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Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (pages 77-81)., Our goal is to understand the functioning of the interbank lending market in times of market stress. Working towards this goal, we conduct theoretical analysis and simulation to study the effects of network structure and shock scenarios on systemic risk in the market. We consider shocks of various sizes at both global and local scales. In terms of risk measures, we study relative systemic loss and the default rate, separating the latter quantity into fundamental default and contagion. Our simulations suggest that all systemic risk measures are similar on the well-studied directed Erdős-Rényi model and the more complex fitness model if we match the mean density and the mean edge weight of these two models. We show through both derivations and simulations that the network size has little effect on systemic risk when the network is sufficiently large. Moreover, as the mean degree grows, the different default rates considered all increase, while relative systemic loss decreases. Furthermore, simulations suggest that local shocks tend to cause more harm than global shocks of the same total size. We also derive upper and lower bounds on a bank's probability of default, only using its neighbors' information. For implementation, we build a method for real-time, automatic, interpretable assessment of financial systemic risk, which only requires temporal snapshots of observable data. Our algorithm takes in partial data, inferring a random graph model, and then generates empirical distributions for risk measures. The first part relies on inferring a fitness model that is compatible with observed information. For the second part, we use simulations to obtain empirical distributions for systemic risk that arises from interbank clearing. We test our method on synthetic data and apply it to the federal funds market using empirical data. Our method is fast enough to be incorporated into algorithms that produce intraday time trajectories of risk prediction. The data requirement is p, by Xianglin Meng., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (pages 77-81)., Our goal is to understand the functioning of the interbank lending market in times of market stress. Working towards this goal, we conduct theoretical analysis and simulation to study the effects of network structure and shock scenarios on systemic risk in the market. We consider shocks of various sizes at both global and local scales. In terms of risk measures, we study relative systemic loss and the default rate, separating the latter quantity into fundamental default and contagion. Our simulations suggest that all systemic risk measures are similar on the well-studied directed Erdős-Rényi model and the more complex fitness model if we match the mean density and the mean edge weight of these two models. We show through both derivations and simulations that the network size has little effect on systemic risk when the network is sufficiently large. Moreover, as the mean degree grows, the different default rates considered all increase, while relative systemic loss decreases. Furthermore, simulations suggest that local shocks tend to cause more harm than global shocks of the same total size. We also derive upper and lower bounds on a bank's probability of default, only using its neighbors' information. For implementation, we build a method for real-time, automatic, interpretable assessment of financial systemic risk, which only requires temporal snapshots of observable data. Our algorithm takes in partial data, inferring a random graph model, and then generates empirical distributions for risk measures. The first part relies on inferring a fitness model that is compatible with observed information. For the second part, we use simulations to obtain empirical distributions for systemic risk that arises from interbank clearing. We test our method on synthetic data and apply it to the federal funds market using empirical data. Our method is fast enough to be incorporated into algorithms that produce intraday time trajectories of risk prediction. The data requirement is p, by Xianglin Meng., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017., Cataloged from PDF version of thesis., Includes bibliographical references (pages 107-108)., We propose and analyze two models to study an intrinsic trade-off between privacy and query complexity in online settings: 1. Our first private optimization model involves an agent aiming to minimize an objective function expressed as a weighted sum of finitely many convex cost functions, where the weights capture the importance the agent assigns to each cost function. The agent possesses as her private information the weights, but does not know the cost functions, and must obtain information on them by sequentially querying an external data provider. The objective of the agent is to obtain an accurate estimate of the optimal solution, x*, while simultaneously ensuring privacy, by making x* difficult to infer for the data provider, who does not know the agent's private weights but only observes the agent's queries. 2. The second private search model we study is also about protecting privacy while searching for an object. It involves an agent attempting to determine a scalar true value, x*, based on querying an external database, whose response indicates whether the true value is larger than or less than the agent's submitted queries. The objective of the agent is again to obtain an accurate estimate of the true value, x*, while simultaneously hiding it from an adversary who observes the submitted queries but not the responses. The main results of this thesis provide tight upper and lower bounds on the agent's query complexity (i.e., number of queries) as a function of desired levels of accuracy and privacy, for both models. We also explicitly construct query strategies whose worst-case query complexity is optimal up to an additive constant., by Zhi Xu., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017., Cataloged from PDF version of thesis., Includes bibliographical references (pages 107-108)., We propose and analyze two models to study an intrinsic trade-off between privacy and query complexity in online settings: 1. Our first private optimization model involves an agent aiming to minimize an objective function expressed as a weighted sum of finitely many convex cost functions, where the weights capture the importance the agent assigns to each cost function. The agent possesses as her private information the weights, but does not know the cost functions, and must obtain information on them by sequentially querying an external data provider. The objective of the agent is to obtain an accurate estimate of the optimal solution, x*, while simultaneously ensuring privacy, by making x* difficult to infer for the data provider, who does not know the agent's private weights but only observes the agent's queries. 2. The second private search model we study is also about protecting privacy while searching for an object. It involves an agent attempting to determine a scalar true value, x*, based on querying an external database, whose response indicates whether the true value is larger than or less than the agent's submitted queries. The objective of the agent is again to obtain an accurate estimate of the true value, x*, while simultaneously hiding it from an adversary who observes the submitted queries but not the responses. The main results of this thesis provide tight upper and lower bounds on the agent's query complexity (i.e., number of queries) as a function of desired levels of accuracy and privacy, for both models. We also explicitly construct query strategies whose worst-case query complexity is optimal up to an additive constant., by Zhi Xu., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016., Cataloged from PDF version of thesis., Includes bibliographical references (pages 131-132)., The problem of maximizing the spread of an opinion inside a social network has been investigated extensively during the past decade. The importance of this problem in applications such as marketing has been amplified by the major expansion of online social networks. In this thesis, we study opinion control policies, first under a broad class of deterministic dynamics governing the interactions inside a network, and then under the classical "Voter Model". In the former case, we design a policy that a controller can follow in order to spread an opinion inside a network with the smallest possible cost. In the latter case, we consider networks whose underlying graph is the d-dimensional integer torus Zd/n, and we design policies that minimize the expected time until the network reaches a consensus. We also show that, in dimension d >/= 2, dynamic policies do not perform significantly better than static policies, while, in dimension d = 1, optimal dynamic policies perform much better than optimal static policies.., by Zied Ben Chaouch., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017., Cataloged from PDF version of thesis., Includes bibliographical references (pages 107-108)., We propose and analyze two models to study an intrinsic trade-off between privacy and query complexity in online settings: 1. Our first private optimization model involves an agent aiming to minimize an objective function expressed as a weighted sum of finitely many convex cost functions, where the weights capture the importance the agent assigns to each cost function. The agent possesses as her private information the weights, but does not know the cost functions, and must obtain information on them by sequentially querying an external data provider. The objective of the agent is to obtain an accurate estimate of the optimal solution, x*, while simultaneously ensuring privacy, by making x* difficult to infer for the data provider, who does not know the agent's private weights but only observes the agent's queries. 2. The second private search model we study is also about protecting privacy while searching for an object. It involves an agent attempting to determine a scalar true value, x*, based on querying an external database, whose response indicates whether the true value is larger than or less than the agent's submitted queries. The objective of the agent is again to obtain an accurate estimate of the true value, x*, while simultaneously hiding it from an adversary who observes the submitted queries but not the responses. The main results of this thesis provide tight upper and lower bounds on the agent's query complexity (i.e., number of queries) as a function of desired levels of accuracy and privacy, for both models. We also explicitly construct query strategies whose worst-case query complexity is optimal up to an additive constant., by Zhi Xu., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016., Cataloged from PDF version of thesis., Includes bibliographical references (pages 131-132)., The problem of maximizing the spread of an opinion inside a social network has been investigated extensively during the past decade. The importance of this problem in applications such as marketing has been amplified by the major expansion of online social networks. In this thesis, we study opinion control policies, first under a broad class of deterministic dynamics governing the interactions inside a network, and then under the classical "Voter Model". In the former case, we design a policy that a controller can follow in order to spread an opinion inside a network with the smallest possible cost. In the latter case, we consider networks whose underlying graph is the d-dimensional integer torus Zd/n, and we design policies that minimize the expected time until the network reaches a consensus. We also show that, in dimension d >/= 2, dynamic policies do not perform significantly better than static policies, while, in dimension d = 1, optimal dynamic policies perform much better than optimal static policies.., by Zied Ben Chaouch., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2017., Cataloged from PDF version of thesis., Includes bibliographical references (pages 107-108)., We propose and analyze two models to study an intrinsic trade-off between privacy and query complexity in online settings: 1. Our first private optimization model involves an agent aiming to minimize an objective function expressed as a weighted sum of finitely many convex cost functions, where the weights capture the importance the agent assigns to each cost function. The agent possesses as her private information the weights, but does not know the cost functions, and must obtain information on them by sequentially querying an external data provider. The objective of the agent is to obtain an accurate estimate of the optimal solution, x*, while simultaneously ensuring privacy, by making x* difficult to infer for the data provider, who does not know the agent's private weights but only observes the agent's queries. 2. The second private search model we study is also about protecting privacy while searching for an object. It involves an agent attempting to determine a scalar true value, x*, based on querying an external database, whose response indicates whether the true value is larger than or less than the agent's submitted queries. The objective of the agent is again to obtain an accurate estimate of the true value, x*, while simultaneously hiding it from an adversary who observes the submitted queries but not the responses. The main results of this thesis provide tight upper and lower bounds on the agent's query complexity (i.e., number of queries) as a function of desired levels of accuracy and privacy, for both models. We also explicitly construct query strategies whose worst-case query complexity is optimal up to an additive constant., by Zhi Xu., S.M.

Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016., Cataloged from PDF version of thesis., Includes bibliographical references (pages 131-132)., The problem of maximizing the spread of an opinion inside a social network has been investigated extensively during the past decade. The importance of this problem in applications such as marketing has been amplified by the major expansion of online social networks. In this thesis, we study opinion control policies, first under a broad class of deterministic dynamics governing the interactions inside a network, and then under the classical "Voter Model". In the former case, we design a policy that a controller can follow in order to spread an opinion inside a network with the smallest possible cost. In the latter case, we consider networks whose underlying graph is the d-dimensional integer torus Zd/n, and we design policies that minimize the expected time until the network reaches a consensus. We also show that, in dimension d >/= 2, dynamic policies do not perform significantly better than static policies, while, in dimension d = 1, optimal dynamic policies perform much better than optimal static policies.., by Zied Ben Chaouch., S.M.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016., Cataloged from PDF version of thesis., Includes bibliographical references (pages 137-141)., We consider the propagation of a contagion process ("epidemic") on a network and study the problem of dynamically allocating a fixed curing budget to the nodes of the graph, at each time instant. We provide a dynamic policy for the rapid containment of a contagion process modeled as an SIS epidemic on a bounded degree undirected graph with n nodes. We show that if the budget r of curing resources available at each time is Q(W), where W is the CutWidth of the graph, and also of order [omega](log n), then the expected time until the extinction of the epidemic is of order O(n/r), which is within a constant factor from optimal, as well as sublinear in the number of nodes. Furthermore, if the CutWidth increases sublinearly with n, a sublinear expected time to extinction is possible with only a sublinearly increasing budget r. In contrast, we provide a lower bound on the expected time to extinction under any such dynamic allocation policy, for bounded degree graphs, in terms of a combinatorial quantity that we call the resistance of the set of initially infected nodes, the available budget, and the number of nodes n. Specifically, we consider the case of bounded degree graphs, with the resistance growing linearly in n. We show that if the curing budget is less than a certain multiple of the resistance, then the expected time to extinction grows exponentially with n. As a corollary, if all nodes are initially infected and the CutWidth of the graph grows linearly in n, while the curing budget is less than a certain multiple of the CutWidth, then the expected time to extinction grows exponentially in n. The combination of these two results establishes a fairly sharp phase transition on the expected time to extinction (sublinear versus exponential) based on the relation between the CutWidth and the curing budget. Finally, in the empirical part of the thesis, we analyze data on the evolution and propagation of influenza across the United States and discover that compartmental, by Kimon Drakopoulos., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., 94, Cataloged from PDF version of thesis., Includes bibliographical references (pages 254-262)., We study the role of partial flexibility in large-scale dynamic resource allocation problems, in which multiple types of processing resources are used to serve multiple types of incoming demands that arrive stochastically over time. Partial flexibility refers to scenarios where (a) only a small fraction of the total processing resources is flexible, or (b) each resource is capable of serving only a small number of demand types. Two main running themes are architecture and information: the former asks how a flexible system should be structured to fully harness the benefits of flexibility, and the latter looks into how information, across the system or from the future, may critically influence performance. Overall, our results suggest that, with the right architecture, information, and decision policies, large-scale systems with partial flexibility can often vastly outperform their inflexible counterparts in terms of delay and capacity, and sometimes be almost as good as fully flexible systems. Our main findings are: 1. Flexible architectures. We show that, just like in fully flexible systems, a large capacity region and a small delay can be achieved even with very limited flexibility, where each resource is capable of serving only a vanishingly small fraction of all demand types. However, the system architecture and scheduling policy need to be chosen more carefully compared to the case of a fully flexible system. (Chapters 3 and 4.) 2. Future information in flexible systems. We show that delay performance in a partially flexible system can be significantly improved by having access to predictive information about future inputs. When future information is sufficient, we provide an optimal scheduling policy under which delay stays bounded in heavy-traffic. Conversely, we show that as soon as future information becomes insufficient, delay diverges to infinity under any policy. (Chapters 5 and 6.) 3. Decentralized partial pooling. For the family of Partial Pool, by Kuang Xu., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., Cataloged from PDF version of thesis., Includes bibliographical references (pages 99-101)., In many situations, the capabilities of firms are better suited to conducting and analyzing field experiments than to analyzing sophisticated demand models. However, the practical value of using field experiments to optimize marketing decisions remains relatively unstudied. We investigate category pricing decisions that require estimating a large matrix of cross-product demand elasticities and ask: how many experiments are required as the number of products in the category grows? Our main result demonstrates that if the categories have a favorable structure, then we can learn faster and reduce the number of experiments that are required: the number of experiments required may grow just logarithmically with the number of products. These findings potentially have important implications for the application of field experiments. Firms may be able to obtain meaningful estimates using a practically feasible number of experiments, even in categories with a large number of products. We also provide a relatively simple mechanism that firms can use to evaluate whether a category has a structure that makes it feasible to use field experiments to set prices. We illustrate how to accomplish this using either a sample of historical data or a pilot set of experiments. Historical data often suffer from the problem of endogeneity bias, but we show that our estimation method is robust to the presence of endogeneity. Besides estimating demand elasticities, firms are also interested in using these elasticities to choose an optimal set of prices in order to maximize profits. We formulate the profit maximization problem and demonstrate that substantial profit gains can also be achieved using a relatively small number of experiments. In addition, we discuss how to evaluate whether field experiments can help optimize other marketing decisions, such as selecting which products to advertise or promote. We adapt our models and methodologies to this setting and show that the main result that r, by Jimmy Qiuyuan Li., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., Cataloged from PDF version of thesis., Includes bibliographical references (pages 173-177)., We study decision making by networked entities and the interplay between networks and outcomes under two different contexts: in the first part of the thesis, we study how strategic agents that share local information coordinate; in the second part of the thesis, we quantify the gain of having access to temporally richer data for learning of influence networks. In the first part of the thesis, we study the role of local information channels in enabling coordination among strategic agents. Building on the standard finite-player global games framework, we show that the set of equilibria of a coordination game is highly sensitive to how information is locally shared among agents. In particular, we show that the coordination game has multiple equilibria if there exists a collection of agents such that (i) they do not share a common signal with any agent outside of that collection; and (ii) their information sets form an increasing sequence of nested sets, referred to as a filtration. Our characterization thus extends the results on the uniqueness and multiplicity of equilibria in global games beyond the well-known case in which agents have access to purely private or public signals. We then provide a characterization of how the extent of equilibrium multiplicity is determined by the extent to which subsets of agents have access to common information: we show that the size of the set of equilibrium strategies is increasing with the extent of variability in the size of the subsets of agents who observe the same signal. We study the set of equilibria in large coordination games, showing that as the number of agents grows, the game exhibits multiple equilibria if and only if a non-vanishing fraction of the agents have access to the same signal. We finally consider an application of our framework in which the noisy signals are interpreted to be the idiosyncratic signals of the agents, which are exchanged through a communication network. In the second part of the thesis, we qu, by Spyridon Ilias Zoumpoulis., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., Cataloged from PDF version of thesis., Includes bibliographical references (pages 99-101)., In many situations, the capabilities of firms are better suited to conducting and analyzing field experiments than to analyzing sophisticated demand models. However, the practical value of using field experiments to optimize marketing decisions remains relatively unstudied. We investigate category pricing decisions that require estimating a large matrix of cross-product demand elasticities and ask: how many experiments are required as the number of products in the category grows? Our main result demonstrates that if the categories have a favorable structure, then we can learn faster and reduce the number of experiments that are required: the number of experiments required may grow just logarithmically with the number of products. These findings potentially have important implications for the application of field experiments. Firms may be able to obtain meaningful estimates using a practically feasible number of experiments, even in categories with a large number of products. We also provide a relatively simple mechanism that firms can use to evaluate whether a category has a structure that makes it feasible to use field experiments to set prices. We illustrate how to accomplish this using either a sample of historical data or a pilot set of experiments. Historical data often suffer from the problem of endogeneity bias, but we show that our estimation method is robust to the presence of endogeneity. Besides estimating demand elasticities, firms are also interested in using these elasticities to choose an optimal set of prices in order to maximize profits. We formulate the profit maximization problem and demonstrate that substantial profit gains can also be achieved using a relatively small number of experiments. In addition, we discuss how to evaluate whether field experiments can help optimize other marketing decisions, such as selecting which products to advertise or promote. We adapt our models and methodologies to this setting and show that the main result that r, by Jimmy Qiuyuan Li., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., Cataloged from PDF version of thesis., Includes bibliographical references (pages 99-101)., In many situations, the capabilities of firms are better suited to conducting and analyzing field experiments than to analyzing sophisticated demand models. However, the practical value of using field experiments to optimize marketing decisions remains relatively unstudied. We investigate category pricing decisions that require estimating a large matrix of cross-product demand elasticities and ask: how many experiments are required as the number of products in the category grows? Our main result demonstrates that if the categories have a favorable structure, then we can learn faster and reduce the number of experiments