bluuebunny/crossref_metadata_2025 huggingface dataset:
The limiting properties of population distributions with particular application to manpower planning
Authors: Woodward Mark
Published: April 2006

A model for predicting expected-value population distributions is developed, assuming that all movements are Markovian and time-homogeneous. Each individual is classified by the amount of time he has spent in the population and by which of a number of classes, of an unspecified nature, he inhabits. The limiting properties of the population distribution are derived, and, in particular, conditions for convergence to a stable distribution are given.

Some discussion of the relevance of the theory to practical applications is given, primarily to manpower planning when recruitment occurs purely to maintain a specified overall population size.
Note on the determination of cluster centers from a realization of a multidimensional Poisson cluster process
Authors: Baudin Michel
Published: April 2006

This is the sequel to a previous paper (Baudin (1981)). The joint probability generating functional of two point processes is introduced as a tool to compute the conditional intensity of the process of cluster centers of a multidimensional Poisson cluster process when a realization is given in a bounded observation window. An explicit formula is derived but it is too complicated for actual use; a linear method for practical estimation is discussed.
Moments of particle size distributions under sequential breakage with applications to species abundance
Authors: Siegel Andrew F. , Sugihara George
Published: April 2006

The sequential broken stick model has appeared in numerous contexts, including biology, physics, engineering and geology. Kolmogorov showed that under appropriate conditions, sequential breakage processes often yield a lognormal distribution of particle sizes. Of particular interest to ecologists is the observed variance of the logarithms of the sizes, which characterizes the evenness of an assemblage of species. We derive the first two moments for the logarithms of the sizes in terms of the underlying distribution used to determine the successive breakages. In particular, for a process yielding n pieces, the expected sample variance behaves asymptotically as log(n). These results also yield a new identity for moments of path lengths in random binary trees.
On the fluctuation of stochastically monotone Markov chains and some applications
Authors: Cohn Harry
Published: April 2006

A Borel–Cantelli-type property in terms of one-step transition probabilities is given for events like {|Xn+1| > a + ε, |Xn|≦a}, a and ε being two positive numbers. Applications to normed sums of i.i.d. random variables with infinite mean and branching processes in varying environment with or without immigration are derived.
A limit theorem for population-size-dependent branching processes
Authors: Klebaner F. C.
Published: April 2006

An analogue of the Kesten–Stigum theorem, and sufficient conditions for the geometric rate of growth in therth mean and almost surely, are obtained for population-size-dependent branching processes.
The stereological estimation of moments of particle volume
Authors: Jensen E. B. , Gundersen H. J. G.
Published: April 2006

In stereology or applied geometric probability quantitative characterization of aggregates of particles from information on lower-dimensional sections plays a major role. Most stereological methods developed for particle aggregates are based on the assumption that the particles are of the same, known (simple) shape. Information on the volume-weighted distribution of particle size may, however, be obtained under fairly general assumptions about particle shape if particle volume is chosen as size parameter. In fact, there exists in this case an unbiased stereological estimator of the first moment under the sole assumption that the particles are convex. In the present paper, we consider a particle aggregate in ℝ and derive estimators of theqth moment of the volume-weighted distribution of particle volume, based on point-sampling of particles and measurements onq-flats through sampled particles. The estimators are valid for arbitrarily shaped particles but if the particles are non-convex it is necessary for the determination of the estimators to be able to identify the different separated parts on aq-flat through the particle aggregate which belong to the same particle. Explicit forms of the estimators are given forq= 1. Forq= 2, an explicit form of one of the estimators is derived for an aggregate of triaxial ellipsoids in three-dimensional space.
Exponential trends of Ornstein–Uhlenbeck first-passage-time densities
Authors: Nobile A. G. , Ricciardi L. M. , Sacerdote L.
Published: April 2006

The asymptotic behaviour of the first-passage-time p.d.f. through a constant boundary for an Ornstein–Uhlenbeck process is investigated for large boundaries. It is shown that an exponential p.d.f. arises, whose mean is the average first-passage time from 0 to the boundary. The proof relies on a new recursive expression of the moments of the first-passage-time p.d.f. The excellent agreement of theoretical and computational results is pointed out. It is also remarked that in many cases the exponential behaviour actually occurs even for small values of time and boundary.
Remarks on a model of competitive bidding for employment
Authors: Pakes Anthony G.
Published: April 2006

Arnold and Laguna introduced a model for income distributions in which the income of the present generation of individuals has the same distribution as the minimum of a random number Nn of independent copies of some random variable and {Nn} is independent. The present paper gives a fairly complete analysis of this model and a number of extensions of it.
Lower tail analysis of the distribution of the strength of load-sharing systems
Authors: Harlow D. G. , Smith R. L. , Taylor H. M.
Published: April 2006

