bluuebunny/crossref_metadata_2025 huggingface dataset:
Five Arabidopsis peroxin 11 homologs individually promote peroxisome elongation, duplication or aggregation
Authors: Lingard Matthew J. , Trelease Richard N.
Published: April 2006

Pex11 homologs and dynamin-related proteins uniquely regulate peroxisome division (cell-cycle-dependent duplication) and proliferation (cell-cycle-independent multiplication). Arabidopsis plants possess five Pex11 homologs designated in this study as AtPex11a, -b, -c, -d and -e. Transcripts for four isoforms were found in Arabidopsis plant parts and in cells in suspension culture; by contrast, AtPex11a transcripts were found only in developing siliques. Within 2.5 hours after biolistic bombardments, myc-tagged or GFP-tagged AtPex11 a, -b, -c, -d and -e individually sorted from the cytosol directly to peroxisomes; none trafficked indirectly through the endoplasmic reticulum. Both termini of myc-tagged AtPex11 b, -c, -d and -e faced the cytosol, whereas the N- and C-termini of myc-AtPex11a faced the cytosol and matrix, respectively. In AtPex11a- or AtPex11e-transformed cells, peroxisomes doubled in number. Those peroxisomes bearing myc-AtPex11a, but not myc-AtPex11e, elongated prior to duplication. In cells transformed with AtPex11c or AtPex11d, peroxisomes elongated without subsequent fission. In AtPex11b-transformed cells, peroxisomes were aggregated and rounded. A C-terminal dilysine motif, present in AtPex11c, -d and -e, was not necessary for AtPex11d-induced peroxisome elongation. However, deletion of the motif from myc-AtPex11e led to peroxisome elongation and fission, indicating that the motif in this isoform promotes fission without elongation. In summary, all five overexpressed AtPex11 isoforms sort directly to peroxisomal membranes where they individually promote duplication (AtPex11a, -e), aggregation (AtPex11b), or elongation without fission (AtPex11c, -d).
Pd-catalysed Capping Removal on a Tri-differentiated α-Cyclodextrin
Authors: Bistri Olivia , Sinaÿ Pierre , Sollogoub Matthieu
Published: April 2006

A chemically novel palladium-catalysed sequential double de-O-allylation to produce a diol is presented and applied to the efficient removal of a cap on a polyfunctionalized cyclodextrin.
The Effects of New Franchisor Partnering Strategies on Franchise System Size
Authors: Shane Scott , Shankar Venkatesh , Aravindakshan Ashwin
Published: April 2006

Many young firms use strategic actions to attract partners who help them increase the size of their operations quickly. This article examines the use of strategic actions to attract partners and increase system size in the context of franchising. We build on research in entrepreneurship, marketing, organization theory, strategic management, and finance to develop specific hypotheses about the influences of franchisor pricing policy and strategic control decisions on system size. We test these hypotheses empirically, using panel data on a sample of 1,292 business format franchise systems from 152 industries that were established in the United States between 1979 and 1996 and followed from their inception forward in time. Our model accounts for the endogeneity of strategic decisions, controls for unobserved firm and industry factors, and accounts for selection effects due to system failure. The results show that franchisors that grow larger (1) lower royalty rates as the systems age, (2) have low up-front franchise fees that rise over time, (3) own a small proportion of outlets and lower that percentage over time, (4) keep franchisees’ initial investment low, and (5) finance their franchisees.
Behind the mask: Eminem and postindustrial minstrelsy
Authors: White Russell
Published: April 2006

Eminem has emerged in the last five years to become perhaps the pre-eminent hip-hop artist of his generation. Despite his success, he is a figure that has polarized audiences in the United States and elsewhere. While frequently criticized for promoting sentiments that are homophobic,
misogynistic and violent, these impulses are presented in a way that is so exaggerated that they slip into and are indeed intended as parody. As such, Eminem provides an excellent example of the way in which rap artists utilize and engage with the traditions of signifying and the carnivalesque.
This study argues that through his lyrics and stage costuming, Eminem is engaged in a form of racial burlesque that is a post-industrial updating of that performed by nineteenth-century blackface minstrels. In doing so, the article examines Eminem's relationship to constructions of authenticity
within hip-hop culture, his coding as white trash, and his relationship to constructions of post-industrial white masculinity.
The Fluence Rate Determines the Synergistic Interaction of UV Radiation and Heat for Mitotic Recombination and Cell Inactivation in Yeasts
Authors: Kim Jin Kyu , Komarova Ludmila N. , Zhurakovskaya Galina P. , Petin Vladislav G.
Published: April 2006

