random observations of marked cox processes time insensitive functionals abstract this article has as an objective to analyze the behavior of multivariate delayed stationary marked cox processes with mutually dependent components about some critical levels the original problems arise in biology computer engineering computer networks software reliability testing and stock market the process under investigation can describe the evolution of stocks indexes cancer cells proliferation of bacteria inventories military conflicts in which the process is being observed only restrictively i e at some specified random epochs given this sometimes limited information it is possible to predict the first passage time when the process crosses the critical level or levels and see the main probability characteristics such as distribution of the components of the process upon the first passage time that occurs at one of the observation times among various questions to arise one is how to choose the frequency of observations to provide more accurate information but not to exceed the budget a quint essence of reliability analysis on the other hand there are ways to scrutinize the available information as to making it analytically more time sensitive without any additional efforts which is one of the primary goals of this investigation we formalize and provide preliminary results for the work to be continued in j math anal appl 293 2004 14 27 about time sensitive functionals and give closed form expressions many examples from science and technology are presented

time sensitive functionals of marked cox processes this paper continues studies on a multivariate marked cox process ct observed upon some random epochs 1 2 initiated in j math anal appl 293 2004 1 13 the goal is to connect the continuous time parameter process ct with c for which closed form transforms were presented in that paper this work does not only restore some or much of the information on ct lost due to its limited observation but it also manages to scrutinize the behavior of c around the first passage time of c that takes place upon one of the observation epochs within some random time intervals again analytically tractable formulas for functionals of c are derived

partially observable markov decision processes incorporating epistemic uncertainties abstract the use of markov decision processes for inspection maintenance and rehabilitation of civil engineering structures relies on the use of several transition matrices related to the stochastic degradation process maintenance actions and imperfect inspections point estimators for these matrices are usually used and they are evaluated using statistical inference methods and or expert evaluation methods thus considerable epistemic uncertainty often veils the true values of these matrices our contribution through this paper is threefold first we present a methodology for incorporating epistemic uncertainties in dynamic programming algorithms used to solve finite horizon markov decision processes which may be partially observable second we propose a methodology based on the use of dirichlet distributions which answers in our sense much of the controversy found in the literature about estimating markov transition matrices third we show how the complexity resulting from the use of monte carlo simulations for the transition matrices can be greatly overcome in the framework of dynamic programming the proposed model is applied to concrete bridge under degradation in order to provide the optimal strategy for inspection and maintenance the influence of epistemic uncertainties on the optimal solution is underlined through sensitivity analysis regarding the input data

strong approximations for time dependent queues a time dependent mt mt 1 queue alternates through periods of under over and critical loading we derive period dependent pathwise asymptotic expansions for its queue length within the framework of strong approximations our main results include time dependent fluid approximations supported by a functional strong law of large numbers and diffusion approximations supported by a functional central limit theorem this complements and extends previous work on asymptotic expansions of the queue length transition probabilities

subspace based fault detection robust to changes in the noise covariances the detection of changes in the eigenstructure of a linear time invariant system by means of a subspace based residual function has been proposed previously while enjoying some success in its applicability in particular in the context of vibration monitoring the robustness of this framework against changes in the noise properties has not been properly addressed yet in this paper a new robust residual is proposed and the robustness of its statistics against changes in the noise covariances is shown the complete theory for hypothesis testing for fault detection is derived and a numerical illustration is provided

minimal area metrics on the swiss cross and punctured torus the closed string theory minimal area problem asks for the conformal metric of least area on a riemann surface with the condition that all non contractible closed curves have length greater than or equal to an arbitrary constant that can be set to one through every point in such a metric there is a geodesic that saturates the length condition and the saturating geodesics in a given homotopy class form a band the extremal metric is unknown when bands of geodesics cross as it happens for surfaces of non zero genus we use recently proposed convex programs to numerically find the minimal area metric on the square torus with a square boundary for various sizes of the boundary for large enough boundary the problem is equivalent to the swiss cross challenge posed by strebel we find that the metric is positively curved in the two band region and flat in the single band regions for small boundary the metric develops a third band of geodesics wrapping around it and has both regions of positive and of negative curvature this surface can be completed to provide the minimal area metric on a once punctured torus representing a closed string tadpole diagram

stochastic differential equations with reflecting boundary conditions on resout des equations differentielles stochastiques a conditions aux limites reflechissantes par une approche directe basee sur le probleme de skorokhod