The Weibull distribution for the strength of a long fiber is reviewed, with emphasis on its derivation via extreme-value theory. It is shown that a corresponding Weibull distribution, but with different scale and shape parameters, is appropriate for the lower tail distribution of a bundle of parallel fibers under general load-sharing assumptions. This result is applied to series-parallel systems. The paper contains discussion of the application of these results to the strength of fibrous materials. It is concluded that the Weibull approximation, developed for series-parallel systems, is appropriate for long thin materials consisting of a small number of parallel fibers.
On queueing systems by retrials
Authors: Kulkarni Vidyadhar G.
Published: April 2006

A general result for queueing systems with retrials is presented. This result relates the expected total number of retrials conducted by an arbitrary customer to the expected total number of retrials that take place during an arbitrary service time. This result is used in the analysis of a special system where two types of customer arrive in an independent Poisson fashion at a single-server service station with no waiting room. The service times of the two types of customer have independent general distributions with finite second moments. When the incoming customer finds the server busy he immediately leaves and tries his luck again after an exponential amount of time. The retrial rates are different for different types of customers. Expressions are derived for the expected number of retrial customers of each type.
The spatial general epidemic and locally dependent random graphs
Authors: Kuulasmaa Kari
Published: April 2006

The threshold behaviour of the stochastic spatial general epidemic model on a discrete location space is investigated by making use of the general percolation theory of McDiarmid.
An optimal parking problem
Authors: Tamari Mitsushi
Published: April 2006

The decision-maker drives a car along a straight highway towards his destination and looks for a parking place. When he finds a parking place, he can either park there and walk the distance to his destination or continue driving. Parking places are assumed to occur in accordance with a Poisson process along the highway. The decision-maker does not know the distance Y to his destination exactly in advance. Only an a priori distribution is assumed for Y and cases of typically important distribution are examined. When we take as loss the distance the decision-maker must walk and wish to minimize the expected loss, the optimal stopping rule and the minimum expected loss are obtained. In Section 3 a generalization to the cases of a non-homogeneous Poisson process and a renewal process is considered.
Records from improving populations
Authors: Ballerini Rocco , Resnick Sidney
Published: April 2006

We consider records from the sequenceYj= Xj, + cj, j ≧1 wherec> 0 if upper records are of interest andc< 0 if lower records are studied. If {Xj} is stationary the record rate is asymptotically constant and if {Xj} is i.i.d. the record rate is, in addition, asymptotically normal. These results are illustrated by analysis of the times in the mile run.
Uniform conditional variability ordering of probability distributions
Authors: Whitt Ward
Published: April 2006

Variability orderings indicate that one probability distribution is more spread out or dispersed than another. Here variability orderings are considered that are preserved under conditioning on a common subset. One density f on the real line is said to be less than or equal to another, g, in uniform conditional variability order (UCVO) if the ratio f(x)/g(x) is unimodal with the model yielding a supremum, but f and g are not stochastically ordered. Since the unimodality is preserved under scalar multiplication, the associated conditional densities are ordered either by UCVO or by ordinary stochastic order. If f and g have equal means, then UCVO implies the standard variability ordering determined by the expectation of all convex functions. The UCVO property often can be easily checked by seeing if f(x)/g(x) is log-concave. This is illustrated in a comparison of open and closed queueing network models.
A queueing system with impatient customers
Authors: De Kok A. G. , Tijms H. C.
Published: April 2006

A queueing situation often encountered in practice is that in which customers wait for service for a limited time only and leave the system if not served during that time. This paper considers a single-server queueing system with Poisson input and general service times, where a customer becomes a lost customer when his service has not begun within a fixed time after his arrival. For performance measures like the fraction of customers who are lost and the average delay in queue of a customer we obtain exact and approximate results that are useful for practical applications.
Inequalities for random flats meeting a convex body
Authors: Schneider Rolf
Published: April 2006

We choose a uniform random point in a given convex bodyKinn-dimensional Euclidean space and through that point the secant ofKwith random direction chosen independently and isotropically. Given the volume ofK, the expectation of the length of the resulting random secant ofKwas conjectured by Enns and Ehlers [5] to be maximal ifKis a ball. We prove this, and we also treat higher-dimensional sections defined in an analogous way. Next, we consider a finite number of independent isotropic uniform random flats meetingK, and we prove that certain geometric probabilities connected with these again become maximal whenKis a ball.
A property of the generalized inverse Gaussian distribution with some applications
Authors: Embrechts Paul
Published: April 2006

An asymptotic convolution property for the generalized inverse Gaussian distribution with λ < 0 is proved. This result is applied to calculate the probability of ruin in the general risk model when these distributions are used to model claim sizes. Some related applications are discussed.
A useful ageing property based on the Laplace transform
Authors: Klefsjö Bengt
Published: April 2006

The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.
Job search: the continuous case
Authors: Zuckerman Dror
Published: April 2006

In this paper we examine a continuous model of job search. An individual is seeking employment continuously over time. There is a search cost of c monetary units per unit time. Job offers are received randomly over time according to a renewal process. The wage offers are assumed to be positive, independent and identically distributed random variables. The only decision the searcher must make is when to stop searching and accept an offer. The objective is to determine a stopping rule that is optimal under the following optimality criteria:

(a)

maximum expected net return,

(b)

maximum expected discounted net return.

