an inventory model with limited production capacity and uncertain demands ii the discounted cost criterion this paper considers a single item periodic review inventory model with uncertain demands we assume a finite production capacity in each period with stationary data a convex one period cost function and a continuous demand distribution we show under a few additional unrestrictive assumptions that a modified basic stock policy is optimal under the discounted cost criterion both for finite and infinite planning horizons in addition we characterize the optimal base stock levels in several ways

cutoff rates for coordinate interleaved qam over rayleigh fading channels cutoff rates for perfect coordinate interleaving over flat rayleigh fading channels are computed for some representative two dimensional 2 d and four dimensional 4 d quadrature amplitude modulation qam schemes and compared to the standard symbol interleaved approaches it is shown that for optimized coordinate interleaving i e using optimum rotation parameters that maximize the cutoff rate for a given signal to noise ratio snr coding gains can be achieved vis a vis symbol interleaving that increases with the dimensionality of the signal constellation perfect coherent detection as well as perfect channel state information are assumed

inverse spectral theory for random jacobi matrices we give necessary and sufficient conditions for a herglotz function to be thew function of a random stationary jacobi matrix

on decoding concatenated codes the correcting properties of concatenated codes with parallel decoding over an additive channel are investigated the ith inner decoder s output is a codeword if the euclidean distance between the received vector and some codeword is less than delta sub i and an erasure otherwise the outer decoders correct errors and erasures the error correcting capability which is taken to be the minimum length of any noise vector that can cause an error is obtained for a bank of z inner and outer decoders as a function of the thresholds used the set of thresholds that maximize the error correcting capability is also found it is shown that for a small number of branches the error correcting capability is nearly as large as any decoder

practical codes for photon communication in a recent paper pierce studied the problems of communicating at optical frequencies using photon counting techniques and concluded that at low temperatures we encounter insuperable problems of encoding long before we approach channel capacity in this paper it is shown that even assuming a noiseless model for photon communication for which capacity measured in nats photon is infinite it is unlikely that a signaling efficiency of even 10 nats photon could be achieved practically on the positive side it is shown that pulse position modulation plus reed solomon coding yields practical results in the range of 2 to 3 nats photon

necessary and sufficient conditions for delay moments in fifo multiserver queues with an application comparing s slow servers with one fast one in this paper we establish the weakest known sufficient conditions for the existence of stationary delay moments in fifogi gi s queues fors 2 these conditions involve not only the service time distribution as in the classic kiefer and wolfowitz conditions but also the interplay of the traffic intensity and the number of servers in the queue we then prove the necessity of our conditions for a large class of service times having finite first but infinite ath moment for some finite a such service time distributions include many but not all of the class of heavy tailed distributions the pareto and cauchy are members the weibull is not our results are then applied to provide one answer to the classic question when ares slow servers operating at rate 1 s better than one fast server operating at rate 1 we consider this question with respect to the rate of decay of the tail of stationary customer delay in a system characterized by service times that have finite mean but lack some higher moments such as are often used to model telecommunications traffic fors greater than a traffic related constant the answer isalways our results help to quantify the benefits of extra servers while also pointing the way towards the derivation of bounds and asymptotics for the stationary delay distribution of multiserver queues having these types of service times such queues are attracting a great deal of academic research motivated by their practical use modeling telecommunications systems

regulated random walks and the lcfs backlog probability analysis and application random walks have been used extensively within operations research models such as inventory systems and single server queues to estimate performance measures in this paper we use sample path analysis to express the steady state probability of a one sided regulated random walk to increase and be above a threshold referred to as the last come first serve lcfs backlog probability we approximate the lcfs backlog probability under mild assumptions on the distribution of the random walk s steps and provide its exact expression when the steps are exponentially distributed and a closed form approximation when the steps are normally distributed in our numerical experiments the average relative gap between the approximated lcfs backlog probabilities and their simulated values is 5 13 we further show that the lcfs backlog probability is an upper bound on the loss probability the probability that a two sided regulated random walk is at a boundary this bound is tighter than the backlog probability the probability that a random walk ever crosses a threshold that also bounds the loss probability in an inventory application we demonstrate that using the lcfs backlog probability rather than the backlog probability reduces the inventory level required to satisfy a service level constraint on the percentage of orders backlogged in our examples this reduction leads to cost savings of 31 on average