The significance of the UV fluence rate for the synergistic interaction of UV light (254 nm) and heat was demonstrated for the frequency of mitotic recombination in a wild‐type diploid yeast of Saccharomyces cerevisiae (strain T1) and for cell inactivation of two wild‐type diploid yeast of S. cerevisiae (strains T1, XS800). It was shown for mitotic recombination that a decrease in the intensity of UV exposure results in the necessity of decreasing the temperature at which UV irradiation occurs to provide the same value of the synergistic enhancement ratio. For cell inactivation, there was a specific temperature maximizing the synergistic effect for any constant fluence rate and the temperature range, synergistically increasing the inactivation effect of UV radiation, should be shifted to lower temperatures with a decrease in the fluence rate. To interpret the results observed, a simple mathematical model of the synergistic interaction was applied. The model suggests that the synergistic interaction of UV light and hyper‐thermia is expected to result from some additional effective damages arising from the interaction of some sublesions induced by both agents. On the basis of data obtained, it was supposed that the synergistic interaction of these factors might take place at small intensities of UV light and temperatures existing in the biosphere. In other words, for a long duration of interaction, which is important for problems of UV light protection and health effects, one can expect a synergistic interaction of this factor with environmental heat or physiological temperatures and thereby an increase in their inactivating and genetic consequences.
Sample path behaviour of Χ2 surfaces at extrema
Authors: Aronowich Michael , Adler Robert J.
Published: April 2006

We study the sample path properties of χ2 random surfaces, in particular in the neighbourhood of their extrema. We show that, as is the case for their Gaussian counterparts, χ2 surfaces at high levels follow the form of certain deterministic paraboloids, but that, unlike their Gaussian counterparts, at low levels their form is much more random. This has a number of interesting implications in the modelling of rough surfaces and the study of the ‘robustness' of Gaussian field models. The general approach of the paper is the study of extrema via the ‘Slepian model process', which, for χ2 fields, is tractable only at asymptotically high or low levels.
Some results on Markovian replacement processes
Authors: Mandl Petr
Published: April 2006

A replacement of type (jk) in a Markov process with rewards means an instantaneous shift of the trajectory from state j into state k. A formula is obtained for the characteristic function of the total reward from the process under an arbitrary non-anticipative replacement policy. From the formula results are deduced concerning Markov policies, optimal policies and policies minimizing the variance of the reward.
Low density inhomogeneous traffic flow
Authors: Mine Hisashi , Ohno Katsuhisa
Published: April 2006

The purpose of this paper is to show some statistical properties of a one-dimensional inhomogeneous flow of particles with their own constant velocities. The most interesting example of such flows is a low-density inhomogeneous road traffic flow; each vehicle drives at his own constant velocity (desired velocity), since passing is freely allowed. Therefore, to give a definite picture to the one-dimensional inhomogeneous flow of particles, the authors deal with a low-density inhomogeneous traffic flow.
On a characterization of Poisson distribution
Authors: Srivastava R. C. , Srivastava A. B. L.
Published: April 2006

Recently Rao (1963) has considered discrete models where an original observation produced by nature is subjected to a destructive process and we observe the undestroyed part of the original observation. Suppose the original observation produced by nature is distributed according to a Poisson distribution with parameter λ and the probability that the original observation n is reduced to r due to the destructive process is Now if Y denotes the resulting random variable (r.v.), then it is easily seen that

Let us call this condition the *-condition. Later Rao and Rubin ({1964),Theorem 1) proved that the *-condition is a characterizing property of the Poisson distribution.
Epidemics with carriers: The large population approximation
Authors: Pettigrew Hugh M. , Weiss George H.
Published: April 2006

This paper applies the constant population approximation to the study of epidemics which involve more than a single type of infective. An example of this would be a situation in which both clinically infected individuals and subclinically infected individuals or carriers are present.

We derive equations for the expected numbers of clinically infected individuals and carriers at any time t for the model with zero latent period and infectious periods having negative exponential distributions. From these equations we derive conditions under which a unimodal incidence curve can result, and expressions for the expected total epidemic size.
Identities for passage times with applications to recurrent events and homogeneous differential functions
Authors: Darroch John N.
Published: April 2006

Let x be a non-negative, non-decreasing, right-continuous function of t defined on the interval [O, T) and let A = x(T–). Define the function y on [O, A] by

Then y is non-decreasing and left-continuous and

If t is a time variable it is natural to call y the passage time function.
Inflow-Stock-Outflow time series, stochastic lag and disaggregation: a note
Authors: Benishay Haskel
Published: April 2006

This note describes a model for inflow-stock-outflow time series which are formed as sums of random numbers of subcomponents of randomly determined sizes and are related via a probabilisticly distributed lag. Such time series may be illustrated by population processes in connection with which not only numbers of units are of interest but also the sizes of the units and the sums of the sizes. Such series may also be illustrated by economic phenomena like new loans made, loans outstanding and loans repaid of a commercial bank; new capital investments, capital stock and depreciated capital for a group of firms as well as accessions to the labor force, labor force outstanding, and secessions from the labor force.
On the relation between customer and time averages in queues
Authors: Brumelle Shelby L.
Published: April 2006

