Fuzzy-Relation-Based Lexicographic Minimum Solution to the P2P Network System

Abstract

In the existing work in the literature, the addition-min fuzzy relation inequalities was applied to describe a peer-to-peer (P2P) network system. In such a model, the total download traffic of a terminal was considered. However, it is more reasonable to consider the largest download traffic in some cases. It is found that max-min fuzzy relation inequalities are more suitable for the P2P network system in such cases. The objective of this work is to reduce the network congestion under some fixed priority grade of the terminals. The concept of a lexicographic minimum solution was first introduced to the max-min fuzzy relation inequalities system to achieve such an objective. Detailed and effective algorithms are proposed for solving the lexicographic minimum solution. Moreover, the validity of our proposed algorithm is formally proved in theory and is demonstrated by some experimental examples.

Upper Bounded Minimal Solution of the Max-Min Fuzzy Relation Inequality System

“…As a consequence, the maximum solution of system (81) is x = (44,50,46,47,50,44). Therefore, we have (44,42,40,35,34,39). That is, the quality levels of T 1 , T 2 , • • • , T 6 are 35Mbps, 42Mbps, 40Mbps, 0Mbps, 0Mbps, 39Mbps, respectively.…”

“…The max-min fuzzy relation inequalities were recently applied to the P2P educational information resource sharing system [38]- [40] (see Fig. 1).…”

“…To decrease network congestion, a minimal solution is usually required. Considering the fixed priority grade of all terminals in a P2P network system, Y. Ma et al [40] studied the lexicographic minimum solution to the corresponding maxmin FRIs. The authors proposed a detailed round-robin algorithm for computing the lexicographic minimum solution.…”