Drop cost and wavelength optimal two-period grooming with ratio 4

We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time, there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and C=4 and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case

Bi-criteria network optimization: problems and algorithms

Several approaches, exact and heuristics, have been designed in order to generate the Pareto frontier for multi-objective combinatorial optimization problems. Although several classes of standard optimization models have been studied in their multi- objective version, there still exists a big gap between the solution techniques and the complexity of the mathematical models that derive from the most recent real world applications. In this thesis such aspect is highlighted with reference to a specific application field, the telecommunication sector, where several emerging optimization problems are characterized by a multi-objective nature. The study of some of these problems, analyzed and solved in the thesis, has been the starting point for an assessment of the state of the art in multicriteria optimization with particular focus on multi-objective integer linear programming. A general two-phase approach for bi-criteria integer network flow problems has been proposed and applied to the bi-objective integer minimum cost flow and the bi-objective minimum spanning tree problem. For both of them the two-phase approach has been designed and tested to generate a complete set of efficient solutions. This procedure, with appropriate changes according to the specific problem, could be applied on other bi-objective integer network flow problems. In this perspective, this work can be seen as a first attempt in the direction of closing the gap between the complex models associated with the most recent real world applications and the methodologies to deal with multi-objective programming. The thesis is structured in the following way: Chapter 1 reports some preliminary concepts on graph and networks and a short overview of the main network flow problems; in Chapter 2 some emerging optimization problems are described, mathematically formalized and solved, underling their multi-objective nature. Chapter 3 presents the state of the art on multicriteria optimization. Chapter 4 describes the general idea of the solution algorithm proposed in this work for bi-objective integer network flow problems. Chapter 5 is focused on the bi-objective integer minimum cost flow problem and on the adaptation of the procedure proposed in Chapter 4 on such a problem. Analogously, Chapter 6 describes the application of the same approach on the bi-objective minimum spanning tree problem. Summing up, the general scheme appears to adapt very well to both problems and can be easily implemented. For the bi-objective integer minimum cost flow problem, the numerical tests performed on a selection of test instances, taken from the literature, permit to verify that the algorithm finds a complete set of efficient solutions. For the bi-objective minimum spanning tree problem, we solved a numerical example using two alternative methods for the first phase, confirming the practicability of the approach

Efficient Spectrum Utilization in Large-Scale RWA and RSA Problems

While the Routing and Wavelength Assignment (RWA) problem has been widely studied, very few studies attempt to solve realistic size instances, namely, with 100 wavelengths per fiber and a few hundred nodes. Indeed, state of the art is closer to around 20 nodes and 30 wavelengths. In this study, we are interested in reducing the gap between realistic data sets and testbed instances, using exact methods. We propose different algorithms that lead to solve exactly or near exactly much larger instances than in the literature, with up to 150 wavelengths and 90 nodes. Extensive numerical experiences are conducted on both the static and the dynamic cases. For the latter, we investigate how much bandwidth is wasted when no lightpath re-arrangement is allowed, and compare it with the number of lightpath re-arrangement it requires in order to fully maximize the grade of service. Results show that the amount of lightpath re-arrangement remains very small in comparison to the amount of wasted bandwidth if not done. The Routing and Spectrum Assignment (RSA) problem is a much more difficult problem than RWA, considered in elastic optical networks. Although investigated extensively, there is still a gap between the size of the instances that can be solved using the current heuristic or exact algorithms, and the size of the instances arising in the industry. As the second objective of this study, we aim to reduce the gap between the two, using a new mathematical modeling, and compare its performance with the best previous algorithms/models on realistic data instances

