a survey on oscillation of impulsive delay differential equations this paper presents a systematic development of the oscillatory results for the linear and nonlinear impulsive delay differential equations we also discuss linearized oscillation theory and give some applications to mathematical biology

fixed width multiple comparison procedures using common random numbers for steady state simulations abstract suppose that there are k 2 different systems i e stochastic processes where each system has an unknown steady state mean performance we consider the problem of running a two stage simulation using common random numbers to construct fixed width confidence intervals for two multiple comparison problems under the assumptions that the stochastic processes representing the simulation output of the different systems satisfy a functional central limit theorem and that the asymptotic covariance matrix satisfies a condition known as sphericity we prove that our confidence intervals are asymptotically valid as the desired half width of the confidence intervals tend to zero we develop both absolute and relative width confidence intervals empirical results are presented indicating the procedures robustness to violations of the sphericity assumption

on the estimation of optimal batch sizes in the analysis of simulation output abstract the estimation of the variance of point estimators is a classical problem of stochastic simulation a more specific problem addresses the estimation of the variance of a sample mean from a steady state autocorrelated process many proposed estimators of the variance of the sample mean are parameterized by batch size a critical problem is to find an appropriate batch size that provides a good tradeoff between bias and variance this paper proposes a procedure for determining the optimal batch size to minimize the mean squared error of estimators of the variance of the sample mean this paper also presents the results of empirical studies of the procedure the experiments involve symmetric two state markov chain models first order autoregressive processes seasonal autoregressive processes and queue waiting times for several m m 1 queueing models the empirical results indicate that the estimation procedure works nearly as well as it would if the parameters of the processes were known

oscillation for solutions of nonlinear neutral differential equations with impulses abstract this paper is concerned with nonlinear neutral differential equations with impulses of the form some oscillation criteria for solutions of this equation are established an interesting example is also given which illustrates that impulses play an important role in giving rise to the oscillation of equations

transient behavior of the m g 1 workload process in this paper we describe the time dependent moments of the workload process in the m g 1 queue the kth moment as a function of time can be characterized in terms of a differential equation involving lower moment functions and the time dependent server occupation probability for general initial conditions we show that the first two moment functions can be represented as the difference of two nondecreasing functions one of which is the moment function starting at zero the two nondecreasing components can be regarded as probability cumulative distribution function cdf s after appropriate normalization the normalized moment functions starting empty are called moment cdf s the other normalized components are called moment difference cdf s we establish relations among these cdf s using stationary excess relations we apply these relations to calculate moments and derivatives at the origin of these cdf s we also obtain results for the covariance function of the stationary workload process it is inte

multiple positive solutions to superlinear repulsive singular impulsive differential equations the existence of multiple positive solutions to superlinear repulsive singular impulsive differential equations is discussed in this paper the proof relies on a nonlinear alternative of leray schauder type and on krasnoselskii fixed point theorem on compression and expansion of cone

on delay differential equations with impulses abstract sufficient conditions are obtained respectively for the asymptotic stability of the trivial solution of x t ax t j 1 bjx tj t tj t tj and for the existence of a nonoscillatory solution conditions are also obtained for all solutions to be oscillatory the asymptotic behaviour of an impulsively perturbed delay logistic equation is investigated as an extension to a nonlinear equation

batch size effects in the analysis of simulation output batching is a commonly used method for calculating confidence intervals on the mean of a sequence of correlated observations arising from a simulation experiment several recent papers have considered the effect of using batch sizes too small to satisfy assumptions of normality and or independence and the resulting incorrect probabilities of the confidence interval covering the mean this paper quantifies the effects of using batch sizes larger than necessary to satisfy normality and independence assumptions these effects include 1 correct probability of covering the mean 2 an increase in expected half length 3 an increase in the standard deviation and coefficient of variation of the half length and 4 an increase in the probability of covering points not equal to the mean for any sample size and independent and normal batch means the results are 1 the effects of less than 10 batches are large and the effects of more than 30 batches small and 2 additional batches have lesser effects on

derivatives of any order of the gaussian hypergeometric function 2f1 a b c z with respect to the parameters a b and c the derivatives to any order of the gaussian hypergeometric function 2f1 a b c z with respect to the parameters a b and c are expressed in terms of generalizations of multivariable kampe de feriet functions several properties are presented in an application to the two body coulomb scattering problem the usefulness of these derivatives is illustrated with the study of the charge dependence of pollaczek like polynomials

