bluuebunny/crossref_metadata_2025 huggingface dataset:
Queueing systems with restricted workload: an explicit solution
Authors: Van Dijk Nico M.
Published: April 2006

Queueing systems with non-exponential service distributions and a capacity restriction on the total residual service requirement (workload) are studied. Closed-form expressions of geometric form in the LCFS case and recursive representations in the FCFS case are obtained for the steady state workload distribution. The proof is of interest in itself and directly leads to extensions.
On extremal service disciplines in single-stage queueing systems
Authors: Righter Rhonda , Shanthikumar J. George , Yamazaki Genji
Published: April 2006

It is shown that among all work-conserving service disciplines that are independent of the future history, the first-come-first-served (FCFS) service discipline minimizes [maximizes] the average sojourn time in a G/GI/1 queueing system with new better [worse] than used in expectation (NBUE[NWUE]) service time distribution. We prove this result using a new basic identity of G/GI/1 queues that may be of independent interest. Using a relationship between the workload and the number of customers in the system with different lengths of attained service it is shown that the average sojourn time is minimized [maximized] by the least-attained-service time (LAST) service discipline when the service time has the decreasing [increasing] mean residual life (DMRL[IMRL]) property.
On the speed of convergence for the queue length process of the GI/G/K system in heavy traffic
Authors: Jin Xing , Wang Rongxin
Published: April 2006

This paper continues the study (initiated in [2]) of the GI/G/K system in heavy traffic. We give a Berry–Esseen type theorem for the rate of convergence of the queue length.
Expected frequencies of DNA patterns using whittle's formula
Authors: Cowan Richard
Published: April 2006

Given a realisation of a Markov chain, one can count the numbers of state transitions of each type. One can ask how many realisations are there with these transition counts and the same initial state. Whittle (1955) has answered this question, by finding an explicit though complicated formula, and has also shown that each realisation is equally likely. In the analysis of DNA sequences which comprise letters from the set {A, C, G, T}, it is often useful to count the frequency of a pattern, say ACGCT, in a long sequence and compare this with the expected frequency for all sequences having the same start letter and the same transition counts (or ‘dinucleotide counts' as they are called in the molecular biology literature). To date, no exact method exists; this paper rectifies that deficiency.
A note on the selection of random variables under a sum constraint
Authors: Rhee Wansoo , Talagrand Michel
Published: April 2006

Consider an i.i.d. sequence of non-negative random variables (X1, · ··, Xn) with known distribution F. Consider decision rules for selecting a maximum number of the subject to the following constraints: (1) the sum of the elements selected must not exceed a given constant c > 0, and (2) the must be inspected in strict sequence with the decision to accept or reject an element being final at the time it is inspected. Coffman et al. (1987) proved that there exists such a rule that maximizes the expected number En(c) of variables selected, and determined the asymptotics of En(c) for special distributions. Here we determine the asymptotics of En(cn) for very general choices of sequences (cn) and of F, by showing that En(c) is very close to an easily computable number. Our proofs are (somewhat deceptively) very simple, and rely on an appropriate stopping-time argument.
The Galton-Watson predator-prey process
Authors: Coffey John , Bühler Wolfgang J.
Published: April 2006

A probabilistic predator-prey model is constructed using linked discrete-time branching-type processes. A necessary and sufficient condition for positive probability of survival of both populations is given.
The superposition of independent discrete Markovian packet streams
Authors: Neuts Marcel F. , Pearce Charles E. M.
Published: April 2006

In a finite, aperiodic, irreducible Markov chain, a visit to some states generates a one; to some others, a zero, while the remaining states are considered silent, in that neither symbol is generated. States during which either a one or a zero is generated are called active states, and sojourns in the set of active states correspond to messages. The output process is called a Markovian packet stream. Informally, a stream is called thin, if the steady-state fraction of time spent in the active states is small and messages are separated by silent periods of long durations. A limit theorem for the superposition of a large number of independent, stochastically identical and appropriately thin Markovian packet streams is obtained. The class of limit processes consists of a family of stationary, integer-valued, discrete-parameter processes of dependent Poisson random variables. Some properties of the limit processes are established.
Bivariate life distributions from Pólya's urn model for contagion
Authors: Marshall Albert W. , Olkin Ingram
Published: April 2006

Shock models based on Poisson processes have been used to derive univariate and multivariate exponential distributions. But in many applications, Poisson processes are not realistic models of physical shock processes because they have independent increments; expanded models that allow for possibly dependent increments are of interest. In this paper, univariate and bivariate Pólya urn schemes are used to derive models of shock sources. The life distributions obtained from these models form a large parametric family that includes the exponential distribution. Even in the univariate case these life distributions have not been widely used, though they form a large and flexible family. In the bivariate case, the family includes the bivariate exponential distributions of Marshall and Olkin as a special case.
Critical behavior of percolation and Markov fields on branching planes
Authors: Wu C. Chris
Published: April 2006