that are required: the number of experiments required may grow just logarithmically with the number of products. These findings potentially have important implications for the application of field experiments. Firms may be able to obtain meaningful estimates using a practically feasible number of experiments, even in categories with a large number of products. We also provide a relatively simple mechanism that firms can use to evaluate whether a category has a structure that makes it feasible to use field experiments to set prices. We illustrate how to accomplish this using either a sample of historical data or a pilot set of experiments. Historical data often suffer from the problem of endogeneity bias, but we show that our estimation method is robust to the presence of endogeneity. Besides estimating demand elasticities, firms are also interested in using these elasticities to choose an optimal set of prices in order to maximize profits. We formulate the profit maximization problem and demonstrate that substantial profit gains can also be achieved using a relatively small number of experiments. In addition, we discuss how to evaluate whether field experiments can help optimize other marketing decisions, such as selecting which products to advertise or promote. We adapt our models and methodologies to this setting and show that the main result that r, by Jimmy Qiuyuan Li., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., Cataloged from PDF version of thesis., Includes bibliographical references (pages 173-177)., We study decision making by networked entities and the interplay between networks and outcomes under two different contexts: in the first part of the thesis, we study how strategic agents that share local information coordinate; in the second part of the thesis, we quantify the gain of having access to temporally richer data for learning of influence networks. In the first part of the thesis, we study the role of local information channels in enabling coordination among strategic agents. Building on the standard finite-player global games framework, we show that the set of equilibria of a coordination game is highly sensitive to how information is locally shared among agents. In particular, we show that the coordination game has multiple equilibria if there exists a collection of agents such that (i) they do not share a common signal with any agent outside of that collection; and (ii) their information sets form an increasing sequence of nested sets, referred to as a filtration. Our characterization thus extends the results on the uniqueness and multiplicity of equilibria in global games beyond the well-known case in which agents have access to purely private or public signals. We then provide a characterization of how the extent of equilibrium multiplicity is determined by the extent to which subsets of agents have access to common information: we show that the size of the set of equilibrium strategies is increasing with the extent of variability in the size of the subsets of agents who observe the same signal. We study the set of equilibria in large coordination games, showing that as the number of agents grows, the game exhibits multiple equilibria if and only if a non-vanishing fraction of the agents have access to the same signal. We finally consider an application of our framework in which the noisy signals are interpreted to be the idiosyncratic signals of the agents, which are exchanged through a communication network. In the second part of the thesis, we qu, by Spyridon Ilias Zoumpoulis., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., Cataloged from PDF version of thesis., Includes bibliographical references (pages 99-101)., In many situations, the capabilities of firms are better suited to conducting and analyzing field experiments than to analyzing sophisticated demand models. However, the practical value of using field experiments to optimize marketing decisions remains relatively unstudied. We investigate category pricing decisions that require estimating a large matrix of cross-product demand elasticities and ask: how many experiments are required as the number of products in the category grows? Our main result demonstrates that if the categories have a favorable structure, then we can learn faster and reduce the number of experiments that are required: the number of experiments required may grow just logarithmically with the number of products. These findings potentially have important implications for the application of field experiments. Firms may be able to obtain meaningful estimates using a practically feasible number of experiments, even in categories with a large number of products. We also provide a relatively simple mechanism that firms can use to evaluate whether a category has a structure that makes it feasible to use field experiments to set prices. We illustrate how to accomplish this using either a sample of historical data or a pilot set of experiments. Historical data often suffer from the problem of endogeneity bias, but we show that our estimation method is robust to the presence of endogeneity. Besides estimating demand elasticities, firms are also interested in using these elasticities to choose an optimal set of prices in order to maximize profits. We formulate the profit maximization problem and demonstrate that substantial profit gains can also be achieved using a relatively small number of experiments. In addition, we discuss how to evaluate whether field experiments can help optimize other marketing decisions, such as selecting which products to advertise or promote. We adapt our models and methodologies to this setting and show that the main result that r, by Jimmy Qiuyuan Li., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., Cataloged from PDF version of thesis., Includes bibliographical references (pages 173-177)., We study decision making by networked entities and the interplay between networks and outcomes under two different contexts: in the first part of the thesis, we study how strategic agents that share local information coordinate; in the second part of the thesis, we quantify the gain of having access to temporally richer data for learning of influence networks. In the first part of the thesis, we study the role of local information channels in enabling coordination among strategic agents. Building on the standard finite-player global games framework, we show that the set of equilibria of a coordination game is highly sensitive to how information is locally shared among agents. In particular, we show that the coordination game has multiple equilibria if there exists a collection of agents such that (i) they do not share a common signal with any agent outside of that collection; and (ii) their information sets form an increasing sequence of nested sets, referred to as a filtration. Our characterization thus extends the results on the uniqueness and multiplicity of equilibria in global games beyond the well-known case in which agents have access to purely private or public signals. We then provide a characterization of how the extent of equilibrium multiplicity is determined by the extent to which subsets of agents have access to common information: we show that the size of the set of equilibrium strategies is increasing with the extent of variability in the size of the subsets of agents who observe the same signal. We study the set of equilibria in large coordination games, showing that as the number of agents grows, the game exhibits multiple equilibria if and only if a non-vanishing fraction of the agents have access to the same signal. We finally consider an application of our framework in which the noisy signals are interpreted to be the idiosyncratic signals of the agents, which are exchanged through a communication network. In the second part of the thesis, we qu, by Spyridon Ilias Zoumpoulis., Ph. D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2014., 94, Cataloged from PDF version of thesis., Includes bibliographical references (pages 254-262)., We study the role of partial flexibility in large-scale dynamic resource allocation problems, in which multiple types of processing resources are used to serve multiple types of incoming demands that arrive stochastically over time. Partial flexibility refers to scenarios where (a) only a small fraction of the total processing resources is flexible, or (b) each resource is capable of serving only a small number of demand types. Two main running themes are architecture and information: the former asks how a flexible system should be structured to fully harness the benefits of flexibility, and the latter looks into how information, across the system or from the future, may critically influence performance. Overall, our results suggest that, with the right architecture, information, and decision policies, large-scale systems with partial flexibility can often vastly outperform their inflexible counterparts in terms of delay and capacity, and sometimes be almost as good as fully flexible systems. Our main findings are: 1. Flexible architectures. We show that, just like in fully flexible systems, a large capacity region and a small delay can be achieved even with very limited flexibility, where each resource is capable of serving only a vanishingly small fraction of all demand types. However, the system architecture and scheduling policy need to be chosen more carefully compared to the case of a fully flexible system. (Chapters 3 and 4.) 2. Future information in flexible systems. We show that delay performance in a partially flexible system can be significantly improved by having access to predictive information about future inputs. When future information is sufficient, we provide an optimal scheduling policy under which delay stays bounded in heavy-traffic. Conversely, we show that as soon as future information becomes insufficient, delay diverges to infinity under any policy. (Chapters 5 and 6.) 3. Decentralized partial pooling. For the family of Partial Pool, by Kuang Xu., Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (p. 145-156)., In this thesis, we investigate the improvement in treatment effectiveness when dynamically optimizing the fractionation scheme in radiation therapy. In the first part of the thesis, we consider delivering a different dose each day depending on the observed patient anatomy. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to a radio-sensitive organ-at-risk when compared to that resulting from standard fractionation. We use the dynamic programming algorithm to solve the problem exactly. Next, we suggest an approach which optimizes the fraction size and selects a treatment plan from a plan library. Computational results from patient datasets indicate this approach is beneficial. In the second part of the thesis, we analyze the effect of repopulation on the optimal fractionation scheme. A dynamic programming framework is developed to determine an optimal fractionation scheme based on a model of cell kill due to radiation and tumor growth in between treatment days. We prove that the optimal dose fractions are increasing over time. We find that the presence of accelerated tumor repopulation suggests larger dose fractions later in the treatment to compensate for the increased tumor proliferation., by Jagdish Ramakrishnan., Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., Cataloged from PDF version of thesis., Includes bibliographical references (p. 125-126)., In this thesis, we develop and analyze a simple grey-box model that describes the pathophysiology of central sleep apnea (CSA). We construct our model following a thorough survey of published approaches. Special attention is given to PNEUMA, a complex, comprehensive model of human respiratory and cardiovascular physiology that brings together many existing physiological models. We perform a sensitivity analysis, concluding that signals of interest in PNEUMA are insensitive to changes in all but approximately twenty parameters. This justifies our goal of developing a small, simple model that captures approximately the same behaviour among signals of interest. The simplicity of our model not only makes it accessible to analytical and intuitive exploration, but also opens up the possibility that its parameters could be reliably estimated from a patient's data records. This could be of great value in developing patient-specific or state-specific treatments for CSA. Our model describes the dynamics of the alveolar gas exchange, blood gas transport, and cerebral gas exchange processes, which together determine the cerebral and arterial partial pressures of carbon dioxide, given ventilation as input. Our model of the ventilatory controller senses both the cerebral and