An Adaptive Load Sharing Algorithm for Heterogeneous Distributed System

Transcription

1 An Aaptive Loa Sharing Algorithm for Heterogeneous Distribute System P.Neelakantan, A.Rama Mohan Rey Abstract Due to the restriction of esigning faster an faster computers, one has to fin the ways to maximize the performance of the available harware. A istribute system consists of several autonomous noes, where some noes are busy with processing, while some noes are ile without any processing. To make better utilization of the harware, the tasks or loa of the overloae noe will be sent to the uner loae noe that has less processing weight to minimize the response time of the tasks. Loa balancing is a tool use effectively for balancing the loa among the systems. Dynamic loa balancing takes into account of the current system state for migration of the tasks from heavily loae noes to the lightly loae noes. In this paper, we evise an aaptive loa-sharing algorithm to balance the loa by taking into consieration of connectivity among the noes, processing capacity of each noe an link capacity. Keywors: Loa balancing, Distribute System, heterogeneous, response time. I. INTRODUCTION An important attribute in a ynamic loa balancing policy is to initiate the loa balancing activity that specifies which noe is responsible for etecting imbalance of the loa among the noes [9]. A loa-balancing algorithm is invoke when loa imbalance among the noes is etecte. The initiation of loa balancing activity will have a higher impact on complexity, overhea an scalability. The loa balancing algorithm is esigne in such a way to make the overloae noe to transfer its excess loa to the unerloae noe which is calle sener initiate an when unerloae noe requests the loa from the overloae noe then it is calle receiverinitiate [6][8]. Domain balancing is use to ecentralize the balancing process by minimizing its scope an ecreasing the time complexity of the loa-balancing algorithm. A omain is efine as subset of noes in a system, such that a loa balancing algorithm can be applie for this subset of noes in a single step. Domain balancing is use in loa balancing algorithms to ecentralize the balancing. The balancing omains are further ivie into two types: The first type is Manuscript submitte May 3, 203, revise Aug 3, 203. P. Neelakantan is with the Department of CSE, SVU College of Engineering, Tirupati-5750 ( pneelakantan@reiffmail.com). Dr.A.Rama Mohan Rey is with the Department of CSE, SVU College of Engineering, Tirupati, ( ramamohansvu@yahoo.com). overlappe omains, which consists of noe initiating the balancing activity an balances its loa by migrating the tasks or loa units with the set of surrouning noes. [3] Global balancing is achieve by balancing every omain an by iffusing the excess loa throughout the overlappe omains in a istribute system. Another important attribute in loa balancing algorithm is the egree of information. The egree of information plays an important role in making the loa balancing ecisions. To achieve global loa balancing in a few steps, the loa balancing shoul get absolute information instea of getting the obsolete information from the noes. In general, the collection of information by a noe is restricte to the omain or nearest neighboring noes (which are irectly connecte to a noe)[4]. Although collecting information from all the noes in a istribute system gives the exact knowlege of the system, it introuces large communication elay, so from this perspective, it will have a negative impact on the loa balancing algorithm. In such cases, it has been observe, that the average response time is kept minimum without loa balancing instea of oing the loa balancing which inuces overhea in migrating the loa from one noe to another noe in the system [5]. In this section, an abstract view of the software etails is presente for loa balancing. The istribute system consists of several noes an the same loa balancing software is installe to run on all the noes in the istribute system. By installing the same software in all the noes, the loa balancing ecision is taken by a noe locally (ecentralize) by collecting the information from the neighboring noes as oppose to the centralize loa balancing policy [4]. The program must use a multi-threae concept to implement loa balancing in a istribute system. Two communication ports are available: TCP an UDP. UDP is preferable as it incurs less communication overhea. In general the architecture provies three layers: Communication layer, Loa balancing process an application layer [4][0]. For storing information two ata structures were use. The communication link is responsible for four phases: noe status information phase, noe status reception, tasks reception an task migration. The noe status information is responsible for isseminating the loa

