bluuebunny/crossref_metadata_2025_split huggingface dataset:
Some British Contributions to Aerodynamics
Authors: Stephens A. V. 
Published: July 2016

A Comprehensive review of British contributions to aerodynamics would fill many volumes and take years to compile. For while some aspects of the science are embarrassingly well documented—every library possesses the monumental reports of the Aeronautical Research Council from 1909 onwards and the no less compendious Journals of the Society—other aspects are hardly illuminated at all.Progress in aerodynamics has flowed in three main streams springing from the work of, first the research establishments and universities, second design offices and flight sections of the aircraft industry and third, the flying schools of the RAF.
Flying-Boats
Authors: Knowler Henry 
Published: July 2016

This Account of Flying-Boats will deal mainly with British craft, and must necessarily have a personal approach from one who has been involved in flyingboat development over nearly the whole of its life history.The prehistoric giant amphibians suffered eclipse through changing environment; similarly changed conditions in Aviation caused the still-evolving flying-boat to come to the end of its economic life. Probably concrete runways were the basic reason for the disappearance of flying-boats for both civil and military use, since landplanes were then no longer restricted either in size of efficiency or aerodrome conditions.
An exponential change of measure for the Feller diffusion and some implications for superprocesses
Authors: Adler Robert J. , Iyer Srikanth K. 
Published: July 2016

Let X

t
be a Feller (branching) diffusion with drift αx. We consider new processes, the probability measures of which are obtained from that of X via changes of measure involving suitably normalized exponential functions of with λ &gt; 0. The new processes can be thought of as ‘self-reinforcing’ versions of the old.
Depending on the values of α, T and λ, the process under the new measure is shown to exhibit explosion in finite time. We also obtain a number of other results related to the new processes.
Since the Feller diffusion is also the total mass process of a superprocess, we relate the finite-time explosion property to the behaviour of superprocesses with local self-interaction, and raise some interesting questions for these.
The fundamental matrix for a certain random walk
Authors: Taylor Howard M. 
Published: July 2016

Consider the random walk {Sn} whose summands have the distributionP(X=0) = 1-(2/π), andP(X= ±n) = 2/[π(4n2−1)], forn≥ 1. This random walk arises when a simple random walk in the integer plane is observed only at those instants at which the two coordinates are equal. We derive the fundamental matrix, or Green function, for the process on the integral [0,N] = {0,1,…,N}, and from this, an explicit formula for the mean timexkfor the random walk starting fromS0=kto exit the interval. The explicit formula yields the limiting behavior ofxkasN→ ∞ withkfixed. For the random walk starting from zero, the probability of exiting the interval on the right is obtained. By lettingN→ ∞ in the fundamental matrix, the Green function on the interval [0,∞) is found, and a simple and explicit formula for the probability distribution of the point of entry into the interval (−∞,0) for the random walk starting fromk= 0 results. The distributions for some related random variables are also discovered.Applications to stress concentration calculations in discrete lattices are briefly reviewed.
On the dependence structure and bounds of correlated parallel queues and their applications to synchronized stochastic systems
Authors: Li Haijun , Xu Susan H. 
Published: July 2016

This paper studies the dependence structure and bounds of several basic prototypical parallel queueing systems with correlated arrival processes to different queues. The marked feature of our systems is that each queue viewed alone is a standard single-server queuing system extensively studied in the literature, but those queues are statistically dependent due to correlated arrival streams. The major difficulty in analysing those systems is that the presence of correlation makes the explicit computation of a joint performance measure either intractable or computationally intensive. In addition, it is not well understood how and in what sense arrival correlation will improve or deteriorate a system performance measure.
The objective of this paper is to provide a better understanding of the dependence structure of correlated queueing systems and to derive computable bounds for the statistics of a joint performance measure. In this paper, we obtain conditions on arrival processes under which a performance measure in two systems can be compared, in the sense of orthant and supermodular orders, among different queues and over different arrival times. Such strong comparison results enable us to study both spatial dependence (dependence among different queues) and temporal dependence (dependence over different time instances) for a joint performance measure. Further, we derive a variety of upper and lower bounds for the statistics of a stationary joint performance measure. Finally, we apply our results to synchronized queueing systems, using the ideas combined from the theory of orthant and supermodular dependence orders and majorization with respect to weighted trees (Xu and Li (2000)). Our results reveal how a performance measure can be affected, favourably or adversely, by different types of dependencies.
New improved bounds for reliability of consecutive-k-out-of-n:F systems
Authors: Muselli Marco 
Published: July 2016