arterial carbon dioxide partial pressures and issues a ventilatory drive command from which the level of ventilation is determined, closing the loop. We develop a linearized small-signal model of our system and determine conditions for its stability. We conclude by comparing the stability predictions suggested by our linear analysis to the stability properties of our original nonlinear model, with promising results., by Ali Kazerani., S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., Cataloged from PDF version of thesis., Includes bibliographical references (p. 103-111)., Using models to simulate and analyze biological networks requires principled approaches to parameter estimation and model discrimination. We use Bayesian and Monte Carlo methods to recover the full probability distributions of free parameters (initial protein concentrations and rate constants) for mass action models of receptor-mediated cell death. The width of the individual parameter distributions is largely determined by non-identifiability but co-variation among parameters, even those that are poorly determined, encodes essential information. Knowledge of joint parameter distributions makes it possible to compute the uncertainty of model-based predictions whereas ignoring it (e.g. by treating parameters as a simple list of values and variances) yields nonsensical predictions. Computing the Bayes factor from joint distributions yields the odds ratio (~20-fold) for competing "direct" and "indirect" apoptosis models having different numbers of parameters. The methods presented in this thesis were then extended to make predictions in eight apoptosis mini-models. Despite topological uncertainty, the simulated predictions can be used to drive experimental design. Our results illustrate how Bayesian approaches to model calibration and discrimination combined with single-cell data represent a generally useful and rigorous approach to discriminating between competing hypotheses in the face of parametric and topological uncertainty., by Hoda Eydgahi., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (p. 203-209)., We study scheduling problems arising in switched queueing networks, a class of stochastic systems that are often used to model data communication networks, such as uplinks and downlinks of cellular networks, networks of data switches, and ad hoc wireless networks. Motivated by empirical evidence of self-similarity and long-range dependence, the networks that we consider receive a mix of heavy-tailed and light-tailed trac. In this setting we evaluate the delay performance of the widely-studied class of Max-Weight scheduling policies. As performance metric we use the notion of delay stability, i.e., whether the steady-state expected delay in a queue is finite or not. Max-Weight policies are known to have excellent stability properties, and also to achieve good delay performance under light-tailed trac. Classical results from queueing theory imply that heavy-tailed queues are delay unstable under any policy, so we focus on the potential impact of heavy tails on light-tailed queues. The main insight derived from this thesis is that the Max-Weight policy performs poorly in the presence of heavy tails, whereas a suitably modified version of Max-Weight achieves much better overall performance. More specifically: (i) under the Max-Weight scheduling policy, any light-tailed queue that conflicts (i.e., cannot be served simultaneously) with a heavy-tailed queue is delay unstable; (ii) delay instability may propagate to light-tailed queues that do not conflict with heavy-tailed queues. The latter can happen through a "domino effect," if a light-tailed queue conflicts with a queue that has become delay unstable because it conflicts with a heavy-tailed queue. The extent of this phenomenon depends on the arrival rates; (iii) under the parameterized Max-Weight- scheduling policy, all light-tailed queues are delay stable provided the -parameters are chosen suitably. On the methodological side, we show how fluid approximations can be combined with renewal theory in order to prove del, by Mihalis G. Markakis., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (p. 145-156)., In this thesis, we investigate the improvement in treatment effectiveness when dynamically optimizing the fractionation scheme in radiation therapy. In the first part of the thesis, we consider delivering a different dose each day depending on the observed patient anatomy. Given that a fixed prescribed dose must be delivered to the tumor over the course of the treatment, such an approach results in a lower cumulative dose to a radio-sensitive organ-at-risk when compared to that resulting from standard fractionation. We use the dynamic programming algorithm to solve the problem exactly. Next, we suggest an approach which optimizes the fraction size and selects a treatment plan from a plan library. Computational results from patient datasets indicate this approach is beneficial. In the second part of the thesis, we analyze the effect of repopulation on the optimal fractionation scheme. A dynamic programming framework is developed to determine an optimal fractionation scheme based on a model of cell kill due to radiation and tumor growth in between treatment days. We prove that the optimal dose fractions are increasing over time. We find that the presence of accelerated tumor repopulation suggests larger dose fractions later in the treatment to compensate for the increased tumor proliferation., by Jagdish Ramakrishnan., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (p. 203-209)., We study scheduling problems arising in switched queueing networks, a class of stochastic systems that are often used to model data communication networks, such as uplinks and downlinks of cellular networks, networks of data switches, and ad hoc wireless networks. Motivated by empirical evidence of self-similarity and long-range dependence, the networks that we consider receive a mix of heavy-tailed and light-tailed trac. In this setting we evaluate the delay performance of the widely-studied class of Max-Weight scheduling policies. As performance metric we use the notion of delay stability, i.e., whether the steady-state expected delay in a queue is finite or not. Max-Weight policies are known to have excellent stability properties, and also to achieve good delay performance under light-tailed trac. Classical results from queueing theory imply that heavy-tailed queues are delay unstable under any policy, so we focus on the potential impact of heavy tails on light-tailed queues. The main insight derived from this thesis is that the Max-Weight policy performs poorly in the presence of heavy tails, whereas a suitably modified version of Max-Weight achieves much better overall performance. More specifically: (i) under the Max-Weight scheduling policy, any light-tailed queue that conflicts (i.e., cannot be served simultaneously) with a heavy-tailed queue is delay unstable; (ii) delay instability may propagate to light-tailed queues that do not conflict with heavy-tailed queues. The latter can happen through a "domino effect," if a light-tailed queue conflicts with a queue that has become delay unstable because it conflicts with a heavy-tailed queue. The extent of this phenomenon depends on the arrival rates; (iii) under the parameterized Max-Weight- scheduling policy, all light-tailed queues are delay stable provided the -parameters are chosen suitably. On the methodological side, we show how fluid approximations can be combined with renewal theory in order to prove del, by Mihalis G. Markakis., Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., Cataloged from PDF version of thesis., Includes bibliographical references (p. 125-126)., In this thesis, we develop and analyze a simple grey-box model that describes the pathophysiology of central sleep apnea (CSA). We construct our model following a thorough survey of published approaches. Special attention is given to PNEUMA, a complex, comprehensive model of human respiratory and cardiovascular physiology that brings together many existing physiological models. We perform a sensitivity analysis, concluding that signals of interest in PNEUMA are insensitive to changes in all but approximately twenty parameters. This justifies our goal of developing a small, simple model that captures approximately the same behaviour among signals of interest. The simplicity of our model not only makes it accessible to analytical and intuitive exploration, but also opens up the possibility that its parameters could be reliably estimated from a patient's data records. This could be of great value in developing patient-specific or state-specific treatments for CSA. Our model describes the dynamics of the alveolar gas exchange, blood gas transport, and cerebral gas exchange processes, which together determine the cerebral and arterial partial pressures of carbon dioxide, given ventilation as input. Our model of the ventilatory controller senses both the cerebral and arterial carbon dioxide partial pressures and issues a ventilatory drive command from which the level of ventilation is determined, closing the loop. We develop a linearized small-signal model of our system and determine conditions for its stability. We conclude by comparing the stability predictions suggested by our linear analysis to the stability properties of our original nonlinear model, with promising results., by Ali Kazerani., S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012., Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections., Includes bibliographical references (p. 167-176)., The overarching goals of this thesis are to quantify the efficiency loss due to market participant strategic behavior, and to design proper pricing mechanisms that reduce the efficiency loss. The concept of efficiency loss is intimately related to the concept of "price of anarchy," which was advanced by Koutsoupias and Papadimitriou, and compares the maximum social welfare with that achieved at a worst Nash equilibrium. This thesis focuses on the following two topics: (i) For a market with an arbitrary number of participants, how much is the Nash equilibrium close, in the sense of price of anarchy, to a social optimum? (ii) For a resource allocation/pricing mechanism, is the social welfare achieved at an economic equilibrium asymptotically optimal, as the number of market participants goes to infinity? Regarding the first topic, we quantify the efficiency loss in classical Cournot oligopoly games, where multiple oligopolists compete by choosing quantities. We also compare the total profit earned at a Cournot equilibrium to the maximum possible total profit that would be obtained if the suppliers were to collude. For the second topic, related to the efficiency in large economics, we analyze the efficiency of Kelly's proportional allocation mechanism in large-scale wireless communication systems. We study a corresponding Bayesian game in which each user has incomplete information on the state or type of the other users, and show that the social welfare achieved at a Bayes-Nash equilibrium is asymptotically optimal, as the number of users increases to infinity. Finally, for electricity delivery systems, we propose a new dynamic pricing mechanism that explicitly encourages consumers to adapt their consumption so as to offset the variability of demand on conventional units. Through a dynamic game-theoretic formulation, we show that the proposed pricing mechanism achieves social optimality asymptotically, as the number of consumers increases to infinity., by Yunjian Xu., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012., Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections., Includes bibliographical references (p. 167-176)., The overarching goals of this thesis are to quantify the efficiency loss due to market participant strategic behavior, and to design proper pricing mechanisms that reduce the efficiency loss. The concept of efficiency loss is intimately related to the concept of "price of anarchy," which was advanced by Koutsoupias and Papadimitriou, and compares the maximum social welfare with that achieved at a worst Nash equilibrium. This thesis focuses on the following two topics: (i) For a market with an arbitrary number of participants, how much is the Nash equilibrium close, in the sense of price of anarchy, to a social optimum? (ii) For a resource allocation/pricing mechanism, is the social welfare achieved at an economic equilibrium asymptotically optimal, as the number of market participants goes to infinity? Regarding the first topic, we quantify the efficiency loss in classical Cournot oligopoly games, where multiple oligopolists compete by choosing quantities. We