Little [8] gave conditions sufficient to obtain the formulaL=λW, whereLis the time average queue size,Wis the expected wait in queue, andλis the arrival rate of customers. This formula is applicable to a very general class of queuing models and is one of the most useful results in queuing theory.
On a solution of the migration process and the application to a problem in epidemiology
Authors: Raman S. , Chiang C. L.
Published: April 2006

In this paper we derive a successive method of solution to a general class of models pertaining to the investigation of the migration process. A specific application of the results to a problem arising in a study of the epidemiology of leprosy has been considered. The application to explorative studies in biological modelling using an interactive computing mode has been discussed.
A note on functions of Markov processes with an application to a sequence of χ2 statistics
Authors: Cameron Murray A.
Published: April 2006

A sufficient condition for a function of a Markov process to be Markovian is obtained by considering a reverse process of the original Markov process. An application of this result provides a simple derivation of the joint distribution of a sequence of Pearson χ2 statistics previously obtained by Zaharov, Sarmanov and Sevast'ianov (1969).
A note on the MX/GY/1, K bulk queueing system
Authors: Bagchi Tapan P. , Templeton J. G. C.
Published: April 2006

Cohen (1969) has studied the transient and stationary queue length distributions for the M/G/1, K queue, with a fixed maximum number of customers, K, in the system at any time. The present note applies Cohen's method to generalize his results to the MX/GY/1, K queue.
Stochastic bounds for heterogeneous-server queues with Erlang service times
Authors: Yu Oliver S.
Published: April 2006

This paper establishes stochastic bounds for the phasal departure times of a heterogeneous-server queue with a recurrent input and Erlang service times. The multi-server queue is bounded by a simple GI/E/1 queue. When the shape parameters of the Erlang service-time distributions of different servers are the same, these relations yield two-sided bounds for customer waiting times and the queue length, which can in turn be used with known results for single-server queues to obtain characterizations of steady-state distributions and heavy-traffic approximations.
Deviations from monotonicity of a Wiener process with drift
Authors: Brockwell P. J.
Published: April 2006

If X(t) is a Wiener process with EX(t) = vt and var X(t) = σ2t (where v > 0) and if M(t) = max0≦τ≦tX(τ) and Ta is the time of first passage through level a (where a > 0) we show that

where is the coefficient of variation of Ta. Applications of the result to the “maturity-time” representation of cell-growth and to queues with heavy traffic are discussed.
Total progeny in a multitype critical age dependent branching process with immigration
Authors: Weiner Howard J.
Published: April 2006

In a multitype critical age dependent branching process with immigration, the numbers of cell types born by t, divided by t2, tends in law to a one-dimensional (degenerate) law whose Laplace transform is explicitily given. The method of proof makes a correspondence between the moments in the m-dimensional case and the one-dimensional case, for which the corresponding limit theorem is known. Other applications are given, a possible relaxation of moment assumptions, and extensions are indicated.
The optimal linear solution of a symmetric team control problem
Authors: Whittle P. , Rudge J.
Published: April 2006

An optimal linear control (4) is deduced for the symmetric team control problem specified by relations (1)–(3). The generating function (6) for the optimal operator is in general irrational if there is more than one agent (controller), indicating that the recursions associated with effective state estimation are no longer of finite order, as in the single-agent case.
Almost sure limit points of record values
Authors: De Haan Laurens , Resnick Sidney I.
Published: April 2006

{Xn, n ≧ 1} are i.i.d. unbounded random variables with continuous d.f. F(x) =1 —e –R(x). Xj is a record value of this sequence if Xj >max {X1, …, Xj-1} The almost sure behavior of the sequence of record values {XLn} is studied. Sufficient conditions are given for lim supn→∞XLn/R–l(n)=ec, lim inf n → ∞XLn/R−1 (n) = e−c, a.s., 0 ≦ c ≦ ∞, and also for lim supn→∞ (XLn—R–1(n))/an =1, lim infn→∞ (XLn—R–1(n))/an = − 1, a.s., for suitably chosen constants an. The a.s. behavior of {XLn} is compared to that of the sequence {Mn}, where Mn = max {X1, …, Xn}. The method is to translate results for the case where the Xn's are exponential to the general case by means of an extended theory of regular variation.
Sufficient optimality conditions for control-limit policy in a semi-Markov process
Authors: Gertsbach I.
Published: April 2006

A finite-state semi-Markov process (SMP) with penalties is considered. A property which is similar to an increasing-hazard-rate property for a Markov chain is defined for an SMP. The SMP is controlled by shifts from the stateEitoimmediately after a transition has occurred. Conditions are given which guarantee that the optimal stationary Markovian policy belongs to a subclass of control-limit policies.
Optimal reserves growth under a Wiener process
Authors: Foster W. F.
Published: April 2006

