh Huang of George Mason Unversty. Students regstered n Dr. Huang's courses at GMU can ake a sngle achnereadable copy and prnt a sngle copy
More informationNear Optimal Online Algorithms and Fast Approximation Algorithms for Resource Allocation Problems
Near Optal Onlne Algorths and Fast Approxaton Algorths for Resource Allocaton Probles Nkhl R Devanur Kaal Jan Balasubraanan Svan Chrstopher A Wlkens Abstract We present algorths for a class of resource
More informationBANDWIDTH ALLOCATION AND PRICING PROBLEM FOR A DUOPOLY MARKET
Yugoslav Journal of Operatons Research (0), Nuber, 6578 DOI: 0.98/YJOR0065Y BANDWIDTH ALLOCATION AND PRICING PROBLEM FOR A DUOPOLY MARKET PengSheng YOU Graduate Insttute of Marketng and Logstcs/Transportaton,
More informationFault tolerance in cloud technologies presented as a service
Internatonal Scentfc Conference Computer Scence 2015 Pavel Dzhunev, PhD student Fault tolerance n cloud technologes presented as a servce INTRODUCTION Improvements n technques for vrtualzaton and performance
More informationVirtual machine resource allocation algorithm in cloud environment
COMPUTE MOELLIN & NEW TECHNOLOIES 2014 1(11) 27924 Le Zheng Vrtual achne resource allocaton algorth n cloud envronent 1, 2 Le Zheng 1 School of Inforaton Engneerng, Shandong Youth Unversty of Poltcal
More informationHow Much to Bet on Video Poker
How Much to Bet on Vdeo Poker Trstan Barnett A queston that arses whenever a gae s favorable to the player s how uch to wager on each event? Whle conservatve play (or nu bet nzes large fluctuatons, t lacks
More informationRevenue Maximization Using Adaptive Resource Provisioning in Cloud Computing Environments
202 ACM/EEE 3th nternatonal Conference on Grd Coputng evenue Maxzaton sng Adaptve esource Provsonng n Cloud Coputng Envronents Guofu Feng School of nforaton Scence, Nanng Audt nversty, Nanng, Chna nufgf@gal.co
More informationAn Analytical Model of Web Server Load Distribution by Applying a Minimum Entropy Strategy
Internatonal Journal of Coputer and Councaton Engneerng, Vol. 2, No. 4, July 203 An Analytcal odel of Web Server Load Dstrbuton by Applyng a nu Entropy Strategy Teeranan Nandhakwang, Settapong alsuwan,
More informationCapacity Planning for Virtualized Servers
Capacty Plannng for Vrtualzed Servers Martn Bchler, Thoas Setzer, Benjan Spetkap Departent of Inforatcs, TU München 85748 Garchng/Munch, Gerany (bchler setzer benjan.spetkap)@n.tu.de Abstract Today's data
More informationA Statistical Model for Detecting Abnormality in StaticPriority Scheduling Networks with Differentiated Services
A Statstcal odel for Detectng Abnoralty n StatcProrty Schedulng Networks wth Dfferentated Servces ng L 1 and We Zhao 1 School of Inforaton Scence & Technology, East Chna Noral Unversty, Shangha 0006,
More informationAn Alternative Way to Measure Private Equity Performance
An Alternatve Way to Measure Prvate Equty Performance Peter Todd Parlux Investment Technology LLC Summary Internal Rate of Return (IRR) s probably the most common way to measure the performance of prvate
More informationOn Monitoring of EndtoEnd Packet Reordering over the Internet
On Montorng of EndtoEnd Packet Reorderng over the Internet Bn Ye 1 Anura P. Jayasuana 1 Nschal M. Pratla 2 1Coputer Networkng Research laboratory, Colorado State Unversty, Fort Collns, CO 8523, USA 2
More informationA R T I C L E S DYNAMIC VEHICLE DISPATCHING: OPTIMAL HEAVY TRAFFIC PERFORMANCE AND PRACTICAL INSIGHTS
A R T I C L E S DYAMIC VEHICLE DISPATCHIG: OPTIMAL HEAVY TRAFFIC PERFORMACE AD PRACTICAL ISIGHTS OAH GAS OPIM Departent, The Wharton School, Unversty of Pennsylvana, Phladelpha, Pennsylvana 191046366