also compare the total profit earned at a Cournot equilibrium to the maximum possible total profit that would be obtained if the suppliers were to collude. For the second topic, related to the efficiency in large economics, we analyze the efficiency of Kelly's proportional allocation mechanism in large-scale wireless communication systems. We study a corresponding Bayesian game in which each user has incomplete information on the state or type of the other users, and show that the social welfare achieved at a Bayes-Nash equilibrium is asymptotically optimal, as the number of users increases to infinity. Finally, for electricity delivery systems, we propose a new dynamic pricing mechanism that explicitly encourages consumers to adapt their consumption so as to offset the variability of demand on conventional units. Through a dynamic game-theoretic formulation, we show that the proposed pricing mechanism achieves social optimality asymptotically, as the number of consumers increases to infinity., by Yunjian Xu., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012., Cataloged from PDF version of thesis., Includes bibliographical references (p. 189-193)., This thesis addresses the design and analysis of resource allocation policies in largescale stochastic systems, motivated by examples such as the Internet, cloud facilities, wireless networks, etc. A canonical framework for modeling many such systems is provided by "stochastic processing networks" (SPN) (Harrison [28, 29]). In this context, the key operational challenge is efficient and timely resource allocation. We consider two important classes of SPNs: switched networks and bandwidth-sharing networks. Switched networks are constrained queueing models that have been used successfully to describe the detailed packet-level dynamics in systems such as input-queued switches and wireless networks. Bandwidth-sharing networks have primarily been used to capture the long-term behavior of the flow-level dynamics in the Internet. In this thesis, we develop novel methods to analyze the performance of existing resource allocation policies, and we design new policies that achieve provably good performance. First, we study performance properties of so-called Maximum-Weight-[alpha] (MW-[alpha]) policies in switched networks, and of a-fair policies in bandwidth-sharing networks, both of which are well-known families of resource allocation policies, parametrized by a positive parameter [alpha] > 0. We study both their transient properties as well as their steady-state behavior. In switched networks, under a MW-a policy with a 2 1, we obtain bounds on the maximum queue size over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property when [alpha] > 1. In the steady-state regime, for any [alpha] >/= 0, we obtain explicit exponential tail bounds on the queue sizes, by relying on a norm-like Lyapunov function, different from the standard Lyapunov function used in the literature. Methods and results are largely parallel for bandwidth-sharing networks. Under an a-fair, by Yuan Zhong., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2012., Cataloged from department-submitted PDF version of thesis. This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections., Includes bibliographical references (p. 167-176)., The overarching goals of this thesis are to quantify the efficiency loss due to market participant strategic behavior, and to design proper pricing mechanisms that reduce the efficiency loss. The concept of efficiency loss is intimately related to the concept of "price of anarchy," which was advanced by Koutsoupias and Papadimitriou, and compares the maximum social welfare with that achieved at a worst Nash equilibrium. This thesis focuses on the following two topics: (i) For a market with an arbitrary number of participants, how much is the Nash equilibrium close, in the sense of price of anarchy, to a social optimum? (ii) For a resource allocation/pricing mechanism, is the social welfare achieved at an economic equilibrium asymptotically optimal, as the number of market participants goes to infinity? Regarding the first topic, we quantify the efficiency loss in classical Cournot oligopoly games, where multiple oligopolists compete by choosing quantities. We also compare the total profit earned at a Cournot equilibrium to the maximum possible total profit that would be obtained if the suppliers were to collude. For the second topic, related to the efficiency in large economics, we analyze the efficiency of Kelly's proportional allocation mechanism in large-scale wireless communication systems. We study a corresponding Bayesian game in which each user has incomplete information on the state or type of the other users, and show that the social welfare achieved at a Bayes-Nash equilibrium is asymptotically optimal, as the number of users increases to infinity. Finally, for electricity delivery systems, we propose a new dynamic pricing mechanism that explicitly encourages consumers to adapt their consumption so as to offset the variability of demand on conventional units. Through a dynamic game-theoretic formulation, we show that the proposed pricing mechanism achieves social optimality asymptotically, as the number of consumers increases to infinity., by Yunjian Xu., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (p. 203-209)., We study scheduling problems arising in switched queueing networks, a class of stochastic systems that are often used to model data communication networks, such as uplinks and downlinks of cellular networks, networks of data switches, and ad hoc wireless networks. Motivated by empirical evidence of self-similarity and long-range dependence, the networks that we consider receive a mix of heavy-tailed and light-tailed trac. In this setting we evaluate the delay performance of the widely-studied class of Max-Weight scheduling policies. As performance metric we use the notion of delay stability, i.e., whether the steady-state expected delay in a queue is finite or not. Max-Weight policies are known to have excellent stability properties, and also to achieve good delay performance under light-tailed trac. Classical results from queueing theory imply that heavy-tailed queues are delay unstable under any policy, so we focus on the potential impact of heavy tails on light-tailed queues. The main insight derived from this thesis is that the Max-Weight policy performs poorly in the presence of heavy tails, whereas a suitably modified version of Max-Weight achieves much better overall performance. More specifically: (i) under the Max-Weight scheduling policy, any light-tailed queue that conflicts (i.e., cannot be served simultaneously) with a heavy-tailed queue is delay unstable; (ii) delay instability may propagate to light-tailed queues that do not conflict with heavy-tailed queues. The latter can happen through a "domino effect," if a light-tailed queue conflicts with a queue that has become delay unstable because it conflicts with a heavy-tailed queue. The extent of this phenomenon depends on the arrival rates; (iii) under the parameterized Max-Weight- scheduling policy, all light-tailed queues are delay stable provided the -parameters are chosen suitably. On the methodological side, we show how fluid approximations can be combined with renewal theory in order to prove del, by Mihalis G. Markakis., Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2013., Cataloged from PDF version of thesis., Includes bibliographical references (p. 125-126)., In this thesis, we develop and analyze a simple grey-box model that describes the pathophysiology of central sleep apnea (CSA). We construct our model following a thorough survey of published approaches. Special attention is given to PNEUMA, a complex, comprehensive model of human respiratory and cardiovascular physiology that brings together many existing physiological models. We perform a sensitivity analysis, concluding that signals of interest in PNEUMA are insensitive to changes in all but approximately twenty parameters. This justifies our goal of developing a small, simple model that captures approximately the same behaviour among signals of interest. The simplicity of our model not only makes it accessible to analytical and intuitive exploration, but also opens up the possibility that its parameters could be reliably estimated from a patient's data records. This could be of great value in developing patient-specific or state-specific treatments for CSA. Our model describes the dynamics of the alveolar gas exchange, blood gas transport, and cerebral gas exchange processes, which together determine the cerebral and arterial partial pressures of carbon dioxide, given ventilation as input. Our model of the ventilatory controller senses both the cerebral and arterial carbon dioxide partial pressures and issues a ventilatory drive command from which the level of ventilation is determined, closing the loop. We develop a linearized small-signal model of our system and determine conditions for its stability. We conclude by comparing the stability predictions suggested by our linear analysis to the stability properties of our original nonlinear model, with promising results., by Ali Kazerani., S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2012., Cataloged from PDF version of thesis., Includes bibliographical references (p. 189-193)., This thesis addresses the design and analysis of resource allocation policies in largescale stochastic systems, motivated by examples such as the Internet, cloud facilities, wireless networks, etc. A canonical framework for modeling many such systems is provided by "stochastic processing networks" (SPN) (Harrison [28, 29]). In this context, the key operational challenge is efficient and timely resource allocation. We consider two important classes of SPNs: switched networks and bandwidth-sharing networks. Switched networks are constrained queueing models that have been used successfully to describe the detailed packet-level dynamics in systems such as input-queued switches and wireless networks. Bandwidth-sharing networks have primarily been used to capture the long-term behavior of the flow-level dynamics in the Internet. In this thesis, we develop novel methods to analyze the performance of existing resource allocation policies, and we design new policies that achieve provably good performance. First, we study performance properties of so-called Maximum-Weight-[alpha] (MW-[alpha]) policies in switched networks, and of a-fair policies in bandwidth-sharing networks, both of which are well-known families of resource allocation policies, parametrized by a positive parameter [alpha] > 0. We study both their transient properties as well as their steady-state behavior. In switched networks, under a MW-a policy with a 2 1, we obtain bounds on the maximum queue size over a given time horizon, by means of a maximal inequality derived from the standard Lyapunov drift condition. As a corollary, we establish the full state space collapse property when [alpha] > 1. In the steady-state regime, for any [alpha] >/= 0, we obtain explicit exponential tail bounds on the queue sizes, by relying on a norm-like Lyapunov function, different from the standard Lyapunov function used in the literature. Methods and results are largely parallel for bandwidth-sharing networks. Under an a-fair, by Yuan Zhong., Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000., Includes bibliographical references (p. 95-97)., This thesis addresses the problem of minimizing a facility's electricity costs by generating optimal responses using an auxiliary generator as the parameter of the control systems. The-goal of the thesis is to find an optimization method that can cope with the uncertainty in the building load while also handles the complex electricity price structures. The building load is the random factor of the stochastic problem and is composed of the weather load and the occupancy load. Several optimization techniques such as Dynamic Programming and Linear Programming (deterministic optimization) are looked at. Stochastic Programming using Nested Bender's Decomposition method is chosen and studied to solve the optimization problem. Stochastic Programming, which is a hybrid of Dynamic Programming and Linear Programming, is used because it can cope with the complex electricity price structures and the uncertainty of the building load while avoiding an explosion in the number of states. However, the method is not suitable for our problem, which is a Mixed Integer Programming problem. Moreover, the random sampling adds some limitations on the method. In addition, the ~high memory requirement and the extensive computational time prohibit the method from being used for a long