on the integral representations for the confluent hypergeometric function in this paper we derive a new contour integral representation for the confluent hypergeometric function as well as for its various special cases consequently we derive expansions of the confluent hypergeometric function in terms of functions of the same kind furthermore we obtain a new identity involving integrals and sums of confluent hypergeometric functions our results generalized several well known results in the literature

the generalized confluent supersymmetry algorithm representations and integral formulas we extend the confluent version of the higher order supersymmetry susy formalism to general linear differential equations of second order closed form representations of transformation functions their wronskians and of the general solutions to susy transformed equations are derived we use these results to construct formulas for resolving multiple integrals of special functions in terms of wronskians

sequencing and routing in multiclass queueing networks part i feedback regulation this paper establishes new criteria for stability and for instability of multiclass network models under a given stationary policy it also extends previous results on the approximation of the solution to the average cost optimality equations through an associated fluid model it is shown that an optimized network possesses a fluid limit model which is itself optimal with respect to a total cost criterion a general framework for constructing control algorithms for multiclass queueing networks is proposed based on these general results network sequencing and routing problems are considered as special cases the following aspects of the resulting feedback regulation policies are developed in the paper the policies are stabilizing and are in fact geometrically ergodic for a markovian model numerical examples are given in each case it is shown that the feedback regulation policy closely resembles the average cost optimal policy a method is proposed for reducing variance in simulation for a network controlled using a feedback regulation policy

derivatives of any order of the hypergeometric function pfq a1 ap b1 bq z with respect to the parameters ai and bi the derivatives of any order of the general hypergeometric function pfq a1 ap b1 bq z with respect to the parameters ai or bi are expressed in compact form in terms of generalizations of multivariable kampe de feriet functions to achieve this use is made of babister s solution to non homogeneous differential equations for pfq a1 ap b1 bq z an application to hahn polynomials which are 3f2 functions is given as an illustration

standardized time series l p norm variance estimators for simulations this paper studies a class of estimators for the variance parameter of a stationary stochastic process the estimators are based on lp norms of standardized time series and they generalize previously studied estimators due to schruben we show that the new estimators have some desirable properties they are asymptotically unbiased and have low asymptotic variance we also illustrate empirically the performance of the lp norm estimators on various stochastic processes

the asymptotic efficiency of simulation estimators a decision theoretic framework is proposed for evaluating the efficiency of simulation estimators the framework includes the cost of obtaining the estimate as well as the cost of acting based on the estimate the cost of obtaining the estimate and the estimate itself are represented as realizations of jointly distributed stochastic processes in this context the efficiency of a simulation estimator based on a given computational budget is defined as the reciprocal of the risk the overall expected cost this framework is appealing philosophically but it is often difficult to apply in practice e g to compare the efficiency of two different estimators because only rarely can the efficiency associated with a given computational budget be calculated however a useful practical framework emerges in a large sample context when we consider the limiting behavior as the computational budget increases a limit theorem established for this model supports and extends a fairly well known efficiency principle

persistent impulsive effects on stability of functional differential equations with finite or infinite delay abstract in this paper the stability problem of impulsive functional differential equations ifdes is considered several criteria ensuring the uniform stability of ifdes with finite or infinite delay are derived by establishing some new razumikhin conditions different with the current existing ones our development results can be applied to delay systems with persistent impulsive effects finally an example and its computer simulation is given to show the effectiveness and advantages of the proposed method

markov chains for exploring posterior distributions several markov chain methods are available for sampling from a posterior distribution two important examples are the gibbs sampler and the metropolis algorithm in addition several strategies are available for constructing hybrid algorithms this paper outlines some of the basic methods and strategies and discusses some related theoretical and practical issues on the theoretical side results from the theory of general state space markov chains can be used to obtain convergence rates laws of large numbers and central limit theorems for estimates obtained from markov chain methods these theoretical results can be used to guide the construction of more efficient algorithms for the practical use of markov chain methods standard simulation methodology provides several variance reduction techniques and also give guidance on the choice of sample size and allocation

a new existence theory for single and multiple positive periodic solutions to volterra integro differential equations with impulse effects this paper presents a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous volterra integro differential equations with impulse effects existence is established by using krasnoselskii fixed point theorem in cones this paper extends some previous results and reports some new results about impulsive differential equation