2 information to the noe that has requeste it. The exchange of the information has a profoun effect on the loa balancing ecision; it has to be one accoring to the preefine intervals of time specifie on each noe[7][4]. The status reception is responsible for receiving the status information from the other noes an it will be upate in the local noe list which is running the status reception phase. Here it is possible to istinguish the ol information from the new information. The technique that is use to fin is to associate the timestamp for the information that it has receive from some noe (say TS (Inf), the time stamp attache to the information receive from j to i). The local noe say i maintaining the status about the noe j is kept in the memory. If any estimate regaring noe j exists in the noe i memory, it will be compare to the receive time stamp message an rops the ol time stamp an the new timestamp message has been save in the memory as the ol time stamp has the obsolete information [][][2]. Once a noe collects the above information, it knows whether it is overloae or unerloae. In case if it is overloae noe, it transmits the excess tasks (loas) to the unerloae noes in a tasks transmission phase. The next initiation of loa balancing activity will be one only when the current migration of loa units to the unerloae noes is complete. The task reception is responsible for listening to the requests an accepts the tasks sent from the other noes. As we can observe from the above situations, the minimum time to initiate the new loa balancing activity takes three time instants. One instant for receiving the status of all the noes an secon time instant for etermining the unerloae noes an computing the excess loa an thir time instant for transferring the excess loa to the unerloae noes which has been etermine in the secon time instant. So, the new loa balancing activity takes place only at the fourth time instant [2] [4]. In a few papers [3] [9] [0], it is assume that the noes will not fail. The problem arises when the noes fail which is common in the istribute systems. Sometimes a communication link will also fail, so the noe will be unreachable. These two aspects i.e., failure of a noe an the communication link will affect greatly the loa balancing algorithms. Let us assume the following scenario. The overloae noe has collecte the loa information from the neighboring noes an foun some of the noes are low loae as iscusse earlier. Now at the given time instant when the noe tries to sen its excess loa to the overloae noe, it will not succee because of the failure of the noe. The noe may fail after sening the status information. If this happens, an alternative must be chosen to avoi a failure of the loa-balancing algorithm. II. NOTATIONS & ASSUMPTIONS N: Number of noes V= {, 2 N} a set of noes in a system q i : Number of tasks in the queue of noe i w i (t): Expecte waiting time experience by a task inserte into the queue at the i th noe in time t A i (t): rate of generation of waiting time on i th noe cause by the aition of tasks in time t. S i (t): rate of reuction in waiting time cause by the service of the tasks at the i th noe in time t. r i (t) : rate of removal(transfer) of the tasks from noe j to noe i at time t by the loa balancing algorithm at noe j. ts i : Average completion time of the task at noe i. b i : Average size of the task in bytes at noe i when it is transferre ij : Transfer rate in bytes/sec between noe i an noe j q (t): Average size of the queue calculate by noe i base on its omain information at time t. D : Neighboring noes to i which is efine as D = {j j V an (i, j) E} where V= {, 2 N} E (t):excess number of tasks at noe i at time t. f ij : Portion of the excess tasks of noe i to be transferre to noe j ecie by the loa balancing algorithm. The following assumptions were mae in this paper:. It is assume that a istribute system consists of N heterogeneous noes interconnecte by an unerlying arbitrary communication network. Each noe i in a system has a processing weight P i >0 an processing capacity S i >0. The loa is efine to be L i = P i /S i. In homogenous case the value of L i =P i. 2. It has been assume that tasks arrive at noe i accoring to Poisson process with rate λ (t). A task arrive at noe i may be processe locally or migrate through the network to another noe j for remote processing. Once the task is migrate it remains there until its completion. 3. It is assume that there is a communication elay incurre when task is transferre from one noe to another before the task can be processe in the system. The communication elays are ifferent for each link. Each noe contains an inepenent queue where arrive tasks are ae to the queue, which results in accumulation of waiting time. Loa balancing must be one repeately to maintain loa balance in the system. Each noe runs the loabalancing algorithm iniviually an hence the propose algorithm is istribute in nature. The secon level of the system is a loa-balancing layer, which consists of loa balancing algorithms. The loa balancing process is initiate by using preefine or ranomly generate time instants, kept in a file. The algorithm etermines the portion of the excess loa to be sent to the unerloae noe base on the current state of the noe an availability of the noes in the network. The loa balancing algorithm must consier the communication elay while migrating the tasks to the other noes. The algorithm selects the tasks to migrate to other noes by setting their status as

