m m 1 queue in two alternating environments and its heavy traffic approximation abstract we investigate an m m 1 queue operating in two switching environments where the switch is governed by a two state time homogeneous markov chain this model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods we first obtain the steady state distribution of the process in terms of a generalized mixture of two geometric distributions in the special case when only one kind of switch is allowed we analyze the transient distribution and investigate the busy period problem the analysis is also performed by means of a suitable heavy traffic approximation which leads to a continuous random process its distribution satisfies a partial differential equation with randomly alternating infinitesimal moments for the approximating process we determine the steady state distribution the transient distribution and a first passage time density

non self adjoint hamiltonians defined by riesz bases we discuss some features of non self adjoint hamiltonians with real discrete simple spectrum under the assumption that the eigenvectors form a riesz basis of hilbert space among other things we give conditions under which these hamiltonians can be factorized in terms of generalized lowering and raising operators

on some time non homogeneous queueing systems with catastrophes computations for non homogeneous birth and death processes with catastrophes applications to queueing and population dynamics problems effect of the periodicity of the rates on the performance of systems with catastrophes non stationary queueing systems subject to catastrophes occurring with time varying intensity are considered the effect of a catastrophe is to make the queue instantly empty the transition probabilities the related moments and the first visit time density to zero state are analyzed particular attention is dedicated to queueing systems in the presence of catastrophes with periodic intensity function various applications are provided including the non stationary birth death process with immigration the queueing systems m t m t 1 and m t m t

fundamental solutions of penny shaped and half infinite plane cracks embedded in an infinite space of one dimensional hexagonal quasi crystal under thermal loading this paper presents fundamental solutions for an infinite space of one dimensional hexagonal quasi crystal medium which contains a penny shaped or half infinite plane crack subjected to two identi

a note on approximating peak congestion in m t g infinity queues with sinusoidal arrivals we study the mt g infinity queue where customers arrive according to a sinusoidal function t a sin 2 t t and the service rate is we show that the expected number of customers in the system during peak congestion can be closely approximated by a for service distributions with coefficient of variation between 0 and 1 motivated by a result derived by eick massey and whitt that the time lag of the peak congestion from the peak of the customer arrivals is 1 2 for models with deterministic service times we show that the time lag for exponential service times is closely approximated by 1 based on a cycle length of 24 hours and regardless of the values of other system parameters these approximations are of the order of 1 accuracy for 1 and the accuracy increases rapidly with increasing

directional derivatives of oblique reflection maps given an oblique reflection map and functions documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document psi chi in mathcal d lim end document the space of k valued functions that have finite left and right limits at every point the directional derivative documentclass aastex usepackage amsbsy usepackage amsfonts usepackage amssymb usepackage bm usepackage mathrsfs usepackage pifont usepackage stmaryrd usepackage textcomp usepackage portland xspace usepackage amsmath amsxtra pagestyle empty declaremathsizes 10 9 7 6 begin document nabla chi gamma psi end document of along evaluated at is defined to be the pointwise limit as documentclass aastex usepackage amsbsy usepackage amsfonts u

unstable asymptotics for nonstationary queues we relate laws of large numbers and central limit theorems for nonstationary counting processes to corresponding limits for their inverse processes we apply these results to develop approximations for queues that are unstable in a nonstationary manner we obtain unstable nonstationary analogs of the queueing relation l w and associated central limit theorem versions for modeling and to obtain the first limits we can construct nonstationary point processes as random time transformations of familiar point processes such as renewal processes and stationary point processes we deduce the asymptotic behavior of the nonstationary point process from the asymptotic behavior of the familiar point process and the time transformation

non self adjoint hamiltonians defined by generalized riesz bases bagarello inoue and trapani j math phys 55 033501 2014 investigated some operators defined by the riesz bases these operators connect with quasi hermitian quantum mechanics and its relatives in this paper we introduce a notion of generalized riesz bases which is a generalization of riesz bases and investigate some operators defined by the generalized riesz bases by changing the frameworks of the operators defined in the work of bagarello inoue and trapani