diffusion approximations for g m n gi queues with state dependent service rates we consider a sequence of many server queueing systems with impatient customers of the type g m n gi in heavy traffic this sequence is indexed by n where the parameter n represents the number of servers in the nth system the state process is considered to be the diffusion scaled total customer count in the system and the service rate is a state dependent perturbation of a given basic service rate 0 0 when the system is critically loaded in the halfin whitt heavy traffic regime we obtain the limiting diffusion for the state processes we also establish the asymptotic relationships among the diffusion scaled processes representing the total customer count virtual waiting time and the number of customer abandonments motivated by the cost structures of telephone call centers we formulate a cost functional and show that the expected value of this cost functional in the nth system converges to that of the limiting diffusion under mild assumptions

consistency and asymptotic normality of some subspace algorithms for systems without observed inputs asymptotic normality for a class of subspace algorithms which estimate the state in a first step is derived expressions for the asymptotic variance are given linear systems with unobserved white noise inputs are considered a class of subspace estimates for the system matrices obtained by estimating the state in the first step is analyzed the main result presented here states asymptotic normality of subspace estimates in addition a consistency result for the system matrix estimates is given an algorithm to compute the asymptotic variances of the estimates is presented in a final section the implications of the result are discussed

maximal flow through a domain in place of flows on a discrete network we study flows described by a vector field x y in a plane domain the analogue of the capacity constraint is c x y and the strength of sources and sinks is n f on the boundary and div f in the interior we show that the largest the maximal flow is determined by the minimal cut as in the discrete case the dual problem has a 0 1 solution given by the characteristic function of the minimal cut for the continuous problem the argument depends on the coarea formula for functions of bounded variation

analysis of the asymptotic properties of the moesp type of subspace algorithms the moesp type of subspace algorithms are used for the identification of linear discrete time finite dimensional state space systems they are based on the geometric structure of covariance matrices and exploit the properties of the state vector extensively in this paper the asymptotic properties of the algorithms are examined the main results include consistency and asymptotic normality for the estimates of the system matrices under suitable assumptions on the noise sequence the input process and the underlying true system

dimensioning large call centers we develop a framework for asymptotic optimization of a queueing system the motivation is the staffing problem of call centers with 100 s of agents or more such a call center is modeled as an m m n queue where the number of agents n is large within our framework we determine the asymptotically optimal staffing level n that trades off agents costs with service quality the higher the latter the more expensive is the former as an alternative to this optimization we also develop a constraint satisfaction approach where one chooses the least n that adheres to a given constraint on waiting cost either way the analysis gives rise to three regimes of operation quality driven where the focus is on service quality efficiency driven which emphasizes agents costs and a rationalized regime that balances and in fact unifies the other two numerical experiments reveal remarkable accuracy of our asymptotic approximations over a wide range of parameters from the very small to the extremely large n is em exactly optimal or it is accurate to within a single agent we demonstrate the utility of our approach by revisiting the square root safety staffing principle which is a long existing rule of thumb for staffing the m m n queue in its simplest form our rule is as follows if c is the hourly cost of an agent and a is the hourly cost of customers delay then n r y a over c sqrt r where r is the offered load and y cdot is a function that is easily computable

a fluid limit for an overloaded x model via a stochastic averaging principle we prove a many server heavy traffic fluid limit for an overloaded markovian queueing system having two customer classes and two service pools known in the call center literature as the x model the system uses the fixed queue ratio with thresholds fqr t control which we proposed in a recent paper as a way for one service system to help another in face of an unexpected overload under fqr t customers are served by their own service pool until a threshold is exceeded then one way sharing is activated with customers from one class allowed to be served in both pools after the control is activated it aims to keep the two queues at a prespecified fixed ratio for large systems that fixed ratio is achieved approximately for the fluid limit or fwlln functional weak law of large numbers we consider a sequence of properly scaled x models in overload operating under fqr t our proof of the fwlln follows the compactness approach i e we show that the sequence of scaled processes is tight and then show that all converging subsequences have the specified limit the characterization step is complicated because the queue difference processes which determine the customer server assignments need to be considered without spatial scaling asymptotically these queue difference processes operate on a faster time scale than the fluid scaled processes in the limit because of a separation of time scales the driving processes converge to a time dependent steady state or local average of a time varying fast time scale process ftsp this averaging principle allows us to replace the driving processes with the long run average behavior of the ftsp

subspace model identification part 2 analysis of the elementary output error state space model identification algorithm the elementary moesp algorithm presented in the first part of this series of papers is analysed in this paper this is done in three different ways first we study the asymptotic properties of the estimated state space model when only considering zero mean white noise perturbations on the output sequence it is shown that in this case the moespl implementation yields asymptotically unbiased estimates an important constraint to this result is that the underlying system must have a finite impulse response and subsequently the size of the hankel matrices constructed from the input and output data at the beginning of the computations depends on the number of non zero markov parameters this analysis however leads to a second implementation of the elementary moesp scheme namely moesp2 the latter implementation has the same asymptotic properties without the finite impulse response constraint secondly we compare the moesp2 algorithm with a classical state space model identification scheme the latter

