Genetic Based Web Cluster Dynamic Load Balancing in Fuzzy Environment

Transcription

1 Genetic Based Web Cluster Dynamic Load Balancing in Fuzzy Environment Chin Wen Cheong & V.Ramachandran Faculty of Information Technology MultiMedia University CyberJaya, Malaysia Abstract In this paper, genetic based Generalized Dimension Exchange (GDE) method is proposed with the intention to uniformly distribute the unprecedented Web cluster workload. Due to the vagueness of workload during redistribution period, fuzzy approach is implemented to model the Web cluster distributed system during workload exchanged. According to experts subjective evaluation, fuzzy system is established to aggregate the fuzzy linguistic term of Web performance metrics into a so-called load-weight index that indicates the s workload intensity. Based on the load-weight, genetic algorithm with robust searching capabilities will equally redistribute the workload among the s with the assistance of fuzzy system. 1. Introduction The exponential growth of Internet population has caused the traffic congestion in /client environment. High popularity Web sites always take precaution on their systems capabilities to handle the bursty traffic[1] especially in the peak hours. Owing to the high demands from Web clients, Web administrators sometimes replicate the information resources by establishing a Web cluster. A Web cluster consists of a collection of mirror s that allow a Web site to deliver information over the Internet[2]. However, no significant network performance improvement is observed in the Web cluster due to unequal workload distribution. Round Robin DNS is one of the well-known methods that is applied in Web cluster load balancing and load sharing. However, for self similar[1] arrival of requests, traditional Round Robin method is not applicable as the method is only practical for the uniformly distributed arrival requests[3]. Additionally, the limited DNS scalability[3] of the reached workload has failed to perform Web cluster optimal resources utilization. To overcome the drawback of traditional DNS approach, adaptive TTL algorithms[4] have been utilized to dynamically selecting the appropriate TTL value. Further, artificial intelligent approaches are also used to prevent the traffic surge. A. Shaout, et al.[5] present a batch job scheduler for a distributed system which utilizes a fuzzy logic algorithm to balance the load on individual processors and maximise the throughput ot the overall system. Abani, K., et at.[6] formulate the load balancing problem with fuzzy sets. A fuzzy decision model for the control and management of large decentralized systemsis more appropriate than the conventional probabilistic models. Park, C., et al.[7] propose a new approach to characterizes the global state uncertainty inherent in a large distributed system in terms of the fuzzy set theory and presents a fuzzy-based distributed load balancing algorithm that explicitly reflects the effect of the uncertainty in the decision making process. Some researches have been carried out in workload modeling. [6]quantified the load intensity as the number of requests in waiting queue where a high load demands transfer of a job, and a low load node can accept a request. However, the simplification of the load indication is insufficient to capture the overall of load characteristic which includes the arrival rate of the request, their total response time, hardware capability and etc[8]. In [9], load balancing system is models by considering the hardware performance, data size, number of work per iteration, total cost of redistribution and etc. Nevertheless, the huge monitoring of parameters has caused unavoidable communication delay and costs. Consequently a dynamic load balancing method should be developed in order to overcome the misallocation of s resources and capable to capture the overall performance metrics uncertainty characteristics as well. Basically, Generalized Dimension Exchange(GDE) method[10] is intensively implemented in parallel computing to equalize the workload between multiprocessors. In this paper, each of the redundant s in the Web cluster is considered analogous to a processor in multicomputer since processor is one of the essential components of a Web. The connector

