Dynamic Replication of Fault-Tolerant Scheduling Algorithm

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1 Send Orders for Reprins o reprins@benhamscience.ae 2670 The Open Cyberneics & Sysemics Journal, 2015, 9, Dynamic Replicaion of Faul-Toleran Scheduling Algorihm Open Access Wang Hongxia * Fang Haoran and Qiu Xin School of Compuer Science and Engineering, Shenyang Ligong Universiy, Shenyang, , P.R. China Absrac: In order o reduce he impac on he grid scheduling caused by he resource error, for complex dependen asks, designed a dynamic replicaion of faul-oleran scheduling algorihm (DRFT). This algorihm build ask model by applying hypergraph heory, using primary-backup ask as backup mode, ake he acive execuion mode combined wih he passive execuion mode o perform he backup ask, se up dynamic backup level according o he level of imporance and resources securiy condiion of dependen ask, pursui ime of he ask execuion is minimized, he simulaion resul shows ha he algorihm can sill be accomplished scheduling quickly in case of error caused by he resource, o make up he shorage of common algorihms in erms of faul-oleran. Keywords: Dependen ask, dynamic replicaion, faul-oleran scheduling, hypergraph. 1. INTRODUCTION In order o improve he reliabiliy of grid sysem, commonly used error prevenion, error verificaion, error predicion and faul-oleran four mehods [1-3]. Among hem, he faul-oleran is a common and efficien soluion. Faul-oleran mehod includes rery, N version of he program design, he recovery block, primary-backup scheduling echnology, he primary-backup scheduling echnique is he mos commonly used of Faul-oleran mehod [4, 5]. The primary-backup scheduling echnique is backup ask on oher resource, if he main ask execuion error, began o perform he backup ask. The execue mehod of backup ask can also be divided ino acive backup mehod, passive backup mehod and he combinaion of acive and passive backup mehod [6-8]. Acive backup mehod, refers o he resource wihou faul are also required o perform he backup ask, his will undoubedly increase he burden on resource; passive backup mehod is a mehod of execuion only afer he main ask execue error, he faul-oleran of such a sysem is no very high; he combinaion of acive and passive backup mehod is a kind of backup ask execuion mode combine wih acive execuion and passive execuion, can achieve a relaively small cos bu also improve he fauloleran of he sysem, so his paper uses he combinaion of acive and passive backup mehod. The researches apply primary-backup mehod o improve faul-oleran on grid sysem are as follows, lieraure [9] were designed mea-ask and dependen ask of primarybackup faul-oleran scheduling algorihm, hough effecively achieve faul-oleran, bu wihou considering he size of he burden he backup o resource; lieraure [10] in order o minimize backup coss as he main arge, designed a differed backup- copy of primary/backup copy, by delay backup-copy sar ime as far as possible, o achieve he purpose of minimize he duy cos, bu he aricle does no consider he imporance of he ask; lieraure [11] designed a primary/backup-copy scheduling algorihm based on dependen ask, o seek he balance beween he minimal cos and he earlies compleion of he backup ask, bu i can no achieve he backup cos and he compleion ime are all small. In a word, he above aricle are no consider he backup issues according o he imporance of he ask, he effec of minimize he backup level and execuion ime is no very obvious. Hypergraph heory [12] was firs proposed by C. Berge in 1970, sudy on he muliple relaionship. Applicaion hypergraph heory o build a model, provides a lo of convenience in describing he problem, conducive o solving pracical problems, herefore, his paper use hypergraph model o express dependencies beween asks, no only can express he basic informaion of ask clearly, bu also can express he inerdependence beween asks. Therefore, his paper aimed a he problem of ask scheduling in grid faul-oleran, designed a dynamic replicaion of faul-oleran scheduling algorihm (DRFT), his mehod akes ino accoun he complexiy of dependen ask, based on he applicaion of hypergraph heory build ask model, using primary-backup ask as backup mode, ake he acive execuion mode combined wih he passive execuion mode o execue he backup asks, se up dynamic backup level according o he level of imporance and resources securiy condiion of dependen ask, pursui ime of he ask execuion is minimized. Compared wih he classical algorihm GS-Min-min algorihm, even in he case of ask execuion error, his mehod is sill able o quickly X/ Benham Open

