bluuebunny/crossref_metadata_2025_split huggingface dataset:
On the Value of Mitigation and Contingency Strategies for Managing Supply Chain Disruption Risks
Authors: Tomlin Brian 
Published: April 2006

We study a single-product setting in which a firm can source from two suppliers, one that is unreliable and another that is reliable but more expensive. Suppliers are capacity constrained, but the reliable supplier may possess volume flexibility. We prove that in the special case in which the reliable supplier has no flexibility and the unreliable supplier has infinite capacity, a risk-neutral firm will pursue a single disruption-management strategy: mitigation by carrying inventory, mitigation by single-sourcing from the reliable supplier, or passive acceptance. We find that a supplier’s percentage uptime and the nature of the disruptions (frequent but short versus rare but long) are key determinants of the optimal strategy. For a given percentage uptime, sourcing mitigation is increasingly favored over inventory mitigation as disruptions become less frequent but longer. Further, we show that a mixed mitigation strategy (partial sourcing from the reliable supplier and carrying inventory) can be optimal if the unreliable supplier has finite capacity or if the firm is risk averse. Contingent rerouting is a possible tactic if the reliable supplier can ramp up its processing capacity, that is, if it has volume flexibility. We find that contingent rerouting is often a component of the optimal disruption-management strategy, and that it can significantly reduce the firm’s costs. For a given percentage uptime, mitigation rather than contingent rerouting tends to be optimal if disruptions are rare.
Evolution of Resistance During Clonal Expansion
Authors: Iwasa Yoh , Nowak Martin A , Michor Franziska 
Published: April 2006

Abstract
Acquired drug resistance is a major limitation for cancer therapy. Often, one genetic alteration suffices to confer resistance to an otherwise successful therapy. However, little is known about the dynamics of the emergence of resistant tumor cells. In this article, we consider an exponentially growing population starting from one cancer cell that is sensitive to therapy. Sensitive cancer cells can mutate into resistant ones, which have relative fitness α prior to therapy. In the special case of no cell death, our model converges to the one investigated by Luria and Delbrück. We calculate the probability of resistance and the mean number of resistant cells once the cancer has reached detection size M. The probability of resistance is an increasing function of the detection size M times the mutation rate u. If Mu ≪ 1, then the expected number of resistant cells in cancers with resistance is independent of the mutation rate u and increases with M in proportion to $\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(M^{1{-}1/\mathrm{{\alpha}}}\) \end{document}$ for advantageous mutants with relative fitness $\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathrm{{\alpha}}{&gt;}1\) \end{document}$, to $\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathrm{ln}M\) \end{document}$ for neutral mutants (α = 1), but converges to an upper limit for deleterious mutants ($\batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \(\mathrm{{\alpha}}{&lt;}1\) \end{document}$). Further, the probability of resistance and the average number of resistant cells increase with the number of cell divisions in the history of the tumor. Hence a tumor subject to high rates of apoptosis will show a higher incidence of resistance than expected on its detection size only.
The caudal characteristic curve of queues
Authors: Neuts Marcel F. 
Published: April 2006

Many queues and related stochastic models, and in particular those that have a matrix-geometric stationary probability vector, have steady-state queue-length densities that are asymptotically geometric. The graph of the asymptotic rate η of these densities as a function of the traffic intensity ρ is the caudal characteristic curve. This is an informative graph from which a number of qualitative inferences about the behavior of the queue may be drawn.The caudal characteristic curve may be computed (by elementary algorithms) for several useful models for which a complete exact numerical solution is not practically feasible. These include queues with certain types of superimposed arrival processes and/or multiple non-exponential servers. The necessary theorems which lead to the algorithmic procedures as well as the interpretation of several numerical examples are discussed.
Damped vibrations excited by white noise
Authors: Orsingher Enzo 
Published: April 2006