bit threads and holographic entanglement the ryu takayanagi rt formula relates the entanglement entropy of a region in a holographic theory to the area of a corresponding bulk minimal surface using the max flow min cut principle a theorem from network theory we rewrite the rt formula in a way that does not make reference to the minimal surface instead we invoke the notion of a flow defined as a divergenceless norm bounded vector field or equivalently a set of planck thickness bit threads the entanglement entropy of a boundary region is given by the maximum flux out of it of any flow or equivalently the maximum number of bit threads that can emanate from it the threads thus represent entanglement between points on the boundary and naturally implement the holographic principle as we explain this new picture clarifies several conceptual puzzles surrounding the rt formula we give flow based proofs of strong subadditivity and related properties unlike the ones based on minimal surfaces these proofs correspond in a transparent manner to the properties information theoretic meanings we also briefly discuss certain technical advantages that the flows oer over minimal surfaces in a mathematical appendix we review the max flow min cut theorem on networks and on riemannian manifolds and prove in the network case that the set of max flows varies lipshitz continuously in the network parameters

heavy traffic limits for queues with many exponential servers two different kinds of heavy traffic limit theorems have been proved for s server queues the first kind involves a sequence of queueing systems having a fixed number of servers with an associated sequence of traffic intensities that converges to the critical value of one from below the second kind which is often not thought of as heavy traffic involves a sequence of queueing systems in which the associated sequences of arrival rates and numbers of servers go to infinity while the service time distributions and the traffic intensities remain fixed with the traffic intensities being less than the critical value of one in each case the sequence of random variables depicting the steady state number of customers waiting or being served diverges to infinity but converges to a nondegenerate limit after appropriate normalization however in an important respect neither procedure adequately represents a typical queueing system in practice because in the heavy traffic limit an arriving customer is either a

stationary distribution convergence for generalized jackson networks in heavy traffic in a recent paper gamarnik and zeevi gamarnik d a zeevi 2006 validity of heavy traffic steady state approximations in open queueing networks ann appl probab 16 1 56 90 it was shown that under suitable conditions stationary distributions of the scaled queue lengths process for a generalized jackson network converge to the stationary distribution of the associated reflected brownian motion in the heavy traffic limit the proof relied on certain exponential integrability assumptions on the primitives of the network in this note we show that the above result holds under much weaker integrability conditions we provide an alternative proof of this result assuming in addition to natural heavy traffic and stability assumptions only standard independence and square integrability conditions on the network primitives that are commonly used in heavy traffic analysis furthermore under additional integrability conditions we establish convergence of moments of stationary distributions

queues with many servers the virtual waiting time process in the qed regime we consider a first come first served multiserver queue in the quality and efficiency driven qed regime in this regime which was first formalized by halfin and whitt the number of servers n is not small servers utilization is efficiency driven while waiting time is quality driven this is equivalent to having the number of servers n being approximately equal to where r is the offered load and is a positive constant for the g dk n queue in the qed regime we analyze the virtual waiting time vn t as n increases indefinitely assuming that the service time distribution has a finite support hence the dk in g dk n it is shown that in the limit the scaled virtual waiting time is representable as a supremum over a random weighted tree s denotes a service time informally it is then argued that for large n here is the averaging of over s and the process is zero mean gaussian that summarizes all relevant information about arrivals and service times arises as a limit of an infinite server g dk process appropriately scaled the results are obtained by using both combinatorial and probabilistic arguments possible applications of our approximations include fast simulation of queues and estimation prediction of customer waiting times in the qed regime

subspace identification by data orthogonalization and model decoupling it has been observed that identification of state space models with inputs may lead to unreliable results in certain experimental conditions even when the input signal excites well within the bandwidth of the system this may be due to ill conditioning of the identification problem which occurs when the state space and the future input space are nearly parallel we have in particular shown in the companion papers automatica 40 4 2004 575 automatica 40 4 2004 677 that under these circumstances subspace methods operating on input output data may be ill conditioned quite independently of the particular algorithm which is used in this paper we indicate that the cause of ill conditioning can sometimes be cured by using orthogonalized data and by recasting the model into a certain natural block decoupled form consisting of a deterministic and a stochastic subsystem the natural subspace algorithm for the identification of the deterministic subsystem is then a weighted version of the pi moesp method of verhaegen and dewilde int j control 56 1993 1187 1211 the analysis shows that under certain conditions methods based on the block decoupled parametrization and orthogonal decomposition of the input output data perform better than traditional joint model based methods in the circumstance of nearly parallel regressors

