An Approximate Solution Using Markov Approximation for a Load Balancing Problem in Communication Networks

With the recent surge in data traffic on information and communication networks, addressing the risk of congestion caused by network bottlenecks has become increasingly critical. Previous studies formulated the UELB problem, which aims to determine a flow configuration that minimizes the maximum link utilization in the network, in order to balance traffic load across communication links. Since this problem is NP-hard, approximation methods based on mathematical programming or heuristic approaches have been proposed. However, these methods do not account for changes in network topology over time and require re-solving the problem from scratch when such changes occur. In this study, we propose a Markov approximation-based method, which is known to be adaptable to dynamic environments, as an approximate approach to the UELB problem. We demonstrate its effectiveness and highlight its potential as an algorithm for flow control in dynamic network environments.