New bounds are found for the reliability of consecutive-k-out-of-n:F systems with equal component failure probabilities. The expressions involved are simple, thus allowing a direct use in the derivation of theoretical properties.
These bounds can also be employed in numerical computations when the value of n or k is so large that the exact calculation of the reliability is not achievable. Comparisons show that the approximation errors exhibited by these new formulas are lower than those of other widely used bounds.
Exact distributions of kin numbers in a Galton-Watson process
Authors: Joffe A. , Waugh W. A. O'n. 
Published: July 2016

The kin number problem involves the relationship between sibship sizes and offspring numbers, and also numbers of relatives of other degrees of affinity of a random member of a population, to be called Ego. The problem has been well known to demographers for some time, but results obtained only gave expected numbers. Recently a study of it, based on the Galton-Watson process, was made, with a view to obtaining joint distributions (Waugh (1981)). In the latter study it was assumed that the population was large, and thus some of the results obtained were approximations.
In the present paper exact distributions are obtained, for any size of population. This can be of use in applications, where the population considered may be a small, isolated tribe or other special group. As a theoretical investigation, it replaces some heuristic arguments with limiting properties that are intrinsic to the process and it makes it possible to evaluate the previous approximations.
Job search: the continuous case
Authors: Zuckerman Dror 
Published: July 2016

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

(a)
maximum expected net return,

(b)
maximum expected discounted net return.

We investigate the case in which the stream of job offers is determined by a Poisson process. We show that under the two optimality criteria defined above an optimal stopping rule is determined by a single critical value ξ. The optimal strategy is to accept the first job offer that exceeds ξ. In the second part of the article, the search model in which offers are received according to a general renewal process is examined.
Probability maximizing approach to a secretary problem by random change-point of the distribution law of the observed process
Authors: Yoshida Minoru 
Published: July 2016

Before some random moment θ, independent identically distributed random variables x
1, · ··, xθ–

1 with common distribution function μ (dx) appear consecutively. After the moment θ, independent random variables xθ, xθ

+1, · ·· have another common distribution function f (x)μ (dx). Our information about θ can be constructed only by successively observed values of the x's.
In this paper we find an optimal stopping policy by which we can maximize the probability that the quantity associated with the stopping time is the largest of all θ + m – 1 quantities for a given integer m.
Negative binomial processes
Authors: Barndorff-Nielsen Ole , Yeo G. F. 
Published: July 2016

Summary
This paper is concerned with negative binomial processes which are essentially mixed Poisson processes whose intensity parameter is given by the sum of squares of a finite number of independently and identically distributed Gaussian processes. A study is made of the distribution of the number of points of a k-dimensional negative binomial process in a compact subset of Rk
, and in particular in the case where the underlying Gaussian processes are independent Ornstein-Uhlenbeck processes when more detailed results may be obtained.
Bonferroni bounds revisited
Authors: Kounias Stratis , Sotirakoglou Kiki 
Published: July 2016

Lower and upper bounds of degree m for the probability of the union of n not necessarily exchangeable events are established. These bounds may be constructed to improve the Bonferroni and the Sobel–Uppuluri bounds.
An application to equi-correlated multivariate normal distribution is given.
A multitrap model for high-intensity reciprocity failure in the photographic grain
Authors: Anderson William J. 
Published: July 2016

The response of the photographic grain to light is a non-deterministic process which is as yet not completely understood. This response, as measured by the photographic density, is usually taken to be a function of the product of incident light intensity and exposure time interval duration, but at extreme values of either of these two quantities, this is no longer true. This latter effect is called reciprocity-law failure.
This paper discusses a probabilistic model, similar to a multiserver queue, for high-intensity reciprocity failure.
On the random coverage of the circle
Authors: Holst L. , Hüsler J. 
Published: July 2016

Place n arcs of equal length a uniformly at random on the circumference of a circle. We discuss the joint limit distributions of the number of gaps, the uncovered proportion of the circle and the lengths of the largest gap and of the smallest gap, depending on how a → 0 as n →∞.
We show that the results may be proved in a unified and simple way by using a result of Le Cam.
The kin number problem in a multitype Galton–Watson population
Authors: Joffe A. , Waugh W. A. O'n. 
Published: July 2016