More informationInventory Control in a MultiSupplier System
3th Intl Workng Senar on Producton Econocs (WSPE), Igls, Autrche, pp.56 Inventory Control n a MultSuppler Syste Yasen Arda and JeanClaude Hennet LAASCRS, 7 Avenue du Colonel Roche, 3077 Toulouse Cedex
More informationCONSTRUCTION OF A COLLABORATIVE VALUE CHAIN IN CLOUD COMPUTING ENVIRONMENT
CONSTRUCTION OF A COLLAORATIVE VALUE CHAIN IN CLOUD COMPUTING ENVIRONMENT Png Wang, School of Econoy and Manageent, Jangsu Unversty of Scence and Technology, Zhenjang Jangsu Chna, sdwangp1975@163.co Zhyng
More informationThe Packing Server for RealTime Scheduling of MapReduce Workflows
The Packng Server for RealTe Schedulng of MapReduce Workflows Shen L, Shaohan Hu, Tarek Abdelzaher Unversty of Illnos at UrbanaChapagn {shenl3, shu7, zaher}@llnos.edu Abstract Ths paper develops new
More informationA Fuzzy Optimization Framework for COTS Products Selection of Modular Software Systems
Internatonal Journal of Fuy Systes, Vol. 5, No., June 0 9 A Fuy Optaton Fraework for COTS Products Selecton of Modular Software Systes Pankaj Gupta, Hoang Pha, Mukesh Kuar Mehlawat, and Shlp Vera Abstract
More informationDynamic Resource Allocation in Clouds: Smart Placement with Live Migration
Dynac Resource Allocaton n Clouds: Sart Placeent wth Lve Mgraton Mahlouf Had Ingéneur de Recherche ahlouf.had@rtsystex.fr Avec : Daal Zeghlache (TSP) daal.zeghlache@telecosudpars.eu FONDATION DE COOPERATION
More informationDEFINING %COMPLETE IN MICROSOFT PROJECT
CelersSystems DEFINING %COMPLETE IN MICROSOFT PROJECT PREPARED BY James E Aksel, PMP, PMISP, MVP For Addtonal Informaton about Earned Value Management Systems and reportng, please contact: CelersSystems,
More informationScan Detection in HighSpeed Networks Based on Optimal Dynamic Bit Sharing
Scan Detecton n HghSpeed Networks Based on Optal Dynac Bt Sharng Tao L Shgang Chen Wen Luo Mng Zhang Departent of Coputer & Inforaton Scence & Engneerng, Unversty of Florda Abstract Scan detecton s one
More informationResearch Article Load Balancing for Future Internet: An Approach Based on Game Theory
Appled Matheatcs, Artcle ID 959782, 11 pages http://dx.do.org/10.1155/2014/959782 Research Artcle Load Balancng for Future Internet: An Approach Based on Gae Theory Shaoy Song, Tngje Lv, and Xa Chen School
More informationNaglaa Raga Said Assistant Professor of Operations. Egypt.
Volue, Issue, Deceer ISSN: 77 8X Internatonal Journal of Adanced Research n Coputer Scence and Software Engneerng Research Paper Aalale onlne at: www.jarcsse.co Optal Control Theory Approach to Sole Constraned
More informationSchedulability Bound of Weighted Round Robin Schedulers for Hard RealTime Systems
Schedulablty Bound of Weghted Round Robn Schedulers for Hard RealTme Systems Janja Wu, JyhCharn Lu, and We Zhao Department of Computer Scence, Texas A&M Unversty {janjaw, lu, zhao}@cs.tamu.edu Abstract
More informationLuby s Alg. for Maximal Independent Sets using Pairwise Independence
Lecture Notes for Randomzed Algorthms Luby s Alg. for Maxmal Independent Sets usng Parwse Independence Last Updated by Erc Vgoda on February, 006 8. Maxmal Independent Sets For a graph G = (V, E), an ndependent
More informationModule 2 LOSSLESS IMAGE COMPRESSION SYSTEMS. Version 2 ECE IIT, Kharagpur
Module LOSSLESS IMAGE COMPRESSION SYSTEMS Lesson 3 Lossless Compresson: Huffman Codng Instructonal Objectves At the end of ths lesson, the students should be able to:. Defne and measure source entropy..