3 inactive to avoi execution of the tasks by current noe application uring the transition perio. After completion of the task transmission activity, the status of the tasks is set to active when they are not transmitte to any noe. When the tasks are transmitte to other noes uring the task transmission phase then those tasks are remove from the task queue of the current noe. Application layer consists of two threas of control: Task input an task execution threas. The task input creates a number of tasks efine in the initialization file an inserts them in the task queue. This task input is also responsible for aing the new tasks to the task queue either from the current noe or from other noes in the system. The task execution threa is responsible for execution of the tasks an upating the QSize variable by removing the task from the task queue. The loa balancing policy must take into account of processing capacity of the noe while migrating the tasks to it. The selecte noe may become a caniate for one or more overloae noe in a given time instant because of the ecentralize policy. Another issue to be consiere is variable task completion times. Taking these issues a priori is not possible so a loa balancing strategy must be aaptive to the ynamic state changes in the system an act accoringly to transfer the tasks. Even this can result in task shuttle between the noes, so a migration limit for a task shoul be set to avoi task thrashing. Another issue to be consiere while migrating the tasks from one noe to another noe in a system is communication overhea. Large communication elays will have a negative impact on the loa balancing policy, so, the transfer elays must be taken into account while migrating the task. When the completion of the task time in current noe is greater than the completion time on task in another noe inclusive of communication overhea, then only a task is consiere for migration. III. MATHEMATICAL MODEL The mathematical moel for loa balancing in a given noe i is given by [] [2] () =A S + r (t) f r (t τ ) () E (t)= q (t)- q (t) r (t) = G (E (t)) f 0, f =0, f = E if y 0 E (t) = 0 if y < 0 When a task is inserte into the task queue of noe i, then it experiences the expecte waiting time which is enote by w i (t). Let the number of tasks in i th noe is enote by q (t). Let the average time neee to service the task at noe i ts. The expecte (average) waiting time is given by at noe i is given by w (t) = q (t)ts. Note that w (t)/ts = q is the number of tasks in the noe i queue. Similarly w (t)/ts = q is the queue length of some noe k. If tasks on noe i were transferre to some noe k, then the waiting time transferre is q ts = (), so that the fraction ts /ts converts waiting time on noe i to waiting time on noe k. A Waiting time generate by aing the task in the i th noe. S : Rate of reuction in waiting time cause by the service of tasks at the i th noe is given by S = ( tp )/tp = for all w (t) > 0. r (t) The rate of removal (transfer) of the tasks from noe i at time t by the loa balancing algorithm at noe i. f is the fraction of i th noe tasks to be sent out to the j th noe. In more etail f ij r i (t) is the rate at which noe i sens waiting time (tasks) to noe i at time t where f ii >=0 an f =0.That is, the transfer from noe i of expecte waiting time (tasks) E (t)t in the interval of time [t, t ] to the other noes is carrie out with the j noe receiving the fraction p (t / t ) u (t)t where the ratio t /t converts the task from waiting time on noe i to waiting time on noe j. As ( f E (t)t ) = E (t)t, this results in removing all of the waiting time E (t)t from noe i.the quantity f E (t τ ) is the rate of increase (rate of transfer) of the expecte waiting time (tasks) at time t from noe i by (to) noe j where τ (τ = 0) is the time elay for the task transfer from noe i to noe j. In this moel, all rates are in units of the rate of change of expecte waiting time, or time/time which is imensionless. As E (t) 0, noe i can only sen tasks to other noes an cannot initiate transfers from another noe to itself. A elay is experience by transmitte tasks before they are receive at the other noe. The control law E (t) = G E (t) states that if the i noe output w (t) is above the omain average ( q (t τ ))/n, then it sens ata to the other noes, while if it is less than the omain average nothing is sent. The j noe receives the fraction (t /t ) u (t)t of F transferre waiting time E (t)t elaye by the time τ.the moel escribe in () is the basic moel for loa balancing, but an important feature is to etermine f ij for each unerloae noe j. One approach is to istribute the excess loa equally to all the unerloae neighbors. f = for i j. Another approach is to use the loa information collecte from the neighbors to etermine the eficit loa of the neighbors. The eficit loa of the neighbours shall be etermine by noe i by using the formula (2) q (t-τ ) q (2) The above formula is use by noe i to compute the eficiency waiting times in the queue of noe j with respect to the omain loa average of noe i. If noe j queue is above the omain average waiting time, then noe i o not sen tasks to it. Therefore (q q (t-

