bluuebunny/crossref_metadata_2025 huggingface dataset:
The busy period of order n in the GI/D/∞ queue
Authors: Dvurečenskij A.
Published: April 2006

The busy period of the GI/D/∞ queue is determined as the time when at least one customer is served. Let v be the number of customers served during this period. The busy period of order n is defined as a busy period for which v ≧ n. In this paper we derive the exact distributions, integral equations, characteristic functions and all moments of those periods. Finally, some properties of the idle periods of order n are established.
Limit laws for kth order statistics from strong-mixing processes
Authors: Dziubdziela W.
Published: April 2006

We present necessary and sufficient conditions for the weak convergence of the distributions of the kth order statistics from a strictly stationary strong-mixing sequence of random variables to limit laws which are represented in terms of a compound Poisson distribution. The obtained limit laws form a class larger than that occurring in the independent case.
A note on the evaluation of first-passage-time probability densities
Authors: Ricciardi L. M. , Sato S.
Published: April 2006

A procedure is indicated to estimate first-passage-time p.d.f.'s through varying boundaries for a class of diffusion processes that can be transformed into the Wiener process by rather general transformations. Although this procedure is adapted to Durbin's [4] algorithm, it could be extended to other existing computation methods.
A rearrangement inequality for the longest run, with an application to network reliability
Authors: Tong Y. L.
Published: April 2006

Let Xl, · ··, Χ n be independent binary variables with parameters θl, · ··, θ n respectively, and let R denote the length of the longest run of 1's. This note concerns a new expression for and a rearrangement inequality. The inequality is applied to solve an optimal permutation problem for consecutive-k-out-of-n: F networks, and its implications on a recent conjecture of Derman et al. (1982) are discussed.
Looking backwards in time in the Moran model in population genetics
Authors: Clifford Peter , Sudbury Aidan
Published: April 2006

The Moran model in population genetics may also be regarded as an invasion process (or voter model) on the complete n-graph. Tracing lines of ancestry is equivalent to studying the dual process. Using this technique certain results concerning lines of ancestry can be derived very rapidly.
Optimal control of a finite dam: average-cost case
Authors: Yeh Lam
Published: April 2006

We consider the problem of minimizing the long-run average cost per unit time of operating a finite dam in the class of the policies of the following type. Assume that the dam is initially empty, the release rate is kept at 0 until the dam storage increases to λ, and as soon as this occurs, water is released at rate M, then the output rate is kept at M as long as the dam storage is more than τ and it must be decreased to 0 if the dam storage becomes τ. We assume that the input of water into the finite dam is a Wiener process with non-negative drift μ and variance parameter σ2. There is a cost in increasing the output rate from 0 to M as well as in decreasing the rate from M to 0 and whenever the dam storage is below level a, there is a penalty cost per unit time depending on the level. A reward is given for each unit of water released. In this paper, the long-run average cost per unit time is determined, and therefore the optimal policy can be found numerically.
The M/G/k loss system with servers subject to breakdown
Authors: Fakinos D.
Published: April 2006

This paper studies the equilibrium behaviour of the M/G/k loss system with servers subject to breakdown. Such a system has k servers, whose customers arrive in a Poisson process. They are served if there is an idle server, otherwise they leave and do not return. Each server is subject to breakdown with probability of occurrence depending on the length of the time the server has been busy since his last repair. On a breakdown the customer waits and his service is continued just after the repair of the server. Among other things, a generalization of the Erlang B-formula is given and it is shown that the equilibrium departure process is Poisson. In fact these results are obtained for the more general case where customers may balk and service and repair rates are state dependent.
A batch-ballot problem and applications
Authors: Mendelson Haim
Published: April 2006

Let (X1, X2, · ··, Xn) be a vector of discrete splittable and interchangeable random variables, and let Sj = Σji = 1Xi. This paper is concerned with probabilities of the form P{Sj < jb – d for j = 1, 2, 3, ···, n | Sn = r}. We focus on applications of these probabilities, study their properties and suggest how they may be computed. The applications are from the areas of computer science, economics, operations management, finance and risk theory.
On the equivalence of flows in networks of queues
Authors: Walrand J.
Published: April 2006

Consider a network of queues in equilibrium. When are the flows observed on two given links of that network equivalent, i.e., when do they have the same law?

The verification of the equivalence of two such point processes is first reduced to an algebraic problem by a technique based on the filtering theory.