The kin number problem in its simplest form is that of the relationship between sibship sizes and offspring numbers. The fact that the distributions are different, and the relationship between the two, is well known to demographers. It is important in such applications as estimating fertility from sibship rather than offspring counts. Further studies have been made, concerning relatives of other degrees of affinity than siblings, but these did not usually yield joint distributions. Recently this aspect of the problem has been studied in the framework of a Galton–Watson process (Waugh (1981), Joffe and Waugh (1982)).
In these studies the population is treated as monotype. Applications such as pedigree studies of diseases require a multitype approach (in the example, two types: victims and others). In this paper such a study is undertaken. The existence of more than one type complicates the time-reversal used in the previous studies, and raises questions about the way in which the focal individual (called ‘Ego') is sampled. These are dealt with, and joint distributions obtained, under a number of sampling schemes which might arise naturally.
On the best order of observation in optimal stopping problems
Authors: Gilat David 
Published: July 2016

For optimal stopping problems in which the player is allowed to choose the order of the random variables as well as the stopping rule, a notion of order equivalence is introduced. It is shown that different (non-degenerate) distributions cannot be order-equivalent.
This result unifies and generalizes two theorems of a similar nature recently obtained by Hill and Hordijk (1985).
The Trivariate Distribution of the Maximum Queue Length, the Number of Customers Served and the Duration of the Busy Period for the M/G/1 Queueing System
Authors: Enns E.G. 
Published: July 2016

In the study of the busy period for a single server queueing system, three variables that have been investigated individually or at most in pairs are:

1.
The duration of the busy period.

2.
The number of customers served during the busy period.

3.
The maximum number of customers in the queue during the busy period.
Bounds for Certain Branching Processes
Authors: Pollak Edward 
Published: July 2016

Summary
We consider a branching process for which the offspring distribution has the generating function f(t) and mean f
'(1) = m &lt; 1. The probability that a line descended from an individual still survives in generation n is asymptotically of the form cmn. A method is derived whereby good bounds for c may be obtained. This method makes use of the first three moments of the distribution of offspring.
Convergence to equilibrium in a traffic model with restricted passing
Authors: Unkelbach Hans Dieter 
Published: July 2016

A road traffic model with restricted passing, formulated by Newell (1966), is described by conditional cluster point processes and analytically handled by generating functionals of point processes.
The traffic distributions in either space or time are in equilibrium, if the fast cars form a Poisson process with constant intensity combined with Poisson-distributed queues behind the slow cars (Brill (1971)). It is shown that this state of equilibrium is stable, which means that this state will be reached asymptotically for general initial traffic distributions. Furthermore the queues behind the slow cars dissolve asymptotically like independent Poisson processes with diminishing rate, also independent of the process of non-queuing cars. To get these results limit theorems for conditional cluster point processes are formulated.
A semi-Markov model for a multigrade population with Poisson recruitment
Authors: McClean Sally I. 
Published: July 2016

We consider a multigrade population with semi-Markov transitions between grades, Poisson arrivals to each grade, and departures from each grade. For this model the joint distribution of the numbers in each grade at any time is found, and the limiting distributions shown to be independently Poisson; this extends a previous result for a multigrade population with Markov transitions and Poisson recruitment.
This model is particularly applicable to manpower planning. The inclusion of semi-Markov transitions allows us to take into account existing knowledge of the distribution of length of service until an individual leaves his firm.
Modelling yeast cell growth using stochastic branching processes
Authors: Green P. J. 
Published: July 2016

This paper aims to demonstrate that the general Crump–Mode–Jagers branching process may be used in a natural way to model the asymmetric growth of budding yeast cells. The models obtained are generalisations of the deterministic model proposed by Hartwell and Unger (1977): all the results that are derived in that paper may be obtained using branching-process methods, but such methods also apply when account is taken of the biologically obvious fact that the various phases of the cell growth are of random rather than fixed duration. In their full generality, branching processes involve more parameters than can be estimated by experiment, but we present below a special case in which this problem is not likely to arise.
A recent paper, Lord and Wheals (1980), discusses more of the biological background than is appropriate here. In the present paper, we show how certain statistical procedures for our model may be developed.
On a stochastic integral equation of the Volterra type in telephone traffic theory
Authors: Padgett W. J. , Tsokos C. P. 
Published: July 2016

In mathematical models of phenomena occurring in the general areas of the engineering, biological, and physical sciences, random or stochastic equations appear frequently. In this paper we shall formulate a problem in telephone traffic theory which leads to a stochastic integral equation which is a special case of the Volterra type of the form

where:

(i)
ω∊Ω, where Ω is the supporting set of the probability measure space (Ω,B,P);

(ii)

x(t; ω) is the unknown random variable for t ∊ R
+, where R
+ = [0, ∞);

(iii)

y(t; ω) is the stochastic free term or free random variable for t ∊ R
+;

(iv)

k(t, τ; ω) is the stochastic kernel, defined for 0 ≦ τ ≦ t &lt; ∞; and

(v)

f(t, x) is a scalar function defined for t ∊ R
+ and x ∊ R, where R is the real line.
A note on linear estimation of the intensity in a doubly stochastic Poisson field
Authors: Grandell Jan 
Published: July 2016

