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© 2017 IEEE. We investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current densities of traffic. The density on each link has first-order dynamics driven by the difference of its incoming and outgoing flows. A link fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities, that is, the maximum flows that can be sustained by the links, are not always better for preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. We show that systemic failures under feasible external inflows can always be averted through proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it provides a practical alternative to building more physical capacity or altering routing decisions that are determined by social behavior.

© 2017 American Automatic Control Council (AACC). In this paper, we investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current particle densities. The density on each link has first order dynamics driven by the difference of its incoming and outgoing flows. A link irreversibly fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities do not necessarily help in preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. Our main result shows that systemic failures under feasible external inflows can always be averted through a proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it is much easier in practice to adjust the speed limits than to build more physical capacity or to alter routing decisions that are determined by social behavior.

© 2017 IEEE. Load-serving entities which procure electricity from the wholesale electricity market to service end-users face significant quantity and price risks due to the volatile nature of electricity demand and quasi-fixed residential tariffs at which electricity is sold. This paper investigates strategies for load serving entities to hedge against such price risks. Specifically, we compute profit-maximizing portfolios of forward contract and call options as a function of uncertain aggregate user demand and wholesale electricity prices. We compare the profit to the case of Demand Response, where users are offered monetary incentives to temporarily reduce their consumption during periods of supply shortages. Using smart meter data of residential customers in California, we simulate optimal portfolios and derive conditions under which Demand Response outperforms call options and forward contracts. Our analysis suggests that Demand Response becomes more competitive as wholesale electricity prices increase.

© 2017 American Automatic Control Council (AACC). In this paper, we investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current particle densities. The density on each link has first order dynamics driven by the difference of its incoming and outgoing flows. A link irreversibly fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities do not necessarily help in preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. Our main result shows that systemic failures under feasible external inflows can always be averted through a proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it is much easier in practice to adjust the speed limits than to build more physical capacity or to alter routing decisions that are determined by social behavior.

© 2017 IEEE. We investigate the use of variable speed limits for resilient operation of transportation networks, which are modeled as dynamical flow networks under local routing decisions. In such systems, some external inflow is injected to the so-called origin nodes of the network. The total inflow arriving at each node is routed to its operational outgoing links based on their current densities of traffic. The density on each link has first-order dynamics driven by the difference of its incoming and outgoing flows. A link fails if it reaches its jam density. Such failures may propagate in the network and cause a systemic failure. We show that larger link capacities, that is, the maximum flows that can be sustained by the links, are not always better for preventing systemic failures under local routing. Accordingly, we propose the use of variable speed limits to operate the links below their capacities, when necessary, to compensate for the lack of global information and coordination in routing decisions. We show that systemic failures under feasible external inflows can always be averted through proper selection of speed limits if the routing decisions are sufficiently responsive to local congestion and the network is initially uncongested. This is an attractive feature as it provides a practical alternative to building more physical capacity or altering routing decisions that are determined by social behavior.

We address the problem of learning the parameters of a mean square stable switched linear systems(SLS) with unknown latent space dimension, or order, from its noisy input-output data. In particular, we focus on learning a good lower order approximation of the underlying model allowed by finite data. This is achieved by constructing Hankel-like matrices from data and obtaining suitable approximations via SVD truncation where the threshold for SVD truncation is purely data dependent. By exploiting tools from theory of model reduction for SLS, we find that the system parameter estimates are close to a balanced truncated realization of the underlying system with high probability.

We investigate the ability of a collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. In a previous paper, we derived upper bounds on the parameters of the batteries that can be emulated, and showed that there is a fundamental trade-off between the abilities of collective load to absorb and release energy at high rates. Here, we introduce a novel class of dynamic priority-driven feedback policies that balance these abilities, and characterize the batteries that they can emulate.

Spurred by the growth of transportation network companies and increasing data capabilities, vehicle routing and ride-matching algorithms can improve the efficiency of private transportation services. However, existing routing solutions do not address where drivers should travel after dropping off a passenger and before receiving the next passenger ride request, i.e., during the between-ride period. We address this problem by developing an efficient algorithm to find the optimal policy for drivers between rides in order to maximize driver profits. We model the road network as a graph, and we show that the between-ride routing problem is equivalent to a stochastic shortest path problem, an infinite dynamic program with no discounting. We prove under reasonable assumptions that an optimal routing policy exists that avoids cycles; policies of this type can be efficiently found. We present an iterative approach to find an optimal routing policy. Our approach can account for various factors, including the frequency of passenger ride requests at different locations, traffic conditions, and surge pricing. We demonstrate the effectiveness of the approach by implementing it on road network data from Boston and New York City.

In coalitional games, traditional coalitional game theory does not apply if different participants hold different opinions about the payoff function that corresponds to each subset of the coalition. In this paper, we propose a framework in which players can exchange opinions about their views of payoff functions and then decide the distribution of the value of the grand coalition. When all players are truth-telling, the problem of opinion consensus is decoupled from the coalitional game, but interesting dynamics will arise when players are strategic in the consensus phase. Assuming that all players are rational, the model implies that, if influential players are risk-averse, an efficient fusion of the distributed data is achieved at pure strategy Nash equilibrium, meaning that the average opinion will not drift. Also, without the assumption that all players are rational, each player can use an algorithmic R-learning process, which gives the same result as the pure strategy Nash equilibrium with rational players.

This paper analyzes the impact of peer effects on electricity consumption of a network of rational, utility-maximizing users. Users derive utility from consuming electricity as well as consuming less energy than their neighbors. However, a disutility is incurred for consuming more than their neighbors. To maximize the profit of the load-serving entity that provides electricity to such users, we develop a two-stage game-theoretic model, where the entity sets the prices in the first stage. In the second stage, consumers decide on their demand in response to the observed price set in the first stage so as to maximize their utility. To this end, we derive theoretical statements under which such peer effects reduce aggregate user consumption. Further, we obtain expressions for the resulting electricity consumption and profit of the load serving entity for the case of perfect price discrimination and a single price under complete information, and approximations under incomplete information. Simulations suggest that exposing only a selected subset of all users to peer effects maximizes the entity's profit.

This paper examines the dependence of network performance measures on network size and considers scaling results for large networks. We connect two performance measures that are well studied, but appear to be unrelated. The first measure is concerned with energy metrics, namely the $H2$-norm of a network, which arises in control theory applications. The second measure is concerned with the notion of “tail risk” which arises in economic and financial networks. We study the question of why such performance measures may deteriorate at a faster rate than the growth rate of the network. We first focus on the energy metric and its well known connection to controllability Gramian of the underlying dynamical system. We show that undirected networks exhibit the most graceful energy growth rates as network size grows. This rate is quantified completely by the proximity of spectral radius to unity or distance to instability. In contrast, we show that the simple characterization of energy in terms of network spectrum does not exist for directed networks. We demonstrate that, for any fixed distance to instability, energy of a directed network can grow at an exponentially faster rate. We provide general methods for manipulating networks to reduce energy. In particular, we prove that certain operations that increase the symmetry in a network cannot increase energy (in an order sense). Additionally, we demonstrate that such operations can effectively reduce energy for many network topologies. Secondly, we focus on tail risk in economic and financial networks. In contrast to H2-norm which arises from computing the expectation of energy in the network, tail risk focuses on tail probability behavior of network variables. Although the two measures differ substantially we show that they are precisely connected through the system Gramian. This surprising result explains why topology considerations rather than specific performance measures dicta

Residential Demand Response has emerged as a viable tool to alleviate supply and demand imbalances of electricity during times when the electric grid is strained. Demand Response providers bid reduction capacity into the wholesale electricity market by asking customers to temporarily reduce consumption in exchange for a monetary incentive. This paper models consumer behavior in response to such incentives by formulating Demand Response in a Mechanism Design framework. In this auction setting, the Demand Response Provider collects price elasticities as bids from its rational, profit-maximizing customers, which allows targeting only the users most susceptible to incentives such that an aggregate reduction target is reached in expectation. We measure reductions by comparing the materialized consumption to the projected consumption, which we model as the '10-in-10'-baseline used by the California Independent System Operator. Due to the suboptimal performance of this baseline, we show, using consumption data of residential customers in California, that Demand Response Providers receive payments for 'virtual reductions', which exist due to the inaccuracies of the baseline rather than actual reductions. Improving the accuracy of the baseline diminishes the contribution of these virtual reductions. Keywords: Load management; Electricity supply industry; Aggregates; Contracts; Elasticity; Buildings