This paper considers a body whose funds accumulate according to a Wiener Process that has parameters which can be controlled at any stage. The process is bounded above by a level at which dividends (or savings) are set aside, and it is bounded below by a level at which a ‘rescue’ policy is invoked to avoid insolvency. Taking long-term dividend maximisation as the optimality criterion, first passage times are used to derive a general first order differential equation for the optimal control of the system at any reserves level, and this equation is solved fully for a certain class of problems. Examples are given of insurance and investment applications.
A singular property of multiserver systems with constant service time
Authors: Halfin S.
Published: April 2006

The behavior of queuing systems with two servers and one waiting room is investigated. It is shown that if the service time is constant, then the difference between the times to service completion of the two servers (phase difference) tends to a constant, for increasing input intensities. This phenomenon holds for a wide class of arrival processes, but not when the service time has even a small variability. These results imply that the delay is not stochastically monotone in the input intensity. In general, we conjecture that the behavior of the phase differences, and delays, depends on whether the size of the waiting room is even or odd.
A limit theorem for two-locus diffusion models in population genetics
Authors: Ethier S. N.
Published: April 2006

A limit theorem of Kurtz for perturbed operator semigroups is applied to show that the two-locus diffusion model in population genetics (allowing for selection, mutation, and migration) converges to a linkage-equilibrium diffusion model as Nc →∞, where N is the population size and c is the recombination fraction; in fact, with an appropriate change of variables, the limiting diffusion is what has been called the independent-loci diffusion model. This generalizes a result of Littler.
Stability and characterisation conditions in negative programming
Authors: Whittle P.
Published: April 2006

Let F be the infinite-horizon minimal cost function, and FKS the minimal cost function for horizon s and terminal cost function K. In Section 2 we define the ‘stable domain' (the set of K for which ), determine some of its properties, and relate these to the questions of stability of the process (whether ) and whether a given solution of the dynamic programming equation can be identified with F These ideas are developed in Sections 3 and 5 for various strengthenings and weakenings of the hypothesis of non-negative costs. In Section 5 we derive a new sufficient condition for stability and for characterisation of F.
Strong consistency of a modified maximum likelihood estimator for controlled Markov chains
Authors: Doshi Bharat , Shreve Steven E.
Published: April 2006

A controlled Markov chain with finite state space has transition probabilities which depend on an unknown parameter α lying in a known finite set A. For each α, a stationary control law ϕ α is given. This paper develops a control scheme whereby at each stage t a parameter α t is chosen at random from among those parameters which nearly maximize the log likelihood function, and the control ut is chosen according to the control law ϕ αt. It is proved that this algorithm leads to identification of the true α under conditions weaker than any previously considered.
Relative extinction times for independent branching processes
Authors: Slud Eric
Published: April 2006

The conditional probability that a Galton-Watson process with initial population j dies out before an independent Galton-Watson process initially i, is computed asymptotically as i or j gets large, given that both processes eventually die out. The results are interpreted qualitatively to discuss parameters of fitness for biological populations, especially with respect to the spread of mutant genes under evolutionary models.
Bounds on the distance of a mixture from its parent distribution
Authors: Shaked Moshe
Published: April 2006

In a series of recent papers, Heyde (1975), Heyde and Leslie (1976), Hall (1979) and Brown (1980) obtained upper bounds on the uniform distance of a scale mixture from its parent distribution. Using a different technique we obtain further bounds which are more meaningful and superior in some applications. The new technique is then applied to obtain bounds on the uniform distance of a location mixture from its parent distribution. Comparison of the new bounds and the earlier ones is given.
Generalized semi-Markov decision processes
Authors: Doshi Bharat T.
Published: April 2006

Various authors have derived the necessary and sufficient conditions for optimality in semi-Markov decision processes in which the state remains constant between jumps. In this paper similar results are presented for a generalized semi-Markov decision process in which the state varies between jumps according to a Markov process with continuous sample paths. These results are specialized to a general storage model and an application to the service rate control in a GI/G/1 queue is indicated.
Random exchanges of information
Authors: Boyd David W. , Steele J. Michael
Published: April 2006

Suppose that n persons each know a different piece of information, and that whenever a pair of persons talk on the telephone each tells the other all the information that he knows at the time. If calls are made at random, we show that the expected number of calls necessary until everyone knows all n pieces of information is asymptotically 1.5 n log n. This sharpens an earlier result of J. W. Moon.
Collapsing supercritical branching processes
Authors: Daly Fergus
Published: April 2006

Characteristics of some collapsing supercritical stochastic population processes where an embedded Galton–Watson process can be isolated are shown to be identical to those of some associated subcritical process.
A diffusion approximation for correlation in queues
Authors: Woodside C. M. , Pagurek B. , Newell G. F.
Published: April 2006

A diffusion model is used to find heavy traffic approximate autocorrelation functions for several variables in queueing systems (i.e. for waiting time, system time, number in system and unfinished work). A table is given by which correlations can easily be found for each variable in any GI/G/1 queue. Further, the infinite sum or integral of the autocorrelations is also found, and the spectral density function. The sum has applications in statistical analysis of queues.