a diffusion approximation for the g gi n m queue we develop a diffusion approximation for the queue length stochastic process in theg gi n m queueing model having a general arrival process independent and identically distributed service times with a general distribution n servers andm extra waiting spaces we use the steady state distribution of that diffusion process to obtain approximations for steady state performance measures of the queueing model focusing especially upon the steady state delay probability the approximations are based on heavy traffic limits in whichn tends to infinity as the traffic intensity increases thus the approximations are intended for largen for thegi m n 8 special case halfin and whitt 1981 showed that scaled versions of the queue length process converge to a diffusion process when the traffic intensity napproaches 1 with 1 n v n i for 0 i 8 a companion paper whitt 2005 extends that limit to a special class ofg gi n m nmodels in which the number of waiting places depends onn and the service time distribution is a mixture of an exponential distribution with probabilityp and a unit point mass at 0 with probability 1 p finite waiting rooms are treated by incorporating the additional limitm n vn for 0 8 the approximation for the more generalg gi n m model developed here is consistent with those heavy traffic limits heavy traffic limits for thegi ph n 8 model with phase type service time distributions established by puhalskii and reiman 2000 imply that our approximating process is not asymptotically correct for nonexponential phase type service time distributions but nevertheless the heuristic diffusion approximation developed here yields useful approximations for key performance measures such as the steady state delay probability the accuracy is confirmed by making comparisons with exact numerical results and simulations

identification of the deterministic part of mimo state space models given in innovations form from input output data the problem of linear multivariable state space model identification from input output data can under the presence of process and measurement noise be solved in a non iterative way when incorporating instrumental variables constructed from both input and output sequences in the recently developed class of multivariable output error state space model class of subspace model identification schemes abstract in this paper we describe two algorithms to identify a linear time invariant finite dimensional state space model from input output data the system to be identified is assumed to be excited by a measurable input and an unknown process tloise and the measurements are disturbed by unknown measurement noise both noise sequences are discrete zero mean white noise the first algorithm gives consistent estimates only for the case where the input also is zero mean white noise while the same result is obtained with the second algorithm without this constraint for the special case where the input signal is discrete zero mean white noise it is explicitly shown that this second algorithm is a special case of the recently developed multivariable output error state space moesp class of algorithms based on instrumental variables the usefulness of the presented schemes is highlighted in a realistic simulation study

hazard rate scaling of the abandonment distribution for the gi m n gi queue in heavy traffic we obtain a heavy traffic limit for the gi m n gi queue which includes the entire patience time distribution our main approach is to scale the hazard rate function of the patience time distribution in such a way that our resulting diffusion approximation contains the entire hazard rate function we then show through numerical studies that for various performance measures our approximations tend to outperform those commonly used in practice the robustness of our results is also demonstrated by applying them to solving constraint satisfaction problems arising in the context of telephone call centers

on the ill conditioning of subspace identification with inputs there is experimental evidence that the performance of standard subspace algorithms from the literature e g the n4sid method may be surprisingly poor in certain experimental conditions this happens typically when the past signals past inputs and outputs and future input spaces are nearly parallel in this paper we argue that the poor behavior may be attributed to a form of ill conditioning of the underlying multiple regression problem which may occur for nearly parallel regressors an elementary error analysis of the subspace identification problem shows that there are two main possible causes of ill conditioning the first has to do with near collinearity of the state and future input subspaces the second has to do with the dynamical structure of the input signal and may roughly be attributed to lack of excitation stochastic realization theory constitutes a natural setting for analyzing subspace identification methods in this setting we undertake a comparative study of three widely used subspace methods n4sid robust n4sid and po moesp the last two methods are proven to be essentially equivalent and the relative accuracy regarding the estimation of the a c parameters is shown to be the same

dynamic scheduling of a multiclass queue in the halfin whitt heavy traffic regime we consider a markovian model of a multiclass queueing system in which a single large pool of servers attends to the various customer classes customers waiting to be served may abandon the queue and there is a cost penalty associated with such abandonments service rates abandonment rates and abandonment penalties are generally different for the different classes the problem studied is that of dynamically scheduling the various classes we consider the halfin whitt heavy traffic regime where the total arrival rate and the number of servers both become large in such a way that the system s traffic intensity parameter approaches one an approximating diffusion control problem is described and justified as a purely formal that is nonrigorous heavy traffic limit the hamilton jacobi bellman equation associated with the limiting diffusion control problem is shown to have a smooth classical solution and optimal controls are shown to have an extremal or bang bang character several useful qualitative insights are derived from the mathematical analysis including a square root rule for sizing large systems and a sharp contrast between system behavior in the halfin whitt regime versus that observed in the conventional heavy traffic regime the latter phenomenon is illustrated by means of a numerical example having two customer classes

