# A Load-Balancing Algorithm for Cluster-based Multi-core Web Servers

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5 G. You et al. /Journal of Computatonal Informaton Systems 7:13 (2011) STGs that are allocated to core. If we defne the number of STGs on core as B, then we can enumerate all the STGs on core : STG, STG,..., STG,..., STG, 1 k B. A A A A 1 2 k B STG A k s the Servce Thread Group that serves request queue A k. If the number of threads on core s X, then X could be calculated by the followng formula: X B = λa k (3) k= 1 So we can get the number of threads on every core: X, X,..., X. We defne D( X ) as the 1 2 N varance of X, X,..., X. If D( X ) s large, t means that the numbers of threads on dfferent cores 1 2 N dffer greatly. So as to keep load balance between cores, the lower value of D( X ) s favorable. Therefore, we defne the ftness functon n the Genetc Algorthm as followng 1 f() e = DX ( ) + 1 (4) where e s a chromosome. Because the lower value of D( X ) s helpful to keep load balance between cores, and sometmes D( X ) mght be zero. So we use the recprocal of D( X ) + 1 as ftness functon. So the larger value of f ( e ) means better load balance between cores. Genetc Algorthm has the followng procedure: (1) Intal Populaton: a populaton s a collecton of chromosomes. The populaton sze L can be determned expermentally. The ntal populaton s usually generated randomly. We can generate L chromosomes by assgnng a random nteger, whch ranges from 0 to N 1, to every gene n chromosome. (2) Calculaton of the Ftness Value: we can use the ftness functon formula (4) and above method to calculate the ftness value of every chromosome n the populaton. (3) Selecton: we select the ftter chromosomes by the roulette wheel method. The greater the ftness values of a chromosome, the larger the probablty to be chosen. We repeat the selecton operaton as many tmes as the number of chromosomes. (4) Crossover: For the randomly selected couple of chromosomes, we decde whether to perform crossover or not based on crossover probablty. If the crossover s allowed, t wll generate a new couple of chromosomes by exchangng portons of the two old chromosomes. (5) Mutaton: we randomly choose a chromosome from the populaton. For a gene of the chromosome, we allow a random change wth very small probablty. If t happens, the gene wll be assgned to random nteger, whch ranges from 0 to N 1 and s dfferent from the orgn value of the gene. (6) Termnaton Condton: n Genetc Algorthm, the generatonal processes (2), (3), (4), and (5) are repeated. The chromosome wth the largest ftness value wll be recorded at each teraton. If the largest ftness value doesn t change for fve tmes, we thnk the teratons should be ended. Fnally, we gan the recorded chromosome wth the largest ftness value. From the chromosome, we can

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