More informationGanesh Subramaniam. American Solutions Inc., 100 Commerce Dr Suite # 103, Newark, DE 19713, USA
238 Int. J. Sulaton and Process Modellng, Vol. 3, No. 4, 2007 Sulatonbased optsaton for ateral dspatchng n VendorManaged Inventory systes Ganesh Subraana Aercan Solutons Inc., 100 Coerce Dr Sute # 103,
More informationProject Networks With MixedTime Constraints
Project Networs Wth MxedTme Constrants L Caccetta and B Wattananon Western Australan Centre of Excellence n Industral Optmsaton (WACEIO) Curtn Unversty of Technology GPO Box U1987 Perth Western Australa
More informationNear Optimal Online Algorithms and Fast Approximation Algorithms for Resource Allocation Problems
Near Optal Onlne Algorths and Fast Approxaton Algorths for Resource Allocaton Probles ABSTRACT Nhl R Devanur Mcrosoft Research Redond WA USA ndev@crosoftco Balasubraanan Svan Coputer Scences Dept Unv of
More informationYixin Jiang and Chuang Lin. Minghui Shi and Xuemin Sherman Shen*
198 Int J Securty Networks Vol 1 Nos 3/4 2006 A selfencrypton authentcaton protocol for teleconference servces Yxn Jang huang Ln Departent of oputer Scence Technology Tsnghua Unversty Beng hna Eal: yxang@csnet1cstsnghuaeducn
More informationA Novel Dynamic RoleBased Access Control Scheme in User Hierarchy
Journal of Coputatonal Inforaton Systes 6:7(200) 24232430 Avalable at http://www.jofcs.co A Novel Dynac RoleBased Access Control Schee n User Herarchy Xuxa TIAN, Zhongqn BI, Janpng XU, Dang LIU School
More informationThe OC Curve of Attribute Acceptance Plans
The OC Curve of Attrbute Acceptance Plans The Operatng Characterstc (OC) curve descrbes the probablty of acceptng a lot as a functon of the lot s qualty. Fgure 1 shows a typcal OC Curve. 10 8 6 4 1 3 4
More information1 Approximation Algorithms
CME 305: Dscrete Mathematcs and Algorthms 1 Approxmaton Algorthms In lght of the apparent ntractablty of the problems we beleve not to le n P, t makes sense to pursue deas other than complete solutons
More informationMaximizing profit using recommender systems
Maxzng proft usng recoender systes Aparna Das Brown Unversty rovdence, RI aparna@cs.brown.edu Clare Matheu Brown Unversty rovdence, RI clare@cs.brown.edu Danel Rcketts Brown Unversty rovdence, RI danel.bore.rcketts@gal.co
More informationINTRODUCTION TO MERGERS AND ACQUISITIONS: FIRM DIVERSIFICATION
XV. INTODUCTION TO MEGES AND ACQUISITIONS: FIM DIVESIFICATION In the ntroducton to Secton VII, t was noted that frs can acqure assets by ether undertakng nternallygenerated new projects or by acqurng
More informationGraph Theory and Cayley s Formula
Graph Theory and Cayley s Formula Chad Casarotto August 10, 2006 Contents 1 Introducton 1 2 Bascs and Defntons 1 Cayley s Formula 4 4 Prüfer Encodng A Forest of Trees 7 1 Introducton In ths paper, I wll
More informationTwoPhase Traceback of DDoS Attacks with Overlay Network
4th Internatonal Conference on Sensors, Measureent and Intellgent Materals (ICSMIM 205) TwoPhase Traceback of DDoS Attacks wth Overlay Network Zahong Zhou, a, Jang Wang2, b and X Chen3, c 2 School of
More informationCommunication Networks II Contents
8 / 1  Communcaton Networs II (Görg)  www.comnets.unbremen.de Communcaton Networs II Contents 1 Fundamentals of probablty theory 2 Traffc n communcaton networs 3 Stochastc & Marovan Processes (SP
More information9.1 The Cumulative Sum Control Chart
Learnng Objectves 9.1 The Cumulatve Sum Control Chart 9.1.1 Basc Prncples: Cusum Control Chart for Montorng the Process Mean If s the target for the process mean, then the cumulatve sum control chart s
More informationJ. Parallel Distrib. Comput.