analysis of state space system identification methods based on instrumental variables and subspace fitting subspace based state space system identification 4sid methods have recently been proposed as an alternative to more traditional techniques for multivariable system identification the advantages are that the user has simple and few design variables and that the methods have robust numerical properties and relatively low computational complexities though subspace techniques have been demonstrated to perform well in a number of cases the performance of these methods is neither fully understood nor analyzed our principal objective is to undertake a statistical investigation of subspace based system identification techniques the studied methods consist of two steps the subspace spanned by the extended observability matrix is first estimated the asymptotic properties of this subspace estimate are derived herein in the second step the structure of the extended observability matrix is used to find a system model estimate two possible methods are considered the simplest one only uses a certain shift invariance property while in the other method a parametric representation of the null space of the observability matrix is exploited explicit expressions for the asymptotic estimation error variances of the corresponding pole estimates are given

quantum max flow min cut the classical max flow min cut theorem describes transport through certain idealized classical networks we consider the quantum analog for tensor networks by associating an integral capacity to each edge and a tensor to each vertex in a flow network we can also interpret it as a tensor network and more specifically as a linear map from the input space to the output space the quantum max flow is defined to be the maximal rank of this linear map over all choices of tensors the quantum min cut is defined to be the minimum product of the capacities of edges over all cuts of the tensor network we show that unlike the classical case the quantum max flow min cut conjecture is not true in general under certain conditions e g when the capacity on each edge is some power of a fixed integer the quantum max flow is proved to equal the quantum min cut however concrete examples are also provided where the equality does not hold we also found connections of quantum max flow min cut with entropy of entanglement and the quantum satisfiability problem we speculate that the phenomena revealed may be of interest both in spin systems in condensed matter and in quantum gravity

subspace based multivariable system identification from frequency response data two noniterative subspace based algorithms which identify linear time invariant mimo multi input multioutput systems from frequency response data are presented the algorithms are related to the recent time domain subspace identification techniques the first algorithm uses equidistantly in frequency spaced data and is strongly consistent under weak noise assumptions the second algorithm uses arbitrary frequency spacing and is strongly consistent under more restrictive noise assumptions promising results are obtained when the algorithms are applied to real frequency data originating from a large flexible structure

service level differentiation in many server service systems via queue ratio routing motivated by telephone call centers we study large scale service systems with multiple customer classes and multiple agent pools each with many agents to minimize staffing costs subject to service level constraints where we delicately balance the service levels sls of the different classes we propose a family of routing rules called fixed queue ratio fqr rules with fqr a newly available agent next serves the customer from the head of the queue of the class from among those he is eligible to serve whose queue length most exceeds a specified proportion of the total queue length the proportions can be set to achieve desired sl targets the fqr rule achieves an important state space collapse ssc as the total arrival rate increases in which the individual queue lengths evolve as fixed proportions of the total queue length in the current paper we consider a variety of service level types and exploit ssc to construct asymptotically optimal solutions for the staffing and routing problem the key assumption in the current paper is that the service rates depend only on the agent pool

range of fluctuation of brownian motion on a complete riemannian manifold we investigate the escape rate of the brownian motion w x t on a complete noncompact riemannian manifold assuming that the manifold has at most polynomial volume growth and that its ricci curvature is bounded below we prove that dist w x t x ct log t for all large t with probability 1 on the other hand if the ricci curvature is nonnegative and the volume growth is at least polynomial of the order n 2 then formula math again for all large t with probability 1 where e 0

queue and idleness ratio controls in many server service systems motivated by call centers we study large scale service systems with multiple customer classes and multiple agent pools each with many agents we propose a family of routing rules called queue and idleness ratio qir rules a newly available agent next serves the customer from the head of the queue of the class from among those he is eligible to serve whose queue length most exceeds a specified state dependent proportion of the total queue length an arriving customer is routed to the agent pool whose idleness most exceeds a specified state dependent proportion of the total idleness we identify regularity conditions on the network structure and system parameters under which qir produces an important state space collapse ssc result in the quality and efficiency driven qed many server heavy traffic limiting regime the ssc result is applied here to prove stochastic process limits and in subsequent papers to solve important staffing and control problems for large scale service systems

routing and staffing in large scale service systems the case of homogeneous impatient customers and heterogeneous servers motivated by call centers we study large scale service systems with homogeneous impatient customers and heterogeneous servers the servers differ with respect to their speed of service for this model we propose staffing and routing rules that are jointly asymptotically optimal in the heavy traffic many server qed ed and ed qed regimes respectively for the qed regime our proposed routing rule is fsf that assigns customers to the fastest server available first in the ed and ed qed regimes all work conserving policies perform asymptotically equally well in all these regimes the form of the asymptotically optimal staffing is consistent with the asymptotically optimal staffing in the same regimes in the single pool case respectively in particular the total service capacity is asymptotically equal to a term that is proportional to the arrival rate plus possibly a term that is proportional to the square root of the arrival rate with both terms being regime dependent our specific proposed approximation for the optimal staffing vector is obtained via a straightforward solution to a deterministic optimization problem subject to a linear feasible region