2 between the s is chosen based on the system desired bandwidth capacity requirement. In GDE method implementation, edge-coloring approach is utilized to pair the Web s with respect to workload distribution. Arbitrary topology of the Web cluster is represented by a graph with its associated vertices. Minimum index orders of dimension are colored using Brelaz Color- Degree Algorithm[11] in order to accelerate the convergence rate to reach the stable stage. The dimension of workload exchange among the s is based on the colored graph and fuzzy system with GA approach will determine the workload allocation for the pair s in every sweep. The proposed GDE method is combined with fuzzy approach and genetic algorithm to equalize the workload among the s. Workload redistribution involves many uncertainties and complexity. It is originating from the instability of network condition, random user surfing behavior and inefficiency of workload handling approach. Due to the nature of the workload uncertainty during workload exchanged, fuzzy approach seems to be a better candidate to model the workload. In this paper, three basic metrics' measurement such requests average size(ω size ), number of request in queue(ω number ) as well as communication overhead(ω com ) are used to determine a so-called load-weight(ω) to indicate the workload intensity of each in certain time period. Each of the metrics parameters is represented by fuzzy linguistic term with predefined membership functions. Fuzzy rules are established under experts subjective judgements[12] where the fuzzy inference system will aggregate the outputs fuzzy sets of each rule into a single fuzzy set. Genetic algorithm robust searching capability is used to optimal selects the workload for each of the s during workload exchange. Binary string will represent the existence of certain workload in the and the fittest genome according to the predefined fitness function will survive as the selection to determine the workload allocation. 2. Genetic Based GDE Approach in Load Balancing The aim of this method is to compare and equalize each neighbor workload in an arbitrary Web cluster topology until the workload distribution reaches the balanced stage. The first step of GDE approach is using edge-coloring to determine the dimension indices. The dimension[10] is defined as edges with the same color while the iterative process for all dimensions in the corresponding system topology is defined as a sweep. Based on the predefined dimensions, neighbor workload exchange is equalized along the order dimension. Fuzzy inference system(fis) is used to determine the load-weight by aggregating three predefined parameters(ω size, ω number, ω com ). Optimal workload distribution among the pair s is determined using FIS and genetic algorithm approach to accelerate the system to achieve the stable stage. The structure of the process flow is illustrated in Figure 1. YES REQUESTS STEADY STATE NO WEB CLUSTER REQUESTS Figure 1 : Process flow 2.1 Web Cluster System Modeling Fuzzy GDE Load FIS Workload Monitoring A given arbitrary graph G(V,E), is representing a Web cluster model where V and E are denoted as the vertex and the edge of the graph respectively. For an arbitrary link oriented network, a vertex (V) represents a and the edge denotes the connection between adjacent for an identical s pair in the model. If the edge coloring of graph G(Vi,Ej) is assigned with k colors, the edges of an identical graph G(Vi,Ej) are colored by minimum number of colors and the adjoining edges are in different colors. The chromatic index of the graph G(Vi,Ej) is denoted by ψ(g) which is based on Vizing s theorem[11], the equivalent ψ(g)= is defined as class I and ψ(g)= +1 is known as class II where is the maximum degree of vertex of a graph. The chromatic index, ψ(g) for the edge between x and y is defined by a 3-tuple (x, y, ψ). In this paper, the edge-coloring is determined as vertex coloring associated with each graph G(Vi,Ej) to its line graph L(G). Hence, the chromatic index of edge coloring is equal to the chromatic number of vertices where ψ(g(vi,ej)) = Ψ(L(G(Vi,Ej))). The first stage of the computation is to identify the Web cluster workload distribution. Fuzzy inference system with predefined rules will imply an so-called index known as load-weight(ω). System distance[13] as a measurement metric will evaluate the efficiency of the current Web workload. The workload-exchange termination is based on the following criterions: a. when the total s load-weight are less than a predefined parameter,ξ and the system balance