indirect estimation via l w for a large class of queueing systems little s law l w helps provide a variety of statistical estimators for the long run time average queue length l and the long run customer average waiting time w we apply central limit theorem versions of little s law to investigate the asymptotic efficiency of these estimators we show that an indirect estimator for l using the natural estimator for w plus the known arrival rate is more efficient than a direct estimator for l provided that the interarrival and waiting times are negatively correlated thus extending a variance reduction principle for the gi g s model due to a m law and j s carson we also introduce a general framework for indirect estimation which can be applied to other problems besides l w we show that the issue of indirect versus direct estimation is related to estimation using nonlinear control variables we also show under mild regularity conditions that any nonlinear control variable scheme is equivalent to a linear control va

asymptotic formulas for markov processes with applications to simulation the simulation run length required to achieve desired statistical precision for a sample mean in a steady state stochastic simulation experiment is largely determined by the asymptotic variance of the sample mean and to a lesser extent by the second order asymptotics of the variance and the asymptotic bias the asymptotic variance the second order asymptotics of the variance and the asymptotic bias of the sample mean of a function of an ergodic markov process can be expressed in terms of solutions of poisson s equation as indicated by positive recurrent potential theory we review this positive recurrent potential theory giving special attention to continuous time markov chains we provide explicit formulas for birth and death processes and diffusion processes and recursive computational procedures for skip free chains these results can be used to help design simulation experiments after approximating the stochastic process of interest by one of the elementary markov processes considered here

arbitrary order jordan chains associated with quantum mechanical hamiltonians representations and integral formulas we consider jordan chains of arbitrary order that are associated with quantum mechanical hamiltonians an explicit formula for the connection between integral and differential representations of the jordan chains is given as a byproduct we obtain a method that allows to resolve certain multiple integrals of special functions

the nonoscillatory solutions of delay differential equations with impulses abstract we obtain a sufficient condition for the impulsive delay differential equation t i 1 n p i t r i t t t k t k t k i k t k k n to have a nonoscillatory solution

queueing simulation in heavy traffic the heavy traffic behavior of a number of standard queueing simulation procedures like sample averaging and regenerative simulation is studied in particular limit theorems based upon brownian approximations are given in a double limit with both the sample size t tending to infinity and the traffic intensity i tending to one the results demonstrate that the growth rate t ti 1 i 2 plays a critical role and it follows both from the present theoretical results and empirical illustrations in a companion paper that negative bias presents a serious problem furthermore the heavy traffic behavior of the limiting variances in the standard large sample theory is found

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

the analysis of time series an introduction 4th ed 1991 the analysis of time series an introduction 4th ed technometrics vol 33 no 3 pp 363 364

existence of positive periodic solutions for a neutral population model with delays and impulse in this paper by using the theory of abstract continuous theorem of k set contractive operator and some analysis techniques we obtain some sufficient conditions for the existence of positive periodic solutions for a neutral population model with delays and impulse

a new existence theory for positive periodic solutions to functional differential equations with impulse effects the principle of this paper is to deal with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments easily verifiable sufficient criteria are established the approach is based on the fixed point theorem in cones the paper extends some previous results and obtains some new results

asymptotic efficiency of the sample mean in markov chain monte carlo schemes in many cases a univariate time series derived from a time reversible stationary markov chain has the property that there is a distribution function on 1 1 0 1 such that for all non negative integers l its lth moment is the ith lag autocorrelation of the time series we discuss some consequences of this property effects of the asymptotic efficiency of the sample mean on the efficiency of subsampling a stationary markov chain are discussed the stationarity assumption is then relaxed we show that under certain regularity conditions the sample mean of a strongly asymptotically stationary process is asymptotically efficient in that it has the smallest mean square error asymptotically in a broad class of linear estimators

derivatives of the pochhammer and reciprocal pochhammer symbols and their use in epsilon expansions of appell and kampe de feriet functions useful expressions of the derivatives to any order of pochhammer and reciprocal pochhammer symbols with respect to their arguments are presented they are building blocks of a procedure recently suggested for obtaining the expansion of functions of the hypergeometric class related to feynman integrals the procedure is applied to some examples of such kind of functions taken from the literature

optimal tests for initialization bias in simulation output we present a family of tests for detecting initialization bias in the mean of a simulation output series using a hypothesis testing framework the null hypothesis is that the output mean does not change throughout the simulation run the alternative hypothesis specifies a general transient mean function the tests are asymptotically optimal based on cumulative sums of deviations about the sample mean a particular test in this family is applied to a variety of simulation models the test requires very modest computation and appears to be both robust and powerful