consistency and relative efficiency of subspace methods we give a consistency proof for two subspace methods we then show the asymptotic equivalence of a special subspace method and the initial estimate proposed by hannan and rissanen finally a simulation study comparing two subspace methods and the maximum likelihood method is performed

heavy traffic limits for the g h2 n m queue we establish heavy traffic stochastic process limits for queue length waiting time and overflow stochastic processes in a class ofg gi n m queueing models withn servers andm extra waiting spaces we let the arrival process be general only requiring that it satisfy a functional central limit theorem to capture the impact of the service time distribution beyond its mean within a markovian framework we consider a special class of service time distributions denoted byh2 which are mixtures of an exponential distribution with probabilityp and a unit point mass at 0 with probability 1 p these service time distributions exhibit relatively high variability having squared coefficients of variation greater than or equal to one as in halfin and whitt 1981 heavy traffic limits for queues with many exponential servers oper res 29 567 588 puhalskii and reiman 2000 the multiclassgi ph n queue in the halfin whitt regime adv appl probab 32 564 595 and garnett mandelbaum and reiman 2002 designing a call center with impatient customers manufacturing service oper management 4 208 227 we consider a sequence of queueing models indexed by the number of servers n and letn tend to infinity along with the traffic intensities nso that v n 1 n for 8 8 to treat finite waiting rooms we letm n v n for 0 8 with the specialh2 service time distribution the limit processes are one dimensional markov processes behaving like diffusion processes with different drift and diffusion functions in two different regions above and below zero we also establish a limit for theg m n m m model having exponential customer abandonments

n4sid subspace algorithms for the identification of combined deterministic stochastic systems abstract recently a great deal of attention has been given to numerical algorithms for subspace state space system identification n4sid in this paper we derive two new n4sid algorithms to identify mixed deterministic stochastic systems both algorithms determine state sequences through the projection of input and output data these state sequences are shown to be outputs of non steady state kalman filter banks from these it is easy to determine the state space system matrices the n4sid algorithms are always convergent non iterative and numerically stable since they only make use of qr and singular value decompositions both n4sid algorithms are similar but the second one trades off accuracy for simplicity these new algorithms are compared with existing subspace algorithms in theory and in practice

modular subspace based system identification from multi setup measurements subspace identification algorithms are efficient for output only eigenstructure identification of linear mimo systems the problem of merging sensor data obtained from moving and nonsimultaneously recorded measurement setups under varying excitation is considered to address the problem of dimension explosion when retrieving the system matrices of the complete system a modular and scalable approach is proposed adapted to a large class of subspace methods observability matrices are normalized and merged to retrieve global system matrices

some facts about the choice of the weighting matrices in larimore type of subspace algorithms in this paper the effect of some weighting matrices on the asymptotic variance of the estimates of linear discrete time state space systems estimated using subspace methods is investigated the analysis deals with systems with white or without observed inputs and refers to the larimore type of subspace procedures the main result expresses the asymptotic variance of the system matrix estimates in canonical form as a function of some of the user choices clarifying the question on how to choose them optimally it is shown that the cca weighting scheme leads to optimal accuracy the expressions for the asymptotic variance can be implemented more efficiently as compared to the ones previously published

an ɛ nash equilibrium with high probability for strategic customers in heavy traffic a multiclass queue with many servers is considered where customers make a join or leave decision upon arrival based on queue length information without knowing the state of other queues a game theoretic formulation is proposed and analyzed that takes advantage of a phenomenon unique to heavy traffic regimes namely reiman s snaphshot principle by which waiting times are predicted with high precision by the information available upon arrival the payoff considered is given as a random variable which depends on the customer s decision accounting for waiting time in the queue and penalty for leaving the notion of an equilibrium is only meaningful in an asymptotic framework which is taken here to be the halfin whitt heavy traffic regime the main result is the identification of an nash equilibrium with probability approaching 1 on the way to proving this result new diffusion limit results for systems with finite buffers are obtained

distance fluctuations and lyapounov exponents we associate certain translation invariant random metrics on r d to brownian motion evolving in a truncated poissonian potential these metrics behave over large distances in an appropriate sense like certain deterministic norms the so called lyapounov exponents we prove here upper bounds on the size of fluctuations of the metrics around their mean under an additional assumption of rotational invariance we also derive upper bounds on the difference between the mean of the metrics and the lyapounov norms