planning period. Hence, a new control system, which is the combination of Stochastic Programming and Linear Programming, is proposed. The key of this proposed method is the reduction of the problem into a two-stage stochastic problem., by Paul Rafiuly., S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000., Includes bibliographical references (p. 95-97)., This thesis addresses the problem of minimizing a facility's electricity costs by generating optimal responses using an auxiliary generator as the parameter of the control systems. The-goal of the thesis is to find an optimization method that can cope with the uncertainty in the building load while also handles the complex electricity price structures. The building load is the random factor of the stochastic problem and is composed of the weather load and the occupancy load. Several optimization techniques such as Dynamic Programming and Linear Programming (deterministic optimization) are looked at. Stochastic Programming using Nested Bender's Decomposition method is chosen and studied to solve the optimization problem. Stochastic Programming, which is a hybrid of Dynamic Programming and Linear Programming, is used because it can cope with the complex electricity price structures and the uncertainty of the building load while avoiding an explosion in the number of states. However, the method is not suitable for our problem, which is a Mixed Integer Programming problem. Moreover, the random sampling adds some limitations on the method. In addition, the ~high memory requirement and the extensive computational time prohibit the method from being used for a long planning period. Hence, a new control system, which is the combination of Stochastic Programming and Linear Programming, is proposed. The key of this proposed method is the reduction of the problem into a two-stage stochastic problem., by Paul Rafiuly., S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000., Includes bibliographical references (p. 95-97)., This thesis addresses the problem of minimizing a facility's electricity costs by generating optimal responses using an auxiliary generator as the parameter of the control systems. The-goal of the thesis is to find an optimization method that can cope with the uncertainty in the building load while also handles the complex electricity price structures. The building load is the random factor of the stochastic problem and is composed of the weather load and the occupancy load. Several optimization techniques such as Dynamic Programming and Linear Programming (deterministic optimization) are looked at. Stochastic Programming using Nested Bender's Decomposition method is chosen and studied to solve the optimization problem. Stochastic Programming, which is a hybrid of Dynamic Programming and Linear Programming, is used because it can cope with the complex electricity price structures and the uncertainty of the building load while avoiding an explosion in the number of states. However, the method is not suitable for our problem, which is a Mixed Integer Programming problem. Moreover, the random sampling adds some limitations on the method. In addition, the ~high memory requirement and the extensive computational time prohibit the method from being used for a long planning period. Hence, a new control system, which is the combination of Stochastic Programming and Linear Programming, is proposed. The key of this proposed method is the reduction of the problem into a two-stage stochastic problem., by Paul Rafiuly., S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Architecture; and, (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2000., Includes bibliographical references (p. 95-97)., This thesis addresses the problem of minimizing a facility's electricity costs by generating optimal responses using an auxiliary generator as the parameter of the control systems. The-goal of the thesis is to find an optimization method that can cope with the uncertainty in the building load while also handles the complex electricity price structures. The building load is the random factor of the stochastic problem and is composed of the weather load and the occupancy load. Several optimization techniques such as Dynamic Programming and Linear Programming (deterministic optimization) are looked at. Stochastic Programming using Nested Bender's Decomposition method is chosen and studied to solve the optimization problem. Stochastic Programming, which is a hybrid of Dynamic Programming and Linear Programming, is used because it can cope with the complex electricity price structures and the uncertainty of the building load while avoiding an explosion in the number of states. However, the method is not suitable for our problem, which is a Mixed Integer Programming problem. Moreover, the random sampling adds some limitations on the method. In addition, the ~high memory requirement and the extensive computational time prohibit the method from being used for a long planning period. Hence, a new control system, which is the combination of Stochastic Programming and Linear Programming, is proposed. The key of this proposed method is the reduction of the problem into a two-stage stochastic problem., by Paul Rafiuly., S.M.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011., Cataloged from PDF version of thesis., Includes bibliographical references (p. 84-85)., In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction p of an available resource is deployed in a centralized manner (e.g., to serve a most-loaded station) while the remaining fraction 1 -p is allocated to local servers that can only serve requests addressed specifically to their respective stations. Using a fluid model approach, we demonstrate a surprising phase transition in the steady-state delay, as p changes: in the limit of a large number of stations, and when any amount of centralization is available (p > 0), the average queue length in steady state scales as log 1/1-p 1/1-[lambda] when the traffic intensity [lambda] goes to 1. This is exponentially smaller than the usual M/M/1-queue delay scaling of 1/1-[lambda], obtained when all resources are fully allocated to local stations (p = 0). This indicates a strong qualitative impact of even a small degree of centralization. We prove convergence to a fluid limit, and characterize both the transient and steady-state behavior of the finite system, in the limit as the number of stations N goes to infinity. We show that the sequence of queue-length processes converges to a unique fluid trajectory (over any finite time interval, as N --> [infinity]), and that this fluid trajectory converges to a unique invariant state vI, for which a simple closedform expression is obtained. We also show that the steady-state distribution of the N-server system concentrates on vI as N goes to infinity., by Kuang Xu., S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010., Cataloged from PDF version of thesis., Includes bibliographical references (p. 129-136)., This thesis will be concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, and robust against unexpected changes in topology such as link failures. We will describe protocols to solve certain control and signal processing problems in this setting. We will demonstrate that a key challenge for such systems is the problem of computing averages in a decentralized way. Namely, we will show that a number of distributed control and signal processing problems can be solved straightforwardly if solutions to the averaging problem are available. The rest of the thesis will be concerned with algorithms for the averaging problem and its generalizations. We will (i) derive the fastest known averaging algorithms in a variety of settings and subject to a variety of communication and storage constraints (ii) prove a lower bound identifying a fundamental barrier for averaging algorithms (iii) propose a new model for distributed function computation which reflects the constraints facing many large-scale networks, and nearly characterize the general class of functions which can be computed in this model., by Alexander Olshevsky., Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011., Cataloged from PDF version of thesis., Includes bibliographical references (p. 84-85)., In this thesis, we propose and analyze a multi-server model that captures a performance trade-off between centralized and distributed processing. In our model, a fraction p of an available resource is deployed in a centralized manner (e.g., to serve a most-loaded station) while the remaining fraction 1 -p is allocated to local servers that can only serve requests addressed specifically to their respective stations. Using a fluid model approach, we demonstrate a surprising phase transition in the steady-state delay, as p changes: in the limit of a large number of stations, and when any amount of centralization is available (p > 0), the average queue length in steady state scales as log 1/1-p 1/1-[lambda] when the traffic intensity [lambda] goes to 1. This is exponentially smaller than the usual M/M/1-queue delay scaling of 1/1-[lambda], obtained when all resources are fully allocated to local stations (p = 0). This indicates a strong qualitative impact of even a small degree of centralization. We prove convergence to a fluid limit, and characterize both the transient and steady-state behavior of the finite system, in the limit as the number of stations N goes to infinity. We show that the sequence of queue-length processes converges to a unique fluid trajectory (over any finite time interval, as N --> [infinity]), and that this fluid trajectory converges to a unique invariant state vI, for which a simple closedform expression is obtained. We also show that the steady-state distribution of the N-server system concentrates on vI as N goes to infinity., by Kuang Xu., S.M.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010., Cataloged from PDF version of thesis., Includes bibliographical references (p. 129-136)., This thesis will be concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, and robust against unexpected changes in topology such as link failures. We will describe protocols to solve certain control and signal processing problems in this setting. We will demonstrate that a key challenge for such systems is the problem of computing averages in a decentralized way. Namely, we will show that a number of distributed control and signal processing problems can be solved straightforwardly if solutions to the averaging problem are available. The rest of the thesis will be concerned with algorithms for the averaging problem and its generalizations. We will (i) derive the fastest known averaging algorithms in a variety of settings and subject to a variety of communication and storage constraints (ii) prove a lower bound identifying a fundamental barrier for averaging algorithms (iii) propose a new model for distributed function computation which reflects the constraints facing many large-scale networks, and nearly characterize the general class of functions which can be computed in this model., by Alexander Olshevsky., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010., Cataloged from PDF version of thesis., Includes bibliographical references (p. 129-136)., This thesis will be concerned with distributed control and coordination of networks consisting of multiple, potentially mobile, agents. This is motivated mainly by the emergence of large scale networks characterized by the lack of centralized access to information and time-varying connectivity. Control and optimization algorithms deployed in such networks should be completely distributed, relying only on local observations and information, and robust against unexpected changes in topology such as link failures. We will describe protocols to solve certain control and signal processing problems in this setting. We will demonstrate that a key challenge for such systems is the problem of computing averages in a decentralized way. Namely, we will show that a number of distributed control and signal processing problems can be solved straightforwardly if solutions to the averaging problem are available. The rest of the thesis will be concerned with algorithms for the averaging problem and its generalizations. We will (i) derive the fastest known averaging algorithms in a variety of settings and subject to a variety of communication and storage constraints (ii) prove a lower bound identifying a fundamental barrier for averaging algorithms (iii) propose a new model for distributed function computation which reflects the constraints facing many large-scale networks, and nearly characterize the general class of functions which can be computed in this model., by Alexander Olshevsky., Ph.D.