J. Parallel Dstrb. Comput. 71 (2011) 62 76 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. journal homepage: www.elsever.com/locate/jpdc Optmzng server placement n dstrbuted systems n
More informationHow Sets of Coherent Probabilities May Serve as Models for Degrees of Incoherence
1 st Internatonal Symposum on Imprecse Probabltes and Ther Applcatons, Ghent, Belgum, 29 June 2 July 1999 How Sets of Coherent Probabltes May Serve as Models for Degrees of Incoherence Mar J. Schervsh
More informationII. THE QUALITY AND REGULATION OF THE DISTRIBUTION COMPANIES I. INTRODUCTION
Fronter Methodology to fx Qualty goals n Electrcal Energy Dstrbuton Copanes R. Rarez 1, A. Sudrà 2, A. Super 3, J.Bergas 4, R.Vllafáfla 5 12 345  CITCEA  UPC UPC., Unversdad Poltécnca de Cataluña,
More informationbenefit is 2, paid if the policyholder dies within the year, and probability of death within the year is ).
REVIEW OF RISK MANAGEMENT CONCEPTS LOSS DISTRIBUTIONS AND INSURANCE Loss and nsurance: When someone s subject to the rsk of ncurrng a fnancal loss, the loss s generally modeled usng a random varable or
More informationWeb Servicebased Business Process Automation Using Matching Algorithms
Web Servcebased Busness Process Autoaton Usng Matchng Algorths Yanggon K and Juhnyoung Lee 2 Coputer and Inforaton Scences, Towson Uversty, Towson, MD 2252, USA, yk@towson.edu 2 IBM T. J. Watson Research
More informationEnabling P2P Oneview Multiparty Video Conferencing
Enablng P2P Onevew Multparty Vdeo Conferencng Yongxang Zhao, Yong Lu, Changja Chen, and JanYn Zhang Abstract MultParty Vdeo Conferencng (MPVC) facltates realtme group nteracton between users. Whle P2P
More informationLecture 3: Force of Interest, Real Interest Rate, Annuity
Lecture 3: Force of Interest, Real Interest Rate, Annuty Goals: Study contnuous compoundng and force of nterest Dscuss real nterest rate Learn annutymmedate, and ts present value Study annutydue, and
More informationPAS: A Packet Accounting System to Limit the Effects of DoS & DDoS. Debish Fesehaye & Klara Naherstedt University of IllinoisUrbana Champaign
PAS: A Packet Accountng System to Lmt the Effects of DoS & DDoS Debsh Fesehaye & Klara Naherstedt Unversty of IllnosUrbana Champagn DoS and DDoS DDoS attacks are ncreasng threats to our dgtal world. Exstng
More informationA Multi Due Date Batch Scheduling Model. on Dynamic Flow Shop to Minimize. Total Production Cost
Conteporary Enneern Scences, Vol. 9, 2016, no. 7, 315324 HIKARI Ltd, www.hkar.co http://dx.do.or/10.12988/ces.2016.617 A Mult Due Date Batch Scheduln Model on Dynac Flow Shop to Mnze Total Producton
More informationRecurrence. 1 Definitions and main statements
Recurrence 1 Defntons and man statements Let X n, n = 0, 1, 2,... be a MC wth the state space S = (1, 2,...), transton probabltes p j = P {X n+1 = j X n = }, and the transton matrx P = (p j ),j S def.
