Schedulng Remote Access to Scentfc Instruments n Cybernfrastructure for Educaton and Research Je Yn 1, Junwe Cao 2,3,*, Yuexuan Wang 4, Lanchen Lu 1,3 and Cheng Wu 1,3 1 Natonal CIMS Engneerng and Research Center, Tsnghua Unversty, Bejng, 100084, P. R. Chna 2 Research Insttute of Informaton Technology, Tsnghua Unversty, Bejng, 100084, P. R. Chna 3 Tsnghua Natonal Laboratory for Informaton Scence and Technology, Bejng, 100084, P. R. Chna 4 Insttute for Theoretcal Computer Scence, Tsnghua Unversty, Bejng, 100084, P. R. Chna *Correspondng emal: jcao@tsnghua.edu.cn Abstract Whle a grd represents a computng nfrastructure for cross doman sharng of computatonal resources, the cybernfrastructure, proposed by the US NSF Blue Rbbon advsory panel, s expected to revolutonzng scence and engneerng by ncludng more computer ntegrated resources, e.g. telescopes and observatores. As a part of the Chna natonal cybernfrastructure for educaton and research, resource sharng of expensve scentfc nstruments s dscussed n ths work. A layered model of nstrument pools s ntroduced and the process from submttng a job to nstrument pools to obtanng results s analyzed. Fuzzy random schedulng algorthms are proposed n nstrument pools when a job s submtted to one of nstruments wthn a pool. The randomness les n the probablty whch nstrument could be chosen for an experment and the fuzzness orgns from vagueness of users feedback opnons on expermental results. Users feedback nformaton s utlzed to mprove overall qualty of servce (QoS) of an nstrument cybernfrastructure. Several algorthms are provded to ncrease utlzaton of nstruments provdng hgher QoS and decrease utlzaton of those wth poor QoS. Ths s demonstrated n detals usng quanttatve smulaton results ncluded n ths paper. 1. Introducton Grd computng, orgnally motvated by wde-area sharng of computatonal resources [4], has evolved to be manstream technologes for enablng large-scale vrtual organzatons [5]. Especally, enterng the new century, the cybernfrastructure vson [1], proposed by the US NSF Blue Rbbon advsory panel, provdes a blueprnt of future nfrastructure n cyberspace for revolutonzng scence and engneerng. Grd technologes are potental to be utlzed for crossdoman sharng of much more computer ntegrated resources, e.g. telescopes and observatores [11]. Current stuaton n Chna s that on one hand some organzatons have expensve scentfc nstruments wth hgh mantenance costs but low utlzaton ratos. On the other hand, many unverstes cannot obtan necessary expermental facltes supportng academc experments and actvtes. As a part of the Chna natonal cybernfrastructure for educaton and research, remote manpulaton of geographcally dstrbuted scentfc nstruments and cross-organzaton sharng of hgh-qualty educaton resources usng grd technologes was dscussed n [16, 17]. Ths work focuses on schedulng remote access of scentfc nstruments wth consderaton of qualty of servce (QoS) ssues. A layered model of nstrument pools s ntroduced. In our prevous work the role of human was not taken nto account and there was no QoS feedback mechansm to reflect whether users are satsfed wth expermental results. In ths paper the feedback nformaton regardng nstrument QoS s consdered to be a fuzzy varable wth one of the followng lngustc values, terrble, bad, normal, good and excellent. The probablty whether an nstrument could be chosen for a job s dynamcally adjusted accordng to users QoS feedback nformaton. As a result, utlzaton of nstruments provdng hgher QoS accordng to users feedback s ncreased so that QoS of an nstrument cybernfrastructure as a whole s dramatcally mproved. Ths s quanttatvely llustrated usng detaled modelng and smulaton results ncluded n ths paper. Resource schedulng ssues for clusters and grds has been dscussed for many years. Especally, usng hstorcal QoS data to mprove schedulng performance has been proved to be very effectve. In a parallel and dstrbuted computng envronment, QoS data can be defned easly usng quanttatve values, e.g. job executon tme [13], queue watng tme [14], data