We investigate the case in which the stream of job offers is determined by a Poisson process. We show that under the two optimality criteria defined above an optimal stopping rule is determined by a single critical value ξ. The optimal strategy is to accept the first job offer that exceeds ξ. In the second part of the article, the search model in which offers are received according to a general renewal process is examined.
The exact and asymptotic formulas for the state probabilities in simple epidemics with m kinds of susceptibles
Authors: Lacayo H. , Langberg Naftali A.
Published: April 2006

A population of susceptible individuals partitioned into m groups and exposed to a contagious disease is considered.

The progress of this simple epidemic is modeled by an m -dimensional stochastic process, whose components are the number of infective individuals in the respective groups at time t. Exact and approximate formulas for the joint and marginal state probabilities are obtained.
The saddlepoint approximation for a general birth process
Authors: Daniels H. E.
Published: April 2006

Saddlepoint approximations to the probabilities for a general time-homogeneous birth process are derived from the known Laplace transform with respect to time. Numerical computations for the simple (logistic) epidemic show the approximation to have a remarkably low relative error over the useful range of times for populations as small as 5. The merit or otherwise of renormalising the approximate probabilities is discussed. To study the accuracy for moderately large population sizes, a special form of birth rate is used, for which the exact probabilities can be computed directly.
On a sufficient condition for superprocesses due to whittle
Authors: Glazebrook K. D.
Published: April 2006

Whittle has given a sufficient condition for a certain class of Markov decision processes to have an optimal strategy of a particularly simple form. We show this condition to be necessary in a certain sense and give some examples of its application.
Shock models leading to increasing failure rate and decreasing mean residual life survival
Authors: Ghosh Malay , Ebrahimi Nader
Published: April 2006

Shock models leading to various univariate and bivariate increasing failure rate (IFR) and decreasing mean residual life (DMRL) distributions are discussed. For proving the IFR properties, shocks are not necessarily assumed to be governed by a Poisson process.
First-passage percolation processes with finite height
Authors: Herrndorf Norbert
Published: April 2006

We consider first-passage percolation in an infinite horizontal strip of finite height. Using methods from the theory of Markov chains, we prove a central limit theorem for first-passage times, and compute the time constants for some special cases.
The slow server problem: a queue with stalling
Authors: Rubinovitch Michael
Published: April 2006

A queue with Poisson arrivals and two different exponential servers is considered. It is assumed that customers are allowed tostall, i.e., to wait for a busy fast server at times when the slow server is free. A stochastic analysis of the queue is given, steady-state probabilities are computed, and policies for overall optimization are characterized and computed. The issue of individual customer's optimization versus overall optimization is also discussed.
A note on a continuous-time Markov manpower model
Authors: Davies G. S.
Published: April 2006

We examine a Markov manpower system in continuous time where demotion rates are 0 and promotion rates are time-dependent. The transient and limiting behaviours of the model are discussed, and illustrated with examples.
A note on the asymptotic properties of correlated random walks
Authors: Roerdink J. B. T. M.
Published: April 2006

We describe a simple relation between the asymptotic behavior of the variance and of the expected number of distinct sites visited during a correlated random walk. The relation is valid for multistate random walks with finite variance in dimensions 1 and 2. A similar relation, valid in all dimensions, exists between the asymptotic behavior of the variance and of the probability of return to the origin.
Cooperation in a repeated game with random payment function
Authors: Eshel Ilan , Weinshall Daphna
Published: April 2006

A model of cooperation versus defection in a sequence of games is analysed under the assumptions that the rules of the game are randomly changed from one encounter to another, that the decisions are to be made each time anew, according to the (random) rules of the specific local game, and that the result of one such game affects the ability of a player to participate and thus, cooperate in the next game. Under plausible assumptions, it is shown that all Nash solutions of the supergame determine cooperation over a non-degenerate range of rules, determining encounters of the prisoner's dilemma type.
Moments Of the stationary waiting time in the Gi/Ph/1 queue
Authors: Ramaswami V. , Lucantoni D. M.
Published: April 2006

Recursive relations for computing the higher moments of the stationary waiting time distribution in a stable GI/PH/1 queue are derived. These provide an accurate and stable technique to compute these moments.
Probabilistic analysis of optimum partitioning
Authors: Karmarkar Narendra , Karp Richard M. , Lueker George S. , Odlyzko Andrew M.
Published: April 2006

