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This paper discusses the problem of finding multiple shortest disjoint paths in modern communication networks, which is essential for ultra-reliable and time-sensitive applications. Dijkstra’s algorithm has been a popular solution for the shortest path problem, but repetitive use of it to find multiple paths is not scalable. The Multiple Disjoint Path Algorithm (MDPAlg), published in 2021, proposes the use of a single full graph to construct multiple disjoint paths. This paper proposes modifications to the algorithm to include a delay constraint, which is important in time-sensitive applications. Different delay constraint least-cost routing algorithms are compared in a comprehensive manner to evaluate the benefits of the adapted MDPAlg algorithm. Fault tolerance, and thereby reliability, is ensured by generating multiple link-disjoint paths from source to destination.