2 Dynamic Replicaion of Faul-oleran Scheduling Algorihm The Open Cyberneics & Sysemics Journal, 2015, Volume complee he scheduling, reduce he impac of resource failure for ask scheduling. 2. MODEL CONSTITUTION In his paper, he backup ask execuion mode using a combinaion of acive and passive execuion mode. In order o reduce he backup excessive use of resources, here is only one backup ask, he backup ask is spli ino acive execuion par and passive execuion par by calculaion uni, execuion mode is he combinaion of acive execuion and passive execuion, ha is he acive execuion iniiaive implemen, passive execuion passive implemen. The acive par of backup asks iniiaive implemen, only when he main ask execuion fails, anoher par of he backup ask, ha is passive par, will be acivaed o execue. So o a cerain exen can reduce backup coss, and if he main ask execuion fails, backup ask can be compleed quickly. Fig. (1) shows he primary-backup ask. 2) rca is he ask compuaion. 3) rs is he sae of he ask, he sae of he ask is divided ino idle sae, has been mached sae, wai sae, execuion sae and finish sae, he sae of he ask changes wih scheduling process. Expressed as follows: rs={rfree, rmach, rwai, rwork, rdone b) RE= {re 1, re 2,,re m is a se of hyperedge, m= RE is he number of hyperedge, hyperedge re i composed by a hree-elemen-array (Pre, Des, rv i ). Pre is all he predecessor ask of he ask se rv i, predecessor ask is ha have a direc dependencies of ask rv i, if and only if afer all asks finished in he se Pre, ask rv i can execue. Des is a collecion of all pos-ask of ask rv i, pos-ask is ha have a direc dependencies of ask rv i, ask rv i finish execuing is a prerequisie for any of he asks can be execued of Des. Any ask node has is corresponding hyperedge, he weigh D i of hyperedge re i is he number of seps of ask node rv i. The number of seps is he maximum number of seps ask node o he exi node. The ask node has no posask is he exi node. Direced hypergraph ask model is shown in Fig. (2). Fig. (1). The Primary-backup ask The Main Task of The Hypergraph Model Because here are inerdependencies beween asks, herefore fusion hypergraph heory building he main ask hypergraph model, ask hypergraph model consis of ask noe and hyperedge, hyperedge can deailed express dependencies beween asks. The ask mainly consider he dependen ask, and all are he compuing ask, dependen ask have inerdependencies beween asks, only he curren ask all predecessor ask is compleed, his ask can execue. Because of he inerdependencies beween asks, hypergraph model is direced hypergraph. Hypohesis resource ransmission speed very quickly, ignore he raffic load problems beween asks. Tasks node consiss of a hree-elemen-array, ha is he ask ID, ask compuaion and he sae of he ask, he sae of he ask includes five saes: idle, have been mached, waiing, execue, finish. The primary ask of direced hypergraph model is described as follows: RH= (RX,RE) is he ask model of he hypergraph represenaion. a) RX ={rv 1,rv 2,,rv rn is he se of node ask, where rv i ={rid, rca, rs is a aribue se of ask node, i [1,rn]. 1) rid is he ask ID. Fig. (2). Direced hypergraph ask model. As shown in Fig. (2), ask rv 1,rv 2,,rv rn, hyperedge re 1, re 2,,re m, e.g. re 3 ({rv 1, {rv 6, rv 7, rv 3 ), he weigh of he re 3 is D 3 =2; re 7 ({rv 1,rv 3, rv 4, rv 5,, {rv 9, rv 7 ), he weigh of he re 7 is D 7 = The Backup Task Model Backup ask are copy from he main ask, so he backup ask inheris is main ask ID, compuaion and dependencies beween asks, he backup ask is one o one corresponding relaion o main ask. In addiion, he backup ask should also have he properies main ask do no have, ha is he acive par and he passive par. Backup ask model and he main ask model are he same, as follows: RH= (RX, RE) is he hypergraph represenaion of backup ask.