Data-driven methods for personalized product recommendation systems

Thesis: Ph. D., Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2018.Cataloged from PDF version of thesis.Includes bibliographical references.The online market has expanded tremendously over the past two decades across all industries ranging from retail to travel. This trend has resulted in the growing availability of information regarding consumer preferences and purchase behavior, sparking the development of increasingly more sophisticated product recommendation systems. Thus, a competitive edge in this rapidly growing sector could be worth up to millions of dollars in revenue for an online seller. Motivated by this increasingly prevalent problem, we propose an innovative model that selects, prices and recommends a personalized bundle of products to an online consumer. This model captures the trade-off between myopic profit maximization and inventory management, while selecting relevant products from consumer preferences. We develop two classes of approximation algorithms that run efficiently in real-time and provide analytical guarantees on their performance. We present practical applications through two case studies using: (i) point-of-sale transaction data from a large U.S. e-tailer, and, (ii) ticket transaction data from a premier global airline. The results demonstrate that our approaches result in significant improvements on the order of 3-7% lifts in expected revenue over current industry practices. We then extend this model to the setting in which consumer demand is subject to uncertainty. We address this challenge using dynamic learning and then improve upon it with robust optimization. We first frame our learning model as a contextual nonlinear multi-armed bandit problem and develop an approximation algorithm to solve it in real-time. We provide analytical guarantees on the asymptotic behavior of this algorithm's regret, showing that with high probability it is on the order of O([square root of] T). Our computational studies demonstrate this algorithm's tractability across various numbers of products, consumer features, and demand functions, and illustrate how it significantly out performs benchmark strategies. Given that demand estimates inherently contain error, we next consider a robust optimization approach under row-wise demand uncertainty. We define the robust counterparts under both polynomial and ellipsoidal uncertainty sets. Computational analysis shows that robust optimization is critical in highly constrained inventory settings, however the price of robustness drastically grows as a result of pricing strategies if the level of conservatism is too high.by Anna Papush.Ph. D

Disaster Resilient Optical Core Networks

During the past few years, the number of catastrophic disasters has increased and its impact sometimes incapacitates the infrastructures within a region. The communication network infrastructure is one of the affected systems during these events. Thus, building a resilient network backbone is essential due to the big role of networks during disaster recovery operations. In this thesis, the research efforts in building a disaster-resilient network are reviewed and open issues related to building disaster-resilient networks are discussed. Large size disasters not necessarily impact the communication networks, but instead it can stimulate events that cause network performance degradation. In this regard, two open challenges that arise after disasters are considered one is the short-term capacity exhaustion and the second is the power outage. First, the post-disaster traffic floods phenomena is considered. The impact of the traffic floods on the optical core network performance is studied. Five mitigation approaches are proposed to serve these floods and minimise the incurred blocking. The proposed approaches explore different technologies such as excess or overprovisioned capacity exploitation, traffic filtering, protection paths rerouting, rerouting all traffic and finally using the degrees of freedom offered by differentiated services. The mitigation approaches succeeded in reducing the disaster induced traffic blocking. Second, advance reservation provisioning in an energy-efficient approach is developed. Four scenarios are considered to minimise power consumption. The scenarios exploit the flexibility provided by the sliding-window advance reservation requests. This flexibility is studied through scheduling and rescheduling scenarios. The proposed scenarios succeeded in minimising the consumed power. Third, the sliding-window flexibility is exploited for the objective of minimising network blocking during post-disaster traffic floods. The scheduling and rescheduling scenarios are extended to overcome the capacity exhaustion and improve the network blocking. The proposed schemes minimised the incurred blocking during traffic floods by exploiting sliding window. Fourth, building blackout resilient networks is proposed. The network performance during power outages is evaluated. A remedy approach is suggested for maximising network lifetime during blackouts. The approach attempts to reduce the required backup power supply while minimising network outages due to limited energy production. The results show that the mitigation approach succeeds in keeping the network alive during a blackout while minimising the required backup power