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Cataloged from student-submitted PDF version of thesis., Includes bibliographical references (p. 73-74)., We investigate a decentralized detection problem in which a set of sensors transmit a summary of their observations to a fusion center, which then decides which one of two hypotheses is true. The focus is on determining the value of feedback in improving performance in the regime of asymptotically many sensors. We formulate the decentralized detection problem for different network configurations of interest under both the Neyman-Pearson and the Bayesian criteria. In a configuration with feedback, the fusion center would make a preliminary decision which it would pass on back to the local sensors; a related configuration, the daisy chain, is introduced: the first fusion center passes the information from a first set of sensors on to a second set of sensors and a second fusion center. Under the Neyman-Pearson criterion, we provide both an empirical study and theoretical results. The empirical study assumes scalar linear Gaussian binary sensors and analyzes asymptotic performance as the signal-to-noise ratio of the measurements grows higher, to show that the value of feeding the preliminary decision back to decision makers is asymptotically negligible. This motivates two theoretical results: first, in the asymptotic regime (as the number of sensors tends to infinity), the performance of the "daisy chain" matches the performance of a parallel configuration with twice as many sensors as the classical scheme; second, it is optimal (in terms of the exponent of the error probability) to constrain all decision rules at the first and second stage of the "daisy chain" to be equal., (cont.) Under the Bayesian criterion, three analytical results are shown. First, it is asymptotically optimal to have all sensors of a parallel configuration use the same decision rule under exponentially skewed priors. Second, again in the asymptotic regime, the decision rules at the second stage of the "daisy chain" can be equal without loss of optimality. Finally, the same result is proven for the first stage., by Spyridon Ilias Zoumpoulis., M.Eng.

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Includes bibliographical references (p. 47-48)., We study the problem of scheduling jobs on a two-machine distributed server, where the job size distribution is heavy-tailed. We focus on two distributions, for which we prove that the performance of the optimal size-independent policy is asymptotically worse than that of a simple size-dependent policy. First, we consider a simple distribution where incoming jobs can only be of two possible sizes. The motivation is that with two largely different sizes, the simple distribution captures the important aspects of a heavy tail. Second, we extend to a bounded Pareto distribution, which has an actual heavy tail. For both cases, we analyze the performance with regards to slowdown (waiting time divided by job size) for several size-independent and size-dependent policies. We see that the size-dependent policies perform better, and then go on to prove that even the best size-independent policy cannot achieve the same performance. We conclude that as we increase the variance of our job size distribution, the gap between size-independent and size-dependent policies grows., by John Nham., M.Eng.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008., Includes bibliographical references (leaves 225-227)., This thesis deals with five important ideas pertaining to supply chains and supply contracts: coordination, flexibility in allocating profit, the push-pull boundary, the valuation of capacity, and cooperation versus competition and its effects on profit and prices. Throughout the thesis, we focus on capacity-constrained supply channels, motivated by the fact that most real-world supply chains have physical or monetary constraints.In the first part of this thesis, we show that when a supply channel is capacity-constrained and the constraint is tight, there is a set of linear wholesale price contracts that coordinates the channel while allowing the supplier to make a profit. We prove this for the one-supplier/one-newsvendor supply channel as well as the many-supplier/one-newsvendor channel configuration (with each supplier selling a unique product). We analyze how this set of wholesale prices changes as we change the channel's capacity constraint. We also explore conditions under which these channel-efficient linear wholesale price contracts result from the equilibrium behavior of a newsvendor procurement game. Our newsvendor procurement game generalizes the Stackelberg game introduced in Lariviere and Porteus (2001) to allow for multiple suppliers as well as a capacity constraint at the newsvendor. In order to convey the worst-case channel performance when these channel-efficient contracts are not used in equilibrium, we quantify the worst-case efficiency loss for the supply channel using a distribution-free method. We also identify the set of Pareto-dominated contracts in a negotiation setting. Furthermore, unlike the unconstrained setting, we show that in the constrained setting wholesale price contracts can be flexible in allocating the channel profit without necessarily sacrificing coordination., (cont.) Finally, we find the set of risk-sharing contracts (such as buy-back and revenue-sharing contracts) that coordinate a constrained supply channel and contrast that set with the set of risk-sharing contracts that coordinate an unconstrained channel. We show that in a capacity constrained channel, even risk-sharing contracts gain extra flexibility because for any given level of risk, there is now a range of possible allocations of the system optimal profit between the supplier and retailer. (Without a capacity constraint, for any given level of risk, there is only one allowable allocation of channel optimal profit between the supplier and retailer.) In other words, in a capacity-constrained environment, using risk-sharing contracts, for any given level of risk, we show there is flexibility in allocating the channel optimal profit.In the second part of this thesis, we consider a supply channel with a capacity constraint in which the retailer makes an order quantity decision that depends only on realized demand rather than a forecast, and instead the supplier is the newsvendor for the channel making a stocking decision based on a forecast. In other words, the retailer now 'pulls' inventory from the supplier as demand is realized which differs from the model in the first part of this thesis wherein the supplier 'pushes' inventory onto the retailer before the sales season begins. We find that for the new supply channel similar results hold. Namely, when the retailer is operating in 'pull-mode', there is a set of 'pull' wholesale price contracts that coordinates the channel while allowing the retailer to make a profit. We analyze how this set of wholesale prices changes as we change the channel's capacity constraint., (cont.) We also explore conditions under which these channel-efficient 'pull' wholesale price contracts result from the equilibrium behavior of a newsvendor procurement game. Our newsvendor procurement game generalizes the Stackelberg game introduced in Cachon and Lariviere (2001) to allow for multiple retailers as well as a capacity constraint at the newsvendor. We assess the worst-case channel performance in equilibrium when these channel-efficient contracts are not selected. Furthermore, we identify the set of Pareto-dominated 'pull' contracts in a negotiation setting. Finally, we identify the wholesale price contracts that coordinate regardless of the supply chain's mode of operation.In the third part of this thesis, we consider a supply channel, operating in 'push'-mode, with multiple suppliers selling differentiated products to one newsvendor with limited capacity, using wholesale price contracts. We show that both in a negotiation setting as well as in an equilibrium setting, with the suppliers selecting wholesale prices followed by the newsvendor choosing order quantities, each supplier incurs an endogenous price for their share of the newsvendor's capacity. We intrepret this price as the value of the newsvendor's capacity and analyze the capacity's price in both a negotiation and an equilibrium setting. Furthermore, we show that our capacity valuation technique can be applied to different supply chain settings by analyzing the capacity price for a different supply chain, operating in 'pull'-mode, with one supplier with limited capacity selling differentiated products to multiple retailers. Finally, we analyze the effects of collusion on prices and profits in both these settings., by Navid Sabbaghi., Ph.D.

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Includes bibliographical references (p. 47-48)., We study the problem of scheduling jobs on a two-machine distributed server, where the job size distribution is heavy-tailed. We focus on two distributions, for which we prove that the performance of the optimal size-independent policy is asymptotically worse than that of a simple size-dependent policy. First, we consider a simple distribution where incoming jobs can only be of two possible sizes. The motivation is that with two largely different sizes, the simple distribution captures the important aspects of a heavy tail. Second, we extend to a bounded Pareto distribution, which has an actual heavy tail. For both cases, we analyze the performance with regards to slowdown (waiting time divided by job size) for several size-independent and size-dependent policies. We see that the size-dependent policies perform better, and then go on to prove that even the best size-independent policy cannot achieve the same performance. We conclude that as we increase the variance of our job size distribution, the gap between size-independent and size-dependent policies grows., by John Nham., M.Eng.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008., Includes bibliographical references (leaves 225-227)., This thesis deals with five important ideas pertaining to supply chains and supply contracts: coordination, flexibility in allocating profit, the push-pull boundary, the valuation of capacity, and cooperation versus competition and its effects on profit and prices. Throughout the thesis, we focus on capacity-constrained supply channels, motivated by the fact that most real-world supply chains have physical or monetary constraints.In the first part of this thesis, we show that when a supply channel is capacity-constrained and the constraint is tight, there is a set of linear wholesale price contracts that coordinates the channel while allowing the supplier to make a profit. We prove this for the one-supplier/one-newsvendor supply channel as well as the many-supplier/one-newsvendor channel configuration (with each supplier selling a unique product). We analyze how this set of wholesale prices changes as we change the channel's capacity constraint. We also explore conditions under which these channel-efficient linear wholesale price contracts result from the equilibrium behavior of a newsvendor procurement game. Our newsvendor procurement game generalizes the Stackelberg game introduced in Lariviere and Porteus (2001) to allow for multiple suppliers as well as a capacity constraint at the newsvendor. In order to convey the worst-case channel performance when these channel-efficient contracts are not used in equilibrium, we quantify the worst-case efficiency loss for the supply channel using a distribution-free method. We also identify the set of Pareto-dominated contracts in a negotiation setting. Furthermore, unlike the unconstrained setting, we show that in the constrained setting wholesale price contracts can be flexible in allocating the channel profit without necessarily sacrificing coordination., (cont.) Finally, we find the set of risk-sharing contracts (such as buy-back and revenue-sharing contracts) that coordinate a constrained supply channel and contrast that set with the set of risk-sharing contracts that coordinate an unconstrained channel. We show that in a capacity constrained channel, even risk-sharing contracts gain extra flexibility because for any given level of risk, there is now a range of possible allocations of the system optimal profit between the supplier and retailer. (Without a capacity constraint, for any given level of risk, there is only one allowable allocation of channel optimal profit between the supplier and retailer.) In other words, in a capacity-constrained environment, using risk-sharing contracts, for any given level of risk, we show there is flexibility in allocating the channel optimal profit.In the second part of this thesis, we consider a supply channel with a