3 state is confirmed based on the following equation Σ ω x ω mean < ξ where ξ is the predefine system s distance threshold with respect to the system overall distance which governed by the topology and the size of the system b. when all the s are idle Web Cluster System Coloring The occurrence of unequal workload distribution among Web s will lead to the GDE dynamic load balancing. Brelaz Color-Degree Algorithm[11] approach will be used in order to color an arbitrary given graph G(Vi,Ej). The vertex coloring algorithm will divide the edge based on the least color degree and provide sequentially the precise chromatic number of a graph, Ψ(L(G(Vi,Ej))). The algorithm is expressed in sequential order as following: Step 1: For a given arbitrary graph G(Vi,Ej), order the vertices in the form of decreasing order of degrees. Step 2: The maximum degree vertex is colored with color C a. Step 3: Choose the largest color-degree vertex and if the vertex is connected to some other vertex/vertices, select any vertex of maximum degree in the uncolored subgraph. Step 4: With the minimum possible color, color the chosen vertex from Step 3. Until all the vertices are colored, end the coloring algorithm. Else go to Step 3. Based on the vertex coloring, the edge colors can be Step 5: determined accordingly before the workload is being exchanged among the neighbor s. 3. Web Cluster Fuzzy Workload Modeling The redundant s in a Web cluster are indicated the load-weight to exhibit the s workload intensity. Generally, for certain time unit, T, the load-weight of each is determine by alternate Web performance metrics that characterized the workload intensity. Workload intensity of a particular is specified by 3-tuple such as ω = {ω size, ω number, ω com } where ω represents the load-weight in a ; ω size represents the average file size in a certain ; ω number represents the number of waiting load in a certain. ω number is the combination of finite set of load f 1, f 2, f 3,, f M in the Web cluster being considered where M is the total number of load in the Web cluster. A Web s (K x ) ω number is illustrated as follows: ω number (K x ) { f 1, f 2, f 3,, f N } where N is the total number of load in a particular. ω number is varying for every in certain time-unit which represent by independent subsets. Let S 1, S 2, S 3, S 4,, S P be the disjoint subsets of ω number in a particular (K 1, K 2, K 3,, K p ) such that no two subsets S m and S n (m n) are identical i.e as well as with the condition f m f n. S m S n = φ and S 1 S 2 S m S n S M = ω total_number where M is the total number of subsets. ω total_number is the total number of the loads in time T. ω com represents the overall communication cost and delay between 2 s, for the sake of simplicity the communication cost is stated as: ω com N workload where N workload is the number of workload has to be immigrated among the paired- in the Web cluster. Due to the vagueness of the distributed system, fuzzy approach is implemented to determine the loadweight(ω). Fuzzy inference system[14] is based on fuzzy set theory and fuzzy rules-based approach in decision analysis and variety of fields, especially dealing with uncertain and complex systems. The portability of fuzzy system allows human linguistic language approach to determine the grade of membership as well as the fuzzy rules for the inference engine. Fuzzy inference system involves some procedures to conclude either a fuzzy or crisp result depending on the user intention. The components of a fuzzy system include fuzzification(fuzzy input memberships), inference engine and defuzzification respectively. According to experts subjective evaluation, each of the tuple is illustrated with fuzzy linguistic term and its associated membership function. For instance the workload metrics values are fuzzified into three fuzzy linguistic spaces as following: ω size, ={Small, Medium, Large} ω number ={Short, Fair, Long} ω com ={Low, Moderate, High} The rule which decide the load-weight values are shown in Table 1. Fuzzy inference system(fis) is used as a max-min composition in the calculation of load-weight value. Fuzzy inference with predefined rules will integrate all the 3-tuples intensity that finalizes a loadweight with seven linguistic term value such as Extremely Heavy, Very Heavy, Heavy, Fair, Low, Very Low, Extremely Low. Figure 2 will illustrate the linguistic input and output of the model system.