3 2672 The Open Cyberneics & Sysemics Journal, 2015, Volume 9 Hongxia e al. a) RX= {rv 1, rv 2,, rv rn is he backup ask node se, where rv i = {rid, vrca, rca, rs, i[1, r n ]. 1) rca is backup ask compuaion of acive execuion, vrca is backup ask compuaion of passive execuion. 2) rs={rfree, rmach, rwai, rwork, vrwork, rdone is he saes of he backup ask, rwork is acive execuion working sae of backup ask, vrwork is passive execuion working sae of backup ask. b) RE= {re 1 re 2 re m is a se of hyperedge, m= RE is he number of hyperedge, hyperedge re i (Pre, Des, rv i ), here consisen wih he main ask model The Resource Model Resource node consiue by resource ID, resource handling, resource load and he safey facor of resource, resources are described as follow: RE= {v 1, v 2,, v n is a se of resource node, where v i is he i-h resource, v i = {ID, P, Load SA is a resource properies collecion, i[1 n]. a) ID is he resource ID. b) P is he abiliy of resource processing. c) Load is a resource load, resource load include he acual load and he virual load. The acual load is he compuaion of backup ask acive execuion par, he virual load is he compuaion of backup ask passive execuion par. Resource load value equal o he acual load value, ha is he load backup asks acually execued. d) SA is he safey facor of resource, se he safey facor for he resource, can dynamically view he securiy of resource, has a direc effec on he scheduling success rae. Number of mission success SA i = (1) Number of mission accep 3. SCHEDULING STRATEGY 3.1. Backup Level Calculaion Faul-oleran backup for dependen asks, wih he influence exen of ask failed o pos-ask execuion, dynamically se of faul-oleran backup level, if he ask error is larger, he more i is necessary o increase he level of backup and here is a direc relaionship beween he level of imporance of ask and he number of sep, he number of sep is he maximum number of seps ask node o he exi node. The larger he number of seps of he ask, he greaer degree of influence on he pos- ask, herefore, he exen of heir backup should be more, and he resource securiy siuaion he main ask of backup ask also need o be considered, so we can ge he formula of he level of backup: -SArv i rcai B( i) = Dmax + 1 Di Di 0 (2) 0 Di =0 SA rvi The safey facor of he main ask of rv i resource; Adjusmen coefficien, can adjus he level of backup; rca The calculaion of ask; D The number of sep; When he number of sep is no zero, he backup level have a relaionship wih ask sep, compuaion and is main ask he safey facor of resources; when he sep number is zero, ask is dependen ask of exi node ask, his ask has no grea influence on he pos-ask, so is no need o backup, ha is backup level is zero. Main ask sequencing and backup level calculaion process: //: sequencing for (all main asks) { Breadh-firs raversal dependen ask graph o ge he number of sep for each ask; Consolidaed he same sep of hyperedge ask and in descending order; hyperedge wihin he same ask, in descending order by prioriy value formula; //: Backup level calculaion for (all backup asks) { Inheri heir main ask dependencies and he number of sep; Calculae he level of he backup; 3.2. Mach Scheduling Breadh-firs raversal ask graph, in descending order based on he mission maximum number of sep, and more han one ask a each sep, so every sep needed o sor. Because of dependencies beween asks, only a predecessor ask complees, all pos-ask can be execued, herefore, he execuion ime of a predecessor ask deermines he sar ime of he pos-ask, if no considered he resource processing capabiliy, he execuion ime of he ask is only concerned wih he compuaional ask. So he prioriy value o each ask is equal o he maximum value of he predecessor ask compuaion and he curren ask o calculae ogeher, see he formula (3). (3) In descending order according o he prioriy value of he ask, herefore, he ask of sor resul deermine ask prioriy maching. Main ask and backup ask can no be on he same resource, because here are differen maching requiremens beween main ask and backup ask, so he main ask and backup ask using differen maching mode a) The main ask of maching According o he ask of sor resul, mach scheduling sar sequenially, maching wih he resources of smalles SL.