4 τ )) is a measure by noe i as how much noe j is behin the omain average waiting time. Noe i performs this computation for all the other noes which are irectly connecte to it an then portions out its tasks among the other noes that fall below the omain queue average of noe i. f = ( ( )) ( ( ) If the enominator (q q (t τ ) =0 then fij are efine to be zero then no waiting times are transferre. If the enominator (q q (t τ ) =0, then(q q (t τ ) 0 j N. However by efinition of the average (q q (t τ ) +q q (t) = (q q (t τ ))=0 which implies q q (t)= (q q (t τ )) > 0 That is, if the enominator is zero, the noe j is not greater than its omain queue average, so E i (t)= G i E i (t))=0, where G is Gain Factor.f ij :Portion of the excess tasks of noe i to be transferre to noe j ecie by the loa balancing algorithm. Except the last three parameters remaining information is known at the time of loa balancing process. Before the instance of loa balancing activity, every variable is upate. Algorithm ALS (3) IV. PROPOSED ALGORITHM The current noe i, performs the followings: a. Calculate the average queue size (q )base on the information receive from the neighbouring noes. q = (q + q ) if (q > q )then E i =(q -q ) * G else Exit. b. Determine the participant noes in loa sharing process. Participants= {j q <q, jn i } c. Calculate the fraction of the loa ( f ) to be sent to the participants f = ( ) ( ( ). Calculate maximum portion of the excess loa (f ) f = ( ) e. fij = Min (f, f ) a. Announce to noe j about its willingness to sen T = fij *E i tasks; b. nowreceive = call proceure acceptancefromnoej() c. if(nowreceive >0) i. Transfer NowReceive to j ii. T =T - NowReceive En if g. Repeat steps from (a) to (f). Proceure acceptancefromnoej() if ((q + T ij ) q nowsen=q q ; else nowsen=-; return now Sen; en acceptancefromnoej In general it is assume that keeping the Gain factor G= will give the goo performance. But in a istribute system with largest elays an the noes that have omain queue average outate gives poor result. This phenomenon was first observe by the loa balancing group at the University of New Mexico [7]. So the G values are set in the way that yiels an optimal result. Another step that is ae in the above algorithm is to test the noe availability. It checks both noe availability as well as the amount of waiting times it can receive. The noe executing the ALS is permitte to sen the tasks to the neighbors after receiving the acknowlegement specifying the amount of the loa they can be able to process.. The time complexity of the propose algorithm is O() shown in table. Table : ALS Operations Sno Actions Operation Compute average queue size 2 Compute Ei 3 Determine the participant noes 4 Compute f 5 Compute f Aition Division Subtraction Comparison Subtraction Division Subtraction Division Quantity, ( is the number of neighbors) Compute T 7 Message to noe Transfer f. For j Participants

5 8 Compute nowreceive Aition Comparison Message Transfer V. SIMULATION To test the performance of the newly propose loabalancing policy, a Java program is evelope to test the performance of the existing an propose algorithms. The existing algorithms ELISA an DOLB are use to compare with the propose algorithm ALS. The DOLB is very much relate to the above problem. The initial settings an parameters are shown in Table 2. The average network transfer rates between each noe are represente by the cost ajacency matrix. The propose algorithm ALS is teste with DOLB & ELISA for the gain values G between 0.3 an with 0. incremental steps. The α parameter introuce in the previous section was set to 0.05 by running several experiments an observing the behavior of the tsi parameter. Note that, the first time the loa-balancing process was triggere after 40s from the start of the system an then the strategy execute regularly at 20s interval. Table 2: Simulation Parameters Number of noes 6,32,64 Initial task istribution [00 000] tasks istribute ranomly at each noe Average task processing Processing time is ranomly time(ts in ms) istribute in a range [ ] Size of task( in KB) 00 Loa balancing instance First time the loa balancing was triggere at 5s then for every 0s the loa balancing is initiate Banwith istribution A cost ajacency matrix ( ) enotes the transfer rate between the noes.it is uniformly istribute in the range [..5] Mbps The above constraint ensures that the ts parameter ha enough time to aapt an reflect the current computational power of each noe before the occurrence of any task migration between the noes. Note that the ratio are fixe over time. The propose an rival methos were evaluate by conucting 0 runs for each value of G between 0.3 an with 0. incremental step. Average task completion time(in ms) Gain values (k) ALS DOLB ELISA Figure : Completion time average over 5 runs vs ifferent gain values K. The graphs shows the results of three policies for system size=64. Average Task Completion time (in ms) Gain Values (k) ALS DOLB ELISA Figure 2: Completion time average over 5 runs vs. ifferent gain values K. The graphs shows the results of three policies for system size=32. NUmber of Tasks exchange Gain values (k) ALS DOLB ELISA Figure 3: Total number of tasks exchange average over 5 runs Vs ifferent Gain values K. The graphs shows the performance of the three policies for system size=6.