Given a set of n items with real-valued sizes, the optimum partition problem asks how it can be partitioned into two subsets so that the absolute value of the difference of the sums of the sizes over the two subsets is minimized. We present bounds on the probability distribution of this minimum under the assumption that the sizes are independent random variables drawn from a common distribution. For a large class of distributions, we determine the asymptotic behavior of the median of this minimum, and show that it is exponentially small.
Aspects of positive ageing
Authors: Deshpande Jayant V. , Kochar Subhash C. , Singh Harshinder
Published: April 2006

The concept of positive ageing describes the adverse effects of age on the lifetime of units. Various aspects of this concept are described in terms of conditional probability distributions of residual lifetimes, failure rates, equilibrium distributions, etc. In this paper we further analyse this concept and relate it to stochastic dominance of first and higher orders. In the process we gain many insights and are able to define several new kinds of ageing criteria which supplement those existing in the literature.
Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules
Authors: Keilson J. , Servi L. D.
Published: April 2006

Processors handling multi-class traffic typically alternate between serving a particular class of traffic and performing other tasks, e.g., secondary service tasks or routine maintenance. The stochastic behavior of such systems is modeled by a newly introduced class of Bernoulli GI/G/1 vacation models. For this model, when a vacation is completed and customers are present, a customer is served. When a customer has just been served and other customers are present, the server accepts a customer with fixed probability p or commences a vacation of prespecified random duration with probability 1 – p. Whenever no customers are present, a vacation is taken. When p = 0 or p = 1 this schedule reduces to the previously introduced single service schedule and the exhaustive service schedule, respectively. An analysis of all three schedules on a state space incorporating server vacations is presented using simple methods in the complex plane. It is shown that the recent decomposition results for exhaustive service extend to the more general class of Bernoulli schedules.
A note on the total size distribution of epidemic models
Authors: Ball Frank
Published: April 2006

A simple coupling argument is used to obtain a new proof of a result of Daniels (1967) concerning the total size distribution of the general stochastic epidemic. The proof admits a straightforward generalisation to multipopulation epidemics and indicates that similar results are unlikely to be available for epidemics with non-exponential infectious periods.
An extremal markovian sequence
Authors: Alpuim M. Teresa
Published: April 2006

In this paper we consider an independent and identically distributed sequence {Yn} with common distribution function F(x) and a random variable X0, independent of the Yi's, and define a Markovian sequence {Xn} as Xi = X0, if i = 0, Xi = k max{Xi− 1, Yi}, if i ≧ 1, k ∈ R, 0 < k < 1. For this sequence we evaluate basic distributional formulas and give conditions on F(x) for the sequence to possess a stationary distribution. We prove that for any distribution function H(x) with left endpoint greater than or equal to zero for which log H(ex) is concave it is possible to construct such a stationary sequence with marginal distributions equal to it. We study the limit laws for extremes and kth order statistics.
On the dependence structure of hitting times of multivariate processes
Authors: Ebrahimi Nader , Ramallingam T.
Published: April 2006

A direct approach to derive dependence properties among the hitting times of bivariate processes has been initiated by Ebrahimi (1987) and explored further by Ebrahimi and Ramallingam (1988). In this paper, new results are obtained for multivariate processes, which help us to identify positive and negative dependence structures among the hitting times of the processes. Applications of our theorems to reliability of systems are given.
Resolvent operators of Markov processes and their applications in the control of a finite dam
Authors: Attia F. A.
Published: April 2006

The resolvent operators of the following two processes are obtained: (a) the bivariate Markov process W = (X, Y), where Y(t) is an irreducible Markov chain and X(t) is its integral, and (b) the geometric Wiener process G(t) = exp{B(t} where B(t) is a Wiener process with non-negative drift μ and variance parameter σ2. These results are then used via a limiting procedure to determine the long-run average cost per unit time of operating a finite dam where the input process is either X(t) or G(t). The system is controlled by a policy (Attia [1], Lam [6]).
Infinite-dimensional stochastic difference equations for particle systems and network flows
Authors: Darling R. W. R.
Published: April 2006

Let V be a countably infinite set, and let {Xn, n = 0, 1, ·· ·} be random vectors in which satisfy Xn = AnXn– 1 + ζn, for i.i.d. random matrices {An} and i.i.d. random vectors {ζ n}. Interpretation: site x in V is occupied by Xn(x) particles at time n; An describes random transport of existing particles, and ζ n(x) is the number of ‘births' at x. We give conditions for (1) convergence of the sequence {Xn} to equilibrium, and (2) a central limit theorem for n–1/2(X1 + · ·· + Xn), respectively. When the matrices {An} consist of 0's and 1's, these conditions are checked in two classes of examples: the ‘drip, stick and flow model' (a stochastic flow with births), and a neural network model.
A sample path analysis of theM/M/1 queue
Authors: Baccelli Francois , Massey William A.
Published: April 2006