queues with many servers and impatient customers the asymptotic many server queue with abandonments g gi n gi is considered in the quality and efficiency driven qed regime here the number of servers and the offered load are related via the square root rule as the number of servers increases indefinitely qed performance entails short waiting times and scarce abandonments high quality jointly with high servers utilization high efficiency which is feasible when many servers cater to a single queue for the g gi n gi queue we derive diffusion approximations for both its queue length and virtual waiting time processes special cases for which closed form analysis is provided are the g m n gi and g d n gi queues thus expanding and generalizing existing results

the ryu takayanagi formula from quantum error correction i argue that a version of the quantum corrected ryu takayanagi formula holds in any quantum error correcting code i present this result as a series of theorems of increasing generality with the final statement expressed in the language of operator algebra quantum error correction in ads cft this gives a purely boundary interpretation of the formula i also extend a recent theorem which established entanglement wedge reconstruction in ads cft when interpreted as a subsystem code to the more general and i argue more physical case of subalgebra codes for completeness i include a self contained presentation of the theory of von neumann algebras on finite dimensional hilbert spaces as well as the algebraic definition of entropy the results confirm a close relationship between bulk gauge transformations edge modes soft hair on black holes and the ryu takayanagi formula they also suggest a new perspective on the homology constraint which basically is to get rid of it in a way that preserves the validity of the formula but which removes any tension with the linearity of quantum mechanics moreover they suggest a boundary interpretation of the bit threads recently introduced by freedman and headrick

risk sensitive control for the parallel server model a markovian queueing model is considered in which servers of various types work in parallel to process jobs from a number of classes at rates mu ij that depend on the class i and the type j the problem of dynamic resource allocation so as to minimize a risk sensitive criterion is studied in a law of large numbers scaling letting x i t denote the number of class i jobs in the system at time t the cost is given by e exp n int 0 th bar x t dt g bar x t where t 0 h and g are given functions satisfying regularity and growth conditions and bar x bar x n n 1 x n cdot it is well known in an analogous context of controlled diffusion and has been shown for some classes of stochastic networks that the limit behavior as n to infty is governed by a differential game dg in which the state dynamics is given by a fluid equation for the formal limit varphi of bar x while the cost consists of int 0 th varphi t dt g varphi t and an additional term th

subspace identification of multivariable linear parameter varying systems a subspace identification method is discussed that deals with multivariable linear parameter varying state space systems with affine parameter dependence it is shown that a major problem with subspace methods for this kind of system is the enormous dimension of the data matrices involved to overcome the curse of dimensionality we suggest using only the most dominant rows of the data matrices in estimating the model an efficient selection algorithm is discussed that does not require the formation of the complete data matrices but processes them row by row

frequency domain subspace identification using frf data from arbitrary signals abstract recently an extension of the frequency domain subspace identification methods was developed that can cope with arbitrary excitation signals and transient effects in this paper the implications of this extended model are investigated for the h 1 estimator it is shown that an extended model makes it possible to start from frequency response functions frfs without suffering from leakage by modelling the initial conditions of each data block used in the averaging procedure of the h 1 estimator in this way the measurements can be averaged in order to reduce both the data set and the noise levels without introducing bias errors caused by leakage phenomena it is shown by both simulations and real life measurements that the presented approach improves the modal parameter estimates and in particular the damping estimates

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

on the invariance principle for the first passage time new results are obtained on the connection between the invariance principle for the first passage time process and that for the underlying processes the main contribution is that the passing process may have general drift an example of the application is given which shows that this is of use in deriving limit theorems for delays from limit theorems for queue lengths when studying queueing systems with queue dependent arrival or and service completion rates

asymptotic variance of subspace methods by data orthogonalization and model decoupling a comparative analysis this is a companion of the paper chiuso and picci 2004d where we do asymptotic error analysis of a weighted pi moesp type method and compare accuracy with respect to estimates obtained by customary joint subspace methods the analysis shows that under certain conditions methods based on orthogonal decomposition of the input output data and block decoupled parametrization perform better than traditional joint model based methods in the circumstance of nearly parallel regressors

a fluid approximation for service systems responding to unexpected overloads in a recent paper we considered two networked service systems each having its own customers and designated service pool with many agents where all agents are able to serve the other customers although they may do so inefficiently usually the agents should serve only their own customers but we want an automatic control that activates serving some of the other customers when an unexpected overload occurs assuming that the identity of the class that will experience the overload or the timing and extent of the overload are unknown we proposed a queue ratio control with thresholds when a weighted difference of the queue lengths crosses a prespecified threshold with the weight and the threshold depending on the class to be helped serving the other customers is activated so that a certain queue ratio is maintained we then developed a simple deterministic steady state fluid approximation based on flow balance under which this control was shown to be optimal and we showed how to calculate the control parameters in this sequel we focus on the fluid approximation itself and describe its transient behavior which depends on a heavy traffic averaging principle the new fluid model developed here is an ordinary differential equation driven by the instantaneous steady state probabilities of a fast time scale stochastic process the averaging principle also provides the basis for an effective gaussian approximation for the steady state queue lengths effectiveness of the approximations is confirmed by simulation experiments