transfer tme [3], CPU workloads [18], whch can be modeled and analyzed usng performance predcton technologes [15] and utlzed to mprove resource schedulng performance. However, t s dffcult for users to characterze nstrument performance quanttatvely snce varous crtera (e.g. tme, cost and precson) may play dfferent roles n dfferent experments. In general, users can only provde an overall mpresson of nstrument QoS. The fuzzy random theory s adopted here, whch s sutable and straghtforward when appled to the schedulng scenaros nvolved n an nstrument cybernfrastructure, though not necessarly provdng the best schedulng soluton. A smlar work usng fuzzy methods for grd schedulng can be found n [2], but the exact model and algorthms are dfferent. The rest of ths paper s organzed as follows. In Secton 2, a layered model of nstrument pools s ntroduced. In Secton 3, we present the fuzzy random schedulng model and algorthms wth consderaton of users QoS feedback nformaton. Smulaton results are gven n Secton 4 and the paper concludes n Secton 5. 2. Scentfc Instrument Sharng requrements. When an nstrument pool receves a job, t wll fnd an avalable nstrument to do t. Every nstrument n Fgure 1 belongs to a certan nstrument pool and can jon and leave the pool dynamcally. All nstrument pools have ther mages n the nstrument pool allance and can also jon and leave the pool allance dynamcally. When a user wants to do an experment and submts t to the nstrument pool allance n Step 1, the nstrument pool allance wll check whether the nstrument cybernfrastructure has the requred nstruments needed to fulfll the experment. If not all resources needed are presented, the pool allance wll reply the user wth refusal nformaton n Step 2. Otherwse the allance wll decompose the experment nto parts and submt the related parts to correspondng pools n Step 3. All the related pools wll fnd sutable resources and submt job parts to chosen nstruments n Step 4. In Step 5, chosen nstruments return results of the experment to pools after the experment was done and the pools return results to the pool allance n Step 6. The pool allance composes all mddle results and returns a fnal result to the user n Step 7. In Step 8, the user feed back hs opnon about the expermental result, whch s mportant to mprove QoS of the nstrument cybernfrastructure as dscussed later. 3. Fuzzy Random Schedulng As we mentoned before, nstrument QoS can be hardly descrbed usng explct parameters. In ths secton, we ntroduce a fuzzy random theory to characterze users feedback QoS nformaton. 3.1 Fuzzy random theory Fgure 1. The process of nvokng a servce n an nstrument cybernfrastructure As shown n Fgure 1, n an nstrument cybernfrastructure, smlar nstruments are organzed nto an nstrument pool and dfferent nstrument pools consttute an nstrument pool allance. When a user wants to do experment va the nstrument cybernfrastructure, he submts the job to the nstrument pool allance, whch analyses the job and verfes whether t can be accomplshed wth exstng pools wthn t. If the job can be fulflled, the nstrument pool allance wll submt t to the requred nstrument pools by order of the job s nherent The fuzzy random theory s an emergng feld n the uncertan theory, a branch of modern mathematcs. It takes two aspects of uncertan factors, randomness and fuzzness, respectvely, nto account and has attracted many research nterests. Some key concepts of the fuzzy random theory are gven n ths secton. A detaled ntroducton can be found n [9]. A fuzzy random varable s a measurable functon from a probablty space to the set of fuzzy varables. In other words, a fuzzy random varable s a random varable takng fuzzy values. The noton of fuzzy random varable was frst ntroduced by Kwakernaak n [7] and [8]. Ths concept was developed n [6], [10] and [12] by dfferent requrements of measurablty. Defnton of fuzzy random varable s as follows [10]: A fuzzy random varable s a functon ξ from a probablty space (Ω, A, Pr) to the set of fuzzy
