delayed feedback based bifurcation control in an internet congestion model in this paper the control of hopf bifurcation in an internet congestion model with a single link accessed by a single source is presented by choosing the gain parameter as a bifurcation parameter it is found that the system without control cannot guarantee a stationary sending rate furthermore hopf bifurcation occurs when the positive gain parameter of the system exceeds a critical value for internet congestion model a control model based on delayed feedback is proposed and analyzed for delaying the onset of undesirable hopf bifurcation numerical simulations are given to justify the validity of delayed feedback controller in bifurcation control

a family of multi path congestion control algorithms with global stability and delay robustness the goal of traffic management is to efficiently allocate network resources via adjustment of source transmission rates and routes selection mathematically it aims to solve a traditional utility maximization problem in a fair and distributed manner in this paper we first develop a generalized multi path utility maximization problem which features a weighted average of the classical kelly s formulation and the voice s model next we design from this broader framework a family of multi path dual congestion control algorithms whose equilibrium point can both achieve a desired bandwidth utilization and preserve a notion of fairness among competing users global stability can be guaranteed for the proposed schemes in the absence of delays by use of a totally novel lyapunov function moreover when heterogeneous propagation delays are taken into account we establish decentralized and scalable sufficient conditions for robust global stability by constructing a reasonable lyapunov krasovskii functional candidate these conditions give estimates for the maximum admissible delays that the controller can tolerate without losing stability finally we verify the results through simulation

the orthogonal decomposition theorems for mimetic finite difference methods accurate discrete analogs of differential operators that satisfy the identities and theorems of vector and tensor calculus provide reliable finite difference methods for approximating the solutions to a wide class of partial differential equations these methods mimic many fundamental properties of the underlying physical problem including conservation laws symmetries in the solution and the nondivergence of particular vector fields i e they are divergence free and should satisfy a discrete version of the orthogonal decomposition theorem this theorem plays a fundamental role in the theory of generalized solutions and in the numerical solution of physical models including the navier stokes equations and in electrodynamics we are deriving mimetic finite difference approximations of the divergence gradient and curl that satisfy discrete analogs of the integral identities satisfied by the differential operators we first define the natural discrete divergence gradient and curl operators based on coordinate invariant definitions such as gauss s theorem for the divergence next we use the formal adjoints of these natural operators to derive compatible divergence gradient and curl operators with complementary domains and ranges of values in this paper we prove that these operators satisfy discrete analogs of the orthogonal decomposition theorem and demonstrate how a discrete vector can be decomposed into two orthogonal vectors in a unique way satisfying a discrete analog of the formula vec a ggrad varphi curl vec b we also present a numerical example to illustrate the numerical procedure and calculate the convergence rate of the method for a spiral vector field

a smooth model of decision making under ambiguity we propose and axiomatize a model of preferences over acts such that the decision maker prefers act f to act g if and only if e e u f e e u g where e is the expectation operator u is a vn m utility function is an increasing transformation and is a subjective probability over the set of probability measures that the decision maker thinks are relevant given his subjective information a key feature of our model is that it achieves a separation between ambiguity identified as a characteristic of the decision maker s subjective information and ambiguity attitude a characteristic of the decision maker s tastes we show that attitudes towards risk are characterized by the shape of u as usual while attitudes towards ambiguity are characterized by the shape of we also derive x 1 e x as the special case of constant ambiguity aversion ambiguity itself is defined behaviorally and is shown to be characterized by properties of the subjective set of measures this characterization of ambiguity is formally related to the definitions of subjective ambiguity advanced by epstein zhang 2001 and ghirardato marinacci 2002 one advantage of this model is that the welldeveloped machinery for dealing with risk attitudes can be applied as well to ambiguity attitudes the model is also distinct from many in the literature on ambiguity in that allows smooth rather than kinked indifference curves this leads to different behavior and improved tractability while still sharing the main features e g ellsberg s paradox etc the maxmin eu model e g gilboa and schmeidler 1989 with a given set of measures may be seen as an extreme case of our model with infinite ambiguity aversion two illustrative applications to portfolio choice are offered

stability of distributed congestion control with heterogeneous feedback delays we investigate how congestion control can achieve efficient usage of network resources in the presence of heterogeneous communication delays between network users and resources to this end we consider a fluid flow model of network behavior we study the stability of the system s behavior under small perturbations around the target equilibrium point local stability we establish several criteria for stability of certain linear delay differential equations via a technique which essentially reduces the question to studying stability of ordinary differential equations these results are then used to derive sufficient conditions for local stability of the network congestion control problem the same issue has been studied by johari et al 2001 where the authors propose a conjecture according to which local stability can be ensured in a distributed way the correctness of the conjecture was established by johari et al only in degenerate cases where feedback delays coincide our results show that a modified form of the conjecture holds true for arbitrary feedback delays

