[Paper Review] Robust Routing in Interdependent Networks

Jianan Zhang, Eytan Modiano|arXiv (Cornell University)|Sep 10, 2017

Complex Network Analysis Techniques27 references3 citations

TL;DR

This paper proposes a robust routing framework for interdependent networks where demand nodes rely on supply nodes, failing only if all their supply nodes fail. It introduces novel metrics for path reliability and d-failure resilience, enabling computation of the most reliable single and paired paths under probabilistic supply node failures, generalizing classical shared risk group models by accounting for multiple dependencies and correlated failures.

ABSTRACT

We consider a model of two interdependent networks, where every node in one network depends on one or more supply nodes in the other network and a node fails if it loses all of its supply nodes. We develop algorithms to compute the failure probability of a path, and obtain the most reliable path between a pair of nodes in a network, under the condition that each supply node fails independently with a given probability. Our work generalizes the classical shared risk group model, by considering multiple risks associated with a node and letting a node fail if all the risks occur. Moreover, we study the diverse routing problem by considering two paths between a pair of nodes. We define two paths to be $d$-failure resilient if at least one path survives after removing $d$ or fewer supply nodes, which generalizes the concept of disjoint paths in a single network, and risk-disjoint paths in a classical shared risk group model. We compute the probability that both paths fail, and develop algorithms to compute the most reliable pair of paths.

Motivation & Objective

• Address the challenge of reliable routing in interdependent networks where demand nodes depend on supply nodes and fail only if all their supply nodes fail.
• Overcome limitations of classical shared risk group models by modeling multiple risks per node and allowing partial failure dependence.
• Develop algorithms to compute the most reliable single path between source-destination pairs under probabilistic supply node failures.
• Introduce and analyze d-failure resilience for diverse routing, ensuring at least one of two paths survives after removal of d or fewer supply nodes.
• Generalize reliability metrics beyond shared risk counts to account for multiplicity of supply nodes and correlated failure patterns.

Proposed method

• Model interdependent networks as two graphs: a demand network and a supply network, where each demand node depends on one or more supply nodes.
• Define failure probability of a path as the probability that all its demand nodes survive, computed via product of individual node survival probabilities.
• Introduce the concept of d-failure resilience: two paths are d-failure resilient if at least one survives after removal of d or fewer supply nodes.
• Use a generalized risk model where a node fails only if all its associated risks (supply nodes) fail, allowing multiple risks per node.
• Derive bounds on failure probabilities using concave function analysis and inequalities involving failure probabilities and their transformations.
• Apply iterative bounding techniques to relate the failure probability of a demand node to the failure probabilities of its supply nodes, using inequalities like (30) to establish reliability bounds.

Experimental results

Research questions

• RQ1 How can the reliability of a path be computed in interdependent networks where demand nodes fail only when all their supply nodes fail?
• RQ2 What is the most reliable single path between a source and destination under probabilistic supply node failures?
• RQ3 How can two paths be designed to be resilient against the failure of up to d supply nodes, generalizing disjoint path concepts?
• RQ4 In what way does the proposed model generalize the classical shared risk group model when multiple supply nodes are involved?
• RQ5 What metrics and algorithms can effectively capture the reliability of diverse routing paths beyond simple risk-disjointness?

Key findings

• The failure probability of a path is determined by the joint survival probability of all its demand nodes, which depends on the product of individual survival probabilities of their supply nodes.
• The most reliable path is not necessarily the one with the fewest supply nodes, as paths with multiple supply nodes per demand node can be more resilient to failures.
• A path with a single supply node is highly vulnerable, as failure of that single node disconnects the entire path, even though it has only one risk.
• The d-failure resilience model generalizes disjoint paths by ensuring that at least one of two paths survives after removal of d or fewer supply nodes, even if the paths share many supply nodes.
• The paper proves that the failure probability of a demand node is bounded by a function of the failure probabilities of its supply nodes, using inequalities that account for multiplicative dependencies.
• The reliability of a path can be bounded using concave function analysis, showing that the ratio of failure probability to failure rate decreases with increasing supply node redundancy, implying improved resilience.