bounds and asymptotics for planning critical safety stocks we develop bounds and approximations for setting base stock levels in production inventory systems with limited production capacity our approximations become exact as inventories become critical meaning either that the target service level is very high or the backorder penalty is very large our bounds apply even without this requirement we consider both single stage and multi stage systems for single stage systems we find tight bounds and asymptotically exact approximations for optimal base stock levels for multistage systems our results give partial characterizations of the optimal levels part of our analysis is a precise connection in the critical regime between a multistage system and an associated single stage system consisting solely of the bottleneck facility

factorization of random jacobi operators and backlund transformations we show that a positive definite random jacobi operatorl over an abstract dynamical systemt x x can be factorized asl d2 whered is again a random jacobi operator but defined over a new dynamical systems y y which is an integral extension oft an isospectral random toda deformation ofl corresponds to an isospectral random volterra deformation ofd the factorization leads to commuting backlund transformations which can be written explicitly in terms of titchmarsh weyl functions in the periodic case the backlund transformations are time 1 maps of a toda flow with a time dependent hamiltonian

the rotation number for almost periodic potentials we define and analyze the rotation number for the almost periodic schrodinger operatorl d2 dx2 q x we use the rotation number to discuss i the spectrum ofl ii its relation to the korteweg de vries equation

ldpc codes for non coherent block fading channels with correlation analysis and design ldpc codes are analyzed and optimized for a noncoherent block fading channel in which there is correlation between the blocks this extends related work in the literature which considered independent blocks low complexity estimation and estimation decoding algorithms based on kalman smoothing are developed and density evolution is used to analyze and optimize the resulting code results indicate that significant gains can be realized by taking inter block correlation into account compared to architectures in which the blocks are assumed to be independent

impact of diversity reception on fading channels with coded modulation ii differential block detection for pt i see ibid vol 45 no 6 p 563 572 1997 we study coded modulation with block differential detection in an arbitrarily correlated rician fading channel with space diversity coded differential q psk is included in our analysis as a special case a metric is chosen that is optimum for perfect interleaving slow fading and independent diversity branches for slow fading we compare the the cutoff rates of the channels resulting from different choices of block length n and diversity index m specifically we show that block detection with diversity may or may not generate a better coding channel than usual differential detection according to the code selected and the combination of values of m and n in particular for low diversity orders m 1 2 and for low to medium code rates differential detection is still an optimal or near optimal solution while for high diversity orders m spl ges 2 and medium to high code rates up to uncoded modulation block detection with n 2 can provide a significant gain an error floor always exists when fading is fast it decreases exponentially with the product of code diversity and space diversity so that the latter emerges as a very effective technique for lowering the error floor of a system affected by fast fading performance examples based on actual coding schemes are also shown

a differential equation approach to the singular value decomposition of bidiagonal matrices we consider the problem of approximating the singular value decomposition of a bidiagonal matrix by a one parameter family of differentiable matrix flows it is shown that this approach can be fully expressed as an autonomous homogeneous and cubic dynamical system asymptotic behavior is justified by the established theory of the toda lattice

low complexity erasure insertion in rs coded sfh spread spectrum communications with partial band interference and nakagami m fading we propose two novel low complexity low delay erasure insertion schemes namely the output threshold test ott and joint maximum output and ratio threshold test mo rtt the employment of the ott and mo rtt is beneficial in the context of the errors and erasures reed solomon rs decoding in a slow frequency hopping spread spectrum sfh ss system using m ary frequency shift keying mfsk the statistics of the erasure insertion related decision variables associated with the ott mo rtt as well as with the ratio threshold test rtt are investigated when the channel of each frequency hopping fh slot is modeled as flat nakagami m fading the transmitted signals also experience both additive white gaussian noise awgn as well as partial band gaussian interference pbgi the properties of these erasure insertion schemes are investigated with the aid of their statistics the performance of the proposed erasure insertion schemes and that of the erasure insertion scheme using the rtt is investigated and compared in the context of rs coded sfh ss systems using mfsk furthermore the performance of the rs coded sfh ss systems is also compared both with and without side information concerning the pbgi

