Open Access A Load Balancing Strategy with Bandwidth Constraint in Cloud Computing. Jing Deng 1,*, Ping Guo 2, Qi Li 3, Haizhu Chen 1

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1 Send Orders for Reprnts to The Open Cybernetcs & Systemcs Journal, 2014, 8, Open Access A Load Balancng Strategy wth Bandwdth Constrant n Cloud Computng Jng Deng 1,*, Png Guo 2, Q L 3, Hazhu Chen 1 1 Department of Computer, Chongqng College of Electronc Engneerng, Chongqng, , Chna; 2 College of Computer Scence, Chongqng Unversty, Chongqng, , Chna; 3 Chna Telecom Corporaton Lmted Chongqng Branch, Chongqng, , Chna Abstract: The schedulng strategy on load balancng, used by data center n cloud computng, plays an mportant role on computng performance, and t s a key technque for the hgh-performance servce. It drectly controls the total performance and the effcency of resource n cloud computng. In ths paper, we ntroduce seven recent patents n the area of load balancng of cloud computng and dscuss some classcal load balancng algorthms (especally Mn-Mn algorthm). Based on Mn-Mn algorthm, a new mproved algorthm named BCLL-Mn-Mn s proposed. It can satsfy the bandwdth constrant and mplement the relatve load balancng schedulng. The smulated experments show that BCLL-Mn-Mn algorthm s wdely avalable for the dverse and uncertan tasks n cloud computng. It mproves the load balance n data center and enhances the throughput n the cluster. Keywords: Cloud computng, load balance, Mn-Mn algorthm, BCLL-Mn-Mn algorthm. 1. INTRODUCTION Cloud computng s a model for enablng ubqutous, convenent, on-demand network access to a shared pool of confgurable computng resources (e.g., networks, servers, storage, applcatons, and servces) that can be rapdly provsoned and released wth mnmal management effort or servce provder nteracton [1]. Cloud computng enables data centers to operate lke the Internet by the process of makng computng and storage resources to be accessed and shared as vrtual resources n a secure and scalable manner. Cloud data centers accommodate a lot of computng and storage equpments, and they provde servces by combnng mult-node servers as a cluster [2]. In the cluster, the balance s dspatched to each node for promotng resource utlzaton and reducng the watng-tme of users. The advanced load balancng strategy s one of the key technques for hghperformance servce, cost savngs and mprovng the cluster throughput [3]. Up to now, several load balance strateges have been presented nto cloud computng. Patent US 0,031,550, ttle Method for mprovng the performance of hgh performance computng applcatons on cloud usng ntegrated load balancng [4], provdes an expected cost set assocated wth an applcaton-specfc task of an applcaton executng on a processng resource n a cloud computng envronment, and communcatng the expected cost set from the processng resource to a cloud management system. Then a task to VM (vrtual machne) assgnment s determned based on the assgnment of the applcaton-specfc task to the specfc computatonal resource. Patent US 0,217,100, ttle Method and system for load balancng content delvery servers [5], presents a cloud computng content delvery system and t ncludes multple content delvery servers (CDSs) confgured to delver content to multple clent devces. The clent devces send requests to the CDS for the mrror lst. Then they send content requests to the frst entry n the lst. Each CDS can update the mrror lst by applyng a load balancng algorthm and provde the mrror lst to a clent devce n the event that one or more CDSs are unavalable. Patent US 0,166,645, ttle Method and apparatus for load balancng n mult-level dstrbuted computatons [6], provdes load balancng n mult-level dstrbuted computatons. A dstrbuted computaton control platform determnes closure capablty data assocated wth respectve levels of a computatonal archtecture, wheren the respectve levels nclude a devce level, an nfrastructure level, and a cloud computng level. The dstrbuted computaton control platform further determnes to cause processng the closure capablty data. Patent CN , ttle Cloud computng load balancng method based on layerng multple agents [7], relates to a cloud computng load balancng method based on layerng multple agents. Two of a pluralty of nodes whch are connected wth a cloud computng platform through the network are used as a task montorng agent and a resource montorng agent, agents are ont management nodes of the cloud computng platform, each management node performs task allocaton accordng to load condtons, dfferent management nodes respectvely take charge of montorng, resource allocatng and the lke. So that a pluralty of cloud computng tasks can be concurrently and effectvely processed, and task processng capacty of the cloud computng platform s mproved. Patent CN , ttle Cloud computng load balancng method and equpment [8], provdes a cloud computng load balancng method and equpment. The load capacty of the server can be changed adaptvely; and the proper servce X/ Bentham Open