4 Dynamic Replicaion of Faul-oleran Scheduling Algorihm The Open Cyberneics & Sysemics Journal, 2015, Volume Load -Load SA -SA P -P i min max i max i SL = + + (4) i Load -Load SA -SA P -P max min max min max min Load i Load of resource i; SA i The safey facor of Resource i; P i Processing capaciy of resource i. By equaion (4) shows, a small value of SL indicaes ha he resource load is small, high safey coefficien and srong processing abiliy, hoping ask o scheduling o such resources. b) Maching backup ask Backup ask mach resource, requires maching high safey coefficien and small load resource, he mos imporan is ha his resource can no be consisen wih he main ask resource. The backup ask scheduling sequence, followed by he main ask. Tha is rv 1, rv 1, rv 2, rv 2,, rv rn, rv rn. If he main ask and he backup ask execuion error, need o reurn o he ask waiing queue, reallocaion of execuion. If he backup ask has no been execued or being execued, and is main ask has been finished, sop execue backup ask, his can reduce backup coss o a cerain exen. Dynamic replicaion of faul-oleran scheduling algorihm (DRFT) scheduling process: Le T be a ask waiing queue, copy of each ask; //: sequencing //: Backup level calculaion for (each ask rv i of T) { main ask rv i mach he minimum value resources of SL; Backup asks rv i '() { Looking for a high safey coefficien resource; Exclude resource of he main ask; Maching resource o which he load is minimal; Scheduling asks rvi o resources v j ; Delee asks rv i, rv i ' in T; Updaed resource load Load, updae ask sae; if (ask execuion success) { if (main ask rv i execuion success) { Oupu scheduling resul; else if (backup asks rv i 'execuion success) { Oupu scheduling resul; else { Task reurns o he waiing queue T, reassigned; Backup ask he acive execuion par is he acual load, he passive execuion par is he virual load. Resource load is he acual load, bu on condiion when he main ask execuion error, passive par is acivaed o execue, a his poin he passive par of he load, which is he virual load will be ransformed ino he acual load, so he acual load and he virual load is consanly changing. 4. PERFORMANCE ANALYSIS The backup ask is an implemenaion of faul-oleran echnology, here is a direc relaionship beween he success of he backup ask execuion and backup ask posiion, ha is for a ask he main ask and is backup ask are no on he same resource, as shown in Fig. (3). Main ask and backup ask of differen asks can be on he same resource, as shown in Fig. (4). Fig. (3). Error backup ask paern. Fig. (4). Correc backup ask paern. Backup 2 Task2 Variable level of faul-oleran backup scheduling is a faul-oleran algorihm based on dependen ask, only under he condiion of he predecessor ask is compleed, o be able o execue pos-ask. If he ask error, and here are oher ask on he backup ask resource, as shown in Fig. (5), if his ask is being execued, as shown in Figure 6, sops he execuion of he ask, reurn o he ask queue waiing o reallocae. Fig. (5) and Fig. (6) shows ha a ime, resource 1 is broken, a his ime he main ask of ask 1 is no finished ye, he acive par of he backup ask of ask 1 is being execued, a his ime need o acivae he passive par of he backup ask, bu he resource is no idle, he passive par is urgen for execuion, hus, he ask 2 will reurn o he ask queue waiing o reallocae. If he main ask is compleed in execuion, i has no ye begin o execue backup asks as shown in Fig. (7), or being

5 2674 The Open Cyberneics & Sysemics Journal, 2015, Volume 9 Hongxia e al. execued as shown in Fig. (8), a his ime he backup ask should sop execuion, o a cerain exen, can reduce he cos of backup, save he scheduling ime. acive execuion and passive execuion, wih he flexibiliy o adjus he cos of backup, pursui of he execuion ime is minimized. Compared wih he classical dependen ask scheduling algorihm GS-Min-min algorihm, in he case of resource error, DRFT algorihm scheduled for execuion can sill be compleed in a shor ime. Task 2 Fig. (5). Failure occurs when he backup ask execuion. Fig. (8). Main ask is complee, backup is being performed. Task 2 Fig. (6). Failure occurred afer he backup ask is compleed. Fig. (9). Backup ask error. Fig. (7). Main ask is complee, backup is no performed. If he backup ask execuion error, a his ime is main ask is execuing sae, as shown in Fig. (9), if he main ask can be execued successfully, will no affec he pos-ask execuion; If he main ask fails, his ask will reurn o he ask queue waiing o reallocae. 5. SIMULATION ANALYSIS This aricle is designed a dynamic replicaion of fauloleran scheduling algorihm (DRFT), according o he imporance level of ask, he ask is spli ino wo pars, GS-Min-min algorihm is based on he dependen ask scheduling, if his algorihm is applied in he faul-oleran sysem, when ask error occurred will reurn o he ask queue waiing o reallocae. Compared he scheduling simulaion experimen of DRFT algorihm and GS-Min-min algorihm, according o he ask dependency of Fig. (2), build differen properies of he ask and he differen aribues of he resource, in he case of he probabiliy of error resource, comparing he maximum compleion ime Makespan. Assuming compuaional ask in he range of 250 o 350, resource processing capaciy in he range of 30 o 60, resource safey facor beween 0.4 and 0.7, a he momen 1=9S, resource 4 fails, a he momen 2=17S, resource 6 fails, assuming resource does no recover afer he failure. Fig. (10) is DRFT algorihm Gan char, Fig. (11) is GS- Min-min algorihm Gan char, from he wo figures i is clear ha even afer he resource fails, DRFT algorihm sill complee he execuion of 23S, bu GS-Min-min algorihm finished execuing using 29S.

