# A new fuzzy-decision based load balancing system for distributed object computing \$

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8 Y.-K. Kwok, L.-S. Cheung / J. Parallel Distrib. Comput. 64 (2004) requests. After defining the above fuzzy variables, a set of inference rules is defined as shown in Table 1. By applying the fuzzy inference rules in Table 1, a decision can be generated based on both antecedents. That is, if RMIT is short and SL is low, then SR is high. Having these fuzzy inference rules and membership graphs, the fuzzification and defuzzification processes can be carried out as follows. First, the input values of RMIT and SL are mapped to their respective membership degree values on their membership graphs. These degree values are compared and the minimum of the two is then projected onto the membership function of their consequence graph. The output graph, usually in the shape of a trapezium [23], then represents the output of one inference rule. After the output graph is generated, defuzzification of the fuzzy output into a crisp or numeric value can be carried out. We used the centroid method [23] to defuzzify the output. The overall centroid of overlapping areas A i for i=1,2,y,n is given by: P N i¼1 %x i A i %x ¼ ; P N A i i¼1 Fig. 7. The membership graph for service rank (SR). Table 1 Fuzzy inference rules SL RMIT L M H S H MH ML M MH M L L M L VL where A i and %x i are the overlapped area and centroid from the triangles or trapeziums obtained in the ith rule, respectively. The centroid and area are calculated for each triangle or trapezium. This process is repeated for other inference rules where the inputs are applied to obtain an area composed of overlapped trapeziums. The defuzzification process generates a centroid value which represents the rank of a service. Fuzzy logic load balancing service can then route client requests to the best service based on the rank obtained. The overall operating sequence of the fuzzy logic controller can be represented by the fuzzy state pattern shown in Fig. 8. It has been noted that the herd effect [29] may occur if the load balancer immediately forwards all requests to a server that is assigned to the highest service rank. It will lead to a sudden degradation in the overall system performance. In order to minimize such effect, the fuzzy logic load balancing service schedules client requests to servers based on the following prioritized round-robin algorithm. Fig. 8. The state pattern.

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