more mathematics for pseudo bosons we propose an alternative definition for pseudo bosons this simplifies the mathematical structure minimizing the required assumptions some physical examples are discussed as well as some mathematical results related to the biorthogonal sets arising out of our framework we also briefly extend the results to the so called nonlinear pseudo bosons

diffusion approximations for some multiclass queueing networks with fifo service disciplines the diffusion approximation is proved for a class of multiclass queueing networks under fifo service disciplines in addition to the usual assumptions for a heavy traffic limit theorem a key condition that characterizes this class is that aj x j matrixg known as the workload contents matrix has a spectral radius less than unity wherej represents the number of service stations the j l th component of matrixg can be interpreted as the long run average amount of future work for stationj that is embodied in a unit of immediate work at stationl this class includes as a special case the feedforward multiclass queueing network and the rybko stolyar network under fifo service discipline a new approach is taken in establishing the diffusion limit theorem the traditional approach is based on an oblique reflection mapping but such a mapping is not well defined for the network under consideration our approach takes two steps arst establishing thec tightness of the scaled queueing processes and then completing the proof for the convergence of the scaled queueing processes by invoking the weak uniqueness for the limiting processes which are semimartingale reflecting brownian motions

asymptotically optimal controls for time inhomogeneous networks a framework is introduced for the identification of controls for single class time varying queueing networks that are asymptotically optimal in the so called uniform acceleration regime a related but simpler first order or fluid control problem is first formulated for a class of performance measures that satisfy a certain continuity property it is then shown that any sequence of policies whose performances approach the infimum in the fluid control problem is asymptotically optimal for the original network problem examples of performance measures with this property are described and simulations implementing asymptotically optimal policies are presented the use of directional derivatives of the reflection map for solving fluid control problems is also illustrated this work serves to complement a large body of literature on asymptotically optimal controls for time homogeneous networks

an empirical investigation of the transient behavior of stationary queueing systems this paper examines the transient behavior of infinite capacity single server markovian queueing systems it estimates q t the expected number of customers in queue at time t by numerically solving the sets of simultaneous first order differential equations that describe these systems empirical results have been drawn from these observations for small values of t the behavior of q t is strongly influenced by the initial state of the queueing system for systems with deterministic initial conditions one can roughly predict which of a small set of patterns this behavior will follow after an initial period of time and independently of initial conditions q t approaches q in a manner that can be approximated through a decaying exponential function on the basis of experimental evidence we have developed an expression that provides a good approximation to the observed values of the time constant associated with this exponential function this expression can also be used to determine an upper b

approximation of the non stationary m t m t c t queue using stationary queueing models the stationary backlog carryover approach this paper proposes a new approach for the time dependent analysis of stochastic and non stationary queueing systems the analysis of a series of stationary queueing models leads to a new approximation of time dependent performance measures based on a stationary backlog carryover sbc approximation of the time dependent expected utilization different approximations of the time dependent expected queue length and the number of customers in the system are discussed limiting results are given for the case of constant rates the accuracy of the sbc approach is shown for non stationary m t m t c t queueing systems with time dependent and piecewise constant arrival rates in numerical experiments we demonstrate the reliability of this approach and compare it with the lagged stationary independent period by period sipp approach in addition the approximation is applied to temporarily overloaded systems that cannot be analyzed by the variants of the sipp approach

on the accuracy of the simple peak hour approximation for markovian queues we empirically explore the accuracy of the simple stationary peak hour approximation spha for estimating peak hour performance in multiserver queuing systems with exponential service times and periodic sinusoidal poisson arrival processes we show that the spha is very good for a range of parameter values corresponding to a reasonably broad spectrum of real systems however we do find and document that there are many situations in which this approximation will be very inaccurate we postulate and then support empirically a set of hypotheses that link the accuracy of the spha and the related point wise stationary approximation psa to key parameter values and model characteristics we also present results on the time dependent behavior of these systems as a function of key parameters finally we present results which indicate that our findings developed for models with sinusoidal input streams may apply to a much broader range of markovian models with more general cyclic inputs

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

the physics of the m t g symbol queue we establish some general structural results and derive some simple formulas describing the time dependent performance of the mt g queue with a nonhomogeneous poisson arrival process we know that for appropriate initial conditions the number of busy servers at time t has a poisson distribution for each t our results show how the time dependent mean function m depends on the time dependent arrival rate function and the service time distribution for example when is quadratic the mean m t coincides with the pointwise stationary approximation t e s where s is a service time except for a time lag and a space shift it is significant that the well known insensitivity property of the stationary m g model does not hold for the nonstationary mt g model the time dependent mean function m depends on the service time distribution beyond its mean the service time stationary excess distribution plays an important role when is decreasing before time t m t is increasing in the service time

the reflection map with discontinuities we study the multidimensional reflection map on the spacesd 0 t r k andd 0 8 r k of right continuous r k valued functions on 0 t or 0 8 with left limits endowed with variants of the skorohod 1956 m1 topology the reflection map was used with the continuous mapping theorem by harrison and reiman 1981 and reiman 1984 to establish heavy traffic limit theorems with reflected brownian motion limit processes for vector valued queue length waiting time and workload stochastic processes in single class open queueing networks since brownian motion and reflected brownian motion have continuous sample paths the topology of uniform convergence over bounded intervals could be used for those results variants of them1 topologies are needed to obtain alternative discontinuous limits approached gradually by the converging processes as occurs in stochastic fluid networks with bursty exogenous input processes e g with on off sources having heavy tailed on periods or off periods having infinite variance we show that the reflection map is continuous at limits without simultaneous jumps of opposite sign in the coordinate functions provided that the productm1 topology is used as a consequence the reflection map is continuous with the productm1 topology at all functions that have discontinuities in only one coordinate at a time that continuity property also holds for more general reflection maps and is sufficient to support limit theorems for stochastic processes in most applications we apply the continuity of the reflection map to obtain limits for buffer content stochastic processes in stochastic fluid networks

asymptotic analysis of a state dependent m g 1 queueing system we present new asymptotic methods for the analysis of queueing systems these methods are applied to a state dependent m g 1 queue we formulate problems for and compute approximations to i the stationary density of the unfinished work ii the mean length of time until the end of a busy period iii the mean length of a busy period and iv the mean time until the unfinished work reaches or exceeds a specified capacity the methods are applied to the full kolmogorov equations scaled so that the arrival rate is rapid and the mean service is small thus we do not truncate equations as in diffusion approximations for state independent m g 1 queues our results are shown to agree with the known exact solutions we include comparisons both analytic and numerical between our results and those obtained from diffusion approximations

the transient solution of time dependent m m 1 queues the transient behavior of time dependent m m 1 queues is studied the boundary probability function pi sub 0 t which is the probability that the queue is empty at time t is shown with analyticity arguments to satisfy a volterra type integral equation the boundary integral equation is derived and a numerical algorithm is used to solve the integral equation and to find the expected queue size from pi sub 0 t the approach can be applied to many other types of time dependent queues examples are given

general theory of regular biorthogonal pairs and its physical operators in this paper we introduce a general theory of regular biorthogonal sequences and its physical operators biorthogonal sequences n and n in a hilbert space h are said to be regular if span n and span n are dense in h the first purpose is to show that there exists a non singular positive self adjoint operator tf in h defined by an orthonormal basis onb f fn in h such that n tffn and n tf 1fn n 0 1 and such an onb f is unique the second purpose is to define and study the lowering operators af and bf the raising operators bf and af and the number operators nf and nf determined by the non singular positive self adjoint operator tf these operators connect with quasi hermitian quantum mechanics and its relatives this paper clarifies and simplifies the mathematical structure of this framework and minimizes the required assumptions

a boundary integral formulation and 2d fundamental solutions for piezoelectric media abstract first based on the basic equations of piezoelectricity the boundary integral formulation is derived by utilizing the reciprocal work theorem second for the plane problem of piezoelectric media one general solution in terms of harmonic functions is derived and the fundamental solutions are therefore obtained numerical calculations by boundary element method bem are performed to give the stress concentration coefficient of an infinite piezoelectric plane with a circular hole as well as the stress and electric intensity factors of a central crack locating on an infinite plate results are found to agree well with the exact solutions

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

the general solution of three dimensional problems in piezoelectric media abstract the governing equations of three dimensional problems in transversely isotropic piezo electric material are composed of four second order partial differential equations in which the displacement components and electric potential functions are the essential unknowns in this paper the so called general solutions of these equations are obtained with the aid of a set of new potential functions which are used to express the components of displacements and the electric potential functions as an application of the general solution the problem of a half space piezoelectrics acted by a concentrated lateral shear force is solved

m t g queues with sinusoidal arrival rates in this paper we describe the mean number of busy servers as a function of time in an mt g queue having a nonhomogeneous poisson arrival process with a sinusoidal arrival rate function for an mt g model with appropriate initial conditions it is known that the number of busy servers at time t has a poisson distribution for each t so that the full distribution is characterized by its mean our formulas show how the peak congestion lags behind the peak arrival rate and how much less is the range of congestion than the range of offered load the simple formulas can also be regarded as consequences of linear system theory because the mean function can be regarded as the image of a linear operator applied to the arrival rate function we also investigate the quality of various approximations for the mean number of busy servers such as the pointwise stationary approximation and several polynomial approximations finally we apply the results for sinusoidal arrival rate functions to treat general periodic arrival rate functions using fourier series these results are intended to provide a better understanding of the behavior of the mt g model and related mt g s r models where some customers are lost or delayed

non self adjoint hamiltonians defined by sesquilinear forms and their physical applications in this paper we introduce a theory of sesquilinear forms with respect to a non self adjoint hamiltonian and its physical operators in particular we discuss some features of non self adjoint operators and sesquilinear forms which are defined starting from biorthogonal sequences that are not riesz bases generalized riesz systems d quasi bases and d e quasi bases

time dependent queues a single server queue is considered having exponentially distributed inter arrival and service times with slowly changing time dependent rates lambda varepsilon t and mu varepsilon t the parameter varepsilon is the ratio of an average inter arrival time to the time over which the rates change appreciably so it is small therefore an asymptotic solution valid for varepsilon small is constructed for the time dependent queue length probability distribution it consists of five typical parts corresponding to five typical time periods they are the initial period the period of light traffic when lambda mu 1 the saturation transition period when lambda mu increases through unity the oversaturation period when lambda mu starts out greater than unity and then decreases below unity and the transition period at the end of oversaturation when the queue returns to the light traffic condition by combining the solutions for these five intervals the solution fo

nonstationary analysis of the loss queue and of queueing networks of loss queues abstract we present an iterative scheme based on the fixed point approximation method for the numerical calculation of the time dependent mean number of customers and blocking probability functions in a nonstationary queueing network with multi rate loss queues we first show how the proposed method can be used to analyze a single class multi class and multi rate nonstationary loss queue subsequently the proposed method is extended to the analysis of a nonstationary queueing network of multi rate loss queues comparisons with exact and simulation results showed that the results are consistently close to the exact results and they are always within simulation confidence intervals

two time scale markov chains and applications to quasi birth death queues aiming at reduction of complexity this work is concerned with two time scale markov chains and applications to quasi birth death queues asymptotic expansions of probability vectors are constructed and justified lumping all states of the markov chain in each subspace into a single state an aggregated process is shown to converge to a continuous time markov chain whose generator is an average with respect to the stationary measures then a suitably scaled sequence is shown to converge to a switching diffusion process extensions of the results are presented together with examples of quasi birth death queues

diffusion approximations for storage processes with general release rules for a sequence of storage processes with general release rate functions which contain as a special case queueing processes we show that under appropriate conditions suitably normalized storage processes converge to a bessel process with negative drift in the sense of law

the skorohod oblique reflection problem in time dependent domains the deterministic skorohod problem plays an important role in the construction and analysis of diffusion processes with reflection in the form studied here the multidimensional skorohod problem w

approximations for networks of queues with overtime this paper presents simple approximations for networks of queues with overtime operation at some stations this type of network is commonly encountered in several manufacturing applications we provide bounds on the performance of the approximations for single and multiple machine stations our results suggest that the methods perform satisfactorily these approximations can be used in conjunction with parametric decomposition methods to analyze queueing networks the computational results indicate that the performance of the decomposition approach does not deteriorate when combined with the methods proposed in this paper

asymptotic analysis of the time dependent m m 1 queue using operator analytic techniques we develop a nonstationary markovian queueing theory starting with the mt mt 1 queue we employ an asymptotic approach quite different from the usual large time analysis instead we uniformly accelerate the queue length process that is we divide the arrival and service rate by a common parameter e then for a fixed time interval we consider the asymptotics for the distribution mean and variance of the queue length process as e goes to zero the effects of e can be quite different for the given time interval this gives us a dynamic asymptotic behavior for the queue length process we can formulate a time dependent traffic intensity parameter that determines when the process is asymptotically stable and when it is asymptotically unstable

asymptotic variability analysis for a two stage tandem queue part i the functional law of the iterated logarithm abstract a functional law of the iterated logarithm lil and its corresponding lil are established for a two stage tandem queue the functional lil and the lil limits quantify the magnitude of asymptotic stochastic fluctuations of stochastic processes compensated by their deterministic fluid limits in two forms the functional and numerical respectively the earliest functional lil and lil concerned are both developed for brownian motion by volker strassen and levy respectively we establish the functional lils and their corresponding lils in twelve cases covering three regimes divided by the traffic intensity the underloaded critically loaded and overloaded for five processes the queue length workload busy idle and departure processes by the primitive data of the first and second moments of the interarrival and service times all the functional lils are expressed into some compact sets of continuous functions and all the corresponding lils are some analytic functions the proofs are based on the fluid approximation and the strong approximation of the queueing system with the fluid approximation characterizing the expected values of the performance functions and the strong approximation approximating discrete performance processes with reflected brownian motions a companion paper asymptotic variability analysis for a two stage tandem queue part ii the law of the iterated logarithm develops another different version of lil which is a later generalization of levy s lil and also quantifies the magnitude of the asymptotic stochastic fluctuations of the performance functions

regular pseudo bosons versus bosons we discuss in which sense the so called regular pseudo bosons recently introduced by trifonov and analyzed in some detail by the author are related to ordinary bosons we repeat the same analysis for pseudo bosons and analyze the role played by certain intertwining operators which may be bounded or not

upper bounds for single server queues with doubly stochastic poisson arrivals consider the following type of single server queues arrivals are according to a doubly stochastic poisson process with a stationary ergodic random intensity t service times are independent identically distributed also independent from arrivals it is proven that the mean stationary work load is not greater than e 0 where a denotes the mean stationary work load in the m gi 1 queue with arrival intensity a and the same service process similar results are given for the mean stationary queue size and the mean stationary delay

performance bounds for nonhomogeneous queues this paper considers nonhomogeneous m t m t 1 queues which can model systems such as communications networks for such systems bounds on moment generating functions and on the tail distribution of the queue process are obtained these bounds are useful for characterizing the quality of service a system can provide to its users an approach utilizing the theory of differential equations is adapted the bounds given in this paper are tighter than those previously available in fact the bounds can be made arbitrarily tight given sufficient computational effort

stochastic orderings for markov processes on partially ordered spaces the purpose of this paper is to develop a unified theory of stochastic ordering for markov processes on countable partially ordered state spaces when such a space is not totally ordered it can induce a wide range of stochastic orderings none of which are equivalent to sample path comparisons similar comparison theorems are also developed for non markov processes that are functions of markov processes and for time inhomogeneous markov processes such alternative orderings can be quite useful when analyzing multi dimensional stochastic models such as queueing networks

biorthogonal vectors sesquilinear forms and some physical operators continuing the analysis undertaken in previous articles we discuss some features of non self adjoint operators and sesquilinear forms which are defined starting from two biorthogonal families of vectors like the so called generalized riesz systems enjoying certain properties in particular we discuss what happens when they forms two d quasi bases

green s functions for a two phase infinite piezoelectric plane first on the basis of the governing equations of piezoelectric materials a displacement function is introduced and the general solutions are derived second by employing the generalized almansi s theorem these solutions are further simplified i e all physical quantities are expressed in three displacement functions i i 1 2 3 which satisfy respectively three similar harmonic secondorder partial differential equations then the green s functions for point forces and point charge acting in the interior of a twophase infinite piezoelectric plane are given using the method of mirror image source the paper is concluded by a discussion of some special cases in which the point force and charge solutions for an infinite uniform piezoelectric plane and for a halfplane with free or fixed straight boundary are given

general solutions for coupled equations for piezoelectric media abstract three general solutions are obtained for the coupled dynamic equations for a transversely isotropic piezoelectric medium these solutions are expressed in terms of the two functions and f where satisfies a second degree partial differential equation and f a sixth degree partial differential equation respectively if the terms concerning the derivatives of time are removed the results become three general solutions for the corresponding equilibrium equations in which the function f can be represented by functions fi i 1 2 3 each of which satisfies a second degree partial differential equation by utilizing a generalized almansi theorem and the solution wang and zheng int j solids structures32 105 115 1995 obtained is proved to be consistent with one case of one of the three general solutions when the constants e15 e31 e33 0 the piezo electric coupling is absent then two of the solutions reduce to the elasticity general solutions for a transversely isotropie medium one of which is the result hu acta scientia sin 2 2 145 151 1953 obtained the other one has not been published last the solution in the limiting explicit form for the problem for a half space with concentrated loads at the boundary is obtained by utilizing the general solutions

the pointwise stationary approximation for m 1 m 1 s green kolesar and svoronos in press and green and kolesar in press use numerical methods to investigate the behavior of multiserver markov queues with a poisson arrival process having a sinusoidal arrival rate for this model they propose an approximation for long run average performance measures called the pointwise stationary approximation psa which consists of an appropriate weighted average of the performance measure that would result at each point in time if the system were stationary with the arrival rate that applies at that point in time in this paper we verify their conjecture that psa is asymptotically correct as the service and arrival rates increase with the instantaneous traffic intensity held fixed corresponding to long arrival rate cycles we actually establish both pointwise and average versions of this result for general time dependent birth and death processes

discrete flow networks bottleneck analysis and fluid approximations we conduct bottleneck analysis of a deterministic dynamic discrete flow network the analysis presupposes only the existence of long run averages and is based on a continuous fluid approximation to the network in terms of these averages the results provide functional strong laws of large numbers for stochastic jackson queueing networks since they apply to their sample paths with probability one

the klauder daubechies construction of the phase space path integral and the harmonic oscillator the canonical operator quantisation formulation corresponding to the klauder daubechies construction of the phase space path integral is considered this formulation is explicitly applied and solved in the case of the harmonic oscillator thereby illustrating in a manner complementary to klauder and daubechies original work some of the promising features offered by their construction of a quantum dynamics the klauder daubechies functional integral involves a regularisation parameter eventually taken to vanish which defines a new physical time scale when extrapolated to the field theory context besides providing a new regularisation of short distance divergences keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems comment 18 pages

the pointwise stationary approximation for queues with nonstationary arrivals we empirically explore the accuracy of an easily computed approximation for long run average performance measures such as expected delay and probability of delay in multiserver queueing systems with exponential service times and periodic sinusoidal poisson arrival processes the pointwise stationary approximation is computed by integrating over time that is taking the expectation of the formula for the stationary performance measure with the arrival rate that applies at each point in time this approximation which has been empirically confirmed as a tight upper bound of the true value is shown to be very accurate for a range of parameter values corresponding to a reasonably broad spectrum of real systems

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

fundamental solutions to contact problems of a magneto electro elastic half space indented by a semi infinite punch abstract this paper presents the fundamental contact solutions of a magneto electro elastic half space indented by a smooth and rigid half infinite punch the material is assumed to be transversely isotropic with the symmetric axis perpendicular to the surface of the half space based on the general solutions the generalized method of potential theory is adopted to solve the boundary value problems the involved potentials are properly assumed and the corresponding boundary integral equations are solved by using the results in literature complete and exact fundamental solutions are derived case by case in terms of elementary functions for the first time the obtained solutions are of significance to boundary element analysis and an important role in determining the physical properties of materials by indentation technique can be expected to play