on delay independent diagonal stability of max min congestion control network feedback in a congestion control system is subject to delay which can significantly affect stability and performance of the entire system while most existing stability conditions explicitly depend on delay di of individual flow i a recent study shows that the combination of a symmetric jacobian a and condition p a 1 guarantees local stability of the system regardless of di however the requirement of symmetry is very conservative and no further results have been obtained beyond this point in this technical note we proceed in this direction and gain a better understanding of conditions under which congestion control systems can achieve delay independent stability towards this end we first prove that if jacobian matrix a satisfies a 1 for any monotonic induced matrix norm the system is locally stable under arbitrary diagonal delay di we then derive a more generic result and prove that delay independent stability is guaranteed as long as a is schur diagonally stable which is also observed to be a necessary condition in simulations utilizing these results we identify several classes of well known matrices that are stable under diagonal delays if rho a 1 and prove stability of mkc with arbitrary parameters alphai and betai

three dimensional magnetotelluric modeling using difference equations theory and comparisons to integral equation solutions we have developed an algorithm for computing the magnetotelluric response of three dimensional 3 d earth models it is a difference equation algorithm that is based on the integral forms of maxwell s equations rather than the differential forms this formulation does not require approximating derivatives of earth properties or electromagnetic fields as happens when using the second order vector diffusion equation rather one must determine how averages are to be computed side boundary values for the h fields are obtained from putting two dimensional 2 d slices of the model into a larger scale 2 d model and solving for the fields at the 3 d boundary positions to solve the 3 d system of equations we propagate an impedance matrix which relates all the horizontal e fields in a layer to all the horizontal h fields in that same layer up through the earth model applying a plane wave source condition and the side boundary h field values allows us to solve for the unknown fields within the model the r

an analysis of finite volume finite element and finite difference methods using some concepts from algebraic topology in this paper we apply the ideas of algebraic topology to the analysis of the finite volume and finite element methods illuminating the similarity between the discretization strategies adopted by the two methods in the light of a geometric interpretation proposed for the role played by the weighting functions in finite elements we discuss the intrinsic discrete nature of some of the factors appearing in the field equations underlining the exception represented by the constitutive term the discretization of which is maintained as the key issue for numerical methods devoted to field problems we propose a systematic technique to perform this task present a rationale for the adoption of two dual discretization grids and point out some optimization opportunities in the combined selection of interpolation functions and cell geometry for the finite volume method finally we suggest an explanation for the intrinsic limitations of the classical finite difference method in the construction of accurate high order formulas for field problems

stability and bifurcation of delayed fractional order dual congestion control algorithms in this technical note fractional order congestion control systems are introduced for the first time in comparison with the conventional integer order dual congestion control algorithms the fractional control algorithms are more accurate and versatile bifurcation theory in fractional order differential equations is still an outstanding problem sufficient conditions for the occurrence of hopf bifurcations are extended from integer order dynamical systems to fractional order cases then these conditions are used to establish the existence of hopf bifurcations for the delayed fractional order model of dual congestion control algorithms proposed in this note finally the onsets of bifurcations are identified where hopf bifurcations occur and a family of oscillations bifurcate from the equilibrium illustrative examples are also provided to demonstrate the theoretical results

global stability analysis of a nonlinear model of internet congestion control with delay we address global stability of a model for the tcp aqm congestion control protocol this model represents the dynamics of a single link and single source and consists of a nonlinear differential equation with a time delay we make use of absolute stability theory and integral quadratic constraints to give conditions under which the dynamics are globally asymptotically stable

ambiguity aversion robustness and the variational representation of preferences we characterize in the anscombe aumann framework the preferences for which there are a utility functionu on outcomes and an ambiguity indexc on the set of probabilities on the states of the world such that for all acts f and g the function u represents the decision maker s risk attitudes while the index c captures his ambiguity attitudes these preferences include the multiple priors preferences of gilboa and schmeidler and the multiplier preferences of hansen and sargent this provides a rigorous decision theoretic foundation for the latter model which has been widely used in macroeconomics and finance

fast simulation of 3d electromagnetic problems using potentials we consider solving three dimensional electromagnetic problems in parameter regimes where the quasi static approximation applies the permeability is constant the conductivity may vary significantly and the range of frequencies is moderate the difficulties encountered include handling solution discontinuities across interfaces and accelerating convergence of traditional iterative methods for the solution of the linear systems of algebraic equations that arise when discretizing maxwell s equations in the frequency domain we use a potential current formulation a with a coulomb gauge the potentials a and decompose the electric field e into components in the active and null spaces of the operator we develop a finite volume discretization on a staggered grid that naturally employs harmonic averages for the conductivity at cell faces after discretization we eliminate the current and the resulting large sparse linear system of equations has a block structure that is diagonally dominant allowing an efficient solution with preconditioned krylov space methods a particularly efficient algorithm results from the combination of bicgstab and an incomplete lu decomposition we demonstrate the efficacy of our method in several numerical experiments

a strong law of large numbers for capacities we consider a totally monotone capacity on a polish space and a sequence of bounded p i i d random variables we show that on a full set any cluster point of empirical averages lies between the lower and the upper choquet integrals of the random variables provided either the random variables or the capacity are continuous