varables such that Cr{ξ(ω) B} s a measurable functon of ω for any Borel set B of R, the real number doman. Ω s a nonempty set, A s an algebra over Ω and Pr s a probablty measure. Cr s the credt of a fuzzy varable, whch s smlar to the probablty of a random varable. Defnton of the expected value of a fuzzy random varable ξ ntroduced n [10] s as follows: + E[ ξ] = Pr{ ω Ω E[ ξ( ω)] r} dr 0 0 Pr{ ω Ω E[ ξ( ω)] r} dr (1), provdng that at least one of the two ntegrals s fnte. From the defnton above, expected value of a fuzzy random varable s a scalar value. In Equaton (1), ξ ( ω) s a fuzzy varable and E n the left of the equaton s the expectaton of a fuzzy random varable, whle E on the rght s the expected value of a fuzzy varable. In most real world nstances, the expectaton calculaton of a fuzzy random varable can be smplfed. 3.2 Schedulng models The fuzzy random schedulng model refers to the schedule process of Step 4 n Fgure 1, whch s an essental step n an nstrument cybernfrastructure for resource sharng. The schedulng model descrbed n ths work take users feedback nformaton nto account and try to satsfy user requrements better. Consder an nstrument pool wth N nstruments n t, as shown n Fgure 2. Fgure 2. The job schedulng n an nstrument pool When a new experment s submtted to an nstrument pool, the probablty that the experment runs on each nstrument s p ( [1, N] ). It s obvous that the followng equaton holds: N p = 1 (2) = 1 When an experment s submtted to any chosen nstrument, there are many factors whch have nfluence on users apprasals, for example the cost of experment ths nstrument charges for, the executon tme and watng tme, whether the result from ths nstrument s relable and whether the precson of the nstrument can satsfy the experment requrement. All these factors dffer wth dfferent nstruments and can be looked as a vrtual parameter of the nstrument. In ths paper, ths parameter s named as QoS of nstrument and denoted by q, and q means the QoS of the th nstrument n an nstrument pool accordng to a specfc experment. The QoS of the same nstrument wll be dfferent when the users constrans changed. The pool adjusts the probablty p accordng to the user s apprasal, Q, to the experment after he receved hs result from the nstrument cybernfrastructure. Both varables q and Q are fuzzy varables because a user can not depct how he satsfed wth a result accurately. Only vague lngustc values lke terrble, bad, normal, good and excellent can express hs apprasal towards the result from the nstrument cybernfrastructure. When a user submts a job wth detaled experment specfcatons to an nstrument cybernfrastructure, the nstrument pool allance wll pass ths job to correspondng nstrument pools. If the experment s submtted to the th nstrument n nstrument pool, q has the value as one of the followng lngustc values, very bad, bad, normal, good and very good. In most cases, a q wth very good value has a large probablty to receve excellent value of Q, good to good, normal to normal, bad to bad and very bad to terrble of Q. Because the value of q to a specfc experment s not known by nstrument pool and can only be reflected by the user s apprasal towards the total process of the experment, the nstrument pool wll adjust p to make the nstrument wth good or very good apprasal hgher utlzaton rato to satsfy users. In some urgent experments, users may attach more mportance on the tme constran. In such case the nstrument wth shorter job executon tme and watng tme wll more satsfed the users. Whle n some experments, users may care more about the cost. Ths fuzzy random schedulng model s a close loop model, whch takes the user s response nto account and s beleved to be able to provde hgher nstrument QoS. Fgure 3 s the system block of the model.