2 116 The Open Cybernetcs & Systemcs Journal, 2014, Volume 8 Deng et al. copy s selected accordng to the load capacty of the server to ensure comparatvely unform load dstrbuton on each copy and realze adaptve load balance of the server. The current schedulng algorthms takes short tme, hgh degree of satsfacton and load balancng as the optmzaton goals and ther algorthms can be classfed nto two types; statc and dynamc. The statc type, whch s based on Posson dstrbuton of the tasks and exponental dstrbuton of response tme, ncludes RR [9], WRR [10]. They are avalable for the statc server systems wth small sze and smple confguraton snce the resources utlzaton s descrbed by a lttle statc feature nformaton and the resources are allocated to the comng task n proper sequence. When the tasks becomes dverse and uncertan, the effect of load balancng wll be undesrable [11] wth a dfference of 10 to 100 tmes. The type of dynamc algorthms s presented subsequently, such as LC, WLC [10]. They wll compute the load of the servers n a perod of tme accordng to dfferent factors before the tasks arrve, so the comng task wll be assgned to a sutable sever. The most dffcult problem n ths type of algorthm s how to choose an approprate coeffcent to compute the load of the servers. Patent CN , ttle Cloud calculatng load balancng schedulng algorthm based on double-weghted least-connecton algorthm [12], dscloses a cloud calculatng load balancng schedulng algorthm based on a double-weghted least-connecton algorthm. In the algorthm, no relatvely large nclnaton of a load of each node s guaranteed when a system s n a long tme operaton state, summaton of all task weghts of each server and weght rato of performances of the servers are calculated by a scheduler before task dstrbuton, new tasks are dstrbuted to the servers wth smallest ratos. The algorthm shortens average accomplshment tme of the cloud calculatng servce system, mproves system effcency and further mproves a load balancng degree of each resource server n a cloud data center. Mn-Mn and TD-Mn-Mn are heurstc schedulng algorthms [13, 14], and shortenng the total completon tme of all tasks s ther optmzaton goal: Mn-Mn algorthm assgns the task accordng to the mappng between vrtual machne and the task whose completon tme s the shortest; whle TD-Mn-Mn algorthm uses the mappng between vrtual machne and the task whose completon tme s the longest. Comparng wth the statc algorthms, the performance of the dynamc ones s better, for they know the realtme load of the servers. But ther performance wll be poor n cloud computng because they are not avalable for the tasks wth dfferent sze and the resources wth bg dversty. The remander of ths paper s organzed as follows: Secton 2 ntroduces the schedulng modes n cloud computng, Mn-Mn and LL-Mn-Mn algorthms [15]; n secton 3, we present BCLL-Mn-Mn that can satsfy the bandwdth constrant and mplement the relatve load balancng schedulng; smulated experments are analyzed n Secton 4; the last secton concludes ths paper. 2. CLASSIC SCHEDULING MODEL AND ALGO- RITHM IN CLOUD COMPUTING The archtecture of cloud computng conssts of three layers: applcaton, platform and nfrastructure layers [16]. Ths archtecture makes the load schedulng n cloud computng a two-level mode [17]. The frst level s the assgnment between user applcaton and vrtual machne, and the task wll be assgned to a sutable vrtual machne accordng to the performance requrements or other lmted factors of the task. Whle the second one s the assgnment between vrtual machne and host, t means that the second level selects the approprate one from the physcal hosts accordng to resource request of each task n the vrtual machne and dynamcally balances the loads of the physcal machnes. Ths model can satsfy all performance requrements of dfferent tasks and the lmted factors. What s more, t can avod ncreasng the executon tme for short of computng resource or wastng the resources snce the dstrbuted resource s more than the task needs. Thanks to the vrtualzaton technology, we can only concern ourselves wth the frst level schedulng of the model n cloudng computng The Task Parameter Model n Cloud Computng Let C = { C1, C2, C3,... Cn} be a gven task sets of cloud computng. And each task C can be represented as: C = { ID, length, ExpB, Bwsat} (1) where, ID unquely dentfes the task, and length s gven as ts estmated completon tme. ExpB s the expected bandwdth and t s the unque measure of the users' satsfacton. Obvously, a task s assgned to a vrtual machne that can perform the task. In partcular, Bwsat s the measure of the satsfyng bandwdth and t can be calculated by: 1 f ExpB <= Bw Bwsat = 0 otherwse where, Bw s the bandwdth of the vrtual machne. Eq.