Kayi Lee

Diverse routing in networks with probabilistic failures

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.

Reliability in layered networks with random link failures

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.

Reliability in Layered Networks with Random Link Failures

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.

Cross-Layer Survivability in WDM Networks with Multiple Failures

We study the survivable lightpath routing problem in the context of multiple failures. We define network metrics to quantify the resilience of lightpath routings, and propose lightpath routing algorithms to maximize network survivability.

Cross-Layer Survivability

The layered architecture of modern communication networks takes advantage of the flexibility of upper layer technology, such as IP, and the high data rates of lower layer technology, such as WDM. In particular, the WDM technology available today can support up to several terabits per second over a single fiber [9], making networks vulnerable to failures, because a failure for even a short period of time can result in a huge loss of data. The main theme of network survivability is to prevent such data loss by provisioning spare resources for recovery. In this chapter, we focus on the impact of layering on network survivability.

Maximizing Reliability in WDM Networks through Lightpath Routing

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.

Reconfigurability of single-hub WDM ring networks

We study the benefit of reconfigurability for single-hub WDM ring networks with dynamic single-hubbed traffic. We show that using reconfigurable wavelength add-drop multiplexers (R- WADMs) in place of non-reconfigurable ones can reduce the number of expensive line terminating equipments (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 R-WADMs 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.