delay constrained capacity with causal feedback a block fading channel model is considered and a k block delay constraint is imposed on data transmission the key consideration is that the channel state information is fed back to the transmitter in a causal manner a general cost function spl mu x is considered in solving the delay constrained transmission problem under the short term and the long term power constraints a causal power adaptation strategy is needed to maximize the cost function hence dynamic programming is found to give the optimum solution the general cost function is then specialized to the cases of expected and outage capacities in the case of expected capacity it is observed that optimizing the transmitted power does not give much benefit at high signal to noise ratio snr but provides a substantial gain at low snr at low snr it is proved that the capacity increases by a factor of approximately log k m due to power adaptation when the channel fades according to the spl chi sub 2m sup 2 statistics in the case of outage capacity it is shown that the optimum power adaptation solution to the long term constraint problem provides a substantial snr gain at both low and high values of snr random coding bounds are derived for the outage capacity algorithms

kotani theory for one dimensional stochastic jacobi matrices we consider families of operators h on l2 given by h u n u n 1 u n 1 v n u n wherev is a stationary bounded ergodic sequence we prove analogs of kotani s results including that for a e ac h is the essential closure of the set ofe where e the lyaponov index vanishes and the result that ifv is non deterministic then ac is empty

clipped diversity combining for channels with partial band interference ii ratio statistic combining for pt i see ibid vol com 3 no 12 p 1320 1987 ratio statistic combining is proposed for mitigating partial band interference in systems with diversity transmission and frequency hop signaling systems with noncoherent demodulation and binary orthogonal signaling are covered the partial band interference is gaussian and gaussian quiescent noise is included in the analysis to account for wideband noise sources the exact probability of error is found for a receiver using ratio statistic combining and this is compared to the exact error probabilities for receivers with optimum combining with perfect side information clipped linear combining the ratio threshold test with majority logic decoding and self normalization diversity combining numerical results are also given for a frequency hop system which uses ratio statistic combining for channels with rayleigh fading and partial band interference it is determined that ratio statistic combining is an excellent diversity combining scheme for systems with partial band interference and fading

channels with block interference a new class of channel models with memory is presented in order to study various kinds of interference phenomena it is shown among other things that when all other parameters are held fixed channel capacity c is an em increasing function of the memory length while the cutoff rate r 0 generally is a em decreasing function calculations with various explicit coding schemes indicate that c is better than r 0 as a performance measure for these channel models as a partial resolution of this c versus r 0 paradox the conjecture is offered that r 0 is more properly a measure of coding delay rather than of coding complexity

generalized affine lie algebras and the solution of a class of flows associated with the qr eigenvalue algorithm in 3 the authors show that the qr algorithm to compute the eigenvalues of a matrix is the integer time evaluation of a completely integrable hamiltonian system here the authors show that all the associated commuting integrals generate flows that can be solved explicitly via a factorization procedure on a suitable finite or infinite dimensional lie algebra

renormalization of random jacobi operators we construct a cantor set open image in new window of limit periodic jacobi operators having the spectrum on the julia setj of the quadratic mapz z2 e for large negative real numberse the density of states of each of these operators is equal to the unique equilibrium measure onj the jacobi operators in open image in new window are defined over the von neumann kakutani system a group translation on the compact topological group of dyadic integers the cantor set open image in new window is an attractor of the iterated function system built up by the two renormalisation maps l d 2 e d to prove the contraction property we use an explicit interpolation of the backlund transformations by toda flows we show that the attractor open image in new window is identical to the hull of the fixed pointl of