The exact solution for the transient distribution of the queue length and busy period of theM/M/1 queue in terms of modified Bessel functions has been proved in a variety of ways. Methods of the past range from spectral analysis (Lederman and Reuter (1954)), combinatorial arguments (Champernowne (1956)), to generating functions coupled with Laplace transforms (Clarke (1956)). In this paper, we present a novel approach that ties the computation of these transient distributions directly to the random sample path behavior of theM/M/1 queue. The use of Laplace transforms is minimized, and the use of generating functions is eliminated completely. This is a method that could prove to be useful in developing a similar transient analysis for queueing networks.
Transient renewal processes in the subexponential case
Authors: Murphree Emily S.
Published: April 2006

A transient renewal process based on a sequence of possibly infinite waiting times is defined. The process is studied when the (rescaled) distribution of the waiting times belongs to the subexponential class of distributions. In this case, even conditional on all waiting times observed by time t being finite, the distributions of the forward and backward delays at t are asymptotically degenerate. Also, the conditional moments of the number of events by time t converge to the same finite limits as the unconditional moments.
Lifetime regression models based on a functional equation of physical nature
Authors: Castillo Enrique , Galambos Janos
Published: April 2006

There are a number of ad hoc regression models for the statistical analysis of lifetime data, but only a few examples exist in which physical considerations are used to characterize the model. In the present paper a complete characterization of a regression model is given by solving a functional equation recurring in the literature for the case of a fatigue problem. The result is that, if the lifetime for given values of the regressor variable and the regressor variable for a given lifetime are both Weibull variables (assumptions which are well founded, at least as approximations, from extreme-value theory in some concrete applications), there are only three families of (conditional) distribution for the lifetime (or for the regressor variable). This model is then applied to a practical problem for illustration.
A stochastic death process with elimination by pairing
Authors: Faddy M. J. , Esty Warren W.
Published: April 2006

A stochastic death process in which particles of two types combine and are removed from the system at a rate proportional to the product of their numbers is derived and analyzed. Exact expressions for the probability distribution and moments are given and an approximating diffusion is obtained. Numerical calculations show close agreement between the exact solution and this diffusion even for small numbers of particles, and reveal the relatively low level of stochastic variation.
Augmented truncations of infinite stochastic matrices
Authors: Gibson Diana , Seneta E.
Published: April 2006

We consider the problem of approximating the stationary distribution of a positive-recurrent Markov chain with infinite transition matrix P, by stationary distributions computed from (n × n) stochastic matrices formed by augmenting the entries of the (n × n) northwest corner truncations of P, as n →∞.
Large deviations of tail estimators based on the Pareto approximation
Authors: Smith Richard L. , Weissman Ishay
Published: April 2006

We consider the relative error of a tail functionwhen this is approximated byy–αusing an estimator of Hill's forα.The results combine recent work of Davis and Resnick on tail estimation with Anderson's work on large deviations in extreme-value theory. Treating separately the domains of attraction of Φαand Λ, we obtain general conditions for the relative error to tend to 0 asu→∞,y →∞ simultaneously. The results serve as warning against the automatic extrapolation of estimates based on extreme-value approximations.
Some remarks on regression with autoregressive errors and their residual processes
Authors: Kulperger R. J.
Published: April 2006

We consider some linear regression modelsY= Σαlfl(z) +X, whereXis an autoregressive (AR) process. The residuals estimate the i.i.d. innovations sequence which drives the AR process. We then consider the partial sum process of the residuals and show they converge to Brownian bridges in certain cases. Some remarks are also made on similar processes when differencing is first applied to remove trends. When an AR process is differenced the residual partial sum can be asymptotically a random polynomial.
Bounds on the expected waiting time in aGI/G/1 queue: upgrading for low traffic intensity
Authors: Rosberg Zvi
Published: April 2006

For aGI/G/1 queue we derive new lower and uper bounds on the expected stationary waiting time which are a function of more than the first two moments of the inter-arrival and service times. When the probability for a delay is low, the bounds tend to be better than other bounds. This is illustrated in an example of a Uniform/Uniform/1 queue.
On aggregated Markov processes
Authors: Fredkin Donald R. , Rice John A.
Published: April 2006

A finite-state Markov process is aggregated into several groups. What can be learned about the underlying process from the aggregated one? We provide some partial answers to this question.
Adventures in applied probability
Authors: Gani J.
Published: April 2006

This article attempts to provide a historical perspective of the author's involvement in applied probability. Several research problems in this area are described, and three organizational experiences of importance to the author outlined. After a brief account of the development of the Applied Probability journals, the article concludes with some philosophical remarks.
Stochastic models and field trials
Authors: Bartlett M. S.
Published: April 2006

A survey of the development of statistical techniques of field experimentation refers to the unified approach of R. A. Fisher, in which analysis and design were closely linked. Randomization of treatment positions bypassed the need for a precise stochastic model, but sometimes at the cost of diminished accuracy.