Extensive comparisons of approximate and exact correlations and their sums are reported, particularly for waiting times and system times, but also including number in system in M/M/1 queues. In general the correlations have similar accuracy to the probability distributions found by diffusion approximations. The percentage error is less for number in system than for waiting time.
A strong approximation for some non-stationary complex Gaussian processes
Authors: Breuer Peter
Published: April 2006

A strong approximation theorem is proved for some non-stationary complex-valued Gaussian processes and an explicit rate of convergence is achieved. The result answers a problem raised by S. Csörgő.
Best-choice problems involving uncertainty of selection and recall of observations
Authors: Petruccelli Joseph D.
Published: April 2006

This paper explores best choice problems which allow both recall of applicants and uncertainty of a current applicant accepting an offer of employment. Properties of optimal selection procedures are derived for the general case. Optimal procedures and the associated probabilities of obtaining the best applicant are found in two special cases. The results unify and extend those of Yang (1974) and Smith (1975).
Level crossings of a constructed process
Authors: Sharpe Ken
Published: April 2006

A method is presented for constructing a continuous, stationary process with a given rate of upcrossings at all levels and for which it is possible to find the exact distribution of the number of upcrossings, in an interval, at all levels.
Oscillating Brownian motion
Authors: Keilson Julian , Wellner Jon A.
Published: April 2006

An ‘oscillating' version of Brownian motion is defined and studied. ‘Ordinary' Brownian motion and ‘reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is established by using results of Stone (1963).
Extreme-value properties of the explosion-time distribution in a pure birth process
Authors: Feigin Paul D. , Yashchin Emmanuel
Published: April 2006

In each of a large number N of independent cells a breakdown mechanism is under way and proceeds until the first of the cells actually fails. At such a time, in each cell, the situation reverts to some initial state and the mechanism restarts. In this paper we consider those mechanisms for which breakdown may be modelled as the explosion of a pure birth process. Of interest is the distribution of time between failures and the possibility of estimating N and/or model parameters by observing a sequence of failure times. Saddlepoint approximation methods are used in the relevant extreme-value theory analysis for two important cases.
A note on some results of Schuh
Authors: Doney R. A.
Published: April 2006

We extend recent results of Schuh on the convergence of , where α ≧ 0 and Sn is the sum of n i.i.d. positive random variables to sums of the form for a large class of functions g, give simpler proofs than those of Schuh, and derive reformulations of the explosion criteria for Markov branching processes with discrete and continuous state space.
Non-strong mixing autoregressive processes
Authors: Andrews Donald W. K.
Published: April 2006

Certain first-order autoregressive processes are shown not to be strong mixing. A direct proof is given. This proof gives considerably more insight into the nature of the result than do proofs by contradiction. The result and proof help to clarify the relation between the autoregressive and strong mixing conditions.
Analysis of transient behaviour of certain processes with return to a central state
Authors: Buckholtz Peter G. , Campbell L. Lorne , Milbourne Ross D. , Wasan M. T.
Published: April 2006

In economics, cash management problems may be modelled by birth-death processes which reset to central states when a boundary is reached. The nature of the transient behaviour of the probability distribution of such processes symmetric about a central state is investigated. A diffusion approximation of such processes is given and the transient probability behaviour derived from the diffusion equation.
On the best-choice problem when the number of observations is random
Authors: Petruccelli Joseph D.
Published: April 2006

We consider the problem of maximizing the probability of choosing the largest from a sequence of N observations when N is a bounded random variable. The present paper gives a necessary and sufficient condition, based on the distribution of N, for the optimal stopping rule to have a particularly simple form: what Rasmussen and Robbins (1975) call an s(r) rule. A second result indicates that optimal stopping rules for this problem can, with one restriction, take virtually any form.
Stationary queue-length characteristics in queues with delayed feedback
Authors: König Dieter , Schmidt Volker
Published: April 2006

A class of two-node queueing networks with general stationary ergodic governing sequence is considered. This means that, in particular, a non-Poissonian arrival process and dependent service times, as well as a non-Bernoulli feedback mechanism are admitted. A mixing condition ensures that the limiting distributions of the number of customers in the nodes observed in continuous time as well as at certain embedded epochs can be expressed by the Palm distributions of appropriately chosen marked point processes. This gives the possibility of connecting the classical concept of embedding with a general point-process approach. Furthermore, it leads to simple proofs of relationships between the limiting distributions. An example is given to illustrate how these relationships can be used to derive explicit formulas for various stationary queueing characteristics.
A coupling proof of weak convergence
Authors: Guttorp Peter , Kulperger Reg , Lockhart Richard
Published: April 2006

Weak convergence to reflected Brownian motion is deduced for certain upwardly drifting random walks by coupling them to a simple reflected random walk. The argument is quite elementary, and also gives the right conditions on the drift. A similar argument works for a corresponding continuous-time problem.
Population-size-dependent branching process with linear rate of growth
Authors: Klebaner F. C.
Published: April 2006