Let v(x, t) denote the displacement of an infinitely long, idealized string performing damped vibrations caused by white noise.Upper and lower bounds for the distribution of maxsv(x, s) and maxxv(x, t) are presented. The results are obtained by adapting Lévy-type inequalities and exploiting a connection of v(x, t) with the Ornstein-Uhlenbeck process through Slepian's theorem.The case of forced-damped vibrations is also analysed. Finally, a section is devoted to the case of a semi-infinite string performing damped vibrations.
Preserving partial balance in continuous-time Markov chains
Authors: Pollett P. K. 
Published: April 2006

Recently a number of authors have considered general procedures for coupling stochastic systems. If the individual components of a system, when considered in isolation, are found to possess the simplifying feature of either reversibility, quasireversibility or partial balance they can be coupled in such a way that the equilibrium analysis of the system is considerably simpler than one might expect in advance. In particular the system usually exhibits a product-form equilibrium distribution and this is often insensitive to the precise specification of the individual components. It is true, however, that certain kinds of components lose their simplifying feature if the specification of the coupling procedure changes. From a practical point of view it is important, therefore, to determine if, and then under what conditions, the revelant feature is preserved.In this paper we obtain conditions under which partial balance in a component is preserved and these often amount to the requirement that there exists a quantity which is unaffected by the internal workings of the component in question. We give particular attention to the components of a stratified clustering process as these most often suffer from loss of partial balance.
Optimal selection of stochastic intervals under a sum constraint
Authors: Coffman E. G. , Flatto L. , Weber R. R. 
Published: April 2006

We model a selection process arising in certain storage problems. A sequence (X1, · ··, Xn) of non-negative, independent and identically distributed random variables is given. F(x) denotes the common distribution of the Xi′s. With F(x) given we seek a decision rule for selecting a maximum number of the Xi′s subject to the following constraints: (1) the sum of the elements selected must not exceed a given constant c > 0, and (2) the Xi′s must be inspected in strict sequence with the decision to accept or reject an element being final at the time it is inspected.We prove first that there exists such a rule of threshold type, i.e. the ith element inspected is accepted if and only if it is no larger than a threshold which depends only on i and the sum of the elements already accepted. Next, we prove that if F(x) ~ Axα as x → 0 for some A, α> 0, then for fixed c the expected number, En(c), selected by an optimal threshold is characterized by

Asymptotics as c → ∞and n → ∞with c/n held fixed are derived, and connections with several closely related, well-known problems are brought out and discussed.
A two-point Markov chain boundary-value problem
Authors: Daley D. J. , Servi L. D. 
Published: April 2006

The two-point Markov chain boundary-value problem discussed in this paper is a finite-time version of the quasi-stationary behaviour of Markov chains. Specifically, for a Markov chain {Xt:t= 0, 1, ·· ·}, given the time interval (0,n), the interest is in describing the chain at some intermediate time point rconditional on knowing boththe behaviour of the chain at the initial time point 0 and that over the interval (0,n) it has avoided some subsetBof the state space. The paper considers both ‘real time' estimates forr=n(i.e. the chain has avoidedBsince 0), anda posterioriestimates forr<nwith at least partial knowledge of the behaviour ofXn.Algorithms to evaluate the distribution ofXrcan be as small asO(n3) (and, for practical purposes, evenO(n2logn)). The estimates may be stochastically ordered, and the process (and hence, the estimates) may be spatially homogeneous in a certain sense. Maximum likelihood estimates of the sample path are furnished, but by example we note that these ML paths may differ markedly from the path consisting of the expected or average states. The scope for two-point boundary-value problems to have solutions in a Markovian setting is noted.Several examples are given, together with a discussion and examples of the analogous problem in continuous time. These examples include the basicM/G/kqueue and variants that include a finite waiting room, reneging, balking, and Bernoulli feedback, a pure birth process and the Yule process. The queueing examples include Larson's (1990) ‘queue inference engine'.
Random high-dimensional orders
Authors: Bollobás Béla , Brightwell Graham 
Published: April 2006