the efficiency of one long run versus independent replication in steady state simulation we evaluate the efficiency of one long run versus independent replications in steady state discrete event simulation assuming that an initial portion of each replication will be deleted to allow the process to approach steady state we provide supporting evidence in favor of one long run but we also show that multiple replications can be more efficient the advantage of one long run increases if the amount deleted increases or if the covariance function decreases more quickly assuming it is nonnegative and decreasing thus assuming that the amount deleted depends on the way the process approaches steady state one long run tends to be efficient when the covariance function decays rapidly compared to the rate the process approaches steady state we also discuss ways to determine the initial portion to delete we consider the case of an exponential covariance function in detail and use it as a basis for approximations we also consider the m g queueing model and reflected brownian motion the latter

simulation run length control in the presence of an initial transient this paper studies the estimation of the steady state mean of an output sequence from a discrete event simulation it considers the problem of the automatic generation of a confidence interval of prespecified width when there is an initial transient present it explores a procedure based on schruben s brownian bridge model for the detection of nonstationarity and a spectral method for estimating the variance of the sample mean the procedure is evaluated empirically for a variety of output sequences the performance measures considered are bias confidence interval coverage mean confidence interval width mean run length and mean amount of deleted data if the output sequence contains a strong transient then inclusion of a test for stationarity in the run length control procedure results in point estimates with lower bias narrower confidence intervals and shorter run lengths than when no check for stationarity is performed if the output sequence contains no initial transient then the performance measures of the procedure with a stationarity test are only slightly degraded from those of the procedure without such a test if the run length is short relative to the extent of the initial transient the stationarity tests may not be powerful enough to detect the transient resulting in a procedure with unreliable point and interval estimates

on integral and differential representations of jordan chains and the confluent supersymmetry algorithm we construct a relationship between integral and differential representation of second order jordan chains conditions to obtain regular potentials through the confluent supersymmetry algorithm when working with the differential representation are obtained using this relationship furthermore it is used to find normalization constants of wave functions of quantum systems that feature energy dependent potentials additionally this relationship is used to express certain integrals involving functions that are solution of schrodinger equations through derivatives

open queueing networks in heavy traffic this paper presents heavy traffic limit theorems for the queue length and sojourn time processes associated with open queueing networks these limit theorems state that properly normalized sequences of queue length and sojourn time processes converge weakly to a certain diffusion as the network traffic intensity converges to unity the limit diffusion is reflected brownian motion on the nonnegative orthant this process behaves like brownian motion on the interior of its state space and reflects instantaneously on the boundaries the reflection direction is a constant for each boundary hyperplane

derivatives of horn hypergeometric functions with respect to their parameters the derivatives of eight horn hypergeometric functions four appell f1 f2 f3 and f4 and four degenerate confluent 1 2 1 and 1 with respect to their parameters are studied the first derivatives are expressed systematically as triple infinite summations or alternatively as single summations of two variable kampe de feriet functions taking advantage of previously established expressions for the derivative of the confluent or gaussian hypergeometric functions the generalization to the nth derivative of horn s functions with respect to their parameters is rather straightforward in most cases the results are expressed in terms of n 2 infinite summations following a similar procedure mixed derivatives are also treated an illustration of the usefulness of the derivatives of f1 with respect to the first and third parameters is given with the study of autoionization of atoms occurring as part of a post collisional process their evaluation setting the coulomb charge to zero provides the

the persistence of nonoscillatory solutions of delay differential equations under impulsive perturbations abstract we obtain a sufficient condition for the persistence of nonoscillatory solutions of the delay differential equation under impulsive perturbations

a weighted least squares approach to computer simulation factor screening in this paper we develop a weighted least squares wls approach to computer simulation factor screening like frequency domain methodology fdm the regression analysis is performed in the frequency domain however unlike fdm where unknown nuisance parameters are eliminated by cancellation in a ratio statistic the wls procedure is designed to estimate these parameters the wls weights and incorporate this information into the regression analysis we propose and compare one and two run approaches for estimating the weights in the wls approach

derivatives of any order of the confluent hypergeometric function f11 a b z with respect to the parameter a or b the derivatives to any order of the confluent hypergeometric kummer function f f11 a b z with respect to the parameter a or b are investigated and expressed in terms of generalizations of multivariable kampe de feriet functions various properties reduction formulas recurrence relations particular cases and series and integral representations of the defined hypergeometric functions are given finally an application to the two body coulomb problem is presented the derivatives of f with respect to a are used to write the scattering wave function as a power series of the sommerfeld parameter

ordinary clt and wlln versions of l λw the familiar queueing principle expressed by the formula l w little s law can be interpreted as a relation among strong laws of large numbers sllns here we prove central limit theorem clt and weak law of large numbers wlln versions of l w for example if the sequence of ordered pairs of interarrival times and waiting times is strictly stationary and satisfies a joint clt then the queue length process also obeys a clt with a related limiting distribution in a previous paper we proved a functional central limit theorem version of l w without stationarity by very different arguments the two papers highlight the differences between establishing ordinary limit theorems and their functional limit theorem counterparts

oscillation and stability of linear impulsive delay differential equations the main results of this paper are that the oscillation and the stability of a linear impulsive delay differential equation are equivalent respectively to the oscillation and the stability of a corresponding linear delay differential equation without impulses the results of this paper can be used to improve and derive some of the known results in the literature

oscillations of second order nonlinear impulsive ordinary differential equations consider the second order impulsive ordinary differential equation r t x t f t x t 0 t t 0 t t k k 1 2 x t k g k x t k x t k h k x t k k 1 2 e where 0 t 0 1 k k t k is any quotient of positive odd integers we obtain some sufficient conditions ensuring that all solutions of e oscillate

two stage stopping procedures based on standardized time series we propose some new two stage stopping procedures to construct absolute width and relative width confidence intervals for a simulation estimator of the steady state mean of a stochastic process the procedures are based on the method of standardized time series proposed by schruben and on stein s two stage sampling scheme we prove that our two stage procedures give rise to asymptotically valid confidence intervals as the prescribed length of the confidence interval approaches zero and the size of the first stage grows to infinity the sole assumption required is that the stochastic process satisfy a functional central limit theorem

coulomb wave functions with complex values of the variable and the parameters the motivation for the present paper lies in the fact that the literature concerning the coulomb wave functions fl and gl is a jungle in which it may be hard to find a safe way when one needs general formulas for the coulomb wave functions with complex values of the variable and the parameters l and for the coulomb wave functions and certain linear combinations of these functions we discuss the connection with the whittaker function the coulomb phase shift wronskians reflection formulas l l 1 integral representations series expansions circuital relations e i and asymptotic formulas on a riemann surface for the variable the parameters l and are allowed to assume complex values

an analytical evaluation of alternative strategies in steady state simulation we consider the simple technique of making independent and probabilistically identical simulation replications to estimate the steady state mean of a stochastic process for a fixed total sample size using a first order autoregressive model with high autocorrelation and time dependent distributions we analytically quantify and investigate the effects of the number of replications and of initial deletions of output on several different measures of point estimator and confidence interval quality this analysis leads to general recommendations on the choice of replications and deletion in particular we conclude that deletion of some amount of the initial output in a replication can be an effective and efficient method of dealing with initialization bias this conclusion differs from several previous studies on the efficacy of deletion

approximating a point process by a renewal process ii superposition arrival processes to queues we develop an approximation for a queue having an arrival process that is the superposition of independent renewal processes i e gi1 g 1 this model is useful for example in analyzing networks of queues where the arrival process to an individual queue is the superposition of departure processes from other queues if component arrival processes are approximated by renewal processes the gi1 g 1 model applies the approximation proposed is a hybrid that combines two basic methods described by whitt all these methods approximate the complex superposition process by a renewal process and yield a gi g 1 queue that can be solved analytically or approximately in the hybrid method the moments of the intervals in the approximating renewal process are a convex combination of the moments determined by the basic methods the weight in the convex combination is identified using the asymptotic properties of the basic methods together with simulation when compared to simulation estimates the error in hybrid

higher order darboux transformations and wronskian representations for schrodinger equations with quadratically energy dependent potentials we construct higher order darboux transformations for schrodinger equations with quadratically energy dependent potentials similar to the case of conventional darboux also known as supersymmetric transformations both the solutions and the potentials of transformed equations are expressed through wronskians we discuss properties of our darboux transformations and provide an application

workload models for stochastic networks value functions and performance evaluation this paper concerns control and performance evaluation for stochastic network models structural properties of value functions are developed for controlled brownian motion cbm and deterministic fluid workload models leading to the following conclusions outside of a null set of network parameters the following hold i the fluid value function is a smooth function of the initial state under further minor conditions the fluid value function satisfies the derivative boundary conditions that are required to ensure it is in the domain of the extended generator for the cbm model exponential ergodicity of the cbm model is demonstrated as one consequence ii the fluid value function provides a shadow function for use in simulation variance reduction for the stochastic model the resulting simulator satisfies an exact large deviation principle while a standard simulation algorithm does not satisfy any such bound iii the fluid value function provides upper and lower bounds on performance for the cbm model this follows from an extension of recent linear programming approaches to performance evaluation

oscillation of impulsive neutral delay differential equations abstract in this paper effective sufficient conditions for the oscillation of all solutions of impulsive neutral delay differential equations of the form x t p t x t q t x t sgn x t 0 t t 0 x t k b k x t k k 1 2 are established our results reveal the fact that the oscillatory properties of all solutions of eqs and may be caused by the impulsive perturbations though the corresponding neutral delay differential equation without impulses i e eq admits a nonoscillatory solution it is also seen that the oscillatory behavior of all solutions of eq can be inherited by eqs and under certain impulsive perturbations some examples are also given to illustrate the applicability of the results obtained

convergence rate of the fuzzy generalized nearest neighbor rule tizzy k nearest neighbor rule k nnr has been applied in a variety of substantive areas yang and chen l described a fuzzy generalized k nn algorithm which is a unified approach to a variety of fuzzy k nnr s they created the strong consistency of posterior risk of the fuzzy generalized nnr in this paper we give their convergence rate that is the convergence rate of posterior risk of the fuzzy generalized nnr is exponentially fast

an approximation method for a single server queue with cyclically indexed arrival and service rates in this paper we develop an approximation scheme for a single server markovian queue with cyclic arrival and or service patterns the arrival and service patterns change cyclically according to a job or customer sequence number the model has found application in production planning for multiple items on constrained resources using cyclic schedules it has also been applied to a computer simulation sensitivity analysis technique called frequency domain methodology the approximation scheme provides results to any desired degree of accuracy performance guidelines for the approximation are established analytically using stochastic ordering in addition performance results are numerically evaluated for the model with cyclic arrival patterns and independent and identically distributed exponential service patterns using a nonlinear optimization model

an interpolation approximation for queueing systems with poisson input for many queueing systems of practical interest it is difficult to obtain exact analytical results it is however often possible to obtain asymptotic results for light and heavy traffic heavy traffic limit theorems yield expressions for normalized quantities of interest in light traffic we can obtain in addition to limits more sensitive information by calculating what are effectively derivatives of the quantity of interest with respect to the arrival rate we can then combine the light and heavy traffic results to yield a polynomial in the arrival rate as an approximation to the normalized quantity of interest for instance by utilizing the heavy traffic limit the light traffic limit and the first derivative we can obtain a quadratic approximation then by reversing the normalization process we can obtain an approximation for the original quantity of interest in this paper we present the details of the above approximation focusing via several examples on applications of the method we then compare the results of the approximation for the examples considered with exact and simulation results in addition we compare our results to some related approximations for the examples considered the approximation works extremely well

exponential families and regression in the monte carlo study of queues and random walks an importance sampling method studied by siegmund and asmussen in the case of waiting time probabilities is extended to the mean and other functionals the ideas involve exponential families of queues and control variates regression and it is found both from theory and practice that the method is dramatically better than standard tools like regenerative simulation or sample mean estimation not least under heavy traffic conditions

mathematical properties of generalized sturmian functions we study some mathematical properties of generalized sturmian functions which are solutions of a schr odinger like equation supplemented by two boundary conditions these generalized functions for any value of the energy are defined in terms of the magnitude of the potential one of the boundary conditions is imposed at the origin of the coordinate where regularity is required the second point is at large distances for negative energies boundlike conditions are imposed for positive or complex energies incoming or outgoing boundary conditions are imposed to deal with scattering problems in this case since scattering conditions are complex the sturmian functions themselves are complex since all of the functions solve a sturm liouville problem they allow us to construct a sturmian basis set which must be orthogonal and complete this is the case even when they are complex here we study some properties of generalized sturmian functions associated with the hulth en potential in particular the spatial organization of their nodes and demonstrate explicitly their orthogonality we also show that the overlap matrix elements which are generally required in scattering or bound state calculations are well defined many of these mathematical properties are expressed in terms of uncommon multivariable hypergeometric functions finally applications to the scattering of a particle by a yukawa and by a hulth en potential serve as

variance and bias reduction techniques for the harmonic gradient estimator abstract gradient estimation techniques are useful for the optimization and sensitivity analysis of discrete event simulation techniques to improve the quality of such estimators are needed to make efficient use of simulation data this paper discusses variance and bias reduction techniques for the steady state simulation response harmonic gradient estimator the variance reduction techniques incorporate two control variates the first control variate is obtained from a noise simulation run output process i e the input parameters are kept fixed during the run the second control variate is obtained from a signal simulation run output process i e the input parameters are varied in sinusoidal patterns during the run two bias reduction techniques are proposed the first approach involves fitting a quadratic regression model to the harmonic coefficient estimates at frequencies in a neighborhood of zero the second approach involves sinusoidally varying the simulation input parameters in batches procedures incorporating these techniques requiring a fixed number of simulation runs independent of the number of input parameters are discussed computational results on simulation models of a m m 1 queueing system and a s s inventory system are included to illustrate the effectiveness and the limitations of these procedures

planning queueing simulations simple heuristic formulas are developed to estimate the simulation run lengths required to achieve desired statistical precision in queueing simulations the formulas are intended to help in the early planning stages before any data have been collected the queueing simulations considered are single replications one long run conducted to estimate steady state characteristics such as expected equilibrium queue lengths the formulas can be applied to design simulation experiments to develop and evaluate queueing approximations in fact this work was motivated by efforts to develop approximations for packet communication networks with multiple classes of traffic having different service characteristics and bursty arrival processes in addition to indicating the approximate simulation run length required in each case of a designed experiment the formulas can help determine what cases to consider what statistical precision to aim for and even whether to conduct the experiment at all the formulas are bas

the continuum schrodinger coulomb and dirac coulomb sturmian functions spherical continuum sturmian functions for the schrodinger coulomb and dirac coulomb problems are constructed by solving appropriate sturm liouville systems it is proved that in the non relativistic case a spectrum of potential strengths is continuous and covers the whole real axis in the relativistic case two sturmian sets may be derived for the relativistic sturm liouville problems their eigenvalue spectra consist of the real axes with zero excluded plus circumferences in the complex plane centred at zero it is shown that as a consequence of a relationship existing between the two families of the continuum dirac coulomb sturmians each family obeys two orthogonality and two closure relations

estimating customer and time averages in this paper we establish a joint central limit theorem for customer and time averages by applying a martingale central limit theorem in a markov framework the limiting values of the two averages appear in the translation terms this central limit theorem helps to construct confidence intervals for estimators and perform statistical tests it thus helps determine which finite average is a more asymptotically efficient estimator of its limit as a basis for testing for pasta poisson arrivals see time averages we determine the variance constant associated with the central limit theorem for the difference between the two averages when pasta holds

a special asymptotic limit of a kampe de feriet hypergeometric function appearing in nonhomogeneous coulomb problems in the investigation of two body coulomb schrodinger equations with some types of nonhomogeneities the particular solution can be expressed in terms of a two variable kampe de feriet hypergeometric function the asymptotic limit of the latter for both variables being large but their ratio being a bound constant is required in order to extract relevant physical information from the solutions in this report the mathematical limit is provided for that purpose a particular series representation of the hypergeometric function in terms of products of kummer and gauss functions is first derived

on poisson approximations for superposition arrival processes in queues we report on simulations of igii m 1 queues the arrival process is the superposition sum of up to 1024 i i d renewal processes and there is a single exponential server as one might anticipate the simulation estimate of the expected number of customers in a igii m 1 queueing system approaches the expected number in an m m 1 queueing system as the number of arrival processes n increases however for a given n the difference between the expected numbers in the m m 1 and igii m 1 queueing systems dramatically increases as the traffic intensity increases from i 0 5 to i 0 9 this difference is approximated by a formula which is a function of the traffic intensity the number of component arrival processes and the squared coefficient of variation of the component interarrival times

analyzing the m m 1 queue in frequency domain experiments abstract frequency domain experiments are a method of performing sensitivity analysis and factor screening and estimating gradients for steady state simulation models the validity of the frequency domain analysis can be assessed by measuring the distance between the expected outputs of the sinusoidally oscillated input parameter system as found in frequency domain experiments and the fixed input parameter system as found in time domain experiments in this paper an upper bound on this distance is derived for an m m 1 queue as the oscillation frequencies of the sinusoidally varied input parameters approach zero this bound is shown to converge to zero as the input parameter oscillation ranges approach zero this bound is also related to a taylor series approximation of the output response function and shown to converge to zero at the same rate as this approximation function in addition this bound is used to assess the bias of the harmonic gradient estimator

approximating a point process by a renewal process i two basic methods this paper initiates an investigation of simple approximations for stochastic point processes the goal is to develop methods for approximately describing complex models such as networks of queues and multiechelon inventory systems the proposed approach is to decouple or decompose the model by replacing all the component flows point processes by independent renewal processes here attention is focused on ways to approximate a single point process by a renewal process this is done in two steps first properties of the point process are used to specify a few moments of the interval between renewals then a convenient distribution is fit to these moments two different methods are suggested for specifying the moments of the renewal interval the stationary interval method equates the moments of the renewal interval with the moments of the stationary interval in the point process to be approximated the asymptotic method in an attempt to account for the dependence among successive intervals determines the moments of the renewal interval by matching the asymptotic behavior of the moments of the sums of successive intervals these two procedures are applied to approximate the superposition merging of point processes the purpose here is to provide a better understanding of these procedures and a general framework for making new approximations in particular the two basic procedures can be used as building blocks to construct refined composite procedures composite procedures for the gi g 1 queue with a superposition arrival process are discussed by albin in part ii albin has developed a hybrid procedure for approximating the mean sequence length and other characteristics in the gi g 1 queue for which the average error when compared with simulated values was 3 over a large number of test systems

current issues in frequency domain experimentation this paper presents an examination of certain issues in frequency domain experimentation fde for discrete event simulation experimental results are presented to demonstrate that i conclusions drawn from fde are dependent on the oscillation frequency and unless frequencies are chosen carefully misleading results can be obtained ii interpretation of results from frequency domain experiments are fundamentally different from the interpretation of results from regression analysis specifically a term found significant by fde is not to be interpreted as a term able to explain a significant portion of the variation in the response over the experimental region and iii basic assumptions required for fde in particular the assumption that input and output processes constitute a time invariant linear system do not hold for m m 1 queues other issues discussed are indexing run length determination computational effort and why fde is not applicable for terminating simulations it is concluded that further developments are needed before fde can be used by practitioners

variance reduction in simulations of loss models we propose a new estimator of steady state blocking probabilities for simulations of stochastic loss models that can be much more efficient than the natural estimator ratio of losses to arrivals the proposed estimator is a convex combination of the natural estimator and an indirect estimator based on the average number of customers in service obtained from little s law l w it exploits the known offered load product of the arrival rate and the mean service time the variance reduction is dramatic when the blocking probability is high and the service times are highly variable the advantage of the combination estimator in this regime is partly due to the indirect estimator which itself is much more efficient than the natural estimator in this regime and partly due to strong correlation most often negative between the natural and indirect estimators in general when the variances of two component estimators are very different the variance reduction from the optimal convex combination is abo

cramer von mises variance estimators for simulations we study estimators for the variance parameter 2 of a stationary process the estimators are based on weighted cramer von mises statistics and certain weightings yield estimators that are first order unbiased for 2 we derive an expression for the asymptotic variance of the new estimators this expression is then used to obtain the first order unbiased estimator having the smallest variance among fixed degree polynomial weighting functions our work is based on asymptotic theory however we present exact and empirical examples to demonstrate the new estimators small sample robustness we use a single batch of observations to derive the estimators asymptotic properties and then we compare the new estimators among one another in real life applications one would use more than one batch we indicate how this generalization can be carried out

existence and multiplicity of positive periodic solutions to functional differential equations with impulse effects abstract this paper deals with a new existence theory for single and multiple positive periodic solutions to a kind of nonautonomous functional differential equations with impulse actions at fixed moments by employing a fixed point theorem in cones easily verifiable sufficient criteria are established the paper extends some previous results and reports some new results about impulsive functional differential equations

oscillation criteria for a first order impulsive neutral differential equation of euler form in this paper we are concerned with the oscillation of a first order impulsive neutral differential equation of euler form with variable delays our results reveal the fact that the oscillatory behavior of all solutions of differential equations without impulses can be inherited by impulsive differential equations under certain impulsive perturbations it is also seen that the oscillatory properties of all solutions of impulsive differential equations may be caused by the impulsive perturbations though the corresponding differential equations without impulses admit a nonoscillatory solution some examples are also given to illustrate the applicability of the results obtained

recursive representation of wronskians in confluent supersymmetric quantum mechanics a recursive form of arbitrary order wronskian associated with transformation functions in the confluent algorithm of supersymmetric quantum mechanics susy is constructed with this recursive form regularity conditions for the generated potentials can be analyzed moreover as byproducts we obtain new representations of solutions to schrodinger equations that underwent a confluent susy transformation