Fgure 3. The system block of an nstrument cybernfrastructure Many good schedulng strateges and algorthms can be desgned on the bass of the fuzzy random model ntroduced above. Most mportantly, users QoS feedback nformaton s used n ths model thus t comples wth the users ntenton better. 3.3 Schedulng algorthms The adjustment of p from users apprasals s descrbed n ths secton. In ths work, the algorthm to adjust p s proportonal to the expected value of fuzzy random varable preq, whch s the predcton of the fuzzy value q, as shown n Equaton (3). The reason why the preq s used n Equaton (3) nstead of q s that the nstrument pool has no nformaton of q and has to predct what the value t s through users apprasals. N p = Epreq [ ]/ Epreq [ ] (3) = 1 In the followng examples, the membershp functon of the fuzzy varable q s shown n Fgure 4. Fgure 4. The QoS membershp functon " Verygood " wth probablty prep " Good " wth probablty prep preq = " Normal" wth probablty prep " Bad " wth probablty prep " VeryBad " wth probablty prep 1 2 3 4 5 (4) The dstrbuton of preq s as Equaton (4). In Equaton (4), prep k (1 k 5) means the probablty that prep equals to kth value n equaton (4). The ntal values of prep k are the same and equal to 0.2. Because preq s a fuzzy random varable, we can calculate ts expected value usng Equaton (1). In ths example the expectaton of preq can be smplfed to Equaton (5). 5 k = k = 1 Epreq [ ] prep c (5), n whch c s defned to be the center of membershp functon and n ths case, they are 17.5, 30, 50, 70 and 82.5 respectvely. It should be noted that when the membershp functon changed, the expected value of preq wll also be dfferent. Accordng to the users feedback nformaton, the prep k wll be adjusted by Algorthm 1. Algorthm 1: swtch ( apprasal ) { case very good : for (=1; <=5; ++) { prep k = prep k * (1 4 * ncrement); } prep 1 = prep 1 + 4 * ncrement; case good : for (=1; <=5; ++) { prep k = prep k * (1 2 * ncrement); } prep 2 = prep 2 + 2 * ncrement; case normal : for (=1; <=5; ++) { prep k = prep k * (1 ncrement); } prep 3 = prep 3 + ncrement; case bad : for (=1; <=5; ++) { prep k = prep k * (1 2 * ncrement);} prep 4 = prep 4 + 2 * ncrement; case very bad : for (=1; <=5; ++) { prep k = prep k * (1 4 * ncrement); } prep 5 = prep 5 + 4 * ncrement; } In the above algorthm, the nstrument that can satsfy users wll have a hgher probablty to be used accordng to Equatons (3) and (5). Parameter ncrement s a constant number. If a new nstrument jons nto the nstrument pool, the followng algorthm works. Algorthm 2: N = N + 1 ; p N = 1 / N ; for ( = 1; < N; ++) { p = p * ( N 1) / N ;}
In Algorthm 2, any new nstrument jonng nto an nstrument pool wll have the average probablty to be used. N s the exstng number of nstruments n a pool. When an nstrument wants to leave the pool, the probabltes are adjusted accordng to Algorthm 3. In Algorthm 3, the kth nstrument n an nstrument pool s supposed to leave the pool. Algorthm 3: totalp=0 ; p k =0 ; for ( =1; <=N; ++ ) { totalp = p + totalp ; } for ( =1; <=N; ++ ) { p = p / p ; } for ( = k; <N; ++) { p = p +1 ; } N = N 1; Algorthm 3 only allows the nstrument wthout any experment runnng on t at that tme to leave. Any nstrument wth job runnng on t s not permtted to leave. If t leaves by some nevtable reasons, the pool wll record the nstrument as unstable and t wll have trouble when next tme t wants to jon the pool. 4. Performance Evaluaton In ths secton three case studes are gven to llustrate the fuzzy random schedulng model and algorthms ntroduced n Secton 3. The programmng language of the smulaton envronment s Java. 4.1 Case study I A smple experment, whch requres only one nstrument, s submtted to the pool allance. An nstrument pool wth N nstruments, whch can run the experment, s chosen by the pool allance. Every nstrument has the same ntal probablty to run the experment. In ths example N equals to 50, and 10 of them have very good QoS and may receve users feedback value of excellent, 10 good, 10 normal, 10 bad and 10 terrble. Fgure 5 s the result when QoS feedback nformaton s used to adjust probabltes of nstruments n 100,000 such experments. The vertcal axs represents the number of jobs and the horzontal axs represents users feedback nformaton n terms of vague values. It s also the case n Fgures 6, 8, 9, 10 and 11. For the purpose of comparson, the result wthout probablty adjustment s also gven n Fgure 5. The parameter ncrement s a constant and n ths example the values are 