4 IF Table 1: Fuzzy rules THEN ω SIZE Operator ω NUMBER Operator ω COM ω (load weight) Large AND Long AND High Extremely heavy Large AND Long AND Moderate Very heavy Large AND Long AND Low Heavy Large AND Fair AND High Very heavy Large AND Fair AND Moderate Heavy Small AND Fair AND Low Very light Small AND Short AND High Light Small AND Short AND Moderate Very light Small AND Short AND Low Extremely light Figure 2. Parameters and associate memberships function 4. GA Approach in Workload Optimal Allocation Basically GA is an optimization search algorithm[15]. The first step of GA is to generate an initial population and formulate a string pattern for the complete solution of the particular model. The chromosome is represents by a binary string depending upon the system condition. Every bit will represent the existence of a load(f p ) in a particular (K a ) with the condition each load only allows to exist once among the s. By applying the operators such as selection, crossover and mutation, the chromosome with the highest fitness is chosen to determine the next time period workload allocation. The major parameters involved in genetic algorithms are Population size of the chromosomes Maximum number of generation Probability of crossover (P cross ) and Probability of mutation (P mute ) Step 1: Step 2: initialization set population size and maximum generation set P cross and P mute set generation = 0 set the bit length for each parameter generation of initial population Step 3: Step 4: Step 5: based on the Web (K a ) load quantity, initial the binary bit where 1 represent the existence and 0 non-existence of the load in the. evaluate the fitness function for each of the string in the current population according to the fitness function. The fitness function is governed by 3 parameters average filesize, number of queueing and communication cost. By using the predefined FIS, determine the fitness function as below: Fitness Function = 1 / (ω x ) -- (ω y ) If the Fitness Function >µ, terminate the searching process, where µ is the predefined fitness function threshold. Else go to Step 4. Set offspring count = 0 and generate the operator according to the crossover rate, mutation rate. Perform crossover with probability P cross. If crossover is not performed, put chromosome into the next generation and go to step 3. Otherwise a. Select mate from population with uniform probability. b. Select crossover point between the string with uniform probability. Repeat the Step 3 if the fitness function threshold, µ is not fulfilled. Step 6: If for consecutive n-th generation the µ is not fulfill, choose the fittest chromosome as the final solution. 4.1 Numerical Example Considers two s with the properties as illustrated in Figure 3, the details of the GA approach and fuzzy system is shown in Table 2. Assume after n-th searching processes, the selected distribution of the pair-s is achieved with the fitness Table 2: Workload allocation in pair-s,k 1 and K 2 1st 2nd 3rd Fitness n-th Fuzzy Based GDE Implementation After the determination of the G(ψ), consider two neighbor s(x, y) with ω x and ω y represent the initial

5 load-weight resulting from the FIS in x and y respectively. Each load(f p ) is indicated with an reference integer and respective file size(f size ) with the condition f m f n, S m S n and f p can only exist in a. Subsequently, workload distribution involves a number of iteration sweeps to reach the uniform distribution for each. System distance as a measurement of the system stability is normalized[13] with the respect maximum possible system distance. A normalized system distance threshold is defined as ξ. The workload interchange between s is resolved by using the subsequent algorithm: Step 1: Identify every s (K i ) workload intensity by using the FIS for time period t. Step 2: If the detects non-existence of steady state, start iterative sweeps in n dimension for the same color edges with the existence of the edge (x,y) and with color n where n=1, n ψ. Step 3: Using GA algorithm(3.1) randomly reallocate the workload in the involves -pair and FIS will determine the workload allocation by concerning the three predefined metrics. Step 4: After one dimension, detect the system state based on the following equation for every K. k t+ 1 ( ω ) ( ωmean ) < ξ i= x, y i If the steady state has not been achieved, go to Step 2. For the next dimension, n=n+1, repeat Step 2 and Step3 (n ψ) until a full sweep has been proceeded. Else, terminate the distribution algorithm. 6. Numerical Estimation t+ 1 Arbitrary, a Web cluster is chosen where the topology of the internal s is in the 3-cube form and the Web cluster consists of 8 s. The edge graph is associated with its line graph and hence the edge coloring can be considered as a vertex coloring. After the determination of Brelaz Color-Degree Algorithm, the hypercube structure is colored with 3 different colors, c 1, c 2 and c 3. The initial workload of the eight s is arbitrarily defined respectively with the associated vertices K 1, K 2, K 3, K 4, K 5, K 6, K 7 and K 8 as illustrated in Table 3. Initially for genetic algorithm approach, the genome length of the encoded chromosomes is represented by 20 randomly distributed binary value where every load is represented by 1 binary bit. The population size, P cross, P mute, µ, number of crossing site and the numbers selected fittest chromosomes are fixed to 0.5, 0.1, 0.30, 1 and 1, respectively. The normalized system distance threshold of the workload is fixed as ξ.