More informationInternational Journal of Industrial Engineering Computations
Internatonal Journal of Industral ngneerng Coputatons 3 (2012) 393 402 Contents lsts avalable at GrowngScence Internatonal Journal of Industral ngneerng Coputatons hoepage: www.growngscence.co/jec Suppler
More informationPRIOR ROBUST OPTIMIZATION. Balasubramanian Sivan. A dissertation submitted in partial fulfillment of the requirements for the degree of
PRIOR ROBUST OPTIMIZATION By Balasubraanan Svan A dssertaton subtted n partal fulfllent of the requreents for the degree of Doctor of Phlosophy (Coputer Scences) at the UNIVERSITY OF WISCONSIN MADISON
More informationA Novel Methodology of Working Capital Management for Large. Public Constructions by Using Fuzzy Scurve Regression
Novel Methodology of Workng Captal Management for Large Publc Constructons by Usng Fuzzy Scurve Regresson ChengWu Chen, Morrs H. L. Wang and TngYa Hseh Department of Cvl Engneerng, Natonal Central Unversty,
More informationInstitute of Informatics, Faculty of Business and Management, Brno University of Technology,Czech Republic
Lagrange Multplers as Quanttatve Indcators n Economcs Ivan Mezník Insttute of Informatcs, Faculty of Busness and Management, Brno Unversty of TechnologCzech Republc Abstract The quanttatve role of Lagrange
More informationTHE DISTRIBUTION OF LOAN PORTFOLIO VALUE * Oldrich Alfons Vasicek
HE DISRIBUION OF LOAN PORFOLIO VALUE * Oldrch Alfons Vascek he amount of captal necessary to support a portfolo of debt securtes depends on the probablty dstrbuton of the portfolo loss. Consder a portfolo
More informationMultiSource Video Multicast in PeertoPeer Networks
ultsource Vdeo ultcast n PeertoPeer Networks Francsco de Asís LópezFuentes*, Eckehard Stenbach Technsche Unverstät ünchen Insttute of Communcaton Networks, eda Technology Group 80333 ünchen, Germany
More informationAnalysis of Clock Synchronization Approaches for Residential Ethernet
Analyss of Clock Synchronzaton Approaches for Resdental Ethernet Geoffrey M. Garner (Consultant) Kees den Hollander SAIT, Sasung Electroncs ggarner@cocast.net, denhollander.c.@sasung.co Abstract Resdental
More informationSecure Cloud Storage Service with An Efficient DOKS Protocol
Secure Cloud Storage Servce wth An Effcent DOKS Protocol ZhengTao Jang Councaton Unversty of Chna z.t.ang@163.co Abstract Storage servces based on publc clouds provde custoers wth elastc storage and ondeand
More informationSTATE HIGHWAY ADMINISTRATION RESEARCH REPORT ENHANCEMENT OF FREEWAY INCIDENT TRAFFIC MANAGEMENT AND RESULTING BENEFITS
MD11 SP009B4Q STATE HIGHWAY ADMINISTRATION RESEARCH REPORT ENHANCEMENT OF FREEWAY INCIDENT TRAFFIC MANAGEMENT AND RESULTING BENEFITS WOON KIM AND MARK FRANZ GANGLEN CHANG DEPARTMENT OF CIVIL AND ENVIRONMENTAL
More informationPerformance Analysis of Energy Consumption of Smartphone Running Mobile Hotspot Application
Internatonal Journal of mart Grd and lean Energy Performance Analyss of Energy onsumpton of martphone Runnng Moble Hotspot Applcaton Yun on hung a chool of Electronc Engneerng, oongsl Unversty, 511 angdodong,
More informationRobust Design of Public Storage Warehouses. Yeming (Yale) Gong EMLYON Business School
Robust Desgn of Publc Storage Warehouses Yemng (Yale) Gong EMLYON Busness School Rene de Koster Rotterdam school of management, Erasmus Unversty Abstract We apply robust optmzaton and revenue management
More informationQuality of Service Analysis and Control for Wireless Sensor Networks
Qualty of ervce Analyss and Control for Wreless ensor Networs Jaes Kay and Jeff Frol Unversty of Veront ay@uv.edu, frol@eba.uv.edu Abstract hs paper nvestgates wreless sensor networ spatal resoluton as
More informationEfficient OnDemand Data Service Delivery to HighSpeed Trains in Cellular/Infostation Integrated Networks
IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. XX, NO. XX, MONTH 2XX 1 Effcent OnDemand Data Servce Delvery to HghSpeed Trans n Cellular/Infostaton Integrated Networks Hao Lang, Student Member,
More informationThe Development of Web Log Mining Based on ImproveKMeans Clustering Analysis
The Development of Web Log Mnng Based on ImproveKMeans Clusterng Analyss TngZhong Wang * College of Informaton Technology, Luoyang Normal Unversty, Luoyang, 471022, Chna wangtngzhong2@sna.cn Abstract.