This method is then used to show that the arrival and departure processes at an M/M/1 node in a Jackson network are not always equivalent, thereby contradicting a conjecture made in [8]. An example where that equivalence holds is also given; it provides new results on the time reversibility of some familiar processes.
On the Distribution and covariance structure of the present value of a random income stream
Authors: Keilson J.
Published: April 2006

The present value is studied when I(t) is a stationary random income stream. The stationary distribution of V(t) for a family of simple streams modeled by stationary finite Markov chains is given explicitly. The process V(t) is shown to be observable in a special sense when I(t) is time-reversible.
Insensitivity of processes with interruptions
Authors: Henderson W. , Taylor P.
Published: April 2006

The theory of insensitivity within generalised semi-Markov processes is extended to cover classes of models in which the generally distributed lifetimes can be terminated prematurely by the deaths of negative exponentially distributed lifetimes. As a consequence of this approach it is shown that there exist classes of processes which are insensitive with respect to characteristics of the general distributions other than the mean. Two examples are given. The first is an analysis of networks of queues in which the generally distributed service times can be interrupted with resulting changes in routing probabilities. The second is a model for the effect of disturbances on the evolution of a vegetation community.
On multitype processes based on progeny length of particles of a supercritical Galton-Watson process
Authors: Gadag V. G. , Rajarshi M. B.
Published: April 2006

Based on infinite and finite line of descent of particles of a one-dimensional supercritical Galton-Watson branching process (GWBP), we construct an associated bivariate process. We show that this bivariate process is a two-dimensional, supercritical GWBP. We also show that this process retains its branching property on appropriate probability spaces, when conditioned on set of non-extinction and set of extinction. Some asymptotic and weak convergence results for this process have been established. A generalisation of these results to a multitype p-dimensional GWBP has also been carried out.
Stochastic control of geometric processes
Authors: Aase Knut K.
Published: April 2006

Stochastic optimization of semimartingales which permit a dynamic description, like a stochastic differential equation, leads normally to dynamic programming procedures. The resulting Bellman equation is often of a very genera! nature, and analytically hard to solve. The models in the present paper are formulated in terms of the relative change, and the optimality criterion is to maximize the expected rate of growth. We show how this can be done in a simple way, where we avoid using the Bellman equation. An application is indicated.
On functionals of the adjusted range process
Authors: Hooghiemstra G.
Published: April 2006

Using a well-known transformation that preserves Wiener measure a theorem is proved that enables one to derive in a non-computational manner distributions of simple functionals of the so-called adjusted range process.
Monotone and associated Markov chains, with applications to reliability theory
Authors: Lindqvist Bo Henry
Published: April 2006

We study monotone and associated Markov chains on finite partially ordered state spaces. Both discrete and continuous time, and both time-homogeneous and time-inhomogeneous chains are considered. The results are applied to binary and multistate reliability theory.
A correlated random walk for the transport and sedimentation of particles
Authors: Gani J.
Published: April 2006

This paper considers a bivariate random walk model on a rectangular lattice for a particle injected into a fluid flowing in a tank. The numbers of jumps of the particle in the x and y directions in this particular model are correlated. It is shown that when the random walk forms a bivariate Markov chain in continuous time, it is possible to obtain the state probabilities pxy(t) through their Laplace transforms. Two exit rules are considered and results for both of them derived.
Approximation of the queue-length distribution of an M/GI/s queue by the basic equations
Authors: Miyazawa Masakiyo
Published: April 2006

We give a unified way of obtaining approximation formulas for the steady-state distribution of the queue length in the M/GI/s queue. The approximations of Hokstad (1978) and Case A of Tijms et al. (1981) are derived again. The main interest of this paper is in considering the theoretical meaning of the assumptions given in the literature. Having done this, we derive new approximation formulas. Our discussion is based on one version of the steady-state equations, called the basic equations in this paper. The basic equations are derived for M/GI/s/k with finite and infinite k. Similar approximations are possible for M/GI/s/k (k < +∞).
Boundary domination and the distribution of the largest nearest-neighbor link in higher dimensions
Authors: Steele J. Michael , Tierney Luke
Published: April 2006

For a sample of points drawn uniformly from either the d-dimensional torus or the d-cube, d ≧ 2, we give limiting distributions for the largest of the nearest-neighbor links. For d ≧ 3 the behavior in the torus is proved to be different from the behavior in the cube. The results given also settle a conjecture of Henze (1982) and throw light on the choice of the cube or torus in some probabilistic models of computational complexity of geometrical algorithms.
A simple proof of the multivariate random time change theorem for point processes
Authors: Brown Timothy C. , Nair M. Gopalan
Published: April 2006

A simple proof of the multivariate random time change theorem of Meyer (1971) is given. This result includes Watanabe's (1964) characterization of the Poisson process; even in this special case the present proof is simpler than existing proofs.
On a model for a time series of cross-sections
Authors: Robinson P. M.
Published: April 2006

Dynamic stationary models for mixed time series and cross-section data are studied. The models are of simple, standard form except that the unknown coefficients are not assumed constant over the cross-section; instead, each cross-sectional unit draws a parameter set from an infinite population. The models are framed in continuous time, which facilitates the handling of irregularly-spaced series, and observation times that vary over the cross-section, and covers also standard cases in which observations at the same regularly-spaced times are available for each unit. A variety of issues are considered, in particular stationarity and distributional questions, inference about the parameter distributions, and the behaviour of cross-sectionally aggregated data.
On the busy period distribution of the M/G/2 queueing system
Authors: Wiens Douglas P.
Published: April 2006

Equations are derived for the distribution of the busy period of the GI/G/2 queue. The equations are analyzed for the M/G/2 queue, assuming that the service times have a density which is an arbitrary linear combination, with respect to both the number of stages and the rate parameter, of Erlang densities. The coefficients may be negative. Special cases and examples are studied.
Optimal inspection policy for a multi-unit machine
Authors: Zuckerman Dror
Published: April 2006

We consider a machine which generates income at rate I during its operating time. The machine is composed of N independent stochastically failing units. A failure of each one of the units causes a breakdown of the machine.