(where ξ. is equivalent to 0.20). The initial workload distribution process will be terminated once the fitness chromosome reached the stationary state for 100 consecutive generation. After the termination, the previous distributed workload will proceed new workload redistribution. The mentioned procedure is repeated until the fixed threshold function is fulfilled. The details of the workload exchanged among the s are illustrated in Figure Conclusion Table 3: Workload initialization i(fi ) Size(MB) i(fi ) Size(MB) In this paper, fuzzy approaches in workload modeling and workload intensity determination enhance the representativeness of the model and ability to capture the vagueness of a Web cluster workload distribution system. Nevertheless, the overall workload characteristics should be studied more detail such as the arrival rate of workload in each, execution time, hardware as well as software requirements. The proposed fuzzy GDE in cluster load balancing shows that it is capable in distributing the unequal s workload. References [1] Crovella M., and Bestavros. A., "Explaining World Wide Web Traffic Self-Similarity", Tech. Rep.BUCS-TR-95F-015, Voston University, CD Dept, Boston MA 02215, [2] Daniel A. Menasce, "Capacity Planning for Web Performance: Metrics, Models & Methods", Prenctice Hall, Inc., [3] Michele Colajanni, P.S. Yu and D.M. Dias, "Scheduling Algorithms for Distributed Web Servers", Proc. ICDCS'97, Baltimore, MD, May [4] V.Cardellini, M Colajanni, and P.S. Yu, DNS Dispatching Algorithms with State Estimators for Scalable Web Server Clusters, World Wide Web J., Baltzer Science, Bussum, Netherlands, Vol.2, No. 2, July [5] Shaout, A.; McAuliffe, P., "Job scheduling using fuzzy load balancing in distributed system",electronics Letters,1998, [6] Kaveh Abini, "Fuzzy Decision Making for Load Balancing in a Distributed System", Proceedings of the 36th Midwest Symposium on Circuits and Systems 1993,

6 [7] Chulhye Park; Kuhl, J.G., "A fuzzy-based distributed load balancing algorithm for large distributed systems", Autonomous Decentralized Systems, Proceedings. ISADS 95., Second International Symposium on, 1995, [8] Wentong Cai, Bu-Sung, Heng,A. and Li Zhu, "A Simulation Sutdy of Dynamic Load Balancing for Network-based Parallel Processing", Proceeding of Parallel Architectures, Algorithms, and Networks, [9] Zaki, M.J.; Wei Li; Parthasarathy, S., Customized Dynamic Load Balancing for A Network of Workstations, High Performance Distributed Computing, 1996, Proceedings of 5th IEEE International Symposium on 1996, [10]ChengZhong Xu, Francis C.M.Lau, "Load Balancing Parallel Computers - Theory and Practice", Kluwer Academic Publishers.,1997. [11] West, Douglas Brent, "Introduction to Graph Theory", Upper Saddlr River, NJ,Prentice Hall [12] V.Ramachandran & V.Sankaranarayanan, Fuzzy Concepts Applied To Statistical Decision Making Methods, 15 th IFIP Conference, Zurich, [13] Bharat S. Joshi, Seyed Hosseini and K.Vairavan, "Stability Analysis of a Load Balancing Algorithm" Proc. of the IEEE Southeast Symposium on System Theory, March [14] J.-S.R. Jang, C.-T. Sun & E. Mizutani, Neuro-Fuzzy and Soft Computing A Computational Approach to Learning and Machine Intelligence, Prentice Hall, Inc., [15] David E.Goldberg, "Genetic Algorithms in Search, Optimization and Machine Learning", Addison-Wesley, STEP 1 STEP 2 SERVER FILE ALLOCATION I(FI ) LOAD-WEIGHT W WMEAN (WMEAN= ) 1, 2, 3, 4, 5, 6, 7, 8, VERY HEAVY , EXTREMELY LIGHT EXTREMELY LIGHT EXTREMELY LIGHT EXTREMELY LIGHT EXTREMELY LIGHT EXTREMELY LIGHT , 12, 13, 14, 15, 16, 17, 18, 19, VERY HEAVY Initially State: Normalized Distance = 1.00 Server FILE ALLOCATION I(FI ) W (LOAD-WEIGHT) W WMEAN (WMEAN= ) 1,4,5,6,7, HEAVY ,3,8, LIGHT EXTREMELY LIGHT EXTREMELY LIGHT EXTREMELY LIGHT EXTREMELY LIGHT ,15,16,18, HEAVY ,20 11,12,13, AVERAGE First Dimension: Normalized Distance = 0.86 STEP 3 STEP 4 SERVER FILE ALLOCATION I(FI ) LOAD-WEIGHT W WMEAN (WMEAN= ) 1,5,6, HEAVY , LIGHT , LIGHT , VERY LIGHT ,19, LIGHT , AVERAGE ,16, HEAVY , AVERAGE Second Dimension: Normalized Distance = 0.22 SERVER FILE ALLOCATION I(FI ) LOAD-WEIGHT W WMEAN (WMEAN= ) 5,6,9, AVERAGE , LIGHT ,7, LIGHT , VERY LIGHT ,15, AVERAGE , AVERAGE , HEAVY , AVERAGE Third Dimension: Normalized Distance = 0.20 Figure 3. Load balancing on a 3-cube Web cluster system