More informationAn Enhanced KAnonymity Model against Homogeneity Attack
JOURNAL OF SOFTWARE, VOL. 6, NO. 10, OCTOBER 011 1945 An Enhanced KAnont Model aganst Hoogenet Attack Qan Wang College of Coputer Scence of Chongqng Unverst, Chongqng, Chna Eal: wangqan@cqu.edu.cn Zhwe
More informationCalculation of Sampling Weights
Perre Foy Statstcs Canada 4 Calculaton of Samplng Weghts 4.1 OVERVIEW The basc sample desgn used n TIMSS Populatons 1 and 2 was a twostage stratfed cluster desgn. 1 The frst stage conssted of a sample
More informationCloudbased Social Application Deployment using Local Processing and Global Distribution
Cloudbased Socal Applcaton Deployment usng Local Processng and Global Dstrbuton Zh Wang *, Baochun L, Lfeng Sun *, and Shqang Yang * * Bejng Key Laboratory of Networked Multmeda Department of Computer
More informationCLoud computing technologies have enabled rapid
1 CostMnmzng Dynamc Mgraton of Content Dstrbuton Servces nto Hybrd Clouds Xuana Qu, Hongxng L, Chuan Wu, Zongpeng L and Francs C.M. Lau Department of Computer Scence, The Unversty of Hong Kong, Hong Kong,
More informationJ. Parallel Distrib. Comput. Environmentconscious scheduling of HPC applications on distributed Cloudoriented data centers
J. Parallel Dstrb. Comput. 71 (2011) 732 749 Contents lsts avalable at ScenceDrect J. Parallel Dstrb. Comput. ournal homepage: www.elsever.com/locate/pdc Envronmentconscous schedulng of HPC applcatons
More informationPSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 12
14 The Chsquared dstrbuton PSYCHOLOGICAL RESEARCH (PYC 304C) Lecture 1 If a normal varable X, havng mean µ and varance σ, s standardsed, the new varable Z has a mean 0 and varance 1. When ths standardsed
More informationA Hybrid Approach to Evaluate the Performance of Engineering Schools
A Hybrd Approach to Evaluate the Perforance of Engneerng Schools School of Engneerng Unversty of Brdgeport Brdgeport, CT 06604 ABSTRACT Scence and engneerng (S&E) are two dscplnes that are hghly receptve
More informationI. SCOPE, APPLICABILITY AND PARAMETERS Scope
D Executve Board Annex 9 Page A/R ethodologcal Tool alculaton of the number of sample plots for measurements wthn A/R D project actvtes (Verson 0) I. SOPE, PIABIITY AD PARAETERS Scope. Ths tool s applcable
More informationTechnical Report, SFB 475: Komplexitätsreduktion in Multivariaten Datenstrukturen, Universität Dortmund, No. 1998,04
econstor www.econstor.eu Der OpenAccessPublkatonsserver der ZBW LebnzInforatonszentru Wrtschaft The Open Access Publcaton Server of the ZBW Lebnz Inforaton Centre for Econocs Becka, Mchael Workng Paper
More informationAn MILP model for planning of batch plants operating in a campaignmode
An MILP model for plannng of batch plants operatng n a campagnmode Yanna Fumero Insttuto de Desarrollo y Dseño CONICET UTN yfumero@santafeconcet.gov.ar Gabrela Corsano Insttuto de Desarrollo y Dseño