The machine's status (good or failed) is observed continuously, by a controller, at zero cost. In the event of a breakdown, exactly one unit is failed, and a series of inspections is performed, in order to identify the failed unit and the reasons for its failure. At any time along the inspection process only one unit can be tested.

An inspection of a given unit is characterized by its cost rate and inspection time. At the end of the inspection process, the failed unit is repaired at a known cost, and a new operating cycle is started.

Our objective is to formulate an optimal inspection strategy under two optimality criteria: long-run average net income, and total expected discounted net income.
Stationary and stability of fork-join networks
Authors: Konstantopoulos Panagiotis , Walrand Jean
Published: April 2006

We consider a fork-join network with arrival and service times forming a stationary and ergodic process. The usual stability condition, namely that the input rate is strictly less than all the service rates, is proved to be valid in this general case. Finally we extend the result to the case where there is random routing.
A non-Markov model for the optimum replacement of self-repairing systems subject to shocks
Authors: Rangan A. , Grace R. Esther
Published: April 2006

A system is subject to shocks; each shock at time t increases the cumulative damage λ (t) by a constant amount, while the system is subject to repair in between the shocks which brings down λ (t) at a constant rate. The shock arrival process is an inhomogeneous Poisson process with intensity function λ (t) and each shock weakens the system making it more expensive to run. The long-run expected cost per unit time of running the system is obtained as well as the variance of the cost which are used to get optimal times of replacement of the system.
A time-reversibility relationship between two Markov chains with exponential stationary distributions
Authors: Chernick M. R. , Daley D. J. , Littlejohn R. P.
Published: April 2006

The stationary non-negative Markov chains {Yn} and {Xn} specified by the relations

for {η n} a sequence of independent identically distributed (i.i.d.) random variables which are independent of {Yn}, and

for {ξ n} a sequence of i.i.d. random variables which are independent of {Xn}, are mutually time-reversed if and only if their common marginal distribution is exponential, relating the exponential autoregressive process of Gaver and Lewis (1980) to the exponential minification process of Tavares (1980).
Extreme values of non-stationary random sequences
Authors: Hüsler Jürg
Published: April 2006

We extend some results of the extreme-value theory of stationary random sequences to non-stationary random sequences. The extremal index, defined in the stationary case, plays a similar role in the extended case. The details show that this index describes not only the behaviour of exceedances above a high level but also above a non-constant high boundary.
Stereological versions of integral geometric formulae for n-dimensional ellipsoids
Authors: Jensen E. B. , Møller J.
Published: April 2006

Recently, unbiased stereological estimators of moments of particle volume, based on measurements on lower-dimensional sections through the particles, have been developed by Jensen and Gundersen (1985). In this note, we derive an explicit form of these unbiased estimators valid for particles in Rn of ellipsoidal shape, and we establish a close relationship between the estimators and a known integral geometric formula for ellipsoids, due to Furstenberg and Tzkoni (1971). Furthermore, a stereological version of another integral geometric formula for n-dimensional ellipsoids, due to Guggenheimer (1973), is derived.
On the null recurrence and transience of a first-order SETAR model
Authors: Guo Meihui , Petruccelli Joseph D.
Published: April 2006

We consider the SETAR(l; 1, ···, 1) model:

where – ∞= r0 < r1, < · ·· < rl = ∞ and for each j {ε t(j)} forms an i.i.d. zero-mean error sequence independent of {ε t(i)} for i ≠ j and having a density positive on the real line. Chan et al. (1985) obtained the region of the parameter space on which the process is ergodic, and showed the process to be transient on a subset of the remainder. They conjectured that the process was null recurrent everywhere else. In this paper we show that conjecture to be incorrect and under the assumption of finite variance of the error distributions we resolve the remaining questions of transience or null recurrence for this process.
On the weak convergence of sequences of circuit processes: a probabilistic approach
Authors: Kalpazidou Sophia
Published: April 2006

The asymptotic behaviour of sequences of Markov processes whose finite distributions depend upon the sample paths ω of a positive recurrent Markov chain ξ is studied. The existence of such sequences depends upon the existence of a unique class of directed weighted circuits having a probabilistic interpretation in terms of the directed circuits occurring along the sample paths of ξ. An application to multiple Markov chains is given.
Useful martingales for stochastic storage processes with Lévy input
Authors: Kella Offer , Whitt Ward
Published: April 2006