dynamics of new product introduction in closed rental systems we study a rental system where a fixed number of heterogeneous users rent one product at a time from a collection of reusable products the online dvd rental firm netflix provides the motivation we assume that rental durations of each user are independent and identically distributed with finite mean we study transient behavior in this system following the introduction of a new product that is desired by all the users we represent the usage process for this new product in terms of an empirical distribution this allows us to characterize the asymptotic behavior of the usage process as the number of users increases without bound via appropriate versions of glivenko cantelli and donsker s theorems analyzing the usage process we demonstrate that an increase in the variability of the rental duration distribution can actually help the firm by allowing it to set lower capacity levels to provide a desired quality of service further we show that the firm is better off not imposing any deadlines for the return of the product

single sample modal identification of a nonstationary stochastic process gauss markov processes excited by nonstationary noises are encountered in the modeling of vibrating systems we prove that the classical instrumental variable method as well as the ho kalman realization algorithm for identifying the pole part modal characteristics of the model are consistent when used on a single sample of the nonstationary signal

nonstationary consistency of subspace methods in this paper we study ldquononstationary consistencyrdquo of subspace methods for eigenstructure identification i e the ability of subspace algorithms to converge to the true eigenstructure despite nonstationarities in the excitation and measurement noises note that such nonstationarities may result in having time varying zeros for the underlying system so the problem is nontrivial in particular likelihood and prediction error related methods do not ensure consistency under such situation because estimation of poles and estimation of zeros are tightly coupled we show in turn that subspace methods ensure such consistency our study carefully separates statistical from nonstatistical arguments therefore enlightening the role of statistical assumptions in this story

selected topics in robust convex optimization robust optimization is a rapidly developing methodology for handling optimization problems affected by non stochastic uncertain but bounded data perturbations in this paper we overview several selected topics in this popular area specifically 1 recent extensions of the basic concept of robust counterpart of an optimization problem with uncertain data 2 tractability of robust counterparts 3 links between ro and traditional chance constrained settings of problems with stochastic data and 4 a novel generic application of the ro methodology in robust linear control

state space formulation a solution to modal parameter estimation abstract as an alternative to fourier techniques based on transfer function fitting modal parameters identification methods derived from a state space formulation of the dynamic equation have been recently studied and developed this formulation leads to the solution of the modal problem via multi dimensional arma model parameters identification in this paper the transition from the dynamic equation to the arma model is described and the algorithms of identification are explained for the very common case of uncontrolled and unmeasured excitation these techniques the qualities of which have been established during extensive processing of offshore structures measurements have been generalized to more complex excitation models such as those of turbo alternators several examples illustrate these different application domains

gaussian limits for a fork join network with nonexchangeable synchronization in heavy traffic we study a fork join network of stations with multiple servers and nonexchangeable synchronization in heavy traffic under the first come first served fcfs discipline tasks are only synchronized if all the tasks associated with the same job are completed service times of parallel tasks of each job can be correlated we jointly consider the number of tasks in each waiting buffer for synchronization with the number of tasks in each parallel service station and the number of synchronized jobs we develop a new approach to show a functional central limit theorem for these processes in the quality driven regime under general assumptions on arrival and service processes specifically we represent these processes as functionals of a sequential empirical process driven by the sequence of service vectors for each job s parallel tasks all of the limiting processes are functionals of two independent processes i e the limiting arrival process and a generalized kiefer process driven by the service vector of

fair dynamic routing in large scale heterogeneous server systems in a call center there is a natural trade off between minimizing customer wait time and fairly dividing the workload among agents of different skill levels the relevant control is the routing policy that is the decision concerning which agent should handle an arriving call when more than one agent is available we formulate an optimization problem for a call center with heterogeneous agent pools in which each pool is distinguished by the speed at which agents in that pool handle calls the objective is to minimize steady state expected customer wait time subject to a fairness constraint on the workload division we first solve the optimization problem by formulating it as a markov decision process mdp and solving a related linear program we note that this approach does not in general lead to an optimal policy that has a simple structure fortunately the optimal policy does appear to have a simple structure as the system size grows large in the halfin whitt many server heavy traffic limit regime therefore we solve the diffusion control problem that arises in this regime and interpret its solution as a policy for the original system the resulting routing policy is a threshold policy that determines server pool priorities based on the total number of customers in the system we prove that a continuous modification of our proposed threshold routing policy is asymptotically optimal in the halfin whitt limit regime we furthermore present simulation results to illustrate that our proposed threshold routing policy outperforms a common routing policy used in call centers that routes to the agent that has been idle the longest