More informationNONCONSTANT SUM REDANDBLACK GAMES WITH BETDEPENDENT WIN PROBABILITY FUNCTION LAURA PONTIGGIA, University of the Sciences in Philadelphia
To appear n Journal o Appled Probablty June 2007 OCOSTAT SUM REDADBLACK GAMES WITH BETDEPEDET WI PROBABILITY FUCTIO LAURA POTIGGIA, Unversty o the Scences n Phladelpha Abstract In ths paper we nvestgate
More informationOn the Interaction between Load Balancing and Speed Scaling
On the Interacton between Load Balancng and Speed Scalng Ljun Chen and Na L Abstract Speed scalng has been wdely adopted n computer and communcaton systems, n partcular, to reduce energy consumpton. An
More informationPowerofTwo Policies for Single Warehouse MultiRetailer Inventory Systems with Order Frequency Discounts
Powerofwo Polces for Sngle Warehouse MultRetaler Inventory Systems wth Order Frequency Dscounts José A. Ventura Pennsylvana State Unversty (USA) Yale. Herer echnon Israel Insttute of echnology (Israel)
More informationExtending Probabilistic Dynamic Epistemic Logic
Extendng Probablstc Dynamc Epstemc Logc Joshua Sack May 29, 2008 Probablty Space Defnton A probablty space s a tuple (S, A, µ), where 1 S s a set called the sample space. 2 A P(S) s a σalgebra: a set
More informationA DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION. Michael E. Kuhl Radhamés A. TolentinoPeña
Proceedngs of the 2008 Wnter Smulaton Conference S. J. Mason, R. R. Hll, L. Mönch, O. Rose, T. Jefferson, J. W. Fowler eds. A DYNAMIC CRASHING METHOD FOR PROJECT MANAGEMENT USING SIMULATIONBASED OPTIMIZATION
More informationA Secure PasswordAuthenticated Key Agreement Using Smart Cards
A Secure PasswordAuthentcated Key Agreement Usng Smart Cards Ka Chan 1, WenChung Kuo 2 and JnChou Cheng 3 1 Department of Computer and Informaton Scence, R.O.C. Mltary Academy, Kaohsung 83059, Tawan,
More informationNasdaq Iceland Bond Indices 01 April 2015
Nasdaq Iceland Bond Indces 01 Aprl 2015 Fxed duraton Indces Introducton Nasdaq Iceland (the Exchange) began calculatng ts current bond ndces n the begnnng of 2005. They were a response to recent changes
More informationRealTime Process Scheduling
RealTme Process Schedulng ktw@cse.ntu.edu.tw (RealTme and Embedded Systems Laboratory) Independent Process Schedulng Processes share nothng but CPU Papers for dscussons: C.L. Lu and James. W. Layland,
More informationTime Series Analysis in Studies of AGN Variability. Bradley M. Peterson The Ohio State University
Tme Seres Analyss n Studes of AGN Varablty Bradley M. Peterson The Oho State Unversty 1 Lnear Correlaton Degree to whch two parameters are lnearly correlated can be expressed n terms of the lnear correlaton
More informationLesson 2 Chapter Two Three Phase Uncontrolled Rectifier
Lesson 2 Chapter Two Three Phase Uncontrolled Rectfer. Operatng prncple of three phase half wave uncontrolled rectfer The half wave uncontrolled converter s the smplest of all three phase rectfer topologes.