6 VI. CONCLUSION The propose algorithm is better when compare to the existing algorithms in the literature. In simulation, we assume the tasks with no preceence an with no ealines. However, in heterogeneous systems, loa balancing technique must take into account of OS scheuling policies like roun robin, priority scheuling an to consier the ealine of the task, In this paper, these factors are not consiere while esigning the propose algorithm. As a future work, these factors must be taken into account in esigning a loabalancing algorithm. References [] M. M. Hayat, S. Dhakal, C. T. Aballah I Dynamic time elay moels for loa balancing. Pan : Stochastic analysis of the effect of elay uncertainty, CNRS-NSF Workshop: Avances in Control of tirne-elay Systems, Paris France, January [2] J. Ghanem, C. T. Aballah, M. M. Hayat, S. Dhakal, J.D Birwell, J. Chiasson, an Z. Tang. Implementation of loa balancing algorithms over a local area network an the internet. 43r IEEE Conference on Decision an Control, Submitte, Bahamas, [3] L. Anan, D. Ghose, an V. Mani, ELISA: An Estimate Loa Information Scheuling Algorithm for Distribute Computing Systems, Int l J. Computers an Math With Applications, vol. 37, no. 8, pp , Apr [4] WEI Wen-hong, XIANG Fei, WANG Wen-feng, et al. Loa Balancing Algorithm in Structure P2P Systems[J],Computer Science, 200, 37(4): [5] Khalifa, A.S.; Fergany, T.A.; Ammar, R.A.; Tolba, M.F, Dynamic online Allocation of Inepenent tasks onto heterogeneous computing systems to maximize loa balancing, IEEE International Symposium on Signal Processing an Information Technology, ISSPIT 2008,Pages: [6] Anras Veres an Miklos Boa. The chaotic nature of TCP congestion control. In Proceeings of the IEEE Infocom, pages , [7] J. Chiasson, J. D. Birwell, Z. Tang, an C.T. Aballah. The effect of time elays in the stability of loa balancing algorithms for parallel computations.ieee CDC, Maui, Hawaii, [8] Ming wu an Xian-He sun, A General Self Aaptive Task Scheuling System for Non Deicate Heterogeneous Computing, In Proceeings of IEEE International Conference on Cluster Computing, PP , Dec [9] Z. Zeng an B. Veeravalli, "Design an Performance Evaluation of Queue-an-Rate-Ajustment Dynamic Loa Balancing Policies for Distribute Networks", presente at IEEE Trans. Computers, 2006, pp [0] K. Lu, R. Subrata, an A. Y. Zomaya, Towars ecentralize loa balancing in a computational gri environment, in: Proceeings of the first International Conference on Gri an Pervasive Computing, 2006, Vol. 3947, pp , Springer- Verlag Press. [] Acker, D., Kulkarni, S A Dynamic Loa Dispersion Algorithm for Loa Balancing in a Heterogeneous Gri System. IEEE Sarnoff Symposium, - 5. [2] M. Luczak an C. McDiarmi. On the maximum queue length in the supermarket moel. The Annals of Probability, 34(2): , [3] Zhou, S. (987). An Experimental Assessment of Resource Queue Lengths as Loa Inices. Proc. Winter USENIX Conf., p [4] J. Ghanem, C. T. Aballah, M. M. Hayat, S. Dhakal, J.D Birwell, J. Chiasson, an Z. Tang. Implementation of loa balancing algorithms over a local area network an the internet. 43r IEEE Conference on Decision an Control, Submitte, Bahamas, P.Neelakantan receive B.E(CSE) from Kuvempu University an M.E (CSE) from Maurai Kamaraj University in the year 2002.Presently he is pursuing Ph. at SV University, Tirupati. Dr. A. Rama Mohan Rey receive the B. Tech. from JNT University, Hyeraba in 986, M. Tech egree in Computer Science from National Institute of Technology in 2000 Warangal an Ph. D in Computer Science an Engineering in 2008 from Sri Venkateswara University, Tirupathi, Anhra Praesh, Inia. He worke as Assistant Professor, Associate Professor of Computer Science an Engineering, Sri Venkateswara University College of Engineering uring the perio 992 an Presently, working as Professor of Computer Science an Engineering, Sri Venkateswara University College of Engineering. He has 28 years of Inustry an Teaching experience. He is life member of ISTE an IE. Research interests inclue Software Architecture, Software Engineering an Data Mining. He has 0 international publications an 4 international conference Publications at International an National level.