For an independent percolation model on , where is a homogeneous tree and is a one-dimensional lattice, it is shown, by verifying that the triangle condition is satisfied, that the percolation probability θ (p) is a continuous function of p at the critical point pc, and the critical exponents , γ, δ, and Δ exist and take their mean-field values. Some analogous results for Markov fields on are also obtained.
Partially observable semi-Markov reward processes
Authors: Masuda Yasushi
Published: April 2006

The main objective of this paper is to investigate the conditional behavior of the multivariate reward process given the number of certain signals where the underlying system is described by a semi-Markov process and the signal is defined by a counting process. To this end, we study the joint behavior of the multivariate reward process and the multivariate counting process in detail. We derive transform results as well as the corresponding real domain expressions, thus providing clear probabilistic interpretation.
Optimal policies for machine repairmen problems
Authors: Frostig Esther
Published: April 2006

n unreliable machines are maintained by m repairmen. Assuming exponentially distributed up-time and repair time we find the optimal policy to allocate the repairmen to the failed machines in order to stochastically minimize the time until all machines work. Considering only one repairman, we find the optimal policy to maximize the expected total discount time that machines work. We find the optimal policy for the cases where the up-time and repair time are exponentially distributed or identically arbitrarily distributed up-times and increasing failure rate distribution repair times.
On Klimov's model by two job classes and exponential processing times
Authors: Chao Xiuli
Published: April 2006

We consider the Klimov model for an open network of two types of jobs. Jobs of type i arrive at station i, have processing times that are exponentially distributed with parameter µi, and when processed either go on to station j with probability pij, or depart the network with probability pi0. Costs are charged at a rate that depends on the number of jobs of the two types in the system. It is shown that for arbitrary arrival processes the policy that gives priority to those jobs for whom the rate of change of the cost function is greatest minimizes the expected cost rate at every time t. This result is stronger than the Klimov result in two ways: arrival processes are arbitrary, and the minimization is at each time t. But the result holds for only two types.
Gaussian integrals on Wiener spaces
Authors: Helfer Adam D. , Zhao Zhongxin
Published: April 2006

We consider integrals on Wiener space of the formsE(expK(x)) andE(expK(x) |L(x) =l) whereKis a quadratic form andLa system of linear forms. We give explicit formulas for these integrals in terms of the operatorsKandL, in the case that these arise from quasilinear functions in the sense of Zhao (1981). As examples, we recover Lévy's area formula in the plane, and derive new formulas for the probability density of the radius of gyration tensor for Brownian paths.
New better than used in expectation processes
Authors: Lam C. Y. Teresa
Published: April 2006

In this paper, we study the new better than used in expectation (NBUE) and new worse than used in expectation (NWUE) properties of Markov renewal processes. We show that a Markov renewal process belongs to a more general class of stochastic processes encountered in reliability or maintenance applications. We present sufficient conditions such that the first-passage times of these processes are new better than used in expectation. The results are applied to the study of shock and repair models, random repair time processes, inventory, and queueing models.
Optimal block replacement policies with multiple choice at failure
Authors: Sheu Shey-Huei
Published: April 2006

A generalization of the block replacement policy (BRP) is proposed and analysed. Under such a policy, an operating system is preventively replaced at timeskT(k= 1, 2, 3, ···), independently of its failure history. At failure an operating system is either replaced by a new or a used one or minimally repaired or remains inactive until the next planned replacement. The cost of theith minimal repair of the new subsystem at ageydepends on the random partC(y) and the deterministic partci(y). The mathematical model is defined and general analytical results are obtained.
Further results on ASTA for general stationary processes and related problems
Authors: Miyazawa Masakiyo , Wolff Ronald W.
Published: April 2006

We consider the equivalence of state probabilities of a general stationary process at an arbitrary time and at embedded epochs of a given point process, which is called ASTA (Arrivals See Time Averages). By using an event-conditonal intensity, we give necessary and sufficient conditions for ASTA for a large class of state sets, which determines a state distribution. We do not need any additional assumptions except that the general process has left-hand limits at all points of time. Especially, for a stationary pure-jump process with a point process, ASTA is obtained for all state sets. As an application of those results, Anti-PASTA is obtained for a pure-jump Markov process and a certain class of GSMP (Generalized Semi-Markov Processes), where Anti-PASTA means that ASTA implies that the arrival process is Poisson.
Optimal stopping problems with generalized objective functions
Authors: Hill T. P. , Kennedy D. P.
Published: April 2006

Optimal stopping of a sequence of random variables is studied, with emphasis on generalized objectives which may be non-monotone functions of EXt, where t is a stopping time, or may even depend on the entire vector (E[X1I{t=l}], · ··, E[XnI{t=n}]), such as the minimax objective to maximize minj{E[XjI{t=j}]}. Convexity is used to establish a prophet inequality and universal bounds for the optimal return, and a method for constructing optimal stopping times for such objectives is given.
Tail behaviour of the stationary density of general non-linear autoregressive processes of order 1
Authors: Diebolt Jean , Guégan Dominique
Published: April 2006