The process we consider is a binary splitting, where the probability of division, , depends on the population size, 2i. We show that Zn converges to ∞ almost surely on a set of positive probability. Zn/n converges in distribution to a proper limit, diverges almost surely on converges almost surely on and there are no constants cn such that Zn/cn converges in probability to a non-degenerate limit.
Limit theorems for the shifting level process
Authors: Cline Daren B. H.
Published: April 2006

This paper studies the asymptotic properties of moment estimators for the general shifting level process (SLP). A law of large numbers and a weak convergence theorem are obtained under conditions involving the unobservable processes which make up SLP. Specific conditions about those underlying processes are added to give explicit results, applicable to a large class of moment estimators. Actual formulae for asymptotic variances, etc. are obtained for a simple example, the GNN model.
Variances and covariances of the grade sizes in manpower systems
Authors: Vassiliou P.-C. G. , Gerontidis I.
Published: April 2006

The asymptotic behaviour of the variances and covariances of the class sizes in closed and open manpower systems is considered. Firstly, the homogeneous case is studied and a theorem is stated which provides the answer to the problem in the most general case for the homogeneous Markov-chain models in manpower systems (open systems) and social mobility models (closed systems). Secondly, the non-homogeneous problem is studied and a theorem is given where under certain conditions it is proved that the vector sequences of means, variances and covariances converge. Finally, we relate our theoretical results to examples from the literature on manpower planning.
A nearly independent, but non-strong mixing, triangular array
Authors: Andrews Donald W. K.
Published: April 2006

The condition of strong mixing for triangular arrays of random variables is a common condition of weak dependence. In this note, it is shown that this condition is not as general as one might believe. In particular, it is shown that there exist triangular arrays of first-order autoregressive random variables which converge almost surely to an independent identically distributed sequence of random variables and for which the central limit theorem holds, but which are not strong mixing triangular arrays. Hence, the strong mixing condition is more restrictive than desired.
Simple derivations of the invariance relations and their applications
Authors: Miyazawa Masakiyo
Published: April 2006

In the literature, various methods have been studied for obtaining invariance relations, for example, L = λW (Little's formula), in queueing models. Recently, it has become known that the theory of point processes provides a unified approach to them (cf. Franken (1976), König et al. (1978), Miyazawa (1979)). This paper is also based on that theory, and we derive a general formula from the inversion formula of point processes. It is shown that this leads to a simple proof for invariance relations in G/G/c queues. Using these results, we discuss a condition for the distribution of the waiting time vector of a G/G/c queue to be identical with that of an M/G/c queue.
On the first-passage times of pure jump processes
Authors: Shaked Moshe , Shanthikumar J. George
Published: April 2006

Let Tx be the time it takes for a pure jump process, which starts at 0, to cross a threshold x > 0. Sufficient conditions on the parameters of this process under which Tx has increasing failure rate average (IFRA), increasing failure rate (IFR) or logconcave density (PF2) are identified. The conditions for IFRA are weaker than those of Drosen (1986). Sufficient conditions on the parameter of a pure jump process for Tx to the IFR or PF2 are not available in the literature.
Limit laws for kth order statistics from conditionally mixing arrays of random variables
Authors: Dziubdziela W.
Published: April 2006

We present sufficient conditions for the weak convergence of the distributions of the kth order statistics from a conditionally mixing array of random variables to limit laws which are represented in terms of a mixed compound Poisson distribution.
Stopping rules for proofreading
Authors: Ferguson T. S. , Hardwick J. P.
Published: April 2006

A manuscript with an unknown random number M of misprints is subjected to a series of proofreadings in an effort to detect and correct the misprints. On the nthproofreading, each remaining misprint is detected independently with probability pn– 1. Each proofreading costs an amount CP > 0, and if one stops after n proofreadings, each misprint overlooked costs an amount cn > 0. Two models are treated based on the distribution of M. In the Poisson model, the optimal stopping rule is seen to be a fixed sample size rule. In the binomial model, the myopic rule is optimal in many important cases. A generalization is made to problems in which individual misprints may have distinct probabilities of detection and distinct overlook costs.
Optimal consumption with stochastic prices in continuous time
Authors: Björk T. , Myhrman J. , Persson M.
Published: April 2006

In this paper we consider an economic agent (the consumer) having initial wealth x(0), which he is allowed to spend during the time interval [0, T]. There are N consumer goods, the prices of which are described by a system of stochastic differential equations, and the consumer can spend his money as he pleases provided that he does not get into debt. The consumer's problem is to maximize his expected utility over [0, T]. Given a separable utility function we show that the optimal consumption policy is linear in the wealth variable regardless of the structure of the price system, and if we assume that the price processes are geometric Brownian motions we can give the optimal consumption policy explicitly.
Run probabilities and the motion of a particle on a given path
Authors: Soltani A. Reza , Khodadadi A.
Published: April 2006