0.02% and 2%, respectvely. As shown n Fgure 5, when feedback nformaton from users apprasals s consdered, those nstruments whch can not satsfy users well wll have fewer chances to be used. If the owners of these nstruments want to have more chances for ther nstruments to be used, they should mprove the QoS of ther nstruments, lke decreasng the prce ther nstruments charge for or shortenng the executon tme of ther nstruments. Fgure 5. Results of users apprasals for 100,000 experments When the probablty adjustment strategy s mproved on the bass of Equaton (3), better results can be obtaned and the occurrence of excellent experments wll ncreased. There are more complcated scenaros for remote nstrument access. For example, an experment may nvolve multple nstruments, whch s dscussed n the case study II. Also servng more tasks wll somehow decrease QoS levels of nstruments, whch s not consdered n ths case. For example, f task arrval rate s hgh enough to exceed processng capablty of an nstrument, respondng delays wll decrease QoS levels of users feedback nformaton. Ths s dscussed n the case study III usng detaled smulaton results. 4.2 Case study II In ths example, two nstruments n two dfferent nstrument pools are requred to complete an experment. The numbers of nstruments n the two pools are N 1 and N 2, respectvely. Every nstrument n each pool has the same ntal probablty to be used. The number of nstruments wth dfferent QoS values n each pool s the same. The fnal QoS value of an experment s q 1 Λq j 2 when the th nstrument n one pool works coordnately wth the jth nstrument n another pool. Ths means the apprasal to the overall experment s the worse one of the two nstruments. In ths example N 1 and N 2 are both 50. The user s
feedback nformaton wll have the same mpact on the two nstruments used. Fgure 6 ncludes smulaton results when feedback nformaton s used to adjust probabltes of both nstrument pools. When feedback nformaton s used, less bad or terrble experments appeared. In comparson wth Fgure 5, no more excellent experments are acheved and there s no obvous QoS mprovement n ths case. Ths s caused by that the two nstruments are coupled n one experment and the user can only provde feedback nformaton on the whole experment nstead of each nstrument. accordng to ths case. λ 1 =5000 results n request arrvals far beyond a pool capablty and λ 2 =1000 corresponds to a stuaton that the request arrval s only slghtly beyond a pool capablty. The other stuaton s that experment requests are wthn the capablty of all nstruments n a pool. Correspondng λ values are λ 3 =600 and λ 4 =100. The followng smulaton results are obtaned usng the flow chart descrbed n Fgure 7. Fgure 6. Results of users apprasals for 100,000 experments each nvolvng 2 nstruments 4.3 Case study III In ths example 100,000 smlar experment requests are submtted to the pool allance and an nstrument pool wll be chose as the executon pool of these experment requests. Smlar to the case study I, there are 50 nstruments n the chosen pool. Dfferent from example 1, job executon tmes are taken nto account. The executon tme of the nstruments wth very good QoS comples wth an exponental dstrbuton and the expected value of the dstrbuton s E 1, E 2 for good, E 3 for normal, E 4 for bad and E 5 for very bad. For the purpose of llustraton and smulaton the fve expected values from E 1 to E 5 n ths example are 1/250, 1/180, 1/150, 1/120 and 1/100, respectvely. The request arrval tme s supposed to be a posson dstrbuton wth λ, where λ s the average arrval rate n a posson dstrbuton. In ths case study, two stuatons are consdered. If experment requests come beyond executon capabltes of an nstrument pool, a queue s unavodable. In ths stuaton, nstruments wth hgh QoS feedback are chosen frst and those wth poor QoS feedback next. In the example, λ 1 and λ 2 are gven Fgure 7. The flow chart of smulatons One thng we should bear n mnd s that too long respondng tme, ncludng watng tme n a queue and executon tme on nstruments, wll degrade users apprasals towards the results they got. Wth consderaton of ths stuaton, addtonal rules are appled. If T 1 < RT < T 2, the apprasal wll degrade by one level. If T 2 < RT, the apprasal wll degrade by two levels. In above rules, RT represents the total respondng tme to an experment request. T 1 and T 2 are two tme lmts that users can bear. We suppose that T 1 and T 2 are about ten to twenty tmes of executon tme, thus T 1 =10 and T 2 =20 n ths example.