More informationMultiplePeriod Attribution: Residuals and Compounding
MultplePerod Attrbuton: Resduals and Compoundng Our revewer gave these authors full marks for dealng wth an ssue that performance measurers and vendors often regard as propretary nformaton. In 1994, Dens
More informationAnalysis of EnergyConserving Access Protocols for Wireless Identification Networks
From the Proceedngs of Internatonal Conference on Telecommuncaton Systems (ITC97), March 223, 1997. 1 Analyss of EnergyConservng Access Protocols for Wreless Identfcaton etworks Imrch Chlamtac a, Chara
More informationA Note on the Decomposition of a Random Sample Size
A Note on the Decomposton of a Random Sample Sze Klaus Th. Hess Insttut für Mathematsche Stochastk Technsche Unverstät Dresden Abstract Ths note addresses some results of Hess 2000) on the decomposton
More informationJoint Scheduling of Processing and Shuffle Phases in MapReduce Systems
Jont Schedulng of Processng and Shuffle Phases n MapReduce Systems Fangfe Chen, Mural Kodalam, T. V. Lakshman Department of Computer Scence and Engneerng, The Penn State Unversty Bell Laboratores, AlcatelLucent
More informationChapter 7. RandomVariate Generation 7.1. Prof. Dr. Mesut Güneş Ch. 7 RandomVariate Generation
Chapter 7 RandomVarate Generaton 7. Contents Inversetransform Technque AcceptanceRejecton Technque Specal Propertes 7. Purpose & Overvew Develop understandng of generatng samples from a specfed dstrbuton
More informationSurvey on Virtual Machine Placement Techniques in Cloud Computing Environment
Survey on Vrtual Machne Placement Technques n Cloud Computng Envronment Rajeev Kumar Gupta and R. K. Paterya Department of Computer Scence & Engneerng, MANIT, Bhopal, Inda ABSTRACT In tradtonal data center
More informationWhat is Candidate Sampling
What s Canddate Samplng Say we have a multclass or mult label problem where each tranng example ( x, T ) conssts of a context x a small (mult)set of target classes T out of a large unverse L of possble
More informationData Broadcast on a MultiSystem Heterogeneous Overlayed Wireless Network *
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 24, 819840 (2008) Data Broadcast on a MultSystem Heterogeneous Overlayed Wreless Network * Department of Computer Scence Natonal Chao Tung Unversty Hsnchu,
More informationTraffic Demand Forecasting for EGCS with Grey Theory Based Multi Model Method
IJCSI Internatonal Journal of Coputer Scence Issues, Vol., Issue, No, January 3 ISSN (Prnt): 694784 ISSN (Onlne): 69484 www.ijcsi.org 6 Traffc Deand Forecastng for EGCS wth Grey Theory Based Mult Model
More informationMultivariate EWMA Control Chart
Multvarate EWMA Control Chart Summary The Multvarate EWMA Control Chart procedure creates control charts for two or more numerc varables. Examnng the varables n a multvarate sense s extremely mportant
More informationDescription of the Force Method Procedure. Indeterminate Analysis Force Method 1. Force Method con t. Force Method con t
Indeternate Analyss Force Method The force (flexblty) ethod expresses the relatonshps between dsplaceents and forces that exst n a structure. Prary objectve of the force ethod s to deterne the chosen set
More informationState function: eigenfunctions of hermitian operators> normalization, orthogonality completeness
Schroednger equaton Basc postulates of quantum mechancs. Operators: Hermtan operators, commutators State functon: egenfunctons of hermtan operators> normalzaton, orthogonalty completeness egenvalues and
More informationMultiResource Fair Allocation in Heterogeneous Cloud Computing Systems
1 MultResource Far Allocaton n Heterogeneous Cloud Computng Systems We Wang, Student Member, IEEE, Ben Lang, Senor Member, IEEE, Baochun L, Senor Member, IEEE Abstract We study the multresource allocaton
More information7.5. Present Value of an Annuity. Investigate
7.5 Present Value of an Annuty Owen and Anna are approachng retrement and are puttng ther fnances n order. They have worked hard and nvested ther earnngs so that they now have a large amount of money on
More information