The randomk-dimensional partial orderPk(n) onnpoints is defined by takingnpoints uniformly at random from [0,1]k. Previous work has concentrated on the case wherekis constant: we consider the model wherekincreases withn.We pay particular attention to the heightHk(n) ofPk(n). We show thatk= (t/logt!) lognis a sharp threshold function for the existence of at-chain inPk(n): ifk –(t/logt!) logntends to + ∞ then the probability thatPk(n) contains at-chain tends to 0; whereas if the quantity tends to − ∞ then the probability tends to 1. We describe the behaviour ofHk(n) for the entire range ofk(n).We also consider the maximum degree ofPk(n). We show that, for each fixedd≧ 2,is a threshold function for the appearance of an element of degreed.Thus the maximum degree undergoes very rapid growth near this value ofk.We make some remarks on the existence of threshold functions in general, and give some bounds on the dimension ofPk(n) for largek(n).
A ratio limit theorem for (sub) Markov chains on {1,2, …} with bounded jumps
Authors: Kesten Harry 
Published: April 2006

We consider positive matricesQ,indexed by {1,2, …}. Assume that there exists a constant 1L <∞ and sequencesu1< u2< · ··andd1d2< · ··such thatQ(i, j) = 0 wheneveri<ur< ur+L < jori > dr+ L > dr> jfor somer. IfQsatisfies some additional uniform irreducibility and aperiodicity assumptions, then fors> 0,Qhas at most one positives-harmonic function and at most ones-invariant measureµ.We use this result to show that ifQis also substochastic, then it has the strong ratio limit property, that isfor a suitableRand someR–1-harmonic functionfandR–1-invariant measureµ.Under additional conditionsµcan be taken as a probability measure on {1,2, …} andexists. An example shows that this limit may fail to exist ifQdoes not satisfy the restrictions imposed above, even thoughQmay have a minimal normalized quasi-stationary distribution (i.e. a probability measureµfor whichR–1µ = µQ).The results have an immediate interpretation for Markov chains on {0,1,2, …} with 0 as an absorbing state. They give ratio limit theorems for such a chain, conditioned on not yet being absorbed at 0 by timen.
The definition of a multi-dimensional generalization of shot noise
Authors: Daley D. J. 
Published: April 2006

The paper studies the formally defined stochastic process where {tj} is a homogeneous Poisson process in Euclidean n-space En and the a.e. finite Em-valued function f(·) satisfies |f(t)| = g(t) (all |t | = t), g(t) ↓ 0 for all sufficiently large t → ∞, and with either m = 1, or m = n and f(t)/g(t) =t/t. The convergence of the sum at (*) is shown to depend on (i)(ii)(iii). Specifically, finiteness of (i) for sufficiently large X implies absolute convergence of (*) almost surely (a.s.); finiteness of (ii) and (iii) implies a.s. convergence of the Cauchy principal value of (*) with the limit of this principal value having a probability distribution independent of t when the limit in (iii) is zero; the finiteness of (ii) alone suffices for the existence of this limiting principal value at t = 0.
On the distribution and moments of the strength of a bundle of filaments
Authors: Suh M. W. , Bhattacharyya B. B. , Grandage A. 
Published: April 2006

SummarySmall sample and large sample properties of the bundle strength of parallel filaments studied earlier by Daniels (1945) and Sen, Bhattacharyya, Suh (1969) have been developed here by probabilistic argument. The statistics belong to a family or class of statistics, each of which forms a reverse semi-martingale sequence. Certain moment properties are also discussed.
Estimation for a family of life distributions with applications to fatigue
Authors: Birnbaum Z.W. , Saunders S.C. 
Published: April 2006