Let {Xn} be a sequence of independent (or Markov dependent) trials taking values in a given set S. Let JR be a given path of length k in S, i.e. R is a run of length k whose elements come from S. {Xn} may indicate the motion of a particle on S. We consider the problem of finding the probability that at trial m, the particle has for the first time moved length l ≦ k on R which is equivalent to finding the probability of the first occurrence of any subrun of length l ≦ k of R. In the case of l = k this gives the result of Schwager [6].
Asymptotic periodicity of the variances and covariances of the state sizes in non-homogeneous Markov systems
Authors: Tsaklidis G. , Vassiliou P.-C. G.
Published: April 2006

In this paper we study the asymptotic periodicity of the sequence of means, variances and covariances of the state sizes of non-homogeneous Markov systems. It is proved that under the assumption that the sequence of the extended stochastic transition matrices converge to a matrix which is an irreducible stochastic matrix of period d, and all the matrices in this sequence have the same incidence matrix, then the sequence of means, variances and covariances splits into d subsequences which converge. Finally, we discuss the application of the present results in a manpower system.
Criteria for the non-ergodicity of stochastic processes: application to the exponential back-off protocol
Authors: Fayolle Guy , Iasnogorodski Rudolph
Published: April 2006

In this paper, we present some simple new criteria for the non-ergodicity of a stochastic process (Yn), n ≧ 0 in discrete time, when either the upward or downward jumps are majorized by i.i.d. random variables. This situation is encountered in many practical situations, where the (Yn) are functionals of some Markov chain with countable state space. An application to the exponential back-off protocol is described.
Joint distribution of successive zero crossing distances for stationary Gaussian processes
Authors: Rychlik Igor
Published: April 2006

As has been shown by de Maré, in a stationary Gaussian process the length of the successive zero-crossing intervals cannot be independent, except for the degenerate case of a pure cosine process. However, no closed-form expression of the distribution of these quantities is known at present. In this paper we present an accurate explicit approximative formula, derived by replacing the Slepian model process by its regression curve.
Chords through a convex body generated from within an embedded body
Authors: Enns E. G. , Ehlers P. F.
Published: April 2006

A body E is completely embedded within a convex body G. A line segment is generated by a measure depending only on E or on both E and G. This line segment is then projected to the surface of G in one or both directions. The distributions of selected line segments of this type are derived.
Some results concerning random arcs on the circle
Authors: Huffer Fred W.
Published: April 2006

Random arcs having random sizes are placed on a circle. Let V be the length of the uncovered portion of the circle and G be the number of uncovered gaps on the circle. Results are presented concerning the joint moments of V and G and the conditional distribution of V given G.
A stochastic explosive reaction system with sampling
Authors: Dawson Donald A. , Fleischmann Klaus
Published: April 2006

Large stochastic systems of marked particles are considered. These ‘populations' grow according to pairwise mutually catalytic reactions and in addition particles may exchange their type (mark) by a sampling procedure. We are interested in the explosive behavior of the model and its high density properties (law of large numbers).
On the non-closure under convolution of the subexponential family
Authors: Leslie J. R.
Published: April 2006

A distribution F of a non-negative random variable belongs to the subexponential family of distributions S if 1 – F(2)(x) ~ 2(1 – F(x)) as x →∞. This family is of considerable interest in branching processes, queueing theory, transient renewal theory and infinite divisibility theory. Much is known about the kind of distributions that belong to S but the question of whether S is closed under convolution has remained unresolved for some time. This paper contains an example which demonstrates that S is not in fact closed.
A perturbation method for solving some queues with processor sharing discipline
Authors: Sengupta Bhaskar
Published: April 2006

In this paper, we present a perturbation method of solving a second-order difference equation with variable coefficients with some additional assumptions. This method can be used to devise an algorithmic solution for the moments of sojourn times in some processor sharing queues. In particular, we examine three queues. The first has exponential service and a fairly general interrupted arrival mechanism. The second is a cyclic queue. The third is a model for a computer system in which finite and infinite sources interact.
Orthant probabilities and Gaussian Markov processes
Authors: Moran P. A. P.
Published: April 2006

A method is given for calculating the probability that n terms of a Gaussian first-order autoregressive series lie between any specified limits where n may be as large as 20 or more.
NBUE and NWUE properties of increasing Markov processes
Authors: Karasu Izi , Özekici Süleyman
Published: April 2006

Consider a device that deteriorates in time according to an increasing Markov process so that it fails as soon as a critical threshold is exceeded. NBUE and NWUE properties of the lifetime of the device are identified to extend the existing literature on the PFr, IFR, IFRA, and NBU cases. In particular, it is shown that NBUE and NWUE characterizations can be made through a monotonicity property on the potential operator of the Markov process.
Next-fit bin packing with random piece sizes
Authors: Halfin Shlomo
Published: April 2006