6 Dynamic Replicaion of Faul-oleran Scheduling Algorihm The Open Cyberneics & Sysemics Journal, 2015, Volume Fig. (10). DRFT algorihm gan char. Fig. (11). GS-min-min algorihm gan char. Resource error will grealy affec he operaion of posask, and can no predic he probabiliy of resource error, Fig. (12). shows wih he probabiliy of resource error increasing, he maximum compleion ime of DRFT algorihm and GS-Min-min algorihm. I was concluded ha he greaer probabiliy of resource error, DRFT algorihm is more superior. In he grid environmen, dynamic resource canno accuraely predic, he probabiliy of resource error can only be based on he sae of pas o predic, mehod o deal wih resource emergency is imporan, ake dynamic backup level scheduling algorihm of primary-backup, can reduce or even does no affec he pos-ask performance. Analysis he simulaion of DRFT algorihm and GS-Min-min algorihm, can be clearly seen he superior of he DRFT algorihm. Fig. (12). The probabiliy of resource error impac on Makespan.

7 2676 The Open Cyberneics & Sysemics Journal, 2015, Volume 9 Hongxia e al. CONCLUSION This aricle designed he dynamic replicaion of fauloleran scheduling algorihm (DRFT), use ask relaionship caused by he imporance of he ask and he securiy of resource of dependen ask as parameers, consiue a variable level of backup and combine wih acive and passive of primary-backup scheduling algorihm, dynamic flexibiliy o adjus he level of backup asks, pursui of scheduling ime is minimized, a he same ime he faul-oleran algorihm perform excellen. Compared wih he classical algorihm GS-Min-min algorihm, even in he case of error resources, he algorihm can sill finish scheduling quickly. CONFLICT OF INTEREST The auhor confirms ha his aricle conen has no conflic of ineres. ACKNOWLEDGEMENTS This research was parially funded by he Naional Naural Science Foundaion of China (Gran No ), suppored by Program for Liaoning Excellen Talens in Universiy (No. LJQ ). REFERENCES [1] M. Amoon, A faul-oleran scheduling sysem for compuaional grids, Compuers & Elecrical Engineering, vol. 38, no. 2, pp , [2] K.J. Naik, and N. Sayanarayana, A novel faul-oleran ask scheduling algorihm for compuaional grids, In: 15h Inernaional Conference on Advanced Compuing Technologies, Rajampe, pp.1-6, [3] S. Jain, and J. Chaudhary, New faul oleran scheduling algorihm implemened using check poining in grid compuing environmen, In: Inernaional Conference on, Opimizaion, Reliabily, and Informaion Technology, Faridabad, pp , [4] S. Xu, Faul-oleran compuing sysems, Hubei:Wuhan Universiy Press, pp , [5] W. Luo, A Real-Time Faul-Toleran Scheduling Algorihm of Periodic Tasks in Heerogeneous Disribued Sysems, Chinese Journal of Compuers, vol. 30, no. 10, pp , [6] C. Yang, G. Deconinck, and W. Gui, Faul-oleran scheduling for real-ime embedded conrol sysems, Journal of Compuer Science and Technology, vol. 19, no. 2, pp , [7] Q. Zheng, B. Veeravalli, and C.K. Tham, On he design of fauloleran scheduling sraegies using primary-backup approach for compuaional girds wih low replicaion coss, IEEE Transacions on compuers, vol. 58, no. 3, pp , [8] A. Benoi, M. Hakem, and Y. Rober, Conenion awareness and faul-oleran scheduling for precedence consrained asks in heerogeneous sysems, Parallel Compuing, vol. 35, no. 2, pp , [9] H. Liu, Research On Primary-Backup Based Faul-Toleran Scheduling Algorihms For Cloud Compuing, M.D. hesis. Zhejiang Gongshang Universiy, On Hangzhou, [10] W. Luo, A Real-Time Faul-Toleran Scheduling Algorihm for Disribued Sysems Based on Deferred Acive Backup-Copy, Journal of Compuer Research and Developmen, vol. 44, no. 3, pp , [11] W. Jing, Faul-oleran scheduling algorihm for precedence consrained asks, Journal of Tsinghua Universiy(Science and Technology), vol. 51, no. S1, pp , [12] C. Berge, Graphs and Hypergraphs, Norh Holland, Amserdam Received: June 10, 2015 Revised: July 29, 2015 Acceped: Augus 15, 2015 Hongxia e al.; Licensee Benham Open. This is an open access aricle licensed under he erms of he (hps://creaivecommons.org/licenses/by/4.0/legalcode), which permis unresriced, noncommercial use, disribuion and reproducion in any medium, provided he work is properly cied.