We examine the main properties of the Markov chainXt=T(Xt– 1) + σ(Xt– 1)εt. Under general and tractable assumptions, we derive bounds for the tails of the stationary density of the process {Xt} in terms of the common density of theεt's.
Estimating the critical values of stochastic growth models
Authors: Buttell L. , Cox J. T. , Durrett R.
Published: April 2006

Interacting particle systems provide an attractive framework for modelling the growth and spread of biological populations and diseases. One problem with their use in applications is that in most cases the existing information about their critical values and equilibrium densities is too crude to be useful. In this paper we describe a method for estimating these quantities that does not require very much computer time and produces fairly accurate results.
Component allocation for a distributed system: reliability maximization
Authors: Revyakov Mikhail
Published: April 2006

An optimal allocation of subsystems depending on the system structure and reliability ordering of inherent subsystem components is determined, in the presence of various external influences on the reliability of components in different locations. It is carried out with the help of L-superadditive functions and Schur-convex functions.
Optimal maintenance strategies for repairable systems with general degree of repair
Authors: Stadje Wolfgang , Zuckerman Dror
Published: April 2006

In this study we examine repairable systems with random lifetime. Upon failure, a maintenance action, specifying the degree of repair, is taken by a controller. The objective is to determine an age-dependent maintenance strategy which minimizes the total expected discounted cost over an infinite planning horizon. Using several properties of the optimal policy which are derived in this study, we propose analytical and numerical methods for determining the optimal maintenance strategy. In order to obtain a better insight regarding the structure and nature of the optimal policy and to illustrate computational procedures, a numerical example is analysed. The proposed maintenance model outlines a new research channel in the area of reliability with interesting theoretical issues and a wide range of potential applications in various fields such as product design, inventory systems for spare parts, and management of maintenance crews.
Cost rate heuristics for semi-Markov decision processes
Authors: Glazebrook K. D. , Bailey Michael P. , Whitaker Lyn R.
Published: April 2006

In response to the computational complexity of the dynamic programming/backwards induction approach to the development of optimal policies for semi-Markov decision processes, we propose a class of heuristics resulting from an inductive process which proceeds forwards in time. These heuristics always choose actions in such a way as to minimize some measure of the current cost rate. We describe a procedure for calculating such cost rate heuristics. The quality of the performance of such policies is related to the speed of evolution (in a cost sense) of the process. A simple model of preventive maintenance is described in detail. Cost rate heuristics for this problem are calculated and assessed computationally.
A Markov chain associated with the minimal quasi-stationary distribution of birth–death chains
Authors: Martínez Servet , Vares Maria Eulália
Published: April 2006

We show that if the limiting conditional distribution for an absorbed birth–death chain exists, then the chain conditioned to non-absorption converges to a Markov chain with transition probabilities given by the matrix associated with the minimal quasi-stationary distribution.
The work of Lajos Takács on probability theory
Authors: Bingham N. H.
Published: April 2006

In more than four decades of prolific scientific activity, Lajos Takács has produced so much that no one contributor to this Festschrift can hope to cover all of it in a balanced way. I thus propose to make a virtue of necessity, and concentrate on those aspects of Takács' work which have particularly interested or influenced me, and on the impact Takács' ideas in these areas have had on the subsequent development of the subject.
Aspects of Lagrangian probability distributions
Authors: Sibuya Masaaki , Miyawaki Norihiko , Sumita Ushio
Published: April 2006

Lagrangian distributions are reviewed from the viewpoint of the Galton-Watson process. They are related to the busy period in queuing systems and to the first visit in random walks.

A property of the distributions is remarked for the application to vacant vehicles in a new transit system. Combinatorial identities of multinomial and binomial coefficients and related recurrences are shown by a probabilistic method. Based on the identities and recurrences, random forests generated by the Poisson and geometric Galton-Watson processes are characterized.
Burgers' equation by non-local shot noise data
Authors: Surgailis Donatas , Woyczynski Wojbor A.
Published: April 2006

We study the scaling limit of random fields which are solutions of a non-linear partial differential equation, known as the Burgers equation, under stochastic initial conditions. These are assumed to be of a non-local shot noise type and driven by a Cox process. Previous work by Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and Funaki et al. (1994) concentrated on the case of local shot noise data which permitted use of techniques from the theory of random fields with finite range dependence. Those are not available for the non-local case being considered in this paper.