A hierarchy of languages, logics, and mathematical theories

We present mathematics from a foundational perspective as a hierarchy in which each tier consists of a language, a logic, and a mathematical theory. Each tier in the hierarchy subsumes all preceding tiers in the sense that its language, logic, and mathematical theory generalize all preceding languages, logics, and mathematical theories. Starting from the root tier, the mathematical theories in this hierarchy are: combinatory logic restricted to the identity I, combinatory logic, ZFC set theory, constructive type theory, and category theory. The languages of the first four tiers correspond to the languages of the Chomsky hierarchy: in combinatory logic Ix = x gives rise to a regular language; the language generated by S, K in combinatory logic is context-free; first-order logic is context-sensitive; and the typed lambda calculus of type theory is recursively enumerable. The logic of each tier can be characterized in terms of the cardinality of the set of its truth values: combinatory logic restricted to I has 0 truth values, while combinatory logic has 1, first-order logic 2, constructive type theory 3, and categeory theory omega_0. We conjecture that the cardinality of objects whose existence can be established in each tier is bounded; for example, combinatory logic is bounded in this sense by omega_0 and ZFC set theory by the least inaccessible cardinal. We also show that classical recursion theory presents a framework for generating the above hierarchy in terms of the initial functions zero, projection, and successor followed by composition and m-recursion, starting with the zero function I in combinatory logic This paper begins with a theory of glossogenesis, i.e. a theory of the origin of language, since this theory shows that natural language has deep connections to category theory and since it was through these connections that the last tier and ultimately the whole hierarchy were discovered. The discussion covers implications of the hierarchy for mathematics, physics, cosmology, theology, linguistics, extraterrestrial communication, and artificial intelligence

Efficient and robust routing of highly variable traffic

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, February 2006.Includes bibliographical references (p. 316-324).Many emerging applications for the Internet are characterized by highly variable traffic behavior over time that is difficult to predict. Classical approaches to network design rely on a model in which a single traffic matrix is estimated. When actual traffic does not conform to such assumptions, desired bandwidth guarantees cannot be provided to the carried traffic. Currently, Internet Service Providers (ISPs) use gross capacity over-provisioning and manual routing adaptation to avoid network congestion caused by unpredictable traffic. These lead to increased network equipment and operational costs. Development of routing infrastructures that optimize network resources while accommodating extreme traffic unpredictability in a robust and efficient manner will be one of the defining themes in the next phase of expansion of the Internet. This thesis proposes two-phase routing as a capacity efficient and robust strategy for handling highly variable traffic. The scheme allows preconfiguration of the network such that all traffic patterns permissible within the network's natural ingress-egress capacity constraints can be routed with bandwidth guarantees without requiring detection of traffic changes in real-time or reconfiguring the network in response to it.(cont.) The scheme routes traffic in two phases -- traffic entering the network is sent from the source to a set of intermediate nodes in predetermined split ratios that depend on the intermediate nodes, and then from the intermediate nodes to the final destination. The scheme has the desirable properties of supporting static optical layer provisioning in IP-over-Optical networks and indirection in specialized service overlay models unlike previous approaches -- like direct source-destination path routing - for handling variable traffic. This thesis represents the first comprehensive study, problem formulation, and algorithm design for many aspects of two-phase routing. Our contributions can be grouped into three broad parts. First, we consider the problems of minimum cost network design and maximum throughput network routing for the scheme. We give a simple solution for minimum cost network design. For maximum throughput network routing. we design linear program.ling based and combinatorial algorithms. We show how the algorithms can handle a total cost constraint for maximum throughput two-phase routing. This can be used to solve the link capacitate version of minimum cost two-phase routing.(cont.) We establish theoretical bounds on the resource requirements of two-phase routing under throughput and cost models with respect to the optimal scheme that is allowed to make the routing dynamically dependent on the current traffic matrix. We also generalize the traffic split ratios to depend not only on the intermediate nodes but also on source and destination of traffic and solve the corresponding optimization problems. Second, we consider making two-phase routing resilient to network failures. Two-phase routing in IP-over-Optical networks can be protected against router node failures through redistribution of traffic split ratio for the failed router node to other intermediate nodes. We propose two different schemes for provisioning the optical layer to handle router node failures. We develop linear programming formulations for both schemes and a fast combinatorial algorithm for the second scheme so as to maximize network throughput. Two-phase routing can be made resilient against link failures by protecting the first and second phase paths using pre-provisioned restoration mechanisms. We consider three such restoration mechanisms - local (link/span) restoration, K-route path restoration, and shared backup path restoration.(cont.) We provide linear programming formulations and combinatorial algorithms for maximum throughput two-phase routing with local restoration and K-route path restoration. We show that the problem of maximum throughput two-phase routing with shared backup path restoration is JVP-hard. Assuming an approximation oracle for a certain disjoint paths problem (which we also show to be AP-hard), we design a combinatorial algorithm with provable guarantees. Third, we consider the application of two-phase routing to multi-hop Wireless Mesh Networks (WMNs). These networks have recently been of much research interest due to their lowered need for wired infrastructure support and due to envisaged new applications like community wireless networks. We extend our optimization framework for maximum throughput two-phase routing in wired networks to handle routing and scheduling constraints that are peculiar to WMNs and arise from the requirement to handle radio transmit/receive diversity and the phenomenon of wireless link interference. We evaluate various aspects of two-phase routing on actual ISP topologies using the developed algorithms. For the WMN application, we use randomly generated WMN topologies for the evaluations.by Sudipta Sengupta.Ph.D

Understanding Behavioral and Physiological Outcomes of Variation in Maternal Care and Glucocorticoids

Behavior is one of the most immediate and effective ways to respond to and cope with environmental and social stressors. Our behavioral response to stressors is proposed to be intimately linked to our hormonal stress response in a bidirectional relationship. Understanding the relationship between these two stress responses in adults and their ontogeny in juveniles helps us understand how animals will respond to rapidly changing environmental pressures and provide more context for understanding the role of individual variation in behavior in natural selection. To investigate this question, I collected hormonal and behavioral data from a wild population of North American red squirrels (Tamiasciurus hudsonicus) in Yukon Territory, Canada. Red squirrels in this region have proven to be amenable to large scale experimental hormone manipulations and offspring growth, hormones, and behavior can be tracked for the entire life of hundreds of individuals each year. Using long-term data on behavior and fecal cortisol, I found no relationship between the hormonal and behavioral stress response as was measured. To better understand the ontogeny of this lack of relationship between the stress responses, I examined the role of the maternal early life environment. Maternal behavior and physiology influence the development of phenotypes, many of which are closely related to fitness. However, maternal behavior is often difficult to observe and measure in wild animals, particularly small mammals. To tackle this problem, I measured maternal motivation by recording the time until mothers return to their pups following researchers removing and returning the pups in the nest, or a “simulated predator intrusion”. I found wide variation in the behavioral response of mothers to this nest intrusion. Some mothers were very vocal and aggressively attempt to protect their pups, other moms hung out in a nearby tree and eat quietly waited for us to return their pups. I found a mother’s maternal style, as measured by latency to return to pups following the intrusion, was repeatable within individuals and played a role in increasing the survival and growth rate of offspring. To further explore the impact of the maternal environment on offspring, I tested hypotheses about the impact of maternal glucocorticoid levels on offspring behavior and physiology by conducting a manipulation with mothers across three years to experimentally elevate circulating glucocorticoids in pregnant or lactating mothers. In offspring from these mothers, I found the behavioral traits of activity and aggression in these juveniles were linked to their hormonal stress reactivity, unlike the adults. Through these studies, I expanded on our understanding of the relationship between behavior and physiology, with a particular focus on maternal effects, in a wild small mammal. I added to the growing body of evidence showing a lack of relationship between behavioral and physiological stress responses in wild animals, suggesting the need to develop a more generalizable model of the relationship between the glucocorticoids and animal personality. Furthermore, I leveraged our ability to closely track reproduction in red squirrels to empirically assess the fitness consequences of individual variation in maternal behavior and conduct a unique field experiment to branch across developmental biology, behavioral ecology, and behavioral endocrinology.PHDPsychologyUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155083/1/westse_1.pd