SummaryThe estimation problem is studied for a new two-parameter family of life length distributions which has been previously derived from a model of fatigue crack growth. Maximum likelihood estimates of both parameters are obtained and iterative computing procedures are given and examined. A simple estimate of the median life is exhibited, shown to be consistent and then compared, favorably, with the maximum likelihood estimate. More important, the asymptotic distribution of this estimate is shown to be within the same class of distributions as the observations themselves. This model, and these estimation procedures, are tried by fitting this distribution to several extensive sets of fatigue data and then some comparisons of practical significance are made.
The Trivariate Distribution of the Maximum Queue Length, the Number of Customers Served and the Duration of the Busy Period for theM/G/1 Queueing System
Authors: Enns E.G. 
Published: April 2006

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.
On the Weak form of Zipf's law
Authors: Chen Wen-Chen 
Published: April 2006

Zipf's laws are probability distributions on the positive integers which decay algebraically. Such laws have been shown empirically to describe a large class of phenomena, including frequency of words usage, populations of cities, distributions of personal incomes, and distributions of biological genera and species, to mention only a few. In this paper we present a Dirichlet–multinomial urn model for describing the above phenomena from a stochastic point of view.We derive the Zipf's law under certain regularity conditions; some limit theorems are also obtained for the urn model under consideration.
Optimal insurance premium rates when the distribution of claims is unknown
Authors: Venezia Itzhak 
Published: April 2006

We analyze here the optimal premium rates for an insurance company for the case where the claims process is a stochastic process with unknown parameters. The beliefs of the insurance company about these parameters are represented by some prior distribution function, and the premium rates are determined on the basis of this distribution. The insurer learns about the unknown parameters from the past behavior of the claims process, and revises the prior distribution whenever new information is obtained (i.e., a claims stream is observed).The learning process introduces multi-period dynamic considerations to the problem of the rate determination, since the rates determined at any period affect the claims process, and thus the information available for future decisions. We show how the optimal rates can be obtained by using some dynamic programming techniques. We also prove that the optimal rates obtained in our case are lower than those determined by an insurance company that does not revise its distribution.
Transient behaviour of queueing networks
Authors: Harrison P. G. 
Published: April 2006

In most contemporary queueing network analysis, the assumption is made that a network is in a state of equilibrium. That is, the network's state space probabilities are assumed to be time independent. It is therefore important to be able to quantify precisely when this assumption is valid. Furthermore there are also situations in which it is desirable to model the transient behaviour of networks which occur in practice, such as computer and communication systems. For example, the immediate effects of component failure or instantaneous alteration of system status may be predicted.In this paper an iterative solution is derived to the time-dependent Kolmogorov equations of queueing networks, and is shown to be convergent. From the solution, modelling of transient situations becomes possible and the time periods during which the equilibrium assumption can and should not be made may be identified; for example in terms of a time constant which is easily computed to a first-order approximation.
A limit theorem for point processes by applications
Authors: Puri Prem S. 
Published: April 2006

Let 0 ≦T1≦T2≦ ·· · represent the epochs in time of occurrences of events of a point processN(t) withN(t) = sup{k:Tk≦t},t≧ 0. Besides certain mild conditions on the processN(t) (see Conditions (A1)– (A3) in the text) we assume that for everyk≧ 1, ast→∞, the vector (t – TN(t),t – TN(t)–1, · ··,t–TN(t)–k+1) converges in law to ak-dimensional distribution which coincides with that of a random vectorξk= (ξ1, · ··,ξk) necessarily satisfyingP(0 ≦ξ1≦ξ2≦ ·· ·≦ξk) = 1. LetR(t) be an arbitrary function defined fort≧ 0, satisfying 0 ≦R(t) ≦ 1, ∀0≦t<∞, and certain mild conditions (see Conditions (B1)– (B4) in the text). Then among other results, it is shown thatThe paper also deals with conditions under which the limit (∗) will be positive. The results are applied to several point processes and to the situations where the role ofR(t) is taken over by an appropriate transform such as a probability generating function, where conditions are given under which the limit (∗) itself will be a transform of an honest distribution. Finally the results are applied to the study of certain characteristics of theGI/G/∞ queue apparently not studied before.
A note on the inverse problem for reducible Markov chains
Authors: Pittenger A. O. 
Published: April 2006