Alternative covariance methods associated with the name of J. S. Papadakis, taking note of the yields of neighbouring plots, have stimulated much research in recent years. The results to date suggest that, while improved accuracy can often be achieved, the assessment of accuracy is more dependent on the stochastic model. Robust methods for such assessment still need to be finalized; with these alternative methods a closer link between analysis and design is also advocated.
Ignatov's theorem: a new and short proof
Authors: Engelen Ron , Tommassen Paul , Vervaat Wim
Published: April 2006

By Ignatov's theorem the sets of values in an i.i.d. sequence that are thekth largest at their appearance (k= 1, 2, ···) are supports of i.i.d. Poisson processes. The present paper contains an elementary and short proof for the case where the underlying distribution functionFis discrete, and then extends the result to generalF.
Restless bandits: activity allocation in a changing world
Authors: Whittle P.
Published: April 2006

We consider a population ofnprojects which in general continue to evolve whether in operation or not (although by different rules). It is desired to choose the projects in operation at each instant of time so as to maximise the expected rate of reward, under a constraint upon the expected number of projects in operation. The Lagrange multiplier associated with this constraint defines an index which reduces to the Gittins index when projects not being operated are static. If one is constrained to operatemprojects exactly then arguments are advanced to support the conjecture that, formandnlarge in constant ratio, the policy of operating themprojects of largest current index is nearly optimal. The index is evaluated for some particular projects.
On the concavity of the waiting-time distribution in some GI/G/1 queues
Authors: Szekli R.
Published: April 2006

In this paper the concavity property for the distribution of a geometric random sum (geometric compound) X, + · ·· + XN is established under the assumption that Xi are i.i.d. and have a DFR distribution. From this and the fact that the actual waiting time in GI/G/1 queues can be written as a geometric random sum, the concavity of the waiting-time distribution in GI/G/1 queues with a DFR service-time distribution is derived. The DFR property of the idle-period distribution in specialized GI/G/1 queues is also mentioned.
Some properties of chord length distributions
Authors: Gates J.
Published: April 2006

The chord length distributions of planar convex sets are discussed, particularly the density values at the extremes of the range; there is a qualitative distinction between polygons and sets with smooth boundaries. The distance between convex sets is related to the distance between distribution functions.
Probability of maintaining or attaining a structure in one step
Authors: Abdallaoui G.
Published: April 2006

Our concern is with a particular problem which arises in connection with a discrete-time Markov chain model for a graded manpower system. In this model, the members of an organisation are classified into distinct classes. As time passes, they move from one class to another, or to the outside world, in a random way governed by fixed transition probabilities. In this paper, the emphasis is placed on evaluating exact values of the probabilities of attaining and maintaining a structure.
Random coverings of the circle by arcs with restricted endpoints
Authors: Janson Svante
Published: April 2006

A circle is covered by random arcs with a given length a and endpoints chosen (independently and uniformly) among m equispaced points on the circle. The asymptotic distribution as a → 0 and m → ∞of the number of arcs required for complete coverage is given. The result connects earlier results for the cases ma = 1 (a discrete problem) and m = ∞ (the continuous limiting case).
A note on cumulative shock models
Authors: Anderson Kevin K.
Published: April 2006

A shock model in which the time intervals between shocks are in the domain of attraction of a stable law of order less than 1 or relatively stable is considered. Weak limit theorems are established for the cumulative magnitude of the shocks and the first time the cumulative magnitude exceeds z without any assumption on the dependence between the intershock interval and shock magnitude.
Smooth first-passage densities for one-dimensional diffusions
Authors: Pauwels E. J.
Published: April 2006

The purpose of this paper is to show that smoothness conditions on the diffusion and drift coefficient of a one-dimensional stochastic differential equation imply the existence and smoothness of a first-passage density.

In order to be able to prove this, we shall show that Brownian motion conditioned to first hit a point at a specified time has the same distribution as a Bessel (3)-process with changed time scale.
Formulas for the reliability of a consecutive-K-Out-of-n: F system
Authors: Papastavridis S. , Hadzichristos I.
Published: April 2006

General exact formulas are established to calculate the reliability of a consecutive-k-out-of-n: F system. The optimality of the system, under permutation of the components, is examined too.
A method for approximating the probability functions of a Markov chain
Authors: Crank Keith N.
Published: April 2006

This paper presents a method of approximating the state probabilities for a continuous-time Markov chain. This is done by constructing a right-shift process and then solving the Kolmogorov system of differential equations recursively. By solving a finite number of the differential equations, it is possible to obtain the state probabilities to any degree of accuracy over any finite time interval.
Modelling dependence in simple and indirect majority systems
Authors: Boland Philip J. , Proschan Frank , Tong Y. L.
Published: April 2006

Majority systems are encountered in both decision theory and reliability theory. In decision theory for example a jury or committee employing a majority rule will make the ‘correct' decision if a majority of the individuals do so. In reliability theory some coherent systems function if and only if a majority of the components work properly. In this paper results concerning the reliability of majority systems are developed which are applicable in both areas. Two models incorporating dependence between individuals or components in majority systems are introduced, and various monotonicity results for their reliability functions are established. Comparisons are also made between direct (or simple) and indirect majority systems.
Ballots, queues and random graphs
Authors: Takács Lajos
Published: April 2006

