We study the reliability maximization problem in wavelength division multiplexing (WDM) networks with random link failures. Reliability in these networks is defined as the probability that the logical network is connected, and it is determined by the underlying lightpath routing, network topologies, and the link failure probability. By introducing the notion of lexicographical ordering for lightpath routings, we characterize precise optimization criteria for maximum reliability in the low failure probability regime. Based on the optimization criteria, we develop lightpath routing algorithms that maximize the reliability, and logical topology augmentation algorithms for further improving reliability. We also study the reliability maximization problem in the high failure probability regime.

We study the reliability maximization problem in WDM networks with random link failures. Reliability in these networks is defined as the probability that the logical network is connected, and it is determined by the underlying lightpath routing and the link failure probability. We show that in general the optimal lightpath routing depends on the link failure probability, and characterize the properties of lightpath routings that maximize the reliability in different failure probability regimes. In particular, we show that in the low failure probability regime, maximizing the ``cross-layer" min cut of the (layered) network maximizes reliability, whereas in the high failure probability regime, minimizing the spanning tree of the network maximizes reliability. Motivated by these results, we develop lightpath routing algorithms for reliability maximization.

We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multilayer setting. Using random sampling techniques, we develop polynomial-time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low-failure-probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability.

In layered networks, a single failure at a lower layer may cause multiple failures in the upper layers. As a result, traditional schemes that protect against single failures may not be effective in multilayer networks. In this paper, we introduce the problem of maximizing the connectivity of layered networks. We show that connectivity metrics in layered networks have significantly different meaning than their single-layer counterparts. Results that are fundamental to survivable single-layer network design, such as the Max-Flow Min-Cut Theorem, are no longer applicable to the layered setting. We propose new metrics to measure connectivity in layered networks and analyze their properties. We use one of the metrics, Min Cross Layer Cut, as the objective for the survivable lightpath routing problem and develop several algorithms to produce lightpath routings with high survivability. This allows the resulting cross-layer architecture to be resilient to failures between layers.

We consider network reliability in layered networks where the lower layer experiences random link failures. In layered networks, each failure at the lower layer may lead to multiple failures at the upper layer. We generalize the classical polynomial expression for network reliability to the multi-layer setting. Using random sampling techniques, we develop polynomial time approximation algorithms for the failure polynomial. Our approach gives an approximate expression for reliability as a function of the link failure probability, eliminating the need to resample for different values of the failure probability. Furthermore, it gives insight on how the routings of the logical topology on the physical topology impact network reliability. We show that maximizing the min cut of the (layered) network maximizes reliability in the low failure probability regime. Based on this observation, we develop algorithms for routing the logical topology to maximize reliability.

We develop diverse routing schemes for dealing with multiple, possibly correlated, failures. While disjoint path protection can effectively deal with isolated single link failures, recovering from multiple failures is not guaranteed. In particular, events such as natural disasters or intentional attacks can lead to multiple correlated failures, for which recovery mechanisms are not well understood. We take a probabilistic view of network failures where multiple failure events can occur simultaneously, and develop algorithms for finding diverse routes with minimum joint failure probability. Moreover, we develop a novel Probabilistic Shared Risk Link Group (PSRLG) framework for modeling correlated failures. In this context, we formulate the problem of finding two paths with minimum joint failure probability as an integer nonlinear program (INLP) and develop approximations and linear relaxations that can find nearly optimal solutions in most cases.

We study the benefit of reconfigurability for wavelength division multiplexed (WDM) ring networks with dynamic single-hubbed traffic. We show that the ability to reconfigure wavelength add-drop multiplexers helps to reduce the number of expensive line terminating equipment (LTEs) by a factor of W, where W is the number of wavelengths in the network. In addition, we show that for a general class of traffic, optical networks using reconfigurable wavelength add-drop multiplexers guarantee to be almost as bandwidth efficient as full wavelength add-drop networks, that is, opaque networks. For such traffic, we introduce several fast algorithms that achieve or approximate the optimal performance guarantees. The comparison between reconfigurable networks and opaque networks is quantified using a performance metric called capacity ratio, which captures the relative throughput performance of a reconfigurable network compared to the opaque network.