Burgers' equation is known to describe various physical phenomena such as non-linear and shock waves, distribution of self-gravitating matter in the universe, and other flow satisfying conservation laws (see e.g. Woyczynski (1993)).
On the rate of Poisson process approximation to a Bernoulli process
Authors: Xia Aihua
Published: April 2006

This note gives the rate for a Wasserstein distance between the distribution of a Bernoulli process on discrete time and that of a Poisson process, using Stein's method and Palm theory. The result here highlights the possibility that the logarithmic factor involved in the upper bounds established by Barbour and Brown (1992) and Barbouret al.(1995) may be superfluous in the true Wasserstein distance between the distributions of a point process and a Poisson process.
Multiple buying or selling with vector offers
Authors: Bruss F. Thomas , Ferguson Thomas S.
Published: April 2006

We consider a generalization of the house-selling problem to selling k houses. Let the offers, X1, X2, · ··, be independent, identically distributed k-dimensional random vectors having a known distribution with finite second moments. The decision maker is to choose simultaneously k stopping rules, N1, · ··, Nk, one for each component. The payoff is the sum over j of the jth component of minus a constant cost per observation until all stopping rules have stopped. Simple descriptions of the optimal rules are found. Extension is made to problems with recall of past offers and to problems with a discount.
Stochastic indicator analysis of contaminated sites
Authors: Christakos George , Hristopulos Dionissios T.
Published: April 2006

We formulate stochastic indicator parameters that characterize pollution levels in geographical regions with heterogeneous contaminant distributions. The indicator parameters are expressed in terms of the random fields representing the contaminant distributions and the critical threshold level specified by health and environmental standards. Certain theoretical results are proven regarding univariate and bivariate indicator parameters. The analytical expressions obtained are general and can be used in practice for various types of contaminant distributions. A test of ergodicity-breaking is suggested for scientific and engineering applications in terms of the indicator parameters. Fractal characteristics of the indicator parameters are discussed. The effects of modelling and observation scale on exceedance contamination analysis are examined. Indicator random field parameters are studied on both continuum and lattice domains using analytical means and numerical simulations.
Optimality of the round-robin routing policy
Authors: Liu Zhen , Towsley Don
Published: April 2006

In this paper we consider the problem of routing customers to identical servers, each with its own infinite-capacity queue. Under the assumptions that (i) the service times form a sequence of independent and identically distributed random variables with increasing failure rate distribution and (ii) state information is not available, we establish that the round-robin policy minimizes, in the sense of a separable increasing convex ordering, the customer response times and the numbers of customers in the queues.
On the clique number of a random overlap graph
Authors: Łuczak Tomasz , Palka Zbigniew
Published: April 2006

The behaviour of the size of the largest complete subgraph contained in an overlap graph of a random acyclic digraph is presented.
Integral equations for compound distribution functions
Authors: Møller Christian Max
Published: April 2006

The aim of the present paper is to introduce some techniques, based on the change of variable formula for processes of finite variation, for establishing (integro) differential equations for evaluating the distribution of jump processes for a fixed period of time. This is of interest in insurance mathematics for evaluating the distribution of the total amount of claims occurred over some period of time, and attention will be given to such issues. Firstly we will study some techniques when the process has independent increments, and then a more refined martingale technique is discussed. The building blocks are delivered by the theory of marked point processes and associated martingale theory. A simple numerical example is given.
Filtering of a branching process given its split times
Authors: Ceci Claudia , Gerardi Anna
Published: April 2006

A filtering problem for a branching process is studied within the tree framework, and the minimal intensity of the splitting process is given.
On the L2-convergence of a superadditive bisexual Galton-Watson branching process
Authors: González M. , Molina M.
Published: April 2006

In this paper the L2-convergence of a superadditive bisexual Galton–Watson branching process is studied. Necessary and sufficient conditions for the convergence of the suitably normed process are given. In the final section, a result about one of the most important bisexual models is proved.
Sooner waiting time problems in a sequence of trinary trials
Authors: Koutras M. V. , Alexandrou V. A.
Published: April 2006

LetX1, X2,· ··be a (linear or circular) sequence of trials with three possible outcomes (sayS, S∗orF) in each trial. In this paper, the waiting time for the first appearance of anS-run of lengthkor anS∗-run of lengthris systematically investigated. Exact formulae and Chen-Stein approximations are derived for the distribution of the waiting times in both linear and circular problems and their asymptotic behaviour is illustrated. Probability generating functions are also obtained when the trials are identical. Finally, practical applications of these results are discussed in some detail.
On the move-to-front scheme with Markov dependent requests
Authors: Phatarfod R. M. , Pryde A. J. , Dyte David
Published: April 2006

In this paper we consider the operation of the move-to-front scheme where the requests form a Markov chain of N states with transition probability matrix P. It is shown that the configurations of items at successive requests form a Markov chain, and its transition probability matrix has eigenvalues that are the eigenvalues of all the principal submatrices of P except those of order N—1. We also show that the multiplicity of the eigenvalues of submatrices of order m is the number of derangements of N — m objects. The last result is shown to be true even if P is not a stochastic matrix.
Limit theorems for the number of occurrences of consecutiveksuccesses innMarkovian trials
Authors: Wang Y. H. , Ji Shuixin
Published: April 2006

We present a method of deriving the limiting distributions of the number of occurrences of success(S)runs of lengthkfor all types of runs under the Markovian structure with stationary transition probabilities. In particular, we consider the following four bestknown types. 1. A string ofSof exact lengthkpreceded and followed by anF, except the first run which may not be preceded by anF, or the last run which may not be followed by anF. 2. A string ofSof lengthkor more. 3. A string ofSof exact lengthk, where recounting starts immediately after a run occurs. 4. A string ofSof exact lengthk, allowing overlapping runs. It is shown that the limits are convolutions of two or more distributions with one of them being either Poisson or compound Poisson, depending on the type of runs in question. The completely stationary Markov case and the i.i.d. case are also treated.
Asymptotic behaviour of Markov population processes by asymptotically linear rate of change
Authors: Klebaner F. C.
Published: April 2006

Multidimensional Markov processes in continuous time with asymptotically linear mean change per unit of time are studied as randomly perturbed linear differential equations. Conditions for exponential and polynomial growth rates with stable type distribution are given. From these conditions results on branching models of populations with stabilizing reproduction for near-supercritical and near-critical cases follow.
Transient solutions for denumerable-state Markov processes
Authors: Hsu Guang-Hui , Yuan Xue-Ming
Published: April 2006

The algorithm for the transient solution for the denumerable state Markov process with an arbitrary initial distribution is given in this paper. The transient queue length distribution for a general Markovian queueing system can be obtained by this algorithm. As examples, some numerical results are presented.
Estimating the home range
Authors: De Haan L. , Resnick Sidney
Published: April 2006

A proposal is given for estimating the home range of an animal based on sequential sightings. We assume the given sightings are independent, identically distributed random vectors X1,· ··, Xn whose common distribution has compact support. If are the polar coordinates of the sightings, then is a sup-measure and corresponds to the right endpoint of the distribution . The corresponding upper semi-continuous function l(θ) is the boundary of the home range. We give a consistent estimator for the boundary l and under the assumption that the distribution of R1 given is in the domain of attraction of an extreme value distribution with bounded support, we are able to give an approximate confidence region.
On the local behaviour of ladder height distributions
Authors: Bertoin J. , Doney R. A.
Published: April 2006

There is a well-known connection between the asymptotic behaviour of the tail of the distribution of the increasing ladder height and the integrated tail of the step distribution of a random walk which either drifts to –∞, or oscillates and whose decreasing ladder height has finite mean. We establish a similar connection in a local sense; this means that in the lattice case we link the asymptotic behaviours of the mass function of the ladder height distribution and of the tail of the step distribution. We deduce the asymptotic behaviour of the mass function of the maximum of the walk, when this is finite, and also treat the non-lattice case.
On an elementary characterization of the increasing convex ordering, by an application
Authors: Makowski Armand M.
Published: April 2006

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.
Weak convergence of conditioned processes on a countable state space
Authors: Jacka S. D. , Roberts G. O.
Published: April 2006

We consider the problem of conditioning a continuous-time Markov chain (on a countably infinite state space) not to hit an absorbing barrier before timeT; and the weak convergence of this conditional process asT→ ∞. We prove a characterization of convergence in terms of the distribution of the process at some arbitrary positive time,t, introduce a decay parameter for the time to absorption, give an example where weak convergence fails, and give sufficient conditions for weak convergence in terms of the existence of a quasi-stationary limit, and a recurrence property of the original process.
A discrete-time proof of Neveu's exchange formula
Authors: Konstantopoulos Takis , Zazanis Michael
Published: April 2006

Neveu's exchange formula relates the Palm probabilities with respect to two jointly stationary simple point processes. We give a new proof of the exchange formula by using a simple result from discrete time stationary stochastic processes.
Moments of the first-passage time of a Wiener process with drift between two elastic barriers
Authors: Dominé Marco
Published: April 2006

The first-passage problem for the one-dimensional Wiener process with drift in the presence of elastic boundaries is considered. We use the Kolmogorov backward equation with corresponding boundary conditions to derive explicit closed-form expressions for the expected value and the variance of the first-passage time. Special cases with pure absorbing and/or reflecting barriers arise for a certain choice of a parameter constellation.
Time-dependent rate conservation laws for a process defined with a stationary marked point process and their applications
Authors: Miyazawa Masakiyo
Published: April 2006

We derive two kinds of rate conservation laws for describing the time-dependent behavior of a process defined with a stationary marked point process and starting at time 0. These formulas are called TRCLs (time-dependent rate conservation laws). It is shown that TRCLs are useful to study the transient behaviors of risk and storage processes with stationary claim and supply processes and with a general premium and release rates, respectively. Detailed discussions are given for the severity for the risk process, and for the workload process of a single-server queue.
Characterizations of life distributions by moments of extremes and sample mean
Authors: Jun Cai
Published: April 2006

We consider two weaker partial orderings among non-negative random variables. We derive some characterizations of the equivalence of two life distributions under the weaker orderings. These results lead to the characterizations of the equality of two non-negative random vectors in distributions by moments of extremes and sample mean. As the application of these results, we get various characterizations of the exponential distribution among HNBUE and HNWUE life distribution classes. The main results of Bhattacharjee and Sethuraman (1990), and Basu and Kirmani (1986) are special cases of these more general results.
Poisson and compound Poisson approximations for random sums of random variables
Authors: Vellaisamy P. , Chaudhuri B.
Published: April 2006

We derive upper bounds for the total variation distance, d, between the distributions of two random sums of non-negative integer-valued random variables. The main results are then applied to some important random sums, including cluster binomial and cluster multinomial distributions, to obtain bounds on approximating them to suitable Poisson or compound Poisson distributions. These bounds are generally better than the known results on Poisson and compound Poisson approximations. We also obtain a lower bound for d and illustrate it with an example.
Characterization of a general class of life-testing models
Authors: Ghitany M. E. , El-saidi M. A. , Khalil Z.
Published: April 2006

In this paper we establish a characterization theorem for a general class of life-testing models based on a relationship between conditional expectation and the failure rate function. As a simple application of the theorem, we characterize the gamma, Weibull, and Gompertz distributions, since they have many probabilistic and statistical properties useful in both biometry and engineering reliability.
The departure process of the M/G/1 queueing model with server vacation and exhaustive service discipline
Authors: Tang Yinghui
Published: April 2006

In this paper we study the departure process of M/G/1 queueing models with a single server vacation and multiple server vacations. The arguments employed are direct probability decomposition, renewal theory and the Laplace–Stieltjes transform. We discuss the distribution of the interdeparture time and the expected number of departures occurring in the time interval (0, t] from the beginning of the state i (i = 0, 1, 2, ···), and provide a new method for analysis of the departure process of the single-server queue.
Stein's method for geometric approximation
Authors: Peköz Erol A.
Published: April 2006

The Stein–Chen method for Poisson approximation is adapted to the setting of the geometric distribution. This yields a convenient method for assessing the accuracy of the geometric approximation to the distribution of the number of failures preceding the first success in dependent trials. The results are applied to approximating waiting time distributions for patterns in coin tossing, and to approximating the distribution of the time when a stationary Markov chain first visits a rare set of states. The error bounds obtained are sharper than those obtainable using related Poisson approximations.
On the distribution of distances in recursive trees
Authors: Dobrow Robert P.
Published: April 2006

Recursive trees have been used to model such things as the spread of epidemics, family trees of ancient manuscripts, and pyramid schemes. A tree Tn with n labeled nodes is a recursive tree if n = 1, or n > 1 and Tn can be constructed by joining node n to a node of some recursive tree Tn–1. For arbitrary nodes i < n in a random recursive tree we give the exact distribution of Xi,n, the distance between nodes i and n. We characterize this distribution as the convolution of the law of Xi,j+1 and n – i – 1 Bernoulli distributions. We further characterize the law of Xi,j+1 as a mixture of sums of Bernoullis. For i = in growing as a function of n, we show that is asymptotically normal in several settings.
Large deviations of heavy-tailed random sums with applications in insurance and finance
Authors: Klüppelberg C. , Mikosch T.
Published: April 2006

We prove large deviation results for the random sum , , where are non-negative integer-valued random variables and are i.i.d. non-negative random variables with common distribution function F, independent of . Special attention is paid to the compound Poisson process and its ramifications. The right tail of the distribution function F is supposed to be of Pareto type (regularly or extended regularly varying). The large deviation results are applied to certain problems in insurance and finance which are related to large claims.
RNA Secondary Structure Analysis Using RNAstructure
Authors: Mathews David H.
Published: April 2006

RNAstructure is a user‐friendly program for the prediction and analysis of RNA secondary structure under Microsoft Windows. This unit provides protocols for RNA secondary structure prediction and prediction of high‐affinity oligonucleotide binding sites to a structured RNA target.
Meat and Meat Products
Authors: Honikel Karl‐Otto
Published: April 2006

The article contains sections titled:

1.Definitions2.History3.Composition of Meat4.Meat Production and Slaughtering5.Fresh Meat Processing6.Processing Techniques6.1.Chilling of Meat6.2.Freezing of Meat6.3.Heating of Meat and Meat Products6.4.Salting and Curing6.5.Use of Additives6.6.Smoking6.7.Drying and Other Means of Preservation7.Types of Meat Products8.Manufacturing of Meat Products8.1.Raw Meat Products8.1.1.Raw Hams8.1.2.Raw Sausages8.2.Cooked Products8.2.1.Emulsion‐Type Sausages8.2.2.Cooked Sausages8.3.Cooked Ham9.Meat Species Identification10.World Meat Production11.Meat Grading
New ways to retire
Authors: Leslie David W.
Published: April 2006

Faculty now have the task of using retirement options creatively, and institutions, of finding common purpose with faculty.
Uncertainty analysis of statistical downscaling methods using Canadian Global Climate Model predictors
Authors: Khan Mohammad Sajjad , Coulibaly Paulin , Dibike Yonas
Published: April 2006

Three downscaling models, namely the Statistical Down‐Scaling Model (SDSM), the Long Ashton Research Station Weather Generator (LARS‐WG) model and an artificial neural network (ANN) model, have been compared in terms of various uncertainty attributes exhibited in their downscaled results of daily precipitation, daily maximum and minimum temperature. The uncertainty attributes are described by the model errors and the 95% confidence intervals in the estimates of means and variances of downscaled data. The significance of those errors has been examined by suitable statistical tests at the 95% confidence level. The 95% confidence intervals in the estimates of means and variances of downscaled data have been estimated using the bootstrapping method and compared with the observed data. The study has been carried out using 40 years of observed and downscaled daily precipitation data and daily maximum and minimum temperature data, starting from 1961 to 2000. In all the downscaling experiments, the simulated predictors of the Canadian Global Climate Model (CGCM1) have been used. The uncertainty assessment results indicate that, in daily precipitation downscaling, the LARS‐WG model errors are significant at the 95% confidence level only in a very few months, the SDSM errors are significant in some months, and the ANN model errors are significant in almost all months of the year. In downscaling daily maximum and minimum temperature, the performance of all three models is similar in terms of model errors evaluation at the 95% confidence level. But, according to the evaluation of variability and uncertainty in the estimates of means and variances of downscaled precipitation and temperature, the performances of the LARS‐WG model and the SDSM are almost similar, whereas the ANN model performance is found to be poor in that consideration. Further assessment of those models, in terms of skewness and average dry‐spell length comparison between observed and downscaled daily precipitation, indicates that the downscaled daily precipitation skewness and average dry‐spell lengths of the LARS‐WG model and the SDSM are closer to the observed data, whereas the ANN model downscaled precipitation underestimated those statistics in all months. Copyright © 2006 John Wiley & Sons, Ltd.
A distributed monthly hydrological model for integrating spatial variations of basin topography and rainfall
Authors: Chen Xi , Chen Yongqin David , Xu Chong‐yu
Published: April 2006

Hydrological models at a monthly time‐scale are important tools for hydrological analysis, such as in impact assessment of climate change and regional water resources planning. Traditionally, monthly models adopt a conceptual, lumped‐parameter approach and cannot account for spatial variations of basin characteristics and climatic inputs. A large requirement for data often severely limits the utility of physically based, distributed‐parameter models. Based on the variable‐source‐area concept, we considered basin topography and rainfall to be two major factors whose spatial variations play a dominant role in runoff generation and developed a monthly model that is able to account for their influences in the spatial and temporal dynamics of water balance. As a hybrid of the Xinanjiang model and TOPMODEL, the new model is constructed by innovatively making use of the highly acclaimed simulation techniques in the two existing models. A major contribution of this model development study is to adopt the technique of implicit representation of soil moisture characteristics in the Xinanjiang model and use the TOPMODEL concept to integrate terrain variations into runoff simulation. Specifically, the TOPMODEL topographic index ln(a/tanβ) is converted into an index of relative difficulty in runoff generation (IRDG) and then the cumulative frequency distribution of IRDG is used to substitute the parabolic curve, which represents the spatial variation of soil storage capacity in the Xinanjiang model. Digital elevation model data play a key role in the modelling procedures on a geographical information system platform, including basin segmentation, estimation of rainfall for each sub‐basin and computation of terrain characteristics. Other monthly data for model calibration and validation are rainfall, pan evaporation and runoff. The new model has only three parameters to be estimated, i.e. watershed‐average field capacity WM, pan coefficient η and runoff generation coefficient α. Sensitivity analysis demonstrates that runoff is least sensitive to WM and, therefore, it can be determined by a prior estimation based on the climate and soil properties of the study basin. The other two parameters can be determined using optimization methods. Model testing was carried out in a number of nested sub‐basins of two watersheds (Yuanjiang River and Dongjiang River) in the humid region in central and southern China. Simulation results show that the model is capable of describing spatial and temporal variations of water balance components, including soil moisture content, evapotranspiration and runoff, over the watershed. With a minimal requirement for input data and parameterization, this terrain‐based distributed model is a valuable contribution to the ever‐advancing technology of hydrological modelling. Copyright © 2006 John Wiley & Sons, Ltd.
Biomechanical evaluation of the interfacial strength of a chemically modified sandblasted and acid‐etched titanium surface
Authors: Ferguson S.J. , Broggini N. , Wieland M. , de Wild M. , Rupp F. , Geis‐Gerstorfer J. , Cochran D.L. , Buser D.
Published: April 2006

The functional capacity of osseointegrated dental implants to bear load is largely dependent on the quality of the interface between the bone and implant. Sandblasted and acid‐etched (SLA) surfaces have been previously shown to enhance bone apposition. In this study, the SLA has been compared with a chemically modified SLA (modSLA) surface. The increased wettability of the modSLA surface in a protein solution was verified by dynamic contact angle analysis. Using a well‐established animal model with a split‐mouth experimental design, implant removal torque testing was performed to determine the biomechanical properties of the bone–implant interface. All implants had an identical cylindrical shape with a standard thread configuration. Removal torque testing was performed after 2, 4, and 8 weeks of bone healing (n = 9 animals per healing period, three implants per surface type per animal) to evaluate the interfacial shear strength of each surface type. Results showed that the modSLA surface was more effective in enhancing the interfacial shear strength of implants in comparison with the conventional SLA surface during early stages of bone healing. Removal torque values of the modSLA‐surfaced implants were 8–21% higher than those of the SLA implants (p = 0.003). The mean removal torque values for the modSLA implants were 1.485 N m at 2 weeks, 1.709 N m at 4 weeks, and 1.345 N m at 8 weeks; and correspondingly, 1.231 N m, 1.585 N m, and 1.143 N m for the SLA implants. The bone–implant interfacial stiffness calculated from the torque–rotation curve was on average 9–14% higher for the modSLA implants when compared with the SLA implants (p = 0.038). It can be concluded that the modSLA surface achieves a better bone anchorage during early stages of bone healing than the SLA surface; chemical modification of the standard SLA surface likely enhances bone apposition and this has a beneficial effect on the interfacial shear strength. © 2006 Wiley Periodicals, Inc. J Biomed Mater Res, 2006
Effect of pH and temperature on the ion‐exchange isotherm of Cd(II) and Pb(II) on clinoptilolite
Authors: Berber‐Mendoza Maria Selene , Leyva‐Ramos Roberto , Alonso‐Davila Pedro , Mendoza‐Barron Jovita , Diaz‐Flores Paola Elizabeth
Published: April 2006

The ion‐exchange equilibrium of Pb(II) and Cd(II) on clinoptilolite from different deposits was studied in this work. The Langmuir isotherm fitted the ion‐exchange equilibrium data of both ions better than the Freundlich isotherm. The capacity of the natural zeolite to exchange Cd(II) and Pb(II) increased, augmenting the solution pH. This behaviour was attributed to the interactions between the ions in solution and the surface charge of the zeolite. Moreover, the capacity of the natural zeolite to exchange Cd(II) and Pb(II) was increased when the temperature was raised from 15 to 35 °C. This tendency was explained by assuming that the ion exchange was an endothermic reaction. The selectivity of the zeolite for the metal cations decreased in the following order: Pb(II) > Cd(II). This order was not modified while reducing the solution pH, but the zeolite selectivity was increased. At pH 2 the selectivity of the zeolite for Pb(II) was nearly three times larger than at pH 4. Copyright © 2006 Society of Chemical Industry
Characterization of the fracture behavior of polyethylene using measured cohesive curves. I: Effects of constraint and rate
Authors: Ting S.K.M. , Williams J.G. , Ivankovic A.
Published: April 2006

The damage and failure mechanisms in polyethylene are investigated using a circumferentially notched tensile specimen subject to constant rate displacement conditions. The fracture process can be quantified, independent of the bulk deformation, using a local traction–separation relation. The study found that the mechanisms of deformation under quasi‐static test speeds depend on the degree of crack tip constraint in addition to rate. This dependency can lead to contrasting deformation‐failure behavior between different grades of polyethylene and hence the overall energy dissipation process. Based on this approach, both gross and subtle differences in the fracture behavior between the grades were readily detected and differentiated. In general, the damage mechanisms changed from a brittle mode under conditions of high constraint to a ductile mode as the level of constraint is reduced. POLYM. ENG. SCI., 46:763–777, 2006. © 2006 Society of Plastics Engineers
Polydiphenylsiloxane–polydimethylsiloxane–polydiphenylsiloxane triblock copolymers
Authors: Gädda Thomas M. , Weber William P.
Published: April 2006

Polydiphenylsiloxane–polydimethylsiloxane–polydiphenylsiloxane triblock copolymers were prepared by two methods. The first approach was the sequential addition of the monomers. The anionic polymerization of hexamethylcyclotrisiloxane initiated by dilithio diphenylsilanolate gave α,ω‐bis(lithio dimethylsilanolate)polydimethylsiloxane, which was added to hexaphenylcyclotrisiloxane at ∼120 °C to yield the desired triblock material. In the other, a convergent approach was used. Excess α‐vinyldimethylsiloxypolydiphenylsiloxane was coupled to α,ω‐bis(hydrido)polydimethylsiloxane by a Pt‐catalyzed hydrosilylation reaction to give the triblock material. The formation of distinct blocks with regular microstructures in these materials was confirmed by 1H, 13C, and 29Si NMR spectroscopy as well as differential scanning calorimetry. The molecular weights were determined by gel permeation chromatography, and the thermal stabilities were evaluated by thermogravimetric analysis. Dynamic mechanical analysis was used to confirm thermal transitions obtained by differential scanning calorimetry and to evaluate the mechanical properties of the materials. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 3629–3639, 2006