long time behaviour of an infinite particle system the long time behaviour of the semi infinite toda lattice is deduced from a set of identities for the squared eigenfunctions of the toda flow

stochastic schrodinger operators and jacobi matrices on the strip we discuss stochastic schrodinger operators and jacobi matrices with wave functions taking values in l so there are 2l lyaponov exponents 1 l 0 l 1 2l 1 our results include the fact that if 1 0 on a set positive measure thenv is deterministic and one that says that e exactly 2j s are zero is the essential support of the a c spectrum of multiplicity 2j

communication over fading channels with delay constraints we consider a user communicating over a fading channel with perfect channel state information data are assumed to arrive from some higher layer application and are stored in a buffer until transmitted we study adapting the user s transmission rate and power based on the channel state information as well as the buffer occupancy the objectives are to regulate both the long term average transmission power and the average buffer delay incurred by the traffic two models for this situation are discussed one corresponding to fixed length variable rate codewords and one corresponding to variable length codewords the tradeoff between the average delay and the average transmission power required for reliable communication is analyzed a dynamic programming formulation is given to find all pareto optimal power delay operating points we then quantify the behavior of this tradeoff in the regime of asymptotically large delay in this regime we characterize simple buffer control policies which exhibit optimal characteristics connections to the delay limited capacity and the expected capacity of fading channels are also discussed

stable non gaussian random processes stochastic models with infinite variance stable random variables on the real line multivariate stable distributions stable stochastic integrals dependence structures of multivariate stable distributions non linear regression complex stable stochastic integrals and harmonizable processes self similar processes chentsov random fields introduction to sample path properties boundedness continuity and oscillations measurability integrability and absolute continuity boundedness and continuity via metric entropy integral representation historical notes and extensions

on the capacity of channels with unknown interference the process of communicating in the presence of interference that is unknown or hostile is modeled as a two person zero sum game with the communicator and the jammer as the players the objective function considered is the rate of reliable communication the communicator s strategies are encoders and distributions on a set of quantizers the jammer s strategies are distributions on the noise power subject to certain constraints various conditions are considered on the jammer s strategy set and on the communicator s knowledge for the case where the decoder is uninformed of the actual quantizer chosen it is shown that from the communicator s perspective the worst case jamming strategy is a distribution concentrated on a finite number of points thereby converting a functional optimization problem into a nonlinear programming problem moreover the worst case distributions can be characterized by means of necessary and sufficient conditions which are easy to verify for the case where the decoder is informed of the actual quantizer chosen the existence of saddle point strategies is demonstrated the analysis is also seen to be valid for a number of situations where the jammer is adaptive

corrected diffusion approximations for a multistage production inventory system we analyze a multistage inventory system with limited production capacity facing stochastic demands each node follows a periodic review base stock policy for echelon inventory in each period each node attempts to produce enough material to restore cumulative down stream inventory to a fixed target level we develop approximations to the key measures of interest average inventories average backorders and service levels by simultaneously letting the mean demand approach the system s bottleneck capacity and letting the base stock level for finished goods increase without bound using a method of siegmund we thus obtain diffusion limits with higher order correction terms a numerical example suggests that the correction terms can substantially improve the accuracy of the approximations

asymptotic performance of m ary orthogonal signals in worst case partial band interference and rayleigh fading it is shown that for worst case partial band jamming the error probability performance for fixed e sub b n sub i becomes worse with increasing m for m 16 the asymptotic probability of error is not zero for any e sub b n sub i ln 2 but decreases inverse linearly with respect to it in the fading case the error probability performance for fixed e sub b n sub 0 improves with m for noncoherent detection but worsens with m for coherent detection for large e sub b n sub 0 the performance of the rayleigh fading channel asymptotically approaches the same limit as the worst case partial band jammed channel however for values of m at least up to 4096 the partial band jammed channel does better while it is unlikely that an m ary orthogonal signal set with m 1024 will be used in a practical situation these results suggest an important theoretical problem namely what signal set achieves reliable communication

amount of rotation about a point and the morse index for the case of exact area preserving monotone twist diffeomorphisms we give formulas relating the amount of rotation about an orbit and certain morse indices

topological entropy of standard type monotone twist maps we study invariant measures of families of monotone twist maps s q p 2q p v q q with periodic morse potential v we prove that there exist a constant c c v such that the topological entropy satisfies htop s log c 3 in particular htop s for we show also that there exist arbitrary large such that s has nonuniformly hyperbolic invariant measures with positive metric entropy for large the measures are hyperbolic and for a class of potentials which includes v q sin q the lyapunov exponent of the map s with invariant measure grows monotonically with

coding for frequency hopped spread spectrum communication with partial band interference part i capacity and cutoff rate the performance of optimal codes on frequency hopped channels with partial band interference is investigated the performance measures considered are channel capacity and cutoff rate worst case partial band gaussian noise interference is assumed with the interference independent of the transmitted signal the capacity and cutoff rate are calculated as a function of the signal to noise ratio we consider soft decision receivers and hard decision receivers with and without side information optimal code rates are found for each of the above cases the required signal to noise ratio for reliable communication when codes are used is determined as a function of the code rate

isospectral deformations of random jacobi operators we show the integrability of infinite dimensional hamiltonian systems obtained by making isospectral deformations of random jacobi operators over an abstract dynamical system the time 1 map of these so called random toda flows can be expressed by aqr decomposition

toda flows with infinitely many variables abstract the toda flow and related flows extend naturally to operators in hilbert space and the purpose of this paper is to describe these flows and to analyse some of their special properties

the importance of power tail distributions for modeling queueing systems power tail distributions are those for which the reliability function is of the form x for large x although they look well behaved they have the singular property that e xl infinity for all l thus it is possible to have a distribution with an infinite variance or even an infinite mean as pathological as these distributions seem to be they occur everywhere in nature from the cpu time used by jobs on main frame computers to sizes of files stored on discs earthquakes or even health insurance claims recently traffic on the electronic super highway was revealed to be of this type too in this paper we first describe these distributions in detail and show their suitability to model self similar behavior e g of the traffic stated above then we show how these distributions can occur in computer system environments and develop a so called truncated analytical model that in the limit is power tail we study and compare the effects on system performance of a gi m 1 model both for the truncated and the limit case and demonstrate the usefulness of these approaches particularly for markov modeling with laqt linear algebraic approach to queueing theory lipsky 1992 techniques

the rotation number for finite difference operators and its properties we discuss a rotation number for second order finite difference operators ifk denotes the integrated density of states thenk 2 for almost periodic operators k is proved to lie in the frequency module whenever is outside the spectrum this yields a labelling of the gaps of the spectrum

pragmatic space time trellis codes gtf based design for block fading channels the pragmatic approach for the construction of space time codes over block fading channels leads to low complexity encoders decoders making them suitable for various applications including cooperative communications we propose a design methodology for pragmatic space time codes which is based on an extension of the concept of generalized transfer function our search algorithm provides code generators for arbitrary number of states antennas and fading rates numerical results show that the performance of the pragmatic space time codes obtained by our design methodology is generally better than that of previously known space time trellis codes in block fading channels

ordinary differential equations and the symmetric eigenvalue problem in this paper the authors develop a general framework for calculating the eigenvalues of a symmetric matrix using ordinary differential equations new algorithms are suggested and old algorithms including qr are interpreted

further results on convolutional code search for block fading channels this correspondence presents results of code search for convolutional codes over block fading channels bfcs search criteria are based on a union bound approach which exploits the concept of generalized transfer function gtf of the error trellis diagram a new asymptotic bound is derived and the performance of the codes found using our search criterion is compared analytically and by numerical simulation with already existing codes

matrix factorizations and integrable systems on montre que les algorithmes qr lij et de cholesky pour calculer les valeurs propres de matrices reelles sont les evaluations a temps entier de flots hamiltoniens completement integrables