(2) means, f the resource of a vrtual machne can be used to perform the task, Bwsat s set by 1. Otherwse, t set by The Vrtual Machne Resource Model n Cloud Computng Let V = { V1, V2, V3,... Vm} be the set of vrtual machnes n cloud computng data center, and each vrtual machne V can be represented as: V = { ID, PE, mps, Ram, Bw, VL} (3) where, ID unquely dentfes the vrtual machne. PE s the number of executve unt n the vrtual machne. mps s the executon speed of the vrtual machne. Ram s the memory sze. Bw s the bandwdth of the vrtual machne and t s compared wth ExpB. VL s the workloads of the vrtual machne. Whle some resource, such as external storage, are not consdered, because they have lttle effect on the workloads of the vrtual machne. (2)

3 A Load Balancng Strategy wth Bandwdth Constrant n Cloud Computng The Open Cybernetcs & Systemcs Journal, 2014, Volume Based on the parameters of the vrtual machnes and the task parameter model, our new algorthm presented bellow wll select the vrtual machne n Eq.(3) for the tasks n Eq.(1) by a sutable load schedulng strategy The Load Model n Cloud Computng Assume that an accurate estmaton of the expected completon tme for each task on each machne s known before the executon and contaned wthn an ETC (namely, expected tme to compute) matrx. ETC[ ][ ] s the estmated completon tme of task on vrtual machne. ETC[ ][ ] s nfluenced by many factors. In ths paper, we assume that ETC[ ][ ] s only nfluenced by length, the length of task, and mps s the executon speed of the vrtual machne. To smplfy the model, we have two conventons as follows: 1) The fnshbg tme of all tasks s fxed when many tasks are executed n a vrtual machne smultaneously. 2) If executng tme of a task s the mnmum on a vrtual machne, the task s executng tme would be the mnmum on other vrtual machne. 3) If the executon speed of a vrtual machne s the maxmum, no matter whch task, ts executon speed s the maxmum. Namely, the executon speed s not related to the task. ETC[ ][ ] can be calculated by: T = length / mps (4) T ETC [ ][ ] = (5) Assume that there are n tasks and m vrtual machnes. The estmated completon tme of n tasks can be calculated by Eqs. (4) and (5) and the result can be expressed by a matrx: T11 T = 21 ETC Tn1 T1 m T 2m Tnm The tasks of dfferent users have nothng n common wth the processng ablty of vrtual machnes n cloud computng data centers and they are dffer from one another. All these ncrease the dffcultes of defnng the workload. In ths paper, two assumptons are gven as followng shows. The frst assumpton, the workload of a task s only related to length of the task. Namely, the longer the length s, the heaver the workload s. The second assumpton, the processng ablty of a vrtual machne s only related to mps, the executon speed of vrtual machne, wthout consderng the bandwdth, the memory sze and so on. mps can be determned to weght accordng to ts hstorcal record. The workload of vrtual machne can be defned as VL and the workload caused by task of vrtual machne can be calculated by: (6) VL = length / mps (7) We know from Eq.(4), the length / mps s equal to the T. So, the workload of vrtual machne s equal to the total sum of all tasks processed n the vrtual machne: VL = T (8) So the load balancng schedulng can be descrbed as all the vrtual machnes have equvalent executng tme of tasks. And a standard measurng load balancng s defned as: = T /T mn max (9) where, T s the mnmal and mn T max s the maxmal completon tme of all vrtual machnes. The results were obtaned as follows accordng to Eq.(9). 1) The tasks are not scheduled when T s equal to 0. max 2) There are dle vrtual machnes when s equal to 0 and T s not equal to 0. max 3) There s the hghest load balance degree when s equal to one, namely, the maxmum s equal to mnmum of workload. Moreover, the closer to 1 s, the hgher the load balance degree s Mn-Mn [13] and LL-Mn-Mn [15] Up tll now, many schedulng algorthm derved from Mn-Mn algorthm. Mn_Mn heurstc begns wth the set U of all unmapped tasks, and then the set of mnmum completon tmes s found. Next, the task wth the overall mnmum completon tme s selected and assgned to the correspondng machne (hence the name Mn_Mn). Last, the newly mapped task s removed from U, and the process repeats untl all