This paper presents five approaches to solve the problem of finding the optimal backup resource assignment which maximizes the survival probability of network functions of middleboxes. In the previous work, no mathematical model to solve this problem is provided, so we formulate the problem as a mixed-integer linear programming (MILP) problem as the first approach. Formulating this MILP problem includes some special steps, which are not considered in the previous work. The MILP problem is not always solved in a practical time when the problem size becomes large. Then, we develop two heuristic approaches by replacing the objective of the original MILP problem relying on the idea of balancing the failure probabilities of functions of connected components. We develop two heuristic approaches by extending the way of assigning functions and servers from the conventional heuristic algorithm. Numerical results show that our four developed heuristic approaches improve the survival probability from the conventional heuristic algorithm in some cases and reduce computation time compared to obtaining the optimal solution. Furthermore, one of our developed heuristic approaches provides exactly the optimal solution with shorter computation time compared to the time solving the original MILP problem in a special case.

本文提出了五种方法来解决寻找最佳备份资源分配问题的方法，该方法可以最大化中间盒网络功能的生存概率。在先前的工作中，没有提供解决该问题的数学模型，因此我们将问题表述为混合整数线性规划（MILP）问题作为第一种方法。阐述此MILP问题包括一些特殊步骤，以前的工作中没有考虑这些步骤。当问题规模变大时，MILP问题并不总是在实际时间内解决。然后，我们通过平衡已连接组件功能的故障概率的思想，通过替换原始MILP问题的目标，开发了两种启发式方法。通过扩展传统启发式算法中分配功能和服务器的方式，我们开发了两种启发式方法。数值结果表明，在某些情况下，我们开发的四种启发式方法比传统的启发式算法提高了生存率，并且与获得最佳解相比，减少了计算时间。此外，与在特殊情况下解决原始MILP问题的时间相比，我们开发的启发式方法之一提供了具有较短计算时间的精确解决方案。