Effects of these rules are also shown n Table 1, whch descrbes relatonshps between users apprasals and the respondng tme. For example, a very good experment n a user s mpresson could be downgraded to be good f respondng tme s longer than T 1 and normal f respondng beyond T 2. Table 1. RT and correspondng users apprasal Level Very Norm Very Good Bad RT good al bad Very Norm Very < T 1 Good Bad good al bad Norm Very Very [T 1,T 2 ] Good Bad al bad bad Norm Very Very Very > T 2 Bad al bad bad bad In Fgures 8 to 11, smulaton results of the case study III are llustrated. In each fgure, smulaton results wth probablty adjustments algorthms descrbed n Secton 3.3 and those wthout probablty adjustments are all gven for the purpose of comparson. As shown n Fgures 8, when request arrval speed s far beyond a pool s processng capablty, the probablty adjustment algorthm does not work well to provde users wth more excellent servce, snce bad servces have to be utlzed anyway. Also when requests arrve too fast and have to wat n a queue, a longer respondng tme wll downgrade users apprasals even f an excellent servce s supposed to be provded. The only way to stll ensure hgh QoS for users s to let more smlar nstruments jon the pool to ncrease the pool s processng capablty. The stuaton s mproved when request arrval speed s lower n Fgure 9. Fgure 10. Results of users apprasals under λ 3 Fgure 8. Results of users apprasals under λ 1 Fgure 11. Results of users apprasals under λ 4 As shown n Fgures 10 and 11, arrval requests are wthn a pool s processng capablty, more satsfactory apprasals wll acheve through the adjustment of probablty n an nstrument pool. Snce a queue seldom appears n these stuatons, requests do not have to be served wth bad nstruments and downgrade rules are not often appled. These results are conformed to those acheved n the case study I. Fgure 9. Results of users apprasals under λ 2
5. Conclusons The contrbuton of ths paper les n the proposal of a fuzzy random schedulng model, whch takes the users QoS feedback nformaton nto account to provde more satsfactory servces for users n an nstrument cybernfrastructure. The QoS apprasals from users can not be represented n an accurate and quanttatve way, snce there are many factors n nstrument QoS that have effects on users apprasals. In many real world scenaros, users feedback nformaton s fuzzy and the fuzzy random model s sutable and straghtforward when appled to the schedulng scenaros descrbed n ths work. The algorthms provded n ths work to ncrease the utlzaton probablty of some nstruments wth hgher QoS and decrease usage of those wth lower QoS, s proved to be effectve n a cybernfrastructure envronment for scentfc nstrument sharng when pool capablty s beyond experment requests. In stuatons when request arrval speed s far beyond processng capablty of an nstrument pool, algorthms supposed to mprove nstrument QoS do not work, snce long queung tme downgrades users apprasals and nstruments wth low QoS feedback have to be used anyway. When applyng the work descrbed n ths paper nto a real world stuaton, addtonal ssues have to be consdered besdes resource management and schedulng. Ongong work nclude an nformaton servce provdng detaled nstrument and experment data, a workflow enactor to mange experments nvolvng multple nstruments, and a layered securty mechansm for authentcaton