tasks are mapped (.e., U s empty). Mn_Mn maps the tasks n the order that changes the machne avalablty status by the least amount that any assgnment could. The expectaton s that a smaller makespan can be obtaned f more tasks are assgned to the machnes that complete them the earlest and also execute them the fastest. LL-Mn-Mn s one of the mproved versons of Mn-Mn and t mplements the relatve load balancng schedulng. In ths algorthm, the task wth the relatvely largest load and the mnmum completon tme s chosen, so each task has an opportunty to be performed n dfferent vrtual machne parallel and the utlzaton percentage of the vrtual machnes can be promoted. The relatve load can descrbe the dfference of the completon tmes of each task n dfferent vrtual machnes, so choosng the maxmum dfferent one from the current task can avod ncreasng the load or the makespan. 3. BCLL-MIN-MIN ALGORITHM When users use cloud computng servce and ask for vrtual machne resource, they rase some vrtual machne performance requests. For example, bandwdth request of tasks, obvously servce provder should satsfy ts users and meet the user demands by dstrbutng suffcent vrtual machne resource. Smultaneously, the completon tme must be short

4 118 The Open Cybernetcs & Systemcs Journal, 2014, Volume 8 Deng et al. Table 1. An example of BCETC matrx (unt: ms). M 1 M 2 M 3 M 1 C C 2 N C 3 N N N 22 C 4 N C 5 N N enough, because t relates to the user's feelng drectly. In concluson, basng on LL-Mn-Mn algorthm and bandwdth constrant, we propose a load balancng strategy wth bandwdth constrant n cloud computng, named as BCLL-Mn- Mn. BCLL-Mn-Mn algorthm's optmstc goal s: loadng balance; satsfy dfferent task bandwdth request; short completon tme. For smplcty, we appont task schedulng that meet two condtons: 1) There s no relaton between two tasks; 2) When a task s dstrbuted to the vrtual machne, other tasks must wat untl t s accomplshed; Base on the above schedulng, we rase schedulng dscplne to realze BCLL-Mn-Mn algorthms optmze goal: 1) If a vrtual machne satsfes the bandwdth requrements, the task wll assgn to the vrtual machne. 2) If there are multple vrtual machnes that meet bandwdth requrements, the task wll be assgned to the one whose executon tme s mnmal The dea of BCLL-Mn-Mn BCLL-Mn-Mn algorthm should meet user s demand for bandwdth and guarantee a certan load balance. The bandwdth requrements can be clarfed by the user s request or by queryng the hstorcal nformaton, and n BCLL-Mn-Mn algorthm, the choce of the bandwdth s based on the user s consderaton. For the bandwdth-demand tasks, ETC that wll meet the bandwdth constrant matrces are named BCETC, and the core of the BCLL-Mn-Mn algorthm s BCETC. The estmated executon tme n BCETC matrx s the same as before when vrtual machne resource meet the user s demand. However, the task cannot be assgned to the vrtual machne and the value of estmated executon tme wll be set N n the same place of BCETC matrx f t does not meet user s need BCETC matrx as shown n the Table 1, the bandwdth n vrtual machne M 1, M 2, M 3, M 4 ncreases successvely. Due to the lower bandwdth requrements of the task C 1, these 4 vrtual machnes satsfy the condton, the frst lne unchanged. But n the second lne, M 1 does not meet the requrement, the value n the [ C 1, M ] wll be set to N, that s 1 not mapped. Smlarly, we can conclude the map between the other tasks and vrtual machnes. Meanwhle, n order to acheve a certan level of load balance, the fewer vrtual machnes wll be gven Prorty schedulng f they satsfy the bandwdth requrements, the procedure of ths sort of schedulng s gven below: Step1: Only one vrtual machne that meet ther requrements. Step2: At least two vrtual machnes that meet ther requrements. Step3: All vrtual machnes that meet ther requrements. Step4: All vrtual machnes that do not meet ther requrements. If we never adopt these schedulng, the tasks of greater coverage wll be performed n the vrtual machne wth a low bandwdth, and t wll result n a serously uneven load. In order to ensure the task and vrtual machnes correspondng to the N n matrx BCETC never be assgned, we set N wth a large value (greater than the sum of all the task completon tme). Therefore, a task wth largest gap n average and mnmum executed tme wll be executed frstly. The less vrtual machnes meet the requrement, the greater the D- value s. Ths algorthm wll preferentally select the task and meet these characterstcs Algorthm Descrpton Algorthm: BCLL-Mn-Mn Input: vrtual machne parameter, tasks parameter Output: mappng scheme Procedure: Step1: generate C to record all tasks; modfy V to record all vrtual machne; defnte CTOV to record current mappng scheme; generate VMLoad to record all vrtual machnes' loadng; Los s an array whch has relatvely loadng of each task; Step2: accordng to tasks' expected nstructon length, vrtual machnes processng speed and bandwdth-demand tasks, we can get the ETC[ ][ ] ; Step3: foreach C n C ; add VMLoad[] to BCETC [][]; foreach C n C ; foreach V n V ;