We apply the general theory of stochastic integration to identify a martingale associated with a Lévy process modified by the addition of a secondary process of bounded variation on every finite interval. This martingale can be applied to queues and related stochastic storage models driven by a Lévy process. For example, we have applied this martingale to derive the (non-product-form) steady-state distribution of a two-node tandem storage network with Lévy input and deterministic linear fluid flow out of the nodes.
Monte Carlo simulation and large deviations theory for uniformly recurrent Markov chains
Authors: Bucklew James A , Ney Peter , Sadowsky John S.
Published: April 2006

Importance sampling is a Monte Carlo simulation technique in which the simulation distribution is different from the true underlying distribution. In order to obtain an unbiased Monte Carlo estimate of the desired parameter, simulated events are weighted to reflect their true relative frequency. In this paper, we consider the estimation via simulation of certain large deviations probabilities for time-homogeneous Markov chains. We first demonstrate that when the simulation distribution is also a homogeneous Markov chain, the estimator variance will vanish exponentially as the sample size n tends to∞. We then prove that the estimator variance is asymptotically minimized by the same exponentially twisted Markov chain which arises in large deviation theory, and furthermore, this optimization is unique among uniformly recurrent homogeneous Markov chain simulation distributions.
Laplace transform inversion and passage-time distributions in Markov processes
Authors: Harrison Peter G.
Published: April 2006

Products of the Laplace transforms of exponential distributions with different parameters are inverted to give a mixture of Erlang densities, i.e. an expression for the convolution of exponentials. The formula for these inversions is expressed both as an explicit sum and in terms of a recurrence relation which is better suited to numerical computation. The recurrence for the inversion of certain weighted sums of these transforms is then solved by converting it into a linear first-order partial differential equation. The result may be used to find the density function of passage times between states in a Markov process and it is applied to derive an expression for cycle time distribution in tree-structured Markovian queueing networks.
A martingale approach to the PASTA property
Authors: Scheutzow Michael
Published: April 2006

It is known (Weizsäcker and Winkler (1990)) that for bounded predictable functions H and a Poisson process with jump times
exists almost surely, and that in this case both limits are equal. Here we relax the boundedness condition on H. Our tool is a law of large numbers for local L2-martingales. We show by examples that our condition is close to optimal. Furthermore we indicate a generalization to point processes on more general spaces. The above property is called PASTA (‘Poisson arrivals see time averages') and is heavily used in queueing theory.
Reliability estimation of a complex renewable system with an unbounded number of repair units
Authors: Solovyev A. D. , Konstant D. G.
Published: April 2006

In this study an asymptotical analysis of the reliability of a complex renewable system with an unbounded number of repair units is provided. The system state is given by a binary vector e(t) = [e1(t), · ··, en(t)], ei(t) = 0(1), if at moment t the ith element is failure-free (failed). We assume that at the state e the ith element has failure intensity λi(e). At the instant of failure of every element the renewal work begins and the renewal time has distribution function Gi(t). Let E_ be the set of failed system states. The goal of this study is the asymptotic estimation of the distribution of the time until the first system failure, .
An optimal repairable replacement model for deteriorating systems
Authors: Yeh Lam
Published: April 2006

In this paper, we study a repair replacement model for a stochastically deteriorating system. For the expected discounted reward case, we show that the optimal replacement policy is of the form ‘replace at the time of the Nth failure'.
Stationary increments of accumulation processes in queues and generalized semi-Markov schemes
Authors: Foley R. D. , Klutke Georgia-Ann , König Dieter
Published: April 2006

Let Tx be the length of time to accumulate x units of a resource. In queueing, the resource could be service. We derive a sufficient condition for the process to have stationary increments where Tx is an additive functional of a Markov process. This condition is satisfied in symmetric queues and generalized semi-Markov schemes with insensitive components. As a corollary, we show that the conditional expected response time in a symmetric queue is linear in the service requirement. A similar result holds for the conditional average residence time of an insensitive component in a GSMS.
A maximum sequence in a critical multitype branching process
Authors: Spåtaru Aurel
Published: April 2006

Let (Zn) be a p-type positively regular and non-singular critical Galton–Watson process with finite second moments. Associated with the spectral radius 1 of the mean matrix of (Zn) consider the right eigenvector u = (u1, · ··, up) > 0, and set . It is shown that lim inf, lim sup whenever Z0 = i, where .
An optimal stopping problem in the excavation of archaeological remains
Authors: Nakai Teruhisa
Published: April 2006