Suppose a physical process is modelled by a Markov chain with transition probability on S1 ∪ S2, S1 denoting the transient states and S2 a set of absorbing states.If v denotes the output distribution on S2, the question arises as to what input distributions (of raw materials) on S1 produce v. In this note we give an alternative to the formulation of Ray and Margo [2] and reduce the problem to one system of linear inequalities. An application to random walk is given and the equiprobability case examined in detail.
The sojourn-time distribution in the M/G/1 queue by processor sharing
Authors: Ott Teunis J. 
Published: April 2006

This paper gives, in the form of Laplace–Stieltjes transforms and generating functions, the joint distribution of the sojourn time and the number of customers in the system at departure for customers in the general M/G/1 queue with processor sharing (M/G/1/PS).Explicit formulas are given for a number of conditional and unconditional moments, including the variance of the sojourn time of an ‘arbitrary' customer.
Age-dependent minimal repair
Authors: Block Henry W. , Borges Wagner S. , Savits Thomas H. 
Published: April 2006

A stochastic model is developed to describe the operation in time of the following maintained system setting. A piece of equipment is put in operation at time 0. Each time it fails, a maintenance action is taken which, with probability p(t), is a complete repair or, with probability q(t)=1– p(t), is a minimal repair, where t is the age of the equipment in use at the failure time. It is assumed that complete repair restores the equipment to its good as new condition, that minimal repair restores the equipment to its condition just prior to failure and that both maintenance actions take negligible time.If the equipment's life distribution F is a continuous function, the successive complete repair times are shown to be a renewal process with interarrival distribution

for t ≧ 0. Preservation and monotone properties of the model extending the results of Brown and Proschan (1983) are obtained.
Conditioned limit theorems for waiting-time processes of the M/G/1 queue
Authors: Hooghiemstra G. 
Published: April 2006

This paper is on conditioned weak limit theorems for imbedded waiting-time processes of an M/G/1 queue. More specifically we study functional limit theorems for the actual waiting-time process conditioned by the event that the number of customers in a busy period exceeds n or equals n. Attention is also paid to the actual waiting-time process with random time index.Combined with the existing literature on the subject this paper gives a complete account of the conditioned limit theorems for the actual waiting-time process of an M/G/1 queue for arbitrary traffic intensity and for a rather general class of service-time distributions.The limit processes that occur are Brownian excursion and meander, while in the case of random time index also the following limit occurs: Brownian excursion divided by an independent and uniform (0, 1) distributed random variable.
Homogeneous row-continuous bivariate markov chains with boundaries
Authors: Keilson J. , Zachmann M. 
Published: April 2006

The matrix-geometric results of M. Neuts are extended to ergodic row-continuous bivariate Markov processes [J(t), N(t)] on state space B = {(j, n)} for which: (a) there is a boundary level N for N(t) associated with finite buffer capacity; (b) transition rates to adjacent rows and columns are independent of row level n in the interior of B. Such processes are of interest in the modelling of queue-length for voice-data transmission in communication systems.One finds that the ergodic distribution consists of two decaying components of matrix-geometric form, the second induced by the finite buffer capacity. The results are obtained via Green's function methods and compensation. Passage-time distributions for the two boundary problems are also made available algorithmically.
Looking forwards and backwards in a bisexual moran model
Authors: Kämmerle K. 
Published: April 2006

In this paper a bisexual Moran model is introduced. The population consists of N pairs of individuals. At times t = 1, 2, ·· ·two individuals are born, who ‘choose their parents randomly' and independently of each other. Then one of the pairs is removed and replaced by the two individuals born at that instant.The extinction probability of the descendants of a single pair and the number of ancestors of a whole generation are studied. A limit result for large population sizes has been derived by diffusion approximation methods.