In this paper, we are concerned with the resilience of locally routed network flows with finite link capacities. In this setting, an external inflow is injected to the so-called origin nodes. The total inflow arriving at each node is routed locally such that none of the outgoing links are overloaded unless the node receives an inflow greater than its total outgoing capacity. A link irreversibly fails if it is overloaded or if there is no operational link in its immediate downstream to carry its flow. For such systems, resilience is defined as the minimum amount of reduction in the link capacities that would result in the failure of all the outgoing links of an origin node. We show that such networks do not necessarily become more resilient as additional capacity is built in the network. Moreover, when the external inflow does not exceed the network capacity, selective reductions of capacity at certain links can actually help averting the cascading failures, without requiring any change in the local routing policies. This is an attractive feature as it is often easier in practice to reduce the available capacity of some critical links than to add physical capacity or to alter routing policies, e.g., when such policies are determined by social behavior, as in the case of road traffic networks. The results can thus be used for real-time monitoring of distance-to-failure in such networks and devising a feasible course of actions to avert systemic failures.

This paper analyzes stability conditions for wholesale electricity markets under real-time retail pricing and realistic consumption models with memory, which explicitly take into account previous electricity prices and consumption levels. By passing on the current retail price of electricity from supplier to consumer and feeding the observed consumption back to the supplier, a closed-loop dynamical system for electricity prices and consumption arises whose stability is to be investigated. Under mild assumptions on the generation cost of electricity and consumers' backlog disutility functions, we show that, for consumer models with price memory only, market stability is achieved if the ratio between the consumers' marginal backlog disutility and the suppliers' marginal cost of supply remains below a fixed threshold. Further, consumer models with price and consumption memory can result in greater stability regions and faster convergence to the equilibrium compared to models with price memory alone, if consumption deviations from nominal demand are adequately penalized.

We investigate the ability of a homogeneous collection of deferrable energy loads to behave as a battery; that is, to absorb and release energy in a controllable fashion up to fixed and predetermined limits on volume, charge rate and discharge rate. We derive bounds on the battery capacity that can be realized and show that there are fundamental tradeoffs between battery parameters. By characterizing the state trajectories under scheduling policies that emulate two illustrative batteries, we show that the trade-offs occur because the states that allow the loads to absorb and release energy at high aggregate rates are conflicting.

We infer local influence relations between networked entities from data on outcomes and assess the value of temporal data by formulating relevant binary hypothesis testing problems and characterizing the speed of learning of the correct hypothesis via the Kullback-Leibler divergence, under three different types of available data: knowing the set of entities who take a particular action; knowing the order that the entities take an action; and knowing the times of the actions., United States. Air Force. Office of Scientific Research (Contract FA9550-09-1-0420).

This paper addresses two fundamental problems in the context of hidden Markov models (HMMs). The first problem is concerned with the characterization and computation of a minimal order HMM that realizes the exact joint densities of an output process based on only finite strings of such densities (known as HMM partial realization problem). The second problem is concerned with learning a HMM from finite output observations of a stochastic process. We review and connect two fields of studies: realization theory of HMMs, and the recent development in spectral methods for learning latent variable models. Our main results in this paper focus on generic situations, namely, statements that will be true for almost all HMMs, excluding a measure zero set in the parameter space. In the main theorem, we show that both the minimal quasi-HMM realization and the minimal HMM realization can be efficiently computed based on the joint probabilities of length N strings, for N in the order of O(logd(k)). In other words, learning a quasi-HMM and an HMM have comparable complexity for almost all HMMs.

Pulsatile release of cortisol from the adrenal glands is governed by pulsatile release of adrenocorticotropic hormone (ACTH) from the anterior pituitary. In return, cortisol has a negative feedback effect on ACTH release. Simultaneous recording of ACTH and cortisol is not typical, and determining the number, timing, and amplitudes of pulsatile events from simultaneously recorded data is challenging because of several factors: 1) stimulator ACTH pulse activity, 2) kinematics of ACTH and cortisol, 3) the sampling interval, and 4) the measurement error. We model ACTH and cortisol secretion simultaneously using a linear differential equations model with Gaussian errors and sparse pulsatile events as inputs to the model. We propose a novel framework for recovering pulses and parameters underlying the interactions between ACTH and cortisol. We recover the timing and amplitudes of pulses using compressed sensing and employ generalized cross validation for determining the number of pulses. We analyze serum ACTH and cortisol levels sampled at 10-min intervals over 24 h from ten healthy women. We recover physiologically plausible timing and amplitudes for these pulses and model the feedback effect of cortisol. We recover 15 to 18 pulses over 24 h, which is highly consistent with the results of another cortisol data analysis approach. Modeling the interactions between ACTH and cortisol allows for accurate quantification of pulsatile events, and normal and pathological states. This could lay the basis for a more physiologically-based approach for administering cortisol therapeutically. The proposed approach can be adapted to deconvolve other pairs of hormones with similar interactions., National Institutes of Health (U.S.) (Grant DP1 OD003646), National Science Foundation (U.S.) (Grant 0836720), National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (Grant 0735956), National Science Foundation (U.S.) (Graduate Research Fellowship), National Institutes of Health (U.S.) (Grant R01GM 53559), National Space Biomedical Research Institute (Grant NCC9-58)

We consider a scenario where price-responsive energy consumers are allowed to optimize their individual utilities via mechanisms of load-shifting in a distribution network subject to capacity constraints. The uncoordinated selfish behavior of the consumers would lead, in general, to requests that could not be served by the distribution network because of such constraints. Thus, a centralized or hierarchically coordination mechanism is required. We derive algorithms and methods to determine in real-time the largest set of consumers' decisions that are compatible with the physical constraints of the network and capable of avoiding congestion phenomena in the future. These methods are shown to be applicable to the design of coordination mechanisms with the aim of providing a large number of degrees of freedom to the users while guaranteeing the integrity of the system., Charles Stark Draper Laboratory (URAD Project), Siemens Corporation, National Science Foundation (U.S.) (CPS-1135843)

We consider network flow over graphs between a single origin-destination pair, where the network state consists of flows and activation status of the links. The evolution of the activation status of a link is given by an irreversible transition that depends on the saturation status of that link and the activation status of the downstream links. The flow dynamics is determined by activation status of the links and node-wise routing policies under the flow balance constraints at the nodes. We formulate a deterministic discrete time dynamics for the network state, where the time epochs correspond to a change in the activation status of the links, and study network resilience towards disturbances that reduce link-wise flow capacities, under distributed routing policies. The margin of resilience is defined as the minimum, among all possible disturbances, of the link-wise sum of reductions in flow capacities, under which the links outgoing from the origin node become inactive in finite time. We propose a backward propagation algorithm to compute an upper bound on the margin of resilience for tree-like network topologies with breadth at most 2, and show that this bound is tight for trees with the additional property of having depth at most 2.

We propose a dynamical model for cascading failures in single-commodity network flows. In the proposed model, the network state consists of flows and activation status of the links. Network dynamics is determined by a, possibly state-dependent and adversarial, disturbance process that reduces flow capacity on the links, and routing policies at the nodes that have access to the network state, but are oblivious to the presence of disturbance. Under the proposed dynamics, a link becomes irreversibly inactive either due to overload condition on itself or on all of its immediate downstream links. The coupling between link activation and flow dynamics implies that links to become inactive successively are not necessarily adjacent to each other, and hence the pattern of cascading failure under our model is qualitatively different than standard cascade models. The magnitude of a disturbance process is defined as the sum of cumulative capacity reductions across time and links of the network, and the margin of resilience of the network is defined as the infimum over the magnitude of all disturbance processes under which the links at the origin node become inactive. We propose an algorithm to compute an upper bound on the margin of resilience for the setting where the routing policy only has access to information about the local state of the network. For the limiting case when the routing policies update their action as fast as network dynamics, we identify sufficient conditions on network parameters under which the upper bound is tight under an appropriate routing policy. Our analysis relies on making connections between network parameters and monotonicity in network state evolution under proposed dynamics.

How can we effectively model situations with large alphabets? On a pragmatic level, any engineered system, be it for inference, communication, or encryption, requires working with a finite number of symbols. Therefore, the most straight-forward model is a finite alphabet. However, to emphasize the disproportionate size of the alphabet, one may want to compare its finite size with the length of data at hand. More generally, this gives rise to scaling models that strive to capture regimes of operation where one anticipates such imbalance. Large alphabets may also be idealized as infinite. The caveat then is that such generality strips away many of the convenient machinery of finite settings. However, some of it may be salvaged by refocusing the tasks of interest, such as by moving from sequence to pattern compression, or by minimally restricting the classes of infinite models, such as via tail properties. In this paper we present an overview of models for large alphabets, some recent results, and possible directions in this area.

Author's final manuscript: September 29, 2011, This paper examines the value of storage in securing reliability of a system with uncertain supply and demand, and supply friction. The storage is frictionless as a supply source, but it cannot be filled up instantaneously. The focus is on application to an energy network in which the nominal supply and demand are assumed to match perfectly, while deviations from the nominal values are modeled as random shocks with stochastic arrivals. Due to friction, the random shocks cannot be tracked by the main supply sources. Storage, when available, can be used to compensate, fully or partially, for the surge in demand or sudden drop in supply. The problem of optimal utilization of storage with the objective of maximizing system reliability is formulated as minimization of the expected discounted cost of blackouts over an infinite horizon. It is shown that when the stage cost is linear in the size of the blackout, the optimal policy is myopic in the sense that all shocks will be compensated by storage up to the available level of storage. However, when the stage cost is strictly convex, it may be optimal to curtail some of the demand and allow a small blackout in the interest of maintaining a higher level of reserve, which may help avoid a large blackout in the future. The value of storage capacity in improving reliability, as well as the effects of the associated optimal policies under different stage costs on the probability distribution of blackouts are examined., National Science Foundation (U.S.), Siemens-MIT Alliance

We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent's payoff is the sum of the payoffs coming from pairwise interaction with each of the neighbors. We first establish that the best response dynamics in this networked game is equivalent to the linear threshold dynamics with heterogeneous thresholds over the agents. While the previous literature has studied such linear threshold models under the assumption that each agent may change actions at most once, a study of best response dynamics in such networked games necessitates an analysis that allows for multiple switches in actions. In this paper, we develop such an analysis. We establish that agent behavior cycles among different actions in the limit, we characterize the length of such limit cycles, and reveal bounds on the time steps required to reach them. We finally propose a measure of network resilience that captures the nature of the involved dynamics. We prove bounds and investigate the resilience of different network structures under this measure., Irwin Mark Jacobs and Joan Klein Jacobs Presidential Fellowship, Siebel Scholarship, United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0420), United States. Army Research Office (Grant W911NF-09-1-0556)

Original manuscript: June 7, 2011, The paper proposes a framework for modeling and analysis of the dynamics of supply, demand, and clearing prices in power systems with real-time retail pricing and information asymmetry. Characterized by passing on the real-time wholesale electricity prices to the end consumers, real-time pricing creates a closed-loop feedback system between the physical layer and the market layer of the system. In the absence of a carefully designed control law, such direct feedback can increase sensitivity and lower the system's robustness to uncertainty in demand and generation. It is shown that price volatility can be characterized in terms of the system's maximal relative price elasticity, defined as the maximal ratio of the generalized price-elasticity of consumers to that of the producers. As this ratio increases, the system may become more volatile. Since new demand response technologies increase the price-elasticity of demand, and since increased penetration of distributed generation can also increase the uncertainty in price-based demand response, the theoretical findings suggest that the architecture under examination can potentially lead to increased volatility. This study highlights the need for assessing architecture systematically and in advance, in order to optimally strike the trade-offs between volatility/robustness and performance metrics such as economic efficiency and environmental efficiency.

Original manuscript March 25, 2011, Robustness of distributed routing policies is studied for dynamical networks, with respect to adversarial disturbances that reduce the link flow capacities. A dynamical network is modeled as a system of ordinary differential equations derived from mass conservation laws on a directed acyclic graph with a single origin-destination pair and a constant total outflow at the origin. Routing policies regulate the way the total outflow at each nondestination node gets split among its outgoing links as a function of the current particle density, while the outflow of a link is modeled to depend on the current particle density on that link through a flow function. The dynamical network is called partially transferring if the total inflow at the destination node is asymptotically bounded away from zero, and its weak resilience is measured as the minimum sum of the link-wise magnitude of disturbances that make it not partially transferring. The weak resilience of a dynamical network with arbitrary routing policy is shown to be upper bounded by the network's min-cut capacity and, hence, is independent of the initial flow conditions. Moreover, a class of distributed routing policies that rely exclusively on local information on the particle densities, and are locally responsive to that, is shown to yield such maximal weak resilience. These results imply that locality constraints on the information available to the routing policies do not cause loss of weak resilience. Fundamental properties of dynamical networks driven by locally responsive distributed routing policies are analyzed in detail, including global convergence to a unique limit flow. The derivation of these properties exploits the cooperative nature of these dynamical systems, together with an additional stability property implied by the assumption of monotonicity of the flow as a function of the density on each link., National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (ARES Grant 0735956), United States. Air Force Office of Scientific Research (Grant FA9950-09-1-0538)

We consider a dynamical formulation of network flows, whereby the network is modeled as a switched system of ordinary differential equations derived from mass conservation laws on directed graphs with a single origin-destination pair and a constant inflow at the origin. The rate of change of the density on each link of the network equals the difference between the inflow and the outflow on that link. The inflow to a link is determined by the total flow arriving to the tail node of that link and the routing policy at that tail node. The outflow from a link is modeled to depend on the current density on that link through a flow function. Every link is assumed to have finite capacity for density and the flow function is modeled to be strictly increasing up to the maximum density. A link becomes inactive when the density on it reaches the capacity. A node fails if all its outgoing links become inactive, and such node failures can propagate through the network due to rerouting of flow. We prove some properties of these dynamical networks and study the resilience of such networks under distributed routing policies with respect to perturbations that reduce link-wise flow functions. In particular, we propose an algorithm to compute upper bounds on the maximum resilience over all distributed routing policies, and discuss examples that highlight the role of cascading failures on the resilience of the network., National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (ARES Grant 0735956), United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0538)

Original manuscript: March 25, 2011, Strong resilience properties of dynamical networks are analyzed for distributed routing policies. The latter are characterized by the property that the way the outflow at a non-destination node gets split among its outgoing links is allowed to depend only on local information about the current particle densities on the outgoing links. The strong resilience of the network is defined as the infimum sum of link-wise flow capacity reductions making the asymptotic total inflow to the destination node strictly less than the total outflow at the origin. A class of distributed routing policies that are responsive to local information is shown to yield the maximum possible strong resilience under such local information constraints for an acyclic dynamical network with a single origin-destination pair. The maximal achievable strong resilience is shown to be equal to the minimum node residual capacity of the network. The latter depends on the limit flow of the unperturbed network and is defined as the minimum, among all the non-destination nodes, of the sum, over all the links outgoing from the node, of the differences between the maximum flow capacity and the limit flow of the unperturbed network. We propose a simple convex optimization problem to solve for equilibrium flows of the unperturbed network that minimize average delay subject to strong resilience guarantees, and discuss the use of tolls to induce such an equilibrium flow in traffic networks. Finally, we present illustrative simulations to discuss the connection between cascaded failures and the resilience properties of the network., National Science Foundation (U.S.). Office of Emerging Frontiers in Research and Innovation (Grant 0735956), United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0538)

This paper investigates the impulse response estimation of linear time-invariant (LTI) systems when only noisy finite-length input-output data of the system is available. The competing parametric candidates are the least square impulse response estimates of possibly different lengths. It is known that the presence of noise prohibits using model sets with large number of parameters as the resulting parameter estimation error can be quite large. Model selection methods acknowledge this problem, hence, they provide metrics to compare estimates in different model classes. Such metrics typically involve a combination of the available least-square output error, which decreases as the number of parameters increases, and a function that penalizes the size of the model. In this paper, we approach the model class selection problem from a different perspective that is closely related to the involved denoising problem. The method primarily focuses on estimating the parameter error in a given model class of finite order using the available least-square output error. We show that such an estimate, which is provided in terms of upper and lower bounds with certain level of confidence, contains the appropriate tradeoffs between the bias and variance of the estimation error. Consequently, these measures can be used as the basis for model comparison and model selection. Furthermore, we demonstrate how this approach reduces to the celebrated AIC method for a specific confidence level. The performance of the method as the noise variance and/or the data length varies is explored, and consistency of the approach as the data length grows is analyzed.