robustness of network flow control against disturbances and time delay this paper studies robustness of kelly s source and link control laws in j oper res soc 49 1998 237 with respect to disturbances and time delays this problem is of practical importance because of unmodelled ows and propagation and queueing delays which are ubiquitous in networks we rst show lp stability for p 1 with respect to additive disturbances we pursue l stability within the input to state stability iss framework of sontag ieee trans automat control 34 1989 435 which makes explicit the vanishing eaect of initial conditions next using this iss property and a loop transformation we prove that global asymptotic stability is preserved for subciently small time delays in forward and return channels for larger delays we achieve global asymptotic stability by scaling down the control gains as in paganini et al proceedings of 2001 conference on decision and control orlando fl december 2001 pp 185 190 c

delay robustness of nonlinear internet congestion control schemes several nonlinear internet congestion control schemes have been proposed in the previous years based on primal and dual decompositions of convex yet centralized optimization problems that describe the bandwidth allocation problem this design methodology uses sub gradient methods for the design of node link dynamics and guarantees nominal functionality for arbitrary system sizes in this technical note we analyze the robustness of such nonlinear schemes to the presence of multiple non commensurate heterogeneous communication delays

global stability of congestion controllers for the internet we consider a single link accessed by a single source which responds to congestion signals from the network the design of controllers for such sources in the presence of feedback delay has received much attention recently here we present conditions for the global asymptotic stability and semiglobal exponential stability of congestion controllers these conditions are natural extensions of conditions obtained through linearized analysis of such systems our result on exponential stability provides the missing link in the proof of how one obtains a single deterministic congestion control equation from a system with many congestion controlled sources and random disturbances using numerical examples we compare the conditions on the congestion control parameters obtained using local and global stability analysis

asymptotic behavior of internet congestion controllers in a many flows regime congestion controllers for the internet are typically designed based on deterministic delay differential equation models in this paper we consider the case of a single link accessed by many tcp like congestion controlled flows and uncontrolled flows that are modeled as stochastic disturbances we show that if the number of flows is large and the link capacity is scaled in proportion to the number of users then under appropriate conditions the trajectory of the stochastic system is eventually well approximated by the trajectory of a delay differential equation our analysis also throws light on the choice of various parameters that ensureglobal asymptotic stability of the limiting deterministic system in the presence of feedback delay numerical examples with some popular congestion feedback mechanisms validate the parameter choices from the analysis the results indicate that a system with multiple tcp like flows is globally stable and thus that a deterministic model is reasonable if the number of flows is large as long asthe product of the throughput and feedback delay per flow is not very small

a non equilibrium analysis and control framework for active queue management we present a non equilibrium analysis and control approach for the active queue management aqm problem in communication networks using simplified fluid models we carry out a bifurcation study of the complex dynamic queue behavior to show that non equilibrium methods are essential for analysis and optimization in the aqm problem we investigate an ergodic theoretic framework for stochastic modeling of the non equilibrium behavior in deterministic models and use it to identify parameters of a fluid model from packet level simulations for computational tractability we use set oriented numerical methods to construct finite dimensional markov models including control markov chains and hidden markov models subsequently we develop and analyze an example aqm algorithm using a markov decision process mdp based control framework the control scheme developed is optimal with respect to a reward function defined over the queue size and aggregate flow rate we implement and simulate our illustrative aqm algorithm in the ns 2 network simulator the results obtained confirm the theoretical analysis and exhibit promising performance when compared with well known alternative schemes under persistent non equilibrium queue behavior

robust global stability to delays of a multi path dual congestion control algorithm abstract global stability has been shown for network congestion control algorithms in the absence of propagation delays by use of the conventional lyapunov function method when heterogeneous delays are taken into account this problem becomes harder and is partly answered until the latest work of papachristodoulou et al where a lyapunov krasovskii functional argument is used to analyze global stability of nonlinear congestion control algorithms but only applicable to the single path case in this paper we develop a new multi path extension to the dual algorithm in the presence of delays by finding a reasonable lyapunov krasovskii functional candidate usually difficult to do in a constructive way we establish a new sufficient condition for robust global stability to delays which includes papachristodoulou s as a special case finally we verify the results through simulations

information and ambiguity toward a foundation of nonexpected utility the concept of ambiguity designates those situations where the information available to the decision maker is insufficient to form a probabilistic view of the world thus it has provided the motivation for departing from the subjective expected utility seu paradigm yet the formalization of the concept is missing this is a grave omission as it leaves nonexpected utility models hanging on shaky ground in particular it leaves unanswered basic questions such as the following 1 does ambiguity exist 2 if so which situations should be labeled as ambiguous 3 why should one depart from seu in the presence of ambiguity 4 if so what kind of behavior should emerge in the presence of ambiguity the present paper fills these gaps specifically it identifies those information structures that are incompatible with seu theory and shows that their mathematical properties are the formal counterpart of the intuitive idea of insufficient information these are used to give a formal definition of ambi