Summary
A realization of a doubly stochastic Poisson field is assumed to be observed in a Borel set S ⊂ Rk. The best linear estimate of the realization of the intensity field (at an arbitrary but fixed point x ∈ S) which generated the observation is obtained.
On the waiting time distribution in a generalized queueing system with uniformly bounded sojourn times
Authors: Loris-Teghem Jacqueline 
Published: July 2016

A generalized queueing system with (N+ 2) types of triplets (delay, service time, probability of joining the queue) and with uniformly bounded sojourn times is considered. An expression for the generating function of the Laplace-Stieltjes transforms of the waiting time distributions is derived analytically, in a case where some of the random variables defining the model have a rational Laplace-Stieltjes transform.The standardKl/Km/1 queueing system with uniformly bounded sojourn times is considered in particular.
Optimal inspection policy for a multi-unit machine
Authors: Zuckerman Dror 
Published: July 2016

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.
Optimal R&D programs in a random environment
Authors: Posner M. J. M. , Zuckerman D. 
Published: July 2016

Our study examines a stochastic R&amp;D model with flexible termination time and without rivalry. Specifically, we assume a stochastic relationship between expenditures rate and the project's status. Furthermore, the termination time of the project is incorporated into the R&amp;D model as a decision variable by allowing the controller to ‘sell' the obtained technology from the project at any point of time. The proposed framework extends the classical approach in the R&amp;D literature.
The main purpose of our study is to determine the optimal stopping time of the project and to characterize qualitatively the firm's expenditure strategy. We show that under certain realistic conditions, the optimal stopping strategy is a control limit policy. Furthermore, the research effort increases monotonically over the development time of the project.
The discrete-time single-server queue with time-inhomogeneous compound Poisson input and general service time distribution
Authors: Minh Do Le 
Published: July 2016

This paper studies a discrete-time, single-server queueing model having a compound Poisson input with time-dependent parameters and a general service time distribution.
All major transient characteristics of the system can be calculated very easily. For the queueing model with periodic arrival function, some explicit results are obtained.
Average delay in queues with non-stationary Poisson arrivals
Authors: Ross Sheldon M. 
Published: July 2016

One of the major difficulties in attempting to apply known queueing theory results to real problems is that almost always these results assume a time-stationary Poisson arrival process, whereas in practice the actual process is almost invariably non-stationary. In this paper we consider single-server infinite-capacity queueing models in which the arrival process is a non-stationary process with an intensity function ∧(t), t ≧ 0, which is itself a random process. We suppose that the average value of the intensity function exists and is equal to some constant, call it λ, with probability 1.
We make a conjecture to the effect that ‘the closer {∧(t), t ≧ 0} is to the stationary Poisson process with rate λ ' then the smaller is the average customer delay, and then we verify the conjecture in the special case where the arrival process is an interrupted Poisson process.
On the transient waiting times for a GI/M/1 priority queue
Authors: Dalen G. , Natvig B. 
Published: July 2016

In this paper we consider the GI/M/1 queueing model with infinite waiting-room capacity. The customer arriving at t = 0 will find k — 1 customers waiting. The latter customers belong to a second priority class, whereas the ones arriving in [0,∞) belong to a first priority class and have the higher priority. Within each class we have a first-in-first-out queueing discipline. A customer, once at the service-point, remains there until his service is completed. Then the next customer for service is the one of highest priority among those queueing.
For this model we derive the transient waiting times for customers belonging to both priority classes. The results are of special interest in appointment systems where customers may not turn up.
On a stopping time of Starr and its use in estimating the number of transmission sources
Authors: Vardi Yehuda 
Published: July 2016

Consider N sources, each of which transmits signals according to a renewal process with a common, known, underlying distribution. Sequential point estimators for N, which are asymptotically efficient in comparison to the best fixed stopping strategy, are derived. Confidence statements for N, and applications to the problem of estimating finite populations are discussed.
The exact limiting distribution, and moments, of the stopping time we use, which was suggested by Starr, are derived.
The probabilistic significance of the rate matrix in matrix-geometric invariant vectors
Authors: Neuts Marcel F. 
Published: July 2016

Many queueing models have embedded Markov chains, whose invariant probability vector is of a (modified) matrix-geometric form. The rate matrix R is shown to have the following probabilistic interpretation:
The element Rvj
is the expected number of visits to the state (i + 1, j), before the first return to the set i = {(i, 1), …,(i, m)}, in a chain starting in the state (i, v).