Investigations into time-slotted communication channels for transmission of data packets led us to analyze the stochastic behavior of the next-fit bin packing algorithm. In this paper we obtain results for general piece-size distributions and truncated distributions, we calculate explicit solutions for the case of the truncated exponential, and we apply the results to calculate the maximal throughput of the time-slotted communication channel.
Realization probability and throughput sensitivity in a closed jackson network
Authors: Cao Xi-Ren
Published: April 2006

Realization probability is a new concept pertaining to perturbation analysis of closed queuing networks. The sensitivities of throughputs in a closed single-class Jackson network can be expressed in terms of realization probabilities. In this paper, based on a discussion of perturbation analysis for networks with state-dependent service rates, we derive some new formulas for sensitivities of throughputs using realization probability.
Some bounds on reliability of coherent systems of IFRA components
Authors: Chaudhuri Gopal , Deshpande Jayant V. , Dharmadhikari Avinash D.
Published: April 2006

In this paper we find new bounds for the reliability of coherent systems of independent components with increasing failure rate average (IFRA) lifetimes. These bounds are based on certain bounds available for the survival functions of IFRA random variables and the fact that the IFRA class of life distributions is closed under the formation of coherent systems. These bounds are compared with other applicable bounds in this case. An illustration of explicit computations of the bounds is provided for the bridge structure with components having independent gamma life distributions.
Absorption and first-passage times for a compound Poisson process in a general upper boundary
Authors: Gallot S. F. L.
Published: April 2006

This paper considers the absorption of a non-decreasing compound Poisson process of finite order in a general upper boundary. The problem is relevant in fields such as risk theory, Kolmogorov–Smirnov statistics and sequential analysis. The probability of absorption and first-passage times are given in terms of a generating function which depends on the boundary only and can be computed readily. Absorption is certain or not as the asymptotic slope of the boundary is greater or less than the expected increase of the process in unit time. The case of the linear boundary is considered in detail.
On the serial correlation for number in system in the stationary GI/M/1 bulk arrival and GI/Em/1 queues
Authors: Stanford D. A. , Pagurek B.
Published: April 2006

The generating functions for the serial covariances for number in system in the stationary GI/M/1 bulk arrival queue with fixed bulk sizes, and the GI/Em/1 queue, are derived. Expressions for the infinite sum of the serial correlation coefficients are also presented, as well as the first serial correlation coefficient in the case of the bulk arrival queue. Several numerical examples are considered.
Further counterexamples to the monotonicity property of t-step maintainable structures
Authors: Haigh John
Published: April 2006

Until Guerry's (1990) counterexample to a conjecture of Davies about three-state hierarchical organisations kept at constant size via annual promotion, wastage and recruitment, it was easy to believe that such structures maintainable in t steps would also be maintainable in t + 1 steps. Here we present further counterexamples, which show that t-step maintainability does not imply (t + 1)-step maintainability, for astonishingly large values of t.
A boundary-crossing result for Brownian motion
Authors: Scheike Thomas H.
Published: April 2006

In this paper we obtain a new crossing result for Brownian motion. The boundary studied is a piecewise linear function consisting of two lines. The expression obtained for the boundary crossing probability is of a simple directly computable form.
On remaining full busy periods of GI/G/c queues and their relation to stationary point processes
Authors: Ghahramani Saeed
Published: April 2006

For a GI/G/c queue, a full busy period is a period commencing when an arrival finds c − 1 customers in the system and ending when, for the first time after that, a departure leaves behind c − 1 customers in the system. We show that given a full busy period is found to be in progress at a random epoch, the remaining full busy period has the equilibrium distribution. Moreover, we demonstrate that this property is typical for a broad class of stationary random processes.
Extreme values of the cyclostationary Gaussian random process
Authors: Konstant D. G. , Piterbarg V.I.
Published: April 2006

In this paper the class of cyclostationary Gaussian random processes is studied. Basic asymptotics are given for the class of Gaussian processes that are centered and differentiable in mean square. Then, under certain conditions on the non-degeneration of the centered cyclostationary Gaussian process with integrable covariance functions, the Gnedenko-type limit formula

is established for and all x > 0.
A note on sojourn times in queuing networks with multiserver nodes
Authors: Hemker Josef
Published: April 2006

Time-reversal arguments can be used to re-derive (and slightly generalize) previous results for sojourn-time distributions in product-form queuing networks.
Steady-state Markov chain models for the Heine and Euler distributions
Authors: Kemp A. W.
Published: April 2006

The paper puts forward steady-state Markov chain models for the Heine and Euler distributions. The models for oil exploration strategies that were discussed by Benkherouf and Bather (1988) are reinterpreted as current-age models for discrete renewal processes. Steady-state success-runs processes with non-zero probabilities that a trial is abandoned, Foster processes, and equilibrium random walks corresponding to elