bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of a modified GEOTEM® system to reconnaissance exploration for kimberlites in the Point Lake area, NWT, Canada
Authors: Smith Richard S. , Annan A. Peter , Lemieux Jean , Pedersen Rolf N.
Published: April 2003

Airborne geophysical surveying with electromagnetic (EM) and magnetic methods is an effective reconnaissance exploration tool for kimberlite pipes because the target can have an associated EM and magnetic anomaly. The EM response of kimberlite pipes is most often attributed to weathering alteration in a near‐surface layer, whereas the magnetic response is attributed to magnetite and ilmenite within the deeper unweathered kimberlite pipe. The discrete shape of kimberlite diatremes results in an easily identifiable anomaly pattern. Diamondiferous kimberlites have recently been found in the Northwest Territories (NWT) of Canada, an area glaciated in the Pleistocene and therefore devoid of a strongly weathered zone. By configuring the GEOTEM® airborne EM system to operate at high frequencies (270 Hz) and to take measurements while the transmitter is switched on, weakly conductive bodies may be detected because there is an adequate contrast with the surrounding highly resistive country rock. System modifications also allow the magnetic field to be sampled at an altitude of only 73 m instead of 120 m and ten times per second instead of once a second. This allows much better definition of weak, small magnetic anomalies. Data sets from two test areas (Point Lake and Willy Nilly, near Lac de Gras, NWT) demonstrate the effectiveness of the airborne system for reconnaissance surveying.
A seismic and gravity study of the McGregor geothermal system, southern New Mexico
Authors: O’Donnell T. M. , Miller K. C. , Witcher J. C.
Published: April 2003

Seismic and gravity studies have proven to be valuable tools in evaluating the geologic setting and economic potential of the McGregor geothermal system of southern New Mexico. An initial gravity study of the system demonstrated that a gravity high coincides with the heat‐flow high. A subsequent seismic reflection survey images a strong reflector, interpreted to be associated with a bedrock high that underlies the gravity and heat‐flow highs. A single reflection, which coincides with the water table, occurs within the Tertiary basin fill above bedrock. This reflector is subhorizontal except above structurally high bedrock, where it dips downward. This observation is consistent with well data that indicate a bedrock water table 30 m lower than water in the basin‐fill aquifer. Velocity models derived from seismic tomography show that the basin fill has velocities in the range of 800 to 4000 m/s and that the bedrock reflector coincides with high velocities of 5000 to 6000 m/s. Low‐velocity zones within the bedrock high are interpreted as karsted bedrock with solution‐collapse breccias and cavities filled with hot water. Higher velocity material that flanks the bedrock high may represent an earlier stage of basin fill or older alluvial‐fan deposits. The heat‐flow anomaly appears to be constrained to the region of shallowest bedrock that lacks these deposits, suggesting that they may act as an aquitard to cap underlying bedrock aquifers or geothermal reservoirs. Taken together, these observations suggest that the geothermal system is associated with karsted and fractured structurally high bedrock that serves as a window for upwelling and outflow of thermal waters. Thermal waters with a temperature as high as 89°C have the potential for space heating, geothermal desalinization, and small‐scale electrical production at McGregor Range.
Estimation of magnetotelluric transfer functions from radio transmitters
Authors: Bastani M. , Pedersen L. B.
Published: April 2003

A new method to estimate magnetotelluric (MT) transfer functions using radio transmitters as the source has been developed using an extended version of Weidelt’s C function expansion. The expansion coefficients are found from solving a mixed determined linear inverse problem by a truncated singular‐value decomposition technique with a truncation level determined automatically from the data. Synthetic tests with both noise‐free and noisy data show the new method is accurate and robust with respect to lack of transmitters in certain bands. A test profile with 42 stations from a dump‐site investigation in the Netherlands shows that the estimated transfer functions are remarkably stable and smooth as a function of frequency and distance along the profile. Compared with the standard band‐averaging technique, even the formal error bars are generally smaller and more realistic with the new method because the bias introduced by assuming that transfer functions are constant in a small subband is removed.
Imaging low‐frequency and dc electromagnetic fields using a simple linear approximation
Authors: Pérez‐Flores M. A. , Méndez‐Delgado S. , Gómez‐Treviño E.
Published: April 2003

We consider that all types of electromagnetic measurements represent weighted averages of the subsurface electrical conductivity distribution, and that to each type of measurement there corresponds a different weighting function. We use this concept for the quantitative interpretation of dc resistivity, magnetometric resistivity, and low‐frequency electric and magnetic measurements at low induction numbers. In all three cases the corresponding inverse problems are nonlinear because the weighting functions depend on the unknown conductivity distribution. We use linear approximations that adapt to the data and do not require reference resistivity values. The problem is formulated numerically as a solution of a system of linear equations. The unknown conductivity values are obtained by minimizing an objective function that includes the quadratic norm of the residuals as well as the spatial derivatives of the unknowns. We also apply constraints through the use of quadratic programming. The final product is the flattest model that is compatible with the data under the assumption of the given weighting functions. This approximate inversion or imaging technique produces reasonably good results for low and moderate conductivity contrasts. We present the results of inverting jointly and individually different data sets using synthetic and field data.
An ultrashallowSH‐wave seismic reflection experiment on a subsurface ground model
Authors: Deidda G. P. , Balia R.
Published: April 2003

An SH‐wave seismic reflection experiment was conducted to evaluate the feasibility and cost effectiveness of reflection imaging ultrashallow targets commonly encountered in engineering, groundwater, and environmental investigations. It was carried out on a purpose‐built subsurface ground model consisting of a concrete layer, at a depth from 2.85–5 m, and a low‐velocity overburden (<80 and 150 m/s for S‐ and P‐waves, respectively), constituted of filling material, with the water table 2.60 m deep. High‐quality CDP data, acquired by using a 10‐kg sledgehammer and newly designed horizontal detectors, allowed us to obtain an extremely detailed stacked section with a minimal amount of processing. Uncertainty in determining the depth and horizontal dimensions of the concrete model was estimated to be 0.2 and 0.3 m, respectively; however, the dominant frequencies lower than 150 Hz, the low‐transmission coefficient at the upper interface, and the relatively high velocity (900 m/s) of the concrete layer prevented us from resolving the layer thickness. The experiment demonstrates that when overburden materials exhibit low velocities (a common condition in near surface), the SH‐wave seismic reflection method is a reliable, detailed, and cost‐effective technique to image ultrashallow targets, even in disturbed material and below the water table.
Three least‐squares minimization approaches to depth, shape, and amplitude coefficient determination from gravity data
Authors: Abdelrahman E. M. , El‐Araby H. M. , El‐Araby T. M. , Abo‐Ezz E. R.
Published: April 2003

Three different least‐squares approaches are developed to determine, successively, the depth, shape (shape factor), and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly. By defining the anomaly value g(max) at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, [Formula: see text]. Formulas are derived for spheres and cylinders. Knowing the depth and applying the least‐squares method, the shape factor and the amplitude coefficient are determined using two simple linear equations. In this way, the depth, shape, and amplitude coefficient are determined individually from all observed gravity data. A procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources. The method is applied to synthetic data with and without random errors. In all the cases examined, the maximum error in depth, shape, and amplitude coefficient is 3%, 1.5%, and 7%, respectively. Finally, the method is tested on a field example from the United States, and the depth and shape obtained by the present method are compared with those obtained from drilling and seismic information and with those published in the literature.
A method to compute terrain corrections for gravimeter stations using a digital elevation model
Authors: Garca‐Abdeslem J. , Martn‐Atienza B.
Published: April 2003

A description is given of a method to compute the terrain corrections for a gravity survey using a digital elevation model. This method is based upon a new forward model solution to compute the gravity effect due to a rectangular prism of uniform mass density that is flat at its base but has a nonflat top. The gravitational attraction of such a prism is evaluated at the gravity station locations by combining analytic and numerical methods of integration. Two simple synthetic examples are provided that show the accuracy of this numerical method, and its performance is illustrated in a field example.
Experimental determination of the elastic coefficients of an orthorhombic material
Authors: Mah M. , Schmitt D. R.
Published: April 2003

In terms of elastic anisotropy, many rocks may be considered to have orthorhombic symmetry. Experimentally determining the nine independent elastic coefficients required for this case remains challenging. Elastic coefficients are most often found from measurements of the phase velocity in a variety of directions throughout a material, but finding this plane‐wave velocity is problematic. Here, quasi‐P and quasi‐S phase speeds are found using the τ‐p transformation through a composite material of orthorhombic symmetry. Arrays of specially constructed transducers (0.65 MHz) with different modes of vibration were placed on a rectangular prism of the material. More than 620 individual measures of phase speed were obtained at different directions and subsequently used in a generalized least‐squares inversion that yields the required elastic coefficients. The analysis does not account for the effects of wave‐speed dispersion evident in the waveforms acquired in the composite material. This dispersion is particularly severe for the in‐plane, quasi‐S polarization and is possibly a consequence of the fine layered structure of the material.
Interactive inversion in geosciences
Authors: Boschetti F. , Moresi L.
Published: April 2003

Inversion algorithms numerically evaluate the mismatch between model and data to guide the search for minima in parameter spaces. In an alternative approach, the numerical evaluation of data misfit can be replaced by subjectively judging the solution’s quality. This widens the class of problems that can be treated within the framework of formal inverse theory—in particular, various geophysical/geological/geodynamic applications in which structural similarity between model and data determines the quality of the fit. In this situation, prior knowledge, experience, and even personal intuition are crucial. This approach also provides a simple way to include such expertise in more traditional numeric applications, e.g., to treat ambiguous problems and disregard geologically unfeasible solutions from the inverse search.
AVO and velocity analysis
Authors: Sarkar D. , Castagna J. P. , Lamb W. J.
Published: April 2003

Velocity analysis using semblance estimates velocities based on a constant amplitude model for seismograms and does not take amplitude variation with offset (AVO) into account. In the presence of AVO, the constant amplitude model becomes inaccurate, particularly for events which exhibit polarity reversals. An AVO sensitive velocity analysis procedure, which is a generalization of the traditional semblance method, can be devised by giving an offset dependence to the modeled seismograms. Incorporating AVO into velocity analysis requires additional parameters to describe the reflectivity. This results in reduced velocity precision. By introducing a regularization term which provides a controlled suppression of the contributions due to AVO effects, we describe an AVO sensitive velocity analysis algorithm that properly deals with events exhibiting polarity reversals or large amplitude variation with offset.
The Ninth International Workshop on Seismic Anisotropy (91WSA)
Authors: Arnaud Jean , Dellinger Joe , Ikelle Luc , Lynn Heloise , MacBeth Colin , Thomsen Leon , Tsvankin Ilya
Published: April 2003

The ninth International Workshop on Seismic Anisotropy (91WSA) was held on March 26–31, 2000, at Camp Allen Conference Center, about 20 miles from Houston, Texas. The 91WSA organization committee is listed above and was chaired by Leon Thomsen. Below are the abstracts of the 58 papers presented at 91WSA. Please see http://www.seg.org/9iwsa for expanded abstracts and proceedings of 91WSA.
Keeping a satellite aloft: two finite fuel stochastic control models
Authors: Jacka S. D.
Published: April 2003

We consider two models for the control of a satellite–in the first, fuel is expended in a linear fashion to move a satellite following a diffusion–where the aim is to keep the satellite above a critical level for as long as possible (or indeed to reach a higher, ‘safe’ level). Under suitable assumptions for the drift and diffusion coefficients, it is shown that the stochastic maximum of the time to fall below the critical level is attained by a policy which imposes a reflecting boundary at the critical level until the fuel is exhausted and jumps the satellite directly to the safe level if this is ever possible. In the second model, there is a nonlinear response to the expenditure of fuel, and no safe level. It is shown that the optimal policy for maximizing the expected discounted time for the satellite to crash is similar, in that equal packets of fuel are used to jump the satellite upwards each time it reaches the critical level.
The Equations of Markovian Random Evolution on the Line
Authors: Kolesnik Alexander
Published: April 2003

We consider a general model of one-dimensional random evolution with n velocities and rates of a switching Poisson process (n ≥ 2). A governing nth-order hyperbolic equation in a determinant form is given. For two important particular cases it is written in an explicit form. Some known hyperbolic equations are obtained as particular cases of the general model
Spectral Factorization of Periodically Correlated MA(1) Processes
Authors: Bentarzi Mohamed , Hallin Marc
Published: April 2003

The spectral factorization problem, i.e. the problem of obtaining all possible MA representations of a process with given autocovariance function, is considered for univariate, d-periodic MA(1) (equivalently, 1-dependent in the second-order sense) processes. The solutions are provided explicitly, and their invertibility properties are investigated. A characterization, in terms of their autocovariance functions, of non-invertible d-periodic 1-dependent processes, extending to the periodic case the traditional unit root condition, is provided.
Increment-Vector Methodology: Transforming Non-Stationary Series to Stationary Series
Authors: Chen Zhao-Guo , Anderson Oliver D.
Published: April 2003

In time series analysis, it is well-known that the differencing operator ∇d may transform a non-stationary series, {Z(t)} say, to a stationary one, {W(t)} = ∇dZ(t)}; and there are many procedures for analysing and modelling {Z(t)} which exploit this transformation. Rather differently, Matheron (1973) introduced a set of measures on Rn that transform an appropriate non-stationary spatial process to stationarity, and Cressie (1988) then suggested that specialized low-order analogues of these measures, called increment-vectors, be used in time series analysis. This paper develops a general theory of increment-vectors which provides a more powerful transformation tool than mere simple differencing. The methodology gives a handle on the second-moment structure and divergence behaviour of homogeneously non-stationary series which leads to many important applications such as determining the correct degree of differencing, forecasting and interpolation.
Optimal Stopping of a Risk Reserve Process with Interest and Cost Rates
Authors: Schöttl A.
Published: April 2003

The risk reserve process of an insurance company within a deteriorating Markov-modulated environment is considered. The company invests its capital with interest rate α; the premiums and claims are increasing with rates β and γ. The problem of stopping the process at a random time which maximizes the expected net gain in order to calculate new premiums is investigated. A semimartingale representation of the risk reserve process yields, under certain conditions, an explicit solution of the problem.
General Conditions for Comparing the Reliability Functions of Systems of Components Sharing a Common Environment
Authors: Garren Steven T. , Richards Donald St. P.
Published: April 2003

We present general criteria for analyzing the crossing characteristics of RI, the reliability function of an m-of-n system of components operating within a laboratory (or test-bench) environment, and RO, the reliability function of the same system now operating subject to an external environment. Inside the laboratory the components' lifetimes may be dependently distributed, and the external environment is modeled using the general approach of Lindley and Singpurwalla (1986). Our techniques, which utilize results basic to the theory of order statistics, apply to broad classes of external environment models.
Continued Fraction Analysis of the Duration of an Excursion in an M/M/∞ System
Authors: Guillemin Fabrice , Pinchon Didier
Published: April 2003

We show in this paper how the Laplace transform θ* of the duration θ of an excursion by the occupation process {Λt} of an M/M/∞ system above a given threshold can be obtained by means of continued fraction analysis. The representation of θ* by a continued fraction is established and the [m−1/m] Padé approximants are computed by means of well known orthogonal polynomials, namely associated Charlier polynomials. It turns out that the continued fraction considered is an S fraction and as a consequence the Stieltjes transform of some spectral measure. Then, using classic asymptotic expansion properties of hypergeometric functions, the representation of the Laplace transform θ* by means of Kummer's function is obtained. This allows us to recover an earlier result obtained via complex analysis and the use of the strong Markov property satisfied by the occupation process {Λt}. The continued fraction representation enables us to further characterize the distribution of the random variable θ.
Partial Orderings of Distributions Based on Right-Spread Functions
Authors: Fernandez-Ponce J. M. , Kochar S. C. , Muñoz-Perez J.
Published: April 2003

In this paper we introduce a quantile dispersion measure. We use it to characterize different classes of ageing distributions. Based on the quantile dispersion measure, we propose a new partial ordering for comparing the spread or dispersion in two probability distributions. This new partial ordering is weaker than the well known dispersive ordering and it retains most of its interesting properties.
Exponential functionals of Brownian motion and disordered systems
Authors: Comtet Alain , Monthus Cécile , Yor Marc
Published: April 2003

The paper deals with exponential functionals of the linear Brownian motion which arise in different contexts, such as continuous time finance models and one-dimensional disordered models. We study some properties of these exponential functionals in relation with the problem of a particle coupled to a heat bath in a Wiener potential. Explicit expressions for the distribution of the free energy are presented.
A canonical representation for aggregated Markov processes
Authors: Larget Bret
Published: April 2003

A deterministic function of a Markov process is called an aggregated Markov process. We give necessary and sufficient conditions for the equivalence of continuous-time aggregated Markov processes. For both discrete- and continuous-time, we show that any aggregated Markov process which satisfies mild regularity conditions can be directly converted to a canonical representation which is unique for each class of equivalent models, and furthermore, is a minimal parameterization of all that can be identified about the underlying Markov process. Hidden Markov models on finite state spaces may be framed as aggregated Markov processes by expanding the state space and thus also have canonical representations.
Subexponential asymptotics of a Markov-modulated random walk with queueing applications
Authors: Jelenković Predrag R. , Lazar Aurel A.
Published: April 2003

Let {(Xn,Jn)} be a stationary Markov-modulated random walk on ℝ x E (E is finite), defined by its probability transition matrix measure F = {Fij}, Fij(B) = ℙ[X1 ∈ B, J1 = j | J0 = i], B ∈ B(ℝ), i, j ∈ E. If Fij([x,∞))/(1-H(x)) → Wij ∈ [0,∞), as x → ∞, for some long-tailed distribution function H, then the ascending ladder heights matrix distribution G+(x) (right Wiener-Hopf factor) has long-tailed asymptotics. If 𝔼Xn < 0, at least one Wij > 0, and H(x) is a subexponential distribution function, then the asymptotic behavior of the supremum of this random walk is the same as in the i.i.d. case, and it is given by ℙ[supn≥0Sn > x] → (−𝔼Xn)−1 ∫x∞ ℙ[Xn > u]du as x → ∞, where Sn = ∑1nXk, S0 = 0. Two general queueing applications of this result are given.

First, if the same asymptotic conditions are imposed on a Markov-modulated G/G/1 queue, then the waiting time distribution has the same asymptotics as the waiting time distribution of a GI/GI/1 queue, i.e., it is given by the integrated tail of the service time distribution function divided by the negative drift of the queue increment process. Second, the autocorrelation function of a class of processes constructed by embedding a Markov chain into a subexponential renewal process, has a subexponential tail. When a fluid flow queue is fed by these processes, the queue-length distribution is asymptotically proportional to its autocorrelation function.
A series expansion approach to the inverse problem
Authors: Angulo J. M. , Ruiz-Medina M. D.
Published: April 2003

We consider the inverse problem of estimating the input random field in a stochastic integral equation relating two random fields. The purpose of this paper is to present an approach to this problem using a Riesz-based or orthonormal-based series expansion of the input random field with uncorrelated random coefficients. We establish conditions under which the input series expansion induces (via the integral equation) a Riesz-based or orthonormal-based series expansion for the output random field. The estimation problem is studied considering two cases, depending on whether data are available from either the output random field alone, or from both the input and output random fields. Finally, we discuss this approach in the case of transmissivity estimation from piezometric head data, which was the original motivation of this work.
On closed support T-Invariants and the traffic equations
Authors: Boucherie Richard J. , Sereno Matteo
Published: April 2003

The traffic equations are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traffic equations are therefore of great importance. This note shows that the new condition stating that each transition is covered by a minimal closed support T-invariant, is necessary and sufficient for the existence of a solution for the traffic equations for batch routing queueing networks and stochastic Petri nets.
Absorption sampling and the absorption distribution
Authors: Kemp Adrienne W.
Published: April 2003

The inverse absorption distribution is shown to be aq-Pascal analogue of the Kemp and Kemp (1991)q-binomial distribution. The probabilities for the direct absorption distribution are obtained via the inverse absorption probabilities and exact expressions for its first two factorial moments are derived usingq-series transformations of its probability generating function. Alternative models for the distribution are given.
The xlogx condition for general branching processes
Authors: Olofsson Peter
Published: April 2003

The xlogx condition is a fundamental criterion for the rate of growth of a general branching process, being equivalent to non-degeneracy of the limiting random variable. In this paper we adopt the ideas from Lyons, Pemantle and Peres (1995) to present a new proof of this well-known theorem. The idea is to compare the ordinary branching measure on the space of population trees with another measure, the size-biased measure.
Wald's equations, first passage times and moments of ladder variables in Markov random walks
Authors: Der Fuh Cheng , Leung Lai Tze
Published: April 2003

Previous work in extending Wald's equations to Markov random walks involves finiteness of moment generating functions and uniform recurrence assumptions. By using a new approach, we can remove these assumptions. The results are applied to establish finiteness of moments of ladder variables and to derive asymptotic expansions for expected first passage times of Markov random walks. Wiener–Hopf factorizations for Markov random walks are also applied to analyse ladder variables and related first passage problems.
Negative binomial sums of random variables and discounted reward processes
Authors: Cooper William L.
Published: April 2003

Given a sequence of random variables (rewards), the Haviv–Puterman differential equation relates the expected infinite-horizon λ-discounted reward and the expected total reward up to a random time that is determined by an independent negative binomial random variable with parameters 2 and λ. This paper provides an interpretation of this proven, but previously unexplained, result. Furthermore, the interpretation is formalized into a new proof, which then yields new results for the general case where the rewards are accumulated up to a time determined by an independent negative binomial random variable with parameters k and λ.
Partition structures and sufficient statistics
Authors: Joyce Paul
Published: April 2003

Is the Ewens distribution the only one-parameter family of partition structures where the total number of types sampled is a sufficient statistic? In general, the answer is no. It is shown that all counterexamples can be generated via an urn scheme. The urn scheme need only satisfy two general conditions. In fact, the conditions are both necessary and sufficient. However, in particular, for a large class of partition structures that naturally arise in the infinite alleles theory of population genetics, the Ewens distribution is the only one in this class where the total number of types is sufficient for estimating the mutation rate. Finally, asymptotic sufficiency for parametric families of partition structures is discussed.
Explicit sufficient invariants for an interacting particle system
Authors: Itoh Yoshiaki , Mallows Colin , Shepp Larry
Published: April 2003

We introduce a new class of interacting particle systems on a graphG. Suppose initially there areNi(0) particles at each vertexiofG, and that the particles interact to form a Markov chain: at each instant two particles are chosen at random, and if these are atadjacentvertices ofG, one particle jumps to the other particle's vertex, each with probability 1/2. The processNenters a death state after a finite time when all the particles are in someindependentsubset of the vertices ofG, i.e. a set of vertices with no edges between any two of them. The problem is to find the distribution of the death state, ηi=Ni(∞), as a function ofNi(0).

We are able to obtain, for some special graphs, thelimitingdistribution ofNiif the total number of particlesN→ ∞ in such a way that the fraction,Ni(0)/S= ξi, at each vertex is held fixed asN→ ∞. In particular we can obtain the limit law for the graphS2, the two-leaf star which has three vertices and two edges.
A minimax optimal stop rule in reliability checking
Authors: Gouweleeuw José M.
Published: April 2003

Consider a machine, which may or may not have a defect, and the probability q that this machine is defective is unknown. In order to determine whether the machine is defective, it is tested. On each test, the defect is found with probability p, if it has not been found yet. Performing n tests costs cn dollars and there is a fine of 1 dollar if there is a defect and it is not found on the tests. When should we stop testing, in order to minimize the cost?

This problem is treated in a minimax setting: we try to find a strategy that works well, even for ‘bad’ q's. It turns out that the minimax optimal stop rule can be unexpectedly complicated. For example, if p = 1/2 and cn = cn = 0.25n, then the optimal rule is to start by performing one test. If a defect is found we stop, otherwise we perform a second test. If a defect is found, then again we stop, else toss a coin and stop if this shows heads. If we still have not stopped, a third and last test is performed.
The stress tensor and the energy of a continuous time homogeneous Markov system with fixed size
Authors: Tsaklidis George M.
Published: April 2003

The set of the attainable structures of a continuous time homogeneous Markov system (HMS) with fixed size, is considered as a continuum and the evolution of the HMS in the Euclidean space corresponds to its motion. Taking account of the velocity field of the HMS, a suitable model of continuum–defined by its stress tensor–is proposed in order to explain the motion of the system. The adoption of this model (equivalently of its stress tensor) enables us to establish the concept of the energy of a structure of the HMS.
Cell loss asymptotics for buffers fed with a large number of independent stationary sources
Authors: Likhanov Nikolay , Mazumdar Ravi R.
Published: April 2003

In this paper we derive asymptotically exact expressions for buffer overflow probabilities and cell loss probabilities for a finite buffer which is fed by a large number of independent and stationary sources. The technique is based on scaling, measure change and local limit theorems and extends the recent results of Courcoubetis and Weber on buffer overflow asymptotics. We discuss the cases when the buffers are of the same order as the transmission bandwidth as well as the case of small buffers. Moreover we show that the results hold for a wide variety of traffic sources including ON/OFF sources with heavy-tailed distributed ON periods, which are typical candidates for so-called ‘self-similar’ inputs, showing that the asymptotic cell loss probability behaves in much the same manner for such sources as for the Markovian type of sources, which has important implications for statistical multiplexing. Numerical validation of the results against simulations are also reported.
Using fuzzy sets in manpower planning
Authors: Guerry M. A.
Published: April 2003

In this paper, given personnel distributions that are not attainable, we introduce the grade of attainability in order to measure the degree to which there exists a similar distribution that is attainable. For constant size systems controlled by recruitment, properties of the most similar distribution to a given distribution are formulated.
Extreme values of phase-type and mixed random variables with parallel-processing examples
Authors: Kang Sungyeol , Serfozo Richard F.
Published: April 2003

A basic issue in extreme value theory is the characterization of the asymptotic distribution of the maximum of a number of random variables as the number tends to infinity. We address this issue in several settings. For independent identically distributed random variables where the distribution is a mixture, we show that the convergence of their maxima is determined by one of the distributions in the mixture that has a dominant tail. We use this result to characterize the asymptotic distribution of maxima associated with mixtures of convolutions of Erlang distributions and of normal distributions. Normalizing constants and bounds on the rates of convergence are also established. The next result is that the distribution of the maxima of independent random variables with phase type distributions converges to the Gumbel extreme-value distribution. These results are applied to describe completion times for jobs consisting of the parallel-processing of tasks represented by Markovian PERT networks or task-graphs. In these contexts, which arise in manufacturing and computer systems, the job completion time is the maximum of the task times and the number of tasks is fairly large. We also consider maxima of dependent random variables for which distributions are selected by an ergodic random environment process that may depend on the variables. We show under certain conditions that their distributions may converge to one of the three classical extreme-value distributions. This applies to parallel-processing where the subtasks are selected by a Markov chain.
Modelling random linear nucleation and growth by a Markov chain
Authors: Quine M. P. , Law J. S.
Published: April 2003

In an attempt to investigate the adequacy of the normal approximation for the number of nuclei in certain growth/coverage models, we consider a Markov chain which has properties in common with related continuous-time Markov processes (as well as being of interest in its own right). We establish that the rate of convergence to normality for the number of ‘drops’ during times 1,2,…n is of the optimal ‘Berry–Esséen’ form, as n → ∞. We also establish a law of the iterated logarithm and a functional central limit theorem.
Setups in polling models: does it make sense to set up if no work is waiting?
Authors: Cooper Robert B. , Niu Shun-Chen , Srinivasan Mandyam M.
Published: April 2003

We compare two versions of a symmetric two-queue polling model with switchover times and setup times. The SI version has State-Independent setups, according to which the server sets up at the polled queue whether or not work is waiting there; and the SD version has State-Dependent setups, according to which the server sets up only when work is waiting at the polled queue. Naive intuition would lead one to believe that the SD version should perform better than the SI version. We characterize the difference in the expected waiting times of these two versions, and we uncover some surprising facts. In particular, we show that, regardless of the server utilization or the service-time distribution, the SD version performs (i) the same as, (ii) worse than, or (iii) better than its SI counterpart if the switchover and setup times are, respectively, (i) both constants, (ii) variable (i.e. non-deterministic) and constant, or (iii) constant and variable. Only (iii) is consistent with naive intuition.
On maximum family size in branching processes
Authors: Rahimov Ibrahim , Yanev George P.
Published: April 2003

The number Yn of offspring of the most prolific individual in the nth generation of a Bienaymé–Galton–Watson process is studied. The asymptotic behaviour of Yn as n → ∞ may be viewed as an extreme value problem for i.i.d. random variables with random sample size. Limit theorems for both Yn and EYn provided that the offspring mean is finite are obtained using some convergence results for branching processes as well as a transfer limit lemma for maxima. Subcritical, critical and supercritical branching processes are considered separately.
Characterizations, stochastic equations, and the Gibbs sampler
Authors: Walker Stephen , Damien Paul
Published: April 2003

We obtain characterizations of densities on the real line and provide solutions to stochastic equations using the Gibbs sampler. Particular stochastic equations considered are of the typeX=dB(X+C) andX=dBX+C.
Excursions of birth and death processes, orthogonal polynomials, and continued fractions
Authors: Guillemin Fabrice , Pinchon Didier
Published: April 2003

On the basis of the Karlin and McGregor result, which states that the transition probability functions of a birth and death process can be expressed via the introduction of an orthogonal polynomial system and a spectral measure, we investigate in this paper how the Laplace transforms and the distributions of different transient characteristics related to excursions of a birth and death process can be expressed by means of the basic orthogonal polynomial system and the spectral measure. This allows us in particular to give a probabilistic interpretation of the series introduced by Stieltjes to study the convergence of the fundamental continued fraction associated with the system. Throughout the paper, we pay special attention to the case when the birth and death process is ergodic. Under the assumption that the spectrum of the spectral measure is discrete, we show how the distributions of different random variables associated with excursions depend on the fundamental continued fraction, the orthogonal polynomial system and the spectral measure.
Search schemes for random optimization algorithms that preserve the asymptotic distribution
Authors: Dorea Chang C. Y. , Gonçalves Cátia R.
Published: April 2003

Markovian algorithms for estimating the global maximum or minimum of real valued functions defined on some domain Ω ⊂ ℝd are presented. Conditions on the search schemes that preserve the asymptotic distribution are derived. Global and local search schemes satisfying these conditions are analysed and shown to yield sharper confidence intervals when compared to the i.i.d. case.
On a single server queue with negative arrivals and request repeated
Authors: Artalejo J. R. , Gomez-Corral A.
Published: April 2003

There is a growing interest in queueing systems with negative arrivals; i.e. where the arrival of a negative customer has the effect of deleting some customer in the queue. Recently, Harrison and Pitel (1996) investigated the queue length distribution of a single server queue of type M/G/1 with negative arrivals. In this paper we extend the analysis to the context of queueing systems with request repeated. We show that the limiting distribution of the system state can still be reduced to a Fredholm integral equation. We solve such an equation numerically by introducing an auxiliary ‘truncated’ system which can easily be evaluated with the help of a regenerative approach.
Hitting time in an M/G/1 queue
Authors: Ross Sheldon M. , Seshadri Sridhar
Published: April 2003

We study the expected time for the work in an M/G/1 system to exceed the level x, given that it started out initially empty, and show that it can be expressed solely in terms of the Poisson arrival rate, the service time distribution and the stationary delay distribution of the M/G/1 system. We use this result to construct an efficient simulation procedure.
Sharp upper bounds on perfect retrieval in the Hopfield model
Authors: Bovier Anton
Published: April 2003

We prove a sharp upper bound on the number of patterns that can be stored in the Hopfield model if the stored patterns are required to be fixed points of the gradient dynamics. We also show corresponding bounds on the one-step convergence of the sequential gradient dynamics. The bounds coincide with the known lower bounds and confirm the heuristic expectations. The proof is based on a crucial idea of Loukianova (1997) using the negative association properties of some random variables arising in the analysis.
On the occurrence of composite events and clusters of points
Authors: Stefanov Valeri T.
Published: April 2003

We derive explicit closed expressions for the moment generating functions of whole collections of quantities associated with the waiting time till the occurrence of composite events in either discrete or continuous-time models. The discrete-time models are independent, or Markov-dependent, binary trials and the events of interest are collections of successes with the property that each two consecutive successes are separated by no more than a fixed number of failures. The continuous-time models are renewal processes and the relevant events are clusters of points. We provide a unifying technology for treating both the discrete and continuous-time cases. This is based on first embedding the problems into similar ones for suitably selected Markov chains or Markov renewal processes, and second, applying tools from the exponential family technology.
Sequential selection of an increasing subsequence from a sample of random size
Authors: Gnedin Alexander V.
Published: April 2003

A random number of independent identically distributed random variables is inspected in strict succession. As a variable is inspected, it can either be selected or rejected and this decision becomes final at once. The selected sequence must increase. The problem is to maximize the expected length of the selected sequence.

We demonstrate decision policies which approach optimality when the number of observations becomes in a sense large and show that the maximum expected length is close to an easily computable value.
The expected time until absorption when absorption is not certain
Authors: Walker D. M.
Published: April 2003

This paper considers continuous-time Markov chains whose state space consists of an irreducible class, 𝒞, and an absorbing state which is accessible from 𝒞. The purpose is to provide a way to determine the expected time to absorption conditional on such time being finite, in the case where absorption occurs with probability less than 1. The results are illustrated by applications to the general birth and death process and the linear birth, death and catastrophe process.
Reward processes for semi-Markov processes: asymptotic behaviour
Authors: Soltani A. Reza , Khorshidian K.
Published: April 2003

The asymptotic behaviour of the cumulative mean of a reward process 𝒵ρ, where the reward function ρ belongs to a rather large class of functions, is obtained. It is proved that E𝒵ρ(t) = C0 + C1t + o(1), t → ∞, where C0 and C1 are fully specified. A section is devoted to the dual process of a semi-Markov process, and a formula is given for the mean of the first passage time from a state i to a state j of the dual process, in terms of the means of passage times of the original process.
Approximating integrals of stochastic processes: extensions
Authors: Benhenni Karim
Published: April 2003

We consider the problem of predicting integrals of second order processes whose covariances satisfy some Hölder regularity condition of order α > 0. When α is an odd integer, linear estimators based on regular sampling designs were constructed and asymptotic results for the approximation error were derived. We extend this result to any α > 0. When 2K < α ≤ 2K + 2, K a non-negative integer, we use an appropriate predictor based on the Euler-MacLaurin formula of order K with regular sampling designs. We give the corresponding result for the mean square error.
On some multi-request move-to-front heuristics
Authors: Phatarfod R. M. , Pryde A. J.
Published: April 2003

We consider the problem of self-organizing a linear list when the list is subjected to a random number of requests. Three separate move-to-front heuristics are considered. The difference between them lies in whether the items in the requested set are moved to the front in random order, or the same order as they were in originally, or in the order opposite to the one they were in originally. The eigenvalues of the transition probability matrices corresponding to the three heuristics are explicitly derived.
On a distributed clustering process of Coffman, Courtois, Gilbert and Piret
Authors: van den Berg J. , Ermakov A.
Published: April 2003

Coffman, Courtois, Gilbert and Piret (1991) have introduced a flow process in graphs, where each vertex gets an initial random resource, and where at each time vertices with large resources tend to attract resources from neighbours. The initial resources are assumed to be i.i.d., with a continuous distribution.

We are mainly interested in the following question: does, with probability 1, the resource of each vertex change only finitely many times?

Coffman et al. concentrate mainly on the case where the graph corresponds with the integer points on the line, in which case it is easily seen that the answer to the above question is positive. For higher-dimensional lattices they make general remarks which suggest that the answer to the above question is still positive. However, no proof seems to be known.

We restrict to the case of the square lattice, and, by a percolation approach, we reduce the question above to the question whether a certain quantity, which can be obtained from a finite computation, is sufficiently small. This computation is, however, still too long to be executed in an acceptable time. We therefore apply Monte Carlo simulation for this finite problem, which gives overwhelming evidence that, for the square lattice, the answer to the main question is positive.
On the stability of polling models with multiple servers
Authors: Down D.
Published: April 2003

The stability of polling models is examined using associated fluid limit models. Examples are presented which generalize existing results in the literature or provide new stability conditions while in both cases providing simple and intuitive proofs of stability. The analysis is performed for both general single server models and specific multiple server models.
Queueing processes in bulk systems under the D-policy
Authors: Dshalalow Jewgeni H.
Published: April 2003

This paper studies the queueing process in a class of D-policy models with Poisson bulk input, general service time, and four different vacation scenarios, among them a multiple vacation, single vacation and idle server. The D-policy specifies a busy period discipline, which requires an idle or vacationing server to resume his service when the workload process crosses some fixed level D. The analysis of the queueing process is based on the theory of fluctuations for three-dimensional marked counting processes presented in the paper. For all models, we derive the stationary distributions for the embedded and continuous time parameter queueing processes in closed analytic forms and illustrate the results by a number of examples and applications.
On critical vaccination coverage in multitype epidemics
Authors: Britton Tom
Published: April 2003

Consider an epidemic outbreak in a large population resulting in an overall proportion infected p~. The proportion needed to be vaccinated in order to prevent the epidemic, the critical vaccination coverage vc, depends on individual and social heterogeneities in the population. In the present note it is shown that vc is larger if, as is likely, individuals differ in terms of susceptibility than if they are equally susceptible.
Bisexual Galton-Watson branching process with population-size-dependent mating
Authors: Molina M. , Mota M. , Ramos A.
Published: April 2003

In this paper, we introduce a bisexual Galton-Watson branching process with mating function dependent on the population size in each generation. Necessary and sufficient conditions for the process to become extinct with probability 1 are investigated for two possible conditions on the sequence of mating functions. Some results for the probability generating functions associated with the process are also given.