On Network Load Balancing

The problem of network load balancing is a practical issue that arises with the growing number of services supported by the network and the increase in network traffic.Network congestion can directly lead to abnormal operation of the entire link,resulting in unstable upper-layer services and severely damaging availability of the network and overall user experience.To solve this problem,many experts and scholars have proposed targeted algorithms for different application scenarios,including policy-based heuristic algorithms and model-based optimization algorithms.However,heuristic algorithms generally cannot guarantee a solution to congestion,while optimization algorithms often have higher complexity.Therefore,studying how to avoid network congestion through network load balancing has important theoretical significance and practical value.Network load balancing algorithms may cause massive changes in the routing paths of the same service after running,resulting in service jitter and increased network scheduling traffic.Therefore,we need a network load balancing model that minimizes the number of newly added paths to solve this problem.We establish a mathematical model for the problem of minimizing the number of newly added paths in network load balancing and analyze the services constraints and link bandwidths constraints that the model should satisfy,as well as how to construct an optimization objective function to achieve the goal of minimizing the number of newly added paths.To overcome the problem of exponential quantity of decision variables in the model,we greatly reduce the complexity of the algorithm through the column generation algorithm framework and parallelization technique.We prove that each column generation subproblem can be solved in polynomial time.Numerical experiment results show that our algorithm can be effectively applied to network load balancing in largescale networks.Furthermore,traditional model-based optimization algorithms for network load balancing typically aim to minimize network congestion,which makes the problem itself NP-hard and difficult to apply to largescale networks.Therefore,we propose a new network load balancing algorithm that can control congestion within a given congestion threshold,maintaining a relative balance between network congestion and overall performance.We establish a linear programming model based on the implicit constraints of the problem and introduce an artificial variable to ensure that the problem is always feasible,facilitating solving of the problem.Numerical experiment results show that compared with traditional algorithms,our algorithm can more effectively eliminate network congestion in both classical and random topologies.In conclusion,this thesis presents a network load balancing model that minimizes the number of newly added paths and a network load balancing algorithm of polynomial time complexity.These algorithms can effectively solve network congestion problems in practical applications and have broad prospects for application.