This paper demonstrates how a simple ballot theorem leads, through the interjection of a queuing process, to the solution of a problem in the theory of random graphs connected with a study of polymers in chemistry. Let Γn(p) denote a random graph with n vertices in which any two vertices, independently of the others, are connected by an edge with probability p where 0 < p < 1. Denote by ρ n(s) the number of vertices in the union of all those components of Γn(p) which contain at least one vertex of a given set of s vertices. This paper is concerned with the determination of the distribution of ρ n(s) and the limit distribution of ρ n(s) as n → ∞and ρ → 0 in such a way that np → a where a is a positive real number.
A generalization of little's law to moments of queue lengths and waiting times in closed, product-form queueing networks
Authors: McKenna James
Published: April 2006

Little's theorem states that under very general conditions L = λW, where L is the time average number in the system, W is the expected sojourn time in the system, and λ is the mean arrival rate to the system. For certain systems it is known that relations of the form E((L)l) = λ lE((W)l) are also true, where (L)l = L(L – 1)· ·· (L – l + 1). It is shown in this paper that closely analogous relations hold in closed, product-form queueing networks. Similar expressions relate Nji and Sji, where Nji is the total number of class j jobs at center i and Sji is the total sojourn time of a class j job at center i, when center i is a single-server, FCFS center. When center i is a c-server, FCFS center, Qji and Wji are related this way, where Qji is the number of class j jobs queued, but not in service at center i and Wji is the waiting time in queue of a class j job at center i. More remarkably, generalizations of these results to joint moments of queue lengths and sojourn times along overtake-free paths are shown to hold.
On some characterizations of the poisson process
Authors: Huang Wen-Jang
Published: April 2006

In this article we give some characterizations of Poisson processes, the model which we consider is inspired by Kimeldorf and Thall (1983) and we generalize the results of Chandramohan and Liang (1985). More precisely, we consider an arbitrarily delayed renewal process, at each arrival time we allow the number of arrivals to be i.i.d. random variables, also the mass of each unit atom can be split into k new atoms with the ith new atom assigned to the process Di, i = 1, ···, k. We shall show that the existence of a pair of uncorrelated processes Di, Dj, i ≠ j, implies the renewal process is Poisson. Some other related characterization results are also obtained.
Time series formed from the superposition of discrete renewal processes
Authors: Blight P. A.
Published: April 2006

The superposition of independent, discrete, renewal processes produces a counting process which is also a discrete time series. The conditional distribution and correlation structure of this kind of time series may be obtained. In suitable conditions the conditional distribution has a spectrum which is exactly or approximately rational. When this is so, an ARMA can be found which matches the spectrum of the superposition.
Structure functions with finite minimal vector sets
Authors: Baxter Laurence A. , Lee Seung Min
Published: April 2006

A continuum structure function (CSF) y is a non-decreasing mapping from the unit hypercube to the unit interval. Define whereas γ (γ) < α for all y < x}, the set of minimal vectors to level α. This paper examines CSFs for which each Pα is finite. It is shown that if γ is such a CSF and X is a vector of independent random variables, the distribution of γ (X) is readily calculated. Further, if γ is an arbitrary right-continuous CSF, the distribution of γ (X) may be approximated arbitrarily closely by that of γ′(X) where γ′ is a right-continuous CSF for which each minimal vector set is finite.
On a system of components with joint lifetimes distributed as a mixture of independent exponential laws
Authors: Lefèvre Claude , Malice Marie-Pierre
Published: April 2006

A system ofnnon-renewable components sharing a common environment is considered. The joint lifetimes of the components are taken distributed as a mixture ofnindependent exponential laws. It is shown how the mixing distribution can affect the number of components functioning and the reliability of ak-out-of-nsystem. The analysis is carried out by using different partial orderings for distribution functions.
Testing for the presence of sinusoidal components
Authors: Quinn B. G.
Published: April 2006

Approximate and asymptotic distributional results are obtained for the likelihood ratio test of the hypothesis that a time series is composed from s sinusoidal components, at unknown frequencies, with additive Gaussian white noise, against the hypothesis that there are an additional r sinusoidal components at unknown frequencies. The work extends that of Fisher (1929), and contains a number of simulations illustrating the results.
Local Gaussian modelling of stochastic dynamical systems in the analysis of non-linear random vibrations
Authors: Ozaki Tohru
Published: April 2006

Stochastic dynamical system models for non-linear random vibrations are considered and their discrete-time version, non-linear time series models are introduced using the local Gaussian modelling method. Some computational problems and implications of the present method in non-linear time series analysis are discussed.
Point-process models with linearly parametrized intensity for application to earthquake data
Authors: Ogata Yosihiko , Katsura Koichi
Published: April 2006

It is demonstrated that linear parametrization of the conditional intensity provides systematic classes of flexible models which are reasonably useful for calculating maximum likelihoods. To exemplify the modelling, seismic activity around Canberra is decomposed into components of evolutionary trend, clustering and periodicity. The causal relationship between earthquake sequences from two seismic regions is also analysed for a certain Japanese earthquake data set.