5 A Load Balancng Strategy wth Bandwdth Constrant n Cloud Computng The Open Cybernetcs & Systemcs Journal, 2014, Volume fnd mnmum completon tme of each task; calculate average tme for each task that remove the mnmum tme; get LL by calculatng the D-value from average tme and mnmum tme; end foreach end foreach choose the task-resource mappng of bggest D-value, and keep n CTOV; Accordng to ETC array refresh VMLoad, delete task that have done from C. end foreach End. BCLL-Mn-Mn algorthm not only dstrbutes tasks preferentally to whose relatve loadng s heavy but also adds user satsfacton. It solves Mn-mn algorthm's problems for optmze goal uncty and load mbalance. 4. SIMULATION EXPERIMENTAL RESULTS AND ANALYSIS In order to verfy the performance of the BCLL-Mn-Mn algorthm, ths secton uses cloud computng smulaton tools CloudSm [9] to do a comparatve experment among BCLL- Mn-Mn algorthm, Round-Robn (CloudSm platform comes wth round-robn schedulng algorthm, referred to as RR algorthm) and Mn-Mn schedulng algorthm (referred to as MM algorthm) n the completon tme of task, load of the vrtual machne and completon of the task bandwdth requrement classes. Patent CN , ttle Cloud computng load balancng evaluaton system and evaluaton method [18], nvents a cloud computng load balancng evaluaton system. In the system, a sgnal output end of a cloud cluster load nformaton collecton module s connected wth a sgnal nput end of an mage converson module, and the sgnal output end of the mage converson module s connected wth a sgnal nput end of a cluster balance analyss module. Accordng to the nventon, the load converson pcture can be generated by adoptng the method for mappng the node comprehensve load value to the grayscale map and s analyzed accordng to the load mage analyss method, thus achevng the purpose of accurately and wholly evaluatng a load. In our prevous work, we take experment and verfcaton n terms of LL-Mn-Mn algorthm for the case of heterogeneous task and unfxed length of the tasks n heterogeneous envronments. Ths paper compares and verfes the case of tasks wth unfxed length based on the strength of Mn-Mn algorthm, observng the mplementaton of tasks n the bandwdth constrants. Ths paper selects the followng two sets of expermental data based on the standard of the total executon tme of the task and load balancng of the vrtual machne: The frst group: 100, 200, 300 tasks and 10 vrtual machnes load schedulng. The man references are task span, vrtual machne load and completon of the task n bandwdth requrements. All parameters are randomly generated, dfference between tasks and vrtual machne performance heterogeneous s lttle, and the rato of bandwdth requrement task s 50%. The second group: adustng the rato of the bandwdth requrement task, 40%, 60% and 80% respectvely; observng the executon tme of three algorthms wth the effect of dfferent rato bandwdth requrement task. As shown n Fg. (1), RR algorthm takes the longest completon tme, BCLL-mn algorthm followed; Mn-mn algorthm s slghtly better than the BCLL-mn algorthm n tme span. RR algorthm s the clearly worst because t does not consder the characterstcs of the vrtual machne and tasks, and t assgns tasks to a vrtual machne sequentally. Mn-mn algorthm has good results n the neat tasks; and t does not consder the bandwdth needs of the users, whch means that t assgns the unsatsfed resources to users; as a result, Mn-mn algorthm s better than BCLL-mn algorthm n executon tme span. Overall, BCLL-mn algorthm meets the basc need n bandwdth requrement, and t guarantees the completon tme. Fg. (1). Comparson of completon tme. Fg. (2). Comparson of loadng balance. The comparson of load balancng of the vrtual machne s shown n Fg. (2). It can be seen that BCLL-mn algorthm has the hghest load balancng vrtual machne under the bandwdth requrements at 50%. Because the bandwdth requrements classes of the task takes only 50%, and the remanng tasks make up for load nequalty caused by bandwdth requrements to a certan extent based on the algorthm characterstcs, achevng optmzaton goal based on load balancng. Performance of Mn-Mn algorthm s good under tasks n certan condtons. But Mn-Mn algorthm s stll worse than BCLL-mn algorthm, whle load balance of these two algorthms perform well when the task ncreases. However, RR algorthm s the worst.

6 120 The Open Cybernetcs & Systemcs Journal, 2014, Volume 8 Deng et al. If tasks wth bandwdth constrants can be performed by some vrtual machnes, the value of Eq.(2) s set by 1. 50% of the bandwdth requrement classes tasks, whch the maxmum s 50, all meet under the case of 100 tasks. Smlarly, 200 tasks are 100 and 300 tasks are 150. The comparson of the completon of the bandwdth tasks s shown n Fg. (3). As Fg. (3) shows, BCLL-Mn algorthm can satsfy bandwdth requrement classes. Whle Mn-Mn algorthm ust can meet a lttle snce t has not the optmzaton goal of bandwdth requrement. However, the RR algorthm wll defntely have some tasks to meet the needs because of the allocaton of a fxed rotaton, and t equally matches Mn- Mn algorthm under the satsfacton of bandwdth requrement. Therefore, compared wth a slght tme dfference n BCLL-mn algorthm, BCLL-mn algorthm acheves a bg satsfacton dfference forthe user tasks. Fg. (5) shows that BCLL-mn algorthm makespan s ncreased wth the lmt of bandwdth requrements constrants, because the satsfed machne lessens after ncreasng the bandwdth lmtng, and t sacrfces some completon tme to meet the tasks. In contrast, Mn-Mn algorthm does not consder bandwdth requrements, so completon tme wth dfferent rato s not much dfferent. However, n general, there wll not be so much tasks of type of bandwdth requrement. Fg. (3). Comparng the bandwdth satsfacton of the tasks. In order to observe tasks wth dfferent rato bandwdth constrants mpact on load schedulng tasks, we adust the rato of bandwdth requrement tasks and ncrease bandwdth for tasks requrement n the second experments. We desgn 200 heterogeneous and lttle dfferent tasks and 10 heterogeneous vrtual machne resources to reflect the comparson between BCLL-mn algorthm and Mn-Mn algorthm based on Mn-Mn algorthm strengths. All parameters are stll randomly generated. The experments results of bandwdth satsfacton wth three ratos are shown n Fg. (4). Fg. (4). Comparson of 200 dfferent proportons tasks satsfacton. From Fg. (4), we can see that BCLL-mn algorthm can bascally meet the bandwdth requrement of users. The growth rate of Mn-Mn algorthm and the RR algorthm s not sgnfcant wth the ncrease n bandwdth rato, and they do not meet bandwdth requrement well. However, wth the rato of bandwdth requrement tasks ncreasng, requrement of bandwdth constrants and lmtng ncreases, meetng the bandwdth requrements wll nevtably lose some tme span. Fg. (5). Comparson of 3 proportons knds of the tme span. Overall, BCLL-mn algorthm s the best under varous condtons, load balance and task completon satsfacton. But task completon tme of BCLL-mn algorthm wll be slghtly reduced wth rato of bandwdth requrement tasks ncreasng. As clearly obtaned from the experments, BCLL-mn algorthm s better than the other two algorthms n heterogeneous task and heterogeneous envronments, and t meets bandwdth requrement. The followng conclusons can be drawn from smulaton experments: 1) Under the number of tasks wth lttle dfference, the load balance of BCLL-mn algorthm s the best. In order to meet bandwdth requrement, the total completon tme of BCLL-mn algorthm s not better than that of Mn-Mn algorthm, not consderng the bandwdth requrement, but much better than that of RR algorthm. 2) Under the number of tasks wth lttle dfference, BCLL-mn algorthm s the best n optmzaton goals and guarantees the load balancng, snce addng bandwdth lmtatons. 3) BCLL-mn algorthm wll have some mpact on task executon tme wth bandwdth constrants condton ncreasng, but t can meet bandwdth requrements tasks at any rato. Meanwhle, BCLL-mn algorthm wll be as effcent as LL-Mn-Mn algorthm f there s no bandwdth requrement. 5. CONCLUSION The computng tasks n cloud computng s not only complcated but also dverse. Consderng on the heterogenety of the vrtual machnes and dversty of the tasks n cloud computng, we mprove classcal Mn-Mn algorthm and LL-Mn-Mn algorthm and present BCLL-Mn-Mn algorthm, whch can satsfy the bandwdth constrants and mplement the relatve load balancng schedulng. The experments performed on smulaton platform CloudSm show that BCLL-Mn-Mn algorthm s more avalable for schedulng the tasks n cloud computng and t can mprove the

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