capacity constraint in which the retailer makes an order quantity decision that depends only on realized demand rather than a forecast, and instead the supplier is the newsvendor for the channel making a stocking decision based on a forecast. In other words, the retailer now 'pulls' inventory from the supplier as demand is realized which differs from the model in the first part of this thesis wherein the supplier 'pushes' inventory onto the retailer before the sales season begins. We find that for the new supply channel similar results hold. Namely, when the retailer is operating in 'pull-mode', there is a set of 'pull' wholesale price contracts that coordinates the channel while allowing the retailer to make a profit. We analyze how this set of wholesale prices changes as we change the channel's capacity constraint., (cont.) We also explore conditions under which these channel-efficient 'pull' wholesale price contracts result from the equilibrium behavior of a newsvendor procurement game. Our newsvendor procurement game generalizes the Stackelberg game introduced in Cachon and Lariviere (2001) to allow for multiple retailers as well as a capacity constraint at the newsvendor. We assess the worst-case channel performance in equilibrium when these channel-efficient contracts are not selected. Furthermore, we identify the set of Pareto-dominated 'pull' contracts in a negotiation setting. Finally, we identify the wholesale price contracts that coordinate regardless of the supply chain's mode of operation.In the third part of this thesis, we consider a supply channel, operating in 'push'-mode, with multiple suppliers selling differentiated products to one newsvendor with limited capacity, using wholesale price contracts. We show that both in a negotiation setting as well as in an equilibrium setting, with the suppliers selecting wholesale prices followed by the newsvendor choosing order quantities, each supplier incurs an endogenous price for their share of the newsvendor's capacity. We intrepret this price as the value of the newsvendor's capacity and analyze the capacity's price in both a negotiation and an equilibrium setting. Furthermore, we show that our capacity valuation technique can be applied to different supply chain settings by analyzing the capacity price for a different supply chain, operating in 'pull'-mode, with one supplier with limited capacity selling differentiated products to multiple retailers. Finally, we analyze the effects of collusion on prices and profits in both these settings., by Navid Sabbaghi., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008., Includes bibliographical references (leaves 225-227)., This thesis deals with five important ideas pertaining to supply chains and supply contracts: coordination, flexibility in allocating profit, the push-pull boundary, the valuation of capacity, and cooperation versus competition and its effects on profit and prices. Throughout the thesis, we focus on capacity-constrained supply channels, motivated by the fact that most real-world supply chains have physical or monetary constraints.In the first part of this thesis, we show that when a supply channel is capacity-constrained and the constraint is tight, there is a set of linear wholesale price contracts that coordinates the channel while allowing the supplier to make a profit. We prove this for the one-supplier/one-newsvendor supply channel as well as the many-supplier/one-newsvendor channel configuration (with each supplier selling a unique product). We analyze how this set of wholesale prices changes as we change the channel's capacity constraint. We also explore conditions under which these channel-efficient linear wholesale price contracts result from the equilibrium behavior of a newsvendor procurement game. Our newsvendor procurement game generalizes the Stackelberg game introduced in Lariviere and Porteus (2001) to allow for multiple suppliers as well as a capacity constraint at the newsvendor. In order to convey the worst-case channel performance when these channel-efficient contracts are not used in equilibrium, we quantify the worst-case efficiency loss for the supply channel using a distribution-free method. We also identify the set of Pareto-dominated contracts in a negotiation setting. Furthermore, unlike the unconstrained setting, we show that in the constrained setting wholesale price contracts can be flexible in allocating the channel profit without necessarily sacrificing coordination., (cont.) Finally, we find the set of risk-sharing contracts (such as buy-back and revenue-sharing contracts) that coordinate a constrained supply channel and contrast that set with the set of risk-sharing contracts that coordinate an unconstrained channel. We show that in a capacity constrained channel, even risk-sharing contracts gain extra flexibility because for any given level of risk, there is now a range of possible allocations of the system optimal profit between the supplier and retailer. (Without a capacity constraint, for any given level of risk, there is only one allowable allocation of channel optimal profit between the supplier and retailer.) In other words, in a capacity-constrained environment, using risk-sharing contracts, for any given level of risk, we show there is flexibility in allocating the channel optimal profit.In the second part of this thesis, we consider a supply channel with a capacity constraint in which the retailer makes an order quantity decision that depends only on realized demand rather than a forecast, and instead the supplier is the newsvendor for the channel making a stocking decision based on a forecast. In other words, the retailer now 'pulls' inventory from the supplier as demand is realized which differs from the model in the first part of this thesis wherein the supplier 'pushes' inventory onto the retailer before the sales season begins. We find that for the new supply channel similar results hold. Namely, when the retailer is operating in 'pull-mode', there is a set of 'pull' wholesale price contracts that coordinates the channel while allowing the retailer to make a profit. We analyze how this set of wholesale prices changes as we change the channel's capacity constraint., (cont.) We also explore conditions under which these channel-efficient 'pull' wholesale price contracts result from the equilibrium behavior of a newsvendor procurement game. Our newsvendor procurement game generalizes the Stackelberg game introduced in Cachon and Lariviere (2001) to allow for multiple retailers as well as a capacity constraint at the newsvendor. We assess the worst-case channel performance in equilibrium when these channel-efficient contracts are not selected. Furthermore, we identify the set of Pareto-dominated 'pull' contracts in a negotiation setting. Finally, we identify the wholesale price contracts that coordinate regardless of the supply chain's mode of operation.In the third part of this thesis, we consider a supply channel, operating in 'push'-mode, with multiple suppliers selling differentiated products to one newsvendor with limited capacity, using wholesale price contracts. We show that both in a negotiation setting as well as in an equilibrium setting, with the suppliers selecting wholesale prices followed by the newsvendor choosing order quantities, each supplier incurs an endogenous price for their share of the newsvendor's capacity. We intrepret this price as the value of the newsvendor's capacity and analyze the capacity's price in both a negotiation and an equilibrium setting. Furthermore, we show that our capacity valuation technique can be applied to different supply chain settings by analyzing the capacity price for a different supply chain, operating in 'pull'-mode, with one supplier with limited capacity selling differentiated products to multiple retailers. Finally, we analyze the effects of collusion on prices and profits in both these settings., by Navid Sabbaghi., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2007., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Includes bibliographical references (p. 175-182)., In the context of patient care for life-threatening illnesses, the presence of uncertainty may compromise the quality of a treatment. In this thesis, we investigate robust approaches to managing uncertainty in radiation therapy treatments for cancer. In the first part of the thesis, we study the effect of breathing motion uncertainty on intensity-modulated radiation therapy treatments of a lung tumor. We construct a robust framework that generalizes current mathematical programming formulations that account for motion. This framework gives insight into the trade-off between sparing the healthy tissues and ensuring that the tumor receives sufficient dose. With this trade-off in mind, we show that our robust solution outperforms a nominal (no uncertainty) solution and a margin (worst-case) solution on a clinical case. Next, we perform an in-depth study into the structure of different intensity maps that were witnessed in the first part of the thesis. We consider parameterized intensity maps and investigate their ability to deliver a sufficient dose to the tumor in the presence of motion that follows a Gaussian distribution. We characterize the structure of optimal intensity maps in terms of certain conditions on the problem parameters., (cont.) Finally, in the last part of the thesis, we study intensity-modulated proton therapy under uncertainty in the location of maximum dose deposited by the beamlets of radiation. We provide a robust formulation for the optimization of proton-based treatments and show that it outperforms traditional formulations in the face of uncertainty. In our computational experiments, we see evidence that optimal robust solutions use the physical characteristics of the proton beam to create dose distributions that are far less sensitive to the underlying uncertainty., by Timothy Ching-Yee Chan., Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008., This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections., Includes bibliographical references (leaves 201-207)., We consider the problem of decentralized binary detection in a network consisting of a large number of nodes arranged as a tree of bounded height. We show that the error probability decays exponentially fast with the number of nodes under both a Neyman-Pearson criterion and a Bayesian criterion, and provide bounds for the optimal error exponent. Furthermore, we show that under the Neyman-Pearson criterion, the optimal error exponent is often the same as that corresponding to a parallel configuration, implying that a large network can be designed to operate efficiently without significantly affecting the detection performance. We provide sufficient, as well as necessary, conditions for this to happen. For those networks satisfying the sufficient conditions, we propose a simple strategy that nearly achieves the optimal error exponent, and in which all non-leaf nodes need only send 1-bit messages. We also investigate the impact of node failures and unreliable communications on the detection performance. Node failures are modeled by a Galton-Watson branching process, and binary symmetric channels are assumed for the case of unreliable communications. We characterize the asymptotically optimal detection performance, develop simple strategies that nearly achieve the optimal performance, and compare the performance of the two types of networks. Our results suggest that in a large scale sensor network, it is more important to ensure that nodes can communicate reliably with each other(e.g.,by boosting the transmission power) than to ensure that nodes are robust to failures. In the case of networks with unbounded height, we establish the validity of a long-standing conjecture regarding the sub-exponential decay of Bayesian detection error probabilities in a tandem network. We also provide bounds for the error probability, and show that under the additional assumption of bounded Kullback-Leibler divergences, the error probability is (e cnd ), for all d> 1/2, with c c(logn)d be, (cont.) Finally, we consider the problem of decentralized detection when sensors have access to side-information that affects the statistics of their measurements, and the network has an overall cost constraint. Nodes can decide whether or not to make a measurement and transmit a message to the fusion center("censoring"), and also have a choice of the transmission function. We study the tradeoff in the detection performance with the cost constraint, and also the impact of sensor cooperation and global sharing of side-information. In particular, we show that if the Type I error probability is constrained to be small, then sensor cooperation is not necessary to achieve the optimal Type II error exponent., by Wee Peng Tay., Ph.D.