Some technical aspects of the modelling and calculations are described.
The risk-sensitive certainty equivalence principle
Authors: Whittle Peter
Published: April 2006

A risk-sensitive certainty equivalence principle is deduced, expressed in Theorem 1, for a model with linear dynamics and observation rules, Gaussian noise and an exponential-quadratic criterion of the form (2). The senses in which one is now to understand certainty equivalence and the separation principle are discussed.
Extremal processes, secretary problems and the 1/e law
Authors: Pfeifer Dietmar
Published: April 2006

We consider a class of secretary problems in which the order of arrival of candidates is no longer uniformly distributed. By a suitable embedding in a time-transformed extremal process it is shown that the asymptotic winning probability is again 1/e as in the classical situation. Extensions of the problem to more than one choice are also considered.
Sojourn times in finite Markov processes
Authors: Rubino Gerardo , Sericola Bruno
Published: April 2006

Sojourn times of Markov processes in subsets of the finite state space are considered. We give a closed form of the distribution of the nth sojourn time in a given subset of states. The asymptotic behaviour of this distribution when time goes to infinity is analyzed, in the discrete time and the continuous-time cases. We consider the usually pseudo-aggregated Markov process canonically constructed from the previous one by collapsing the states of each subset of a given partition. The relation between limits of moments of the sojourn time distributions in the original Markov process and the moments of the corresponding holding times of the pseudo-aggregated one is also studied.
Shepp statistic for Markov chains application to a long-run average cost criterion
Authors: Ksir Brahim
Published: April 2006

This paper is a generalization to Markov chains of the work of Shepp [6] in the i.i.d case. Shepp studies the limiting values of the averagesTn= (Sn+f(n)–Sn)/f(n) whereSn=X0+X1+ · ·· +Xn,X0= 0,n= 1, 2, ···, is a sum of mutually independent and identically distributed random variables. The functionftakes positive integer values and non-decreasingly tends to infinity. Here we take a class of functionsfin central positionf(n) = [clogn],c> 0,n= 1, 2, ···. There are many refinements of the functionfin the i.i.d case [1], [2]. Here we consider the more general case whereX1,· ··,Xnis an irreducible and recurrent Markov chain. The state space of the chain is either compact or countable.
On a duality between a non-Markoyian storage/production process and a Markovian dam process with state-dependent input and output
Authors: Kaspi Haya , Perry David
Published: April 2006

We consider a storage/production process where the production rate is state dependent, the demand arrival is a renewal process, and the sizes of the demands are i.i.d exponentially distributed random variables. The resulting content process is non-Markovian but regenerative. We construct a dual Markovian dam process with drift, jump rate and jump sizes that are state dependent and use it to compute the limiting one-dimensional distribution of the content process.
A characterization of Gumbel's bivariate exponential and lindley and Singpurwalla's bivariate lomax distributions
Authors: Roy Dilip
Published: April 2006

A bivariate exponential distribution due to Gumbel and a bivariate Lomax distribution due to Lindley and Singpurwalla have been characterized through a bivariate extension of a univariate characterizing property of the exponential and the Lomax distribution; the characterization is based on mean residual lives and hazard rates.
Further results for dynamic scheduling of multiclassG/G/1 queues
Authors: Hirayama Tetsuji , Kijima Masaaki , Nishimura Shoichi
Published: April 2006

We consider discrete-time dynamic scheduling problems of the following three types ofG/G/1 queue withKdifferent customer classes: (i) aG/DFR/1 queue withKclasses under preemptive resume service discipline, (ii) aG/IFR/1 queue with two classes under preemptive resume service discipline, and (iii) aG/G/1 queue with two classes under non-preemptive service discipline. Interchange arguments are used to show that simple index policies of different type minimize the total holding cost of customers in a finite-horizon scheduling period for the three cases. Our results extend the result for aG/M/1 queue by Buyukkoc et al. (1985) to general queues.
Pareto processes
Authors: Yeh Hsiaw-Chan , Arnold Barry C. , Robertson Christopher A.
Published: April 2006

An autoregressive process ARP(1) with Pareto-distributed inputs, analogous to those of Lawrance and Lewis (1977), (1980), is defined and its properties developed. It is shown that the stationary distributions are Pareto. Further, the maximum and minimum processes are asymptotically Weibull, and the ARP(1) process is shown to be closed under maximization or minimization when the number of terms is geometrically distributed. The ARP(1) process leads naturally to an extremal process in the sense of Lamperti (1964). Statistical inference for the ARP(1) process is developed. An absolutely continuous variant of the Pareto process is described.