and authorzaton of remote nstrument access. Acknowledgement Ths work s supported by Mnstry of Educaton of Chna under the 211/15 cybernfrastructure project Natonal Unversty Instrument and Resource Sharng Systems, Mnstry of Scence and Technology of Chna under the natonal 863 hgh-tech R&D program grants No. 2006AA10Z237 and No. 2006AA10Z216, and Natonal Scence Foundaton of Chna under the grant No. 60604033. References [1]. D. E. Atkns, K. K. Droegemeer, S. I. Feldman, H. Garca- Molna, M. L. Klen, D. G. Messerschmtt, P. Messna, et. al., Revolutonzng Scence and Engneerng through Cybernfrastructure, Natonal Scence Foundaton Blue Rbbon Advsory Panel on Cybernfrastructure, January 2003. [2]. J. Cao, S. A. Jarvs, S. San and G. R. Nudd, GrdFlow: Workflow Management for Grd Computng, n Proceedngs of 3 rd IEEE/ACM Internatonal Symposum on Cluster Computng and the Grd, Tokyo, Japan, pp. 198-205, 2003. [3]. M. Faerman, A. Su, R. Wolsk and F. Berman, Adaptve Performance Predcton for Dstrbuted Data-Intensve Applcatons, n Proceedngs of ACM/IEEE Supercomputng Conference, 1999. [4]. I. Foster and C. Kesselman, The Grd: Blueprnt for a New Computng Infrastructure, Morgan-Kaufmann, 1998. [5]. I. Foster, C. Kesselman and S. Tuecke, The Anatomy of the Grd: Enablng Scalable Vrtual Organzatons, Internatonal Journal of Supercomputer Applcatons, Vol. 15, No. 3, 2001. [6]. R. Kruse and K. D. Meyer, Statstcs wth Vague Data, D. Redel Publshng Company, Dordrecht, 1987. [7]. H. Kwakernaak, Fuzzy Random Varables-I. Defntons and Theorems, Informaton Scences, Vol. 15, pp. 1-29, 1978. [8]. H. Kwakernaak, Fuzzy Random Varables-II. Algorthms and Examples for the Dscrete Case, Informaton Scences, Vol. 17, pp. 253-278, 1979. [9]. B. Lu and J. Peng, A Course n Uncertanty Theory, Tsnghua Unversty Press, Bejng, 2005. [10]. Y. K. Lu and B. Lu, Fuzzy Random Varables: a Scalar Expected Value Operator, Fuzzy Optmzaton and Decson Makng, Vol. 2, No. 2, pp. 143-160, 2003. [11]. NSF Cybernfrastructure Councl, NSF s Cybernfrastructure Vson for 21 st Century Dscovery, Verson 5.0, January 20, 2006. [12]. M. L. Pur and D. Ralescu, Fuzzy Random Varables, Journal of Mathematcal Analyss and Applcatons, Vol. 114, pp. 409-422, 1986. [13]. W. Smth, V. Taylor and I. Foster, Predctng Applcaton Run Tmes Usng Hstorcal Informaton, Job Schedulng Strateges for Parallel Processng, LNCS Vol. 1459, Sprnger Verlag, pp. 122-142, 1998. [14]. W. Smth, V. Taylor and I. Foster, Usng Run-Tme Predctons to Estmate Queue Wat Tmes and Improve Scheduler Performance, Job Schedulng Strateges for Parallel Processng, LNCS Vol. 1659, Sprnger Verlag, pp. 202-219, 1999. [15]. D. P. Spooner, S. A. Jarvs, J. Cao, S. San and G. R. Nudd, Local Grd Schedulng Technques Usng Performance Predcton, IEE Proceedngs Computers and Dgtal Technques, Vol. 150, No. 2, pp. 87-96, 2003. [16]. Y. Wang, L. Lu, C. Wu and W. N, Research on Equpment Resource Schedulng n Grds, Grd and Cooperatve Computng, LNCS Vol. 3251, Sprnger Verlag, pp. 927-930, 2004. [17]. Y. Wang and C. Wu, A Study on Educaton Resource Sharng Grd, Internatonal Journal of Informaton Technology, Specal Issue on Grd Computng I, Vol. 11, No. 3, pp. 73-80, 2005. [18]. L. Yang, J. M. Schopf and I. Foster, Conservatve Schedulng: Usng Predcted Varance to Improve Schedulng Decsons n Dynamc Envronments, n Proceedngs of ACM/IEEE Supercomputng Conference, 2003.