In the excavation of archaeological remains of high value, a search tool with low cost can be used at first, but if we reach a stratum which is very likely to contain valuable material we must use a search tool with high efficiency to reduce the risk of destruction of the remains even if this is more expensive. Which tool should we use at each time? Furthermore, if the search costs too much in comparison with the reward of detection, it is not profitable to go on searching for ever. When should we stop the search? We answer these questions for continuous and discrete models.
Joint simulation of backward and forward recurrence times in a superposition of independent renewal processes
Authors: Lam C. Y. Teresa
Published: April 2006

It is shown that, in a superposition of finitely many independent renewal processes, an observation from the limiting (when t →∞) joint distribution of backward and forward recurrence times at t can be simulated by simulating an observation of the pair (UW, (1 – U)W), where U and Ware independent random variables with U ~ uniform(0, 1) and W distributed according to the limiting total life distribution of the superposition process.
Monotonicity property of t-step maintainable structures in three-grade manpower systems: a counterexample
Authors: Guerry M. A.
Published: April 2006

In this paper the t-step maintainable regions Mt are examined in a three-graded system under the following conditions: the total size of the system remains constant during each intermediate step, demotions do not occur and recruitment control is considered.

A counterexample, showing that the monotonicity property Mt ⊆ Mt+1 does not exist in general, refutes the conjecture of Davies [3].
The equality of the workload and total attained waiting time in average
Authors: Yamazaki Genji , Miyazawa Masakiyo
Published: April 2006

It has recently been shown that, for the FCFS G/G/1 queue, the workload and attained waiting time of a customer in service have the same stationary distribution. We show that, for a general queueing system setting, the workload and total attained waiting time of customers in service are identical in average but the equality of the distributions is not true in general except for the FCFS G/G/1 queue.
Quasi-limiting distributions of Markov chains that are skip-free to the left in continuous time
Authors: Kijima Masaaki
Published: April 2006

A continuous-time Markov chain on the non-negative integers is called skip-free to the left (right) if the governing infinitesimal generator A = (aij) has the property that aij = 0 for j ≦ i ‒ 2 (i ≦ j – 2). If a Markov chain is skip-free both to the left and to the right, it is called a birth-death process. Quasi-limiting distributions of birth–death processes have been studied in detail in their own right and from the standpoint of finite approximations. In this paper, we generalize, to some extent, results for birth-death processes to Markov chains that are skip-free to the left in continuous time. In particular the decay parameter of skip-free Markov chains is shown to have a similar representation to the birth-death case and a result on convergence of finite quasi-limiting distributions is obtained.
On the empty cells of Poisson histograms
Authors: Kendall Wilfrid S.
Published: April 2006

This paper considers the histogram of unit cell size built up from m independent observations on a Poisson (μ) distribution. The following question is addressed: what is the limiting probability of the event that there are no unoccupied cells lying to the left of occupied cells of the histogram? It is shown that the probability of there being no such isolated empty cells (or isolated finite groups of empty cells) tends to unity as the number m of observations tends to infinity, but that the corresponding almost sure convergence fails. Moreover this probability does not tend to unity when the Poisson distribution is replaced by the negative binomial distribution arising when μ is randomized by a gamma distribution. The relevance to empirical Bayes statistical methods is discussed.
Utilization of the method of linear matrix equations to solve a quasi-birth-death problem
Authors: Feldman Richard M. , Deuermeyer Bryan L. , Valdez-Flores Ciriaco
Published: April 2006

The steady-state analysis of a quasi-birth-death process is possible by matrix geometric procedures in which the root to a quadratic matrix equation is found. A recent method that can be used for analyzing quasi-birth–death processes involves expanding the state space and using a linear matrix equation instead of the quadratic form. One of the difficulties of using the linear matrix equation approach regards the boundary conditions and obtaining the norming equation. In this paper, we present a method for calculating the boundary values and use the operator-machine interference problem as a vehicle to compare the two approaches for solving quasi-birth-death processes.
On the existence of quasi-stationary distributions in denumerable R-transient Markov chains
Authors: Kijima Masaaki
Published: April 2006

Let {Xn, n = 0, 1, 2, ···} be a transient Markov chain which, when restricted to the state space 𝒩 + = {1, 2, ···}, is governed by an irreducible, aperiodic and strictly substochastic matrix 𝐏 = (pij), and let pij(n) = P ∈ Xn = j, Xk ∈ 𝒩+ for k = 0, 1, ···, n | X0 = i], i, j 𝒩 +. The prime concern of this paper is conditions for the existence of the limits, qij say, of as n →∞. If the distribution (qij) is called the quasi-stationary distribution of {Xn} and has considerable practical importance. It will be shown that, under some conditions, if a non-negative non-trivial vector x = (xi) satisfying rxT = xT𝐏 and exists, where r is the convergence norm of 𝐏, i.e. r = R–1 and and T denotes transpose, then it is unique, positive elementwise, and qij(n) necessarily converge to xj as n →∞. Unlike existing results in the literature, our results can be applied even to the R-null and R-transient cases. Finally, an application to a left-continuous random walk whose governing substochastic matrix is R-transient is discussed to demonstrate the usefulness of our results.
Stochastic convexity of sums of i.i.d. non-negative random variables with applications
Authors: Makowski Armand M. , Philips Thomas K.
Published: April 2006

We present some monotonicity and convexity properties for the sequence of partial sums associated with a sequence of non-negative independent identically distributed random variables. These results are applied to a system of parallel queues with Bernoulli routing, and are useful in establishing a performance comparison between two scheduling strategies in multiprocessor systems.
Optimal control of a finite dam using PMλΤ policies and penalty cost: total discounted and long run average cases
Authors: Abdel-hameed M. , Nakhi Y.
Published: April 2006

Zuckermann [10] considers the problem of optimal control of a finite dam using policies, assuming that the input process is Wiener with drift term μ ≧ 0. Lam Yeh and Lou Jiann Hua [7] treat the case where the input is a Wiener process with a reflecting boundary at zero, with drift term μ ≧ 0, using the long-run average cost and total discounted cost criteria. Attia [1] obtains results similar to those of Lam Yeh and Lou Jiann Hua for the long-run average case and extends them to include μ < 0. In this paper we look further into the results of Zuckerman [10], simplify some of the work of Attia [1], [2], offering corrections to some of his formulae and extend the results of Lam Yeh and Lou Jiann Hua [7].
Correlation and variability in birth processes
Authors: Donnelly Peter , Kurtz Thomas , Marjoram Paul
Published: April 2006

Faddy (1990) has conjectured that the variability of a pure birth process is increased, relative to the linear case, if the birth rates are convex and decreased if they are concave. We prove the conjecture by relating variability to the correlation structure of certain more informative versions of the process. A correlation inequality due to Harris (1977) is used to derive the necessary positive and negative correlation results.
Autoregressive processes and first-hit probabilities for randomized random walks
Authors: Feldman Raisa Epstein
Published: April 2006

We find the first-hit distributions of symmetric randomized random walks on ℝ with exponential lifetime using prediction formulas for Gaussian stationary autoregressive processes, associated with the random walks.
Some generalized variability orderings among life distributions with reliability applications
Authors: Bhattacharjee M. C.
Published: April 2006

We investigate a generalized variability ordering and its weaker versions among non-negative random variables (lifetimes of components). Our results include a necessary and sufficient condition which justifies the generalized variability interpretation of this dominance relation between life distributions, relationships to some weakly aging classes in reliability theory, closure properties and inequalities for the mean life of series and parallel systems under such ordering.
Sojourn times in vacation and polling systems with Bernoulli feedback
Authors: Takine T. , Takagi H. , Hasegawa T.
Published: April 2006

We study sojourn times in M/G/1 multiple vacation systems and multiqueue cyclic-service (polling) systems with instantaneous Bernoulli feedback. Three service disciplines, exhaustive, gated, and 1-limited, are considered for both M/G/1 vacation and polling systems. The Laplace-Stieltjes transforms of the sojourn time distributions in the three vacation systems are derived. For polling systems, we provide explicit expressions for the mean sojourn times in symmetric cases. Furthermore a pseudo-conservation law with respect to the mean sojourn times is derived for a polling system with a mixture of the three service disciplines.
Response time distributions in tandem G-networks
Authors: Harrison Peter G. , Pitel Edwige
Published: April 2006

The Laplace transform of the probability distribution of the end-to-end delay in tandem networks is obtained where the first and/or second queue are G-queues, i.e. they have negative arrivals. For the most general case the method is based on the solution of a boundary value problem on a closed contour in the complex plane, which itself reduces to the solution of a Fredholm integral equation of the second kind. We also consider the dependence or independence of the sojourn times at each queue in the two special cases where only one of the queues is a G-queue, the other having no negative arrivals.
A stochastic model of fragment formation when DNA replicates
Authors: Cowan Richard , Chiu S. N.
Published: April 2006

The double-stranded molecule, DNA, has the unique property of replication and, because of this, it is the central molecule of life. The mechanism of replication for each single strand is intricate, involving enzymes which move along each of the single strands building a complementary copy. At the frontier of this action, the events have a strong stochastic character due to the random location on the DNA of key ‘sites' where copying commences. A model of this process is analysed. The central problem of interest is the mean length of certain ‘islands' of newly replicated DNA developed at the randomly located ‘sites'. These islands, which have been observed experimentally, are called Okazaki fragments.
Simple random walk statistics. Part II: Continuous time results
Authors: Böhm W. , Panny W.
Published: April 2006

In this paper various statistics for randomized random walks and their distributions are presented. The distributional results are derived by means of a limiting procedure applied to the pertaining discrete time process, which has been considered in part I of this work (Katzenbeisser and Panny 1996). This basic approach, originally due to Meisling (1958), seems to offer certain technical advantages, since it avoids the use of Laplace transforms and is even simpler than Feller's randomization technique.
More on n-point, win-by-k games
Authors: Haigh John
Published: April 2006

When Siegrist (1989) derived an expression for the probability that player A wins a game that consists of a sequence of Bernoulli trials, the winner being the first player to win n trials and have a lead of at least k, he noted the desirability of giving a direct probabilistic argument. Here we present such an argument, and extend the domain of applicability of the results beyond Bernoulli trials, including cases (such as the tie-break in lawn tennis) where the probability of winning each trial cannot reasonably be taken as constant, and to where there is Markov dependence between successive trials.
A note on disjoint-occurrence inequalities for marked Poisson point processes
Authors: van den Berg J.
Published: April 2006

For (marked) Poisson point processes we give, for increasing events, a new proof of the analog of the BK inequality. In contrast to other proofs, which use weak-convergence arguments, our proof is ‘direct' and requires no extra topological conditions on the events. Apart from some well-known properties of Poisson point processes, the proof is self-contained.
A note on the Volterra integral equation for the first-passage-time probability density
Authors: Jáimez R. Gutiérrez , Román P. Román , Ruiz F. Torres
Published: April 2006

In this paper we prove the validity of the Volterra integral equation for the evaluation of first-passage-time probability densities through varying boundaries, given by Buonocore et al. [1], for the case of diffusion processes not necessarily time-homogeneous. We study, specifically those processes that can be obtained from the Wiener process in the sense of [5]. A study of the kernel of the integral equation, in the same way as that by Buonocore et al. [1], is done. We obtain the boundaries for which closed-form solutions of the integral equation, without having to solve the equation, can be obtained. Finally, a few examples are given to indicate the actual use of our method.
Adaptive linear list reorganization under a generalized query system
Authors: Valiveti R. S. , Oommen B. J. , Zgierski J. R.
Published: April 2006

We consider the problem of reorganizing a linear list, when the individual queries consist of accesses to a subset of the elements stored, as opposed to the individual elements themselves. In this paper, which to our knowledge represents the first reported result in this model of query processing, we first propose a simple model for a query generator which emits set queries. Subsequently, we present extensions to the classical move-to-front (MTF) and transposition (TR) rules under this generalized query generation mechanism and analyze their performance.
Non-explosivity of limits of conditioned birth and death processes
Authors: Roberts G. O. , Jacka S. D. , Pollett P. K.
Published: April 2006

Let X be a birth and death process on with absorption at zero and suppose that X is suitably recurrent, irreducible and non-explosive. In a recent paper, Roberts and Jacka (1994) showed that as T → ∞ the process conditioned to non-absortion until time T converges weakly to a time-homogeneous Markov limit, X∞, which is itself a birth and death process. However the question of the possibility of explosiveness of X∞ remained open. The major result of this paper establishes that X∞ is always non-explosive.
The value of an Asian option
Authors: Rogers L. C. G. , Shi Z.
Published: April 2006

This paper approaches the problem of computing the price of an Asian option in two different ways. Firstly, exploiting a scaling property, we reduce the problem to the problem of solving a parabolic PDE in two variables. Secondly, we provide a lower bound which is so accurate that it is essentially the true price.
On a conjecture for the non-existence of the expectation of randomly stopped sums
Authors: Lefèvre Claude , Utev Sergey
Published: April 2006

In a recent paper on the validity of Wald's equation, Roters (1994) raised an important question on the non-existence of the expectation of randomly stopped sums. The purpose of this note is to answer the question in the affirmative. As a consequence, an old question by Taylor (1972) also gets a positive answer.
Simpler proofs of some properties of the fundamental period of the MAP/G/1 queue
Authors: Lucantoni David M. , Neuts Marcel F.
Published: April 2006

By an argument which involves matching sample paths, some useful equations for the probability distribution of the fundamental period in the MAP/G/1 queue are derived with less calculational effort than in earlier proofs. It is further shown that analogous equations hold for the MAP/SM/1 queueing model. These results are then used to derive explicit formulas for the mean vectors of the number served during and the duration of the fundamental period.
A limit theorem for the replication time of a DNA molecule
Authors: Cowan Richard , Chiu S. N. , Holst Lars
Published: April 2006

The DNA of higher animals replicates by an interesting mechanism. Enzymes recognise specific sites randomly scattered on the molecule and establish a bidirectional process of unwinding and replication from these sites. We investigate the limiting distribution of the completion time for this process by considering related coverage problems investigated by Janson (1983) and Hall (1988).
A simple derivation of exact reliability formulas for linear and circular consecutive-k-of-n: F systems
Authors: Peköz Erol A. , Ross Sheldon M.
Published: April 2006

Exact reliability formulas for linear and circular consecutive-k-of-n: F systems are derived in the case of equal component reliabilities.
Drift vectors are not sufficient to determine recurrence of a Markov chain on ℤ3+
Authors: Kotler Mitchell
Published: April 2006

For a Markov chain in n = 2, drift vectors (conditional expected jumps) on the interior and the boundaries distinguish between recurrence and transience. The result of this paper is that the analogous proposition in the n = 3 case fails.
Measles Cases Are Spreading in the US—Here’s What to Know
Authors: Suran Melissa
Published: February 2024

This Medical News article discusses measles cases spreading in the US.
Spesolimab Response in a Girl With Acrodermatitis Continua of Hallopeau
Authors: Wang Youcong , Zhang Li , Zheng Jie , Li Xia , Chen Lihong
Published: February 2024

This case report summarizes the treatment of acrodermatitis continua of Hallopeau with spesolimab in a 9-year-old girl.
Hourly Heat Exposure and Acute Ischemic Stroke
Authors: Zhu Xinlei , Chen Renjie , Yuan Jing , Liu Yang , Wang Yong , Ji Xunming , Kan Haidong , Zhao Jing
Published: February 2024

Importance

Previous studies have demonstrated the associations of daily high temperature with hospitalizations and mortality from ischemic stroke, but the hourly association of ambient heat and acute ischemic stroke (AIS) onset has been rarely examined.

Objectives

To evaluate the association between hourly high ambient temperature and the onset of AIS.

Design, Setting, and Participants

This time-stratified case-crossover study was conducted using a nationwide registry that collects data from more than 200 stroke centers in China. Participants were adult patients with AIS who were hospitalized in the warm seasons between January 1, 2019, and December 31, 2021.

Exposures

Hourly temperature and single-hour temperature exposure lag up to 24 hours before the AIS onset (lag 0 hours to lag 24 hours).

Main Outcomes and Measures

The main outcome was onset of AIS. Associations between hourly mean temperatures and AIS onset were analyzed using conditional logistic regression integrated with the distributed lag nonlinear model. Stratification analyses were applied to examine potential association modifiers. Several sensitivity analyses were conducted to examine the robustness of the results.

Results

A total of 82 455 patients with AIS (mean [SD] age, 65.8 [11.9] years; 52 267 males [63.4%]) were included in the final analysis. A monotonically increasing risk of AIS onset was associated with higher temperatures. The excess AIS risk occurred immediately at lag 0 hours and persisted for 10 hours. Compared with the reference temperature (12.1 °C), the cumulative odds ratio (OR) over lag 0 to 10 hours of AIS onset associated with extremely high temperature (33.3 °C) was 1.88 (95% CI, 1.65-2.13) nationwide. The exposure-response curve was steeper in the north than in the south (OR, 1.80 [95% CI, 1.53-2.11] vs 1.57 [95% CI, 1.31-1.87]). The ORs were greater for males and patients with a history of dyslipidemia or atrial fibrillation, but the differences were not significant.

Conclusions and Relevance

Results of this study suggest that hourly heat exposure is associated with increased risk of AIS onset. This finding may benefit the formulation of public health strategies to reduce cerebrovascular risk associated with high ambient temperature under global warming.
Real‐time route planning for low observable unmanned combat aerial vehicle
Authors: Yang Yuanchao
Published: February 2024

The next generation of low observable (LO) unmanned combat aerial vehicle (UCAV) with highly autonomy to implement a penetration mission requires advanced methods for flyable and safe route planning (i.e., respecting physical capability of vehicle and threat coverage by hostile air defense radars) at a real‐time manner. Currently, the main challenge of real‐time route planning for LO UCAV is to achieve computationally efficiency under dynamic (pop‐up/moving) threats by air defense radars. In this paper, a real‐time planning paradigm in compliance with complex penetration requirements is proposed, and a complete modeling of route planning for LO UCAV's penetration as an optimal control problem is designed. The paper at first devises a direct method to transform the optimal control problem into a nonlinear programming (NLP) problem and then solves the formulated NLP problem under a moving planning horizon. The proposed method can give computationally efficient route planning results for LO UCAV's penetration under multiple kinds of radar threats. Numerical test results based on F‐16 uninhabited platform demonstrate the effectiveness of the proposed method.
Structure and Validation of a Kinematic Surface Simulation Model for the Direct Laser Writing Process
Authors: Wieland Fabian , Gärtner Eric , Wieland Sebastian
Published: February 2024

The article introduces the structure and validation of a kinematic surface simulation model for the replication of laser‐structured surfaces and their impressions after hot embossing. The surface replication is accomplished by the stepwise Boolean intersection of a structured and digitized point ablation with the workpiece. The resulting surface is characterized according to ISO 25178. Resulting from the kinematic simulation principle, the model can be applied to a wide range of material–machine combinations in the field of laser structuring and enables a time–efficient, nanometer‐resolved replication of representative surfaces with a size up to several square millimeters. Within the validation process it was proven that the main surface characteristics can be predicted by the model. Compared to AI approaches and numerical or multiphysical simulations, preliminary studies are only needed to a very small extent. Furthermore, complex influences such as material and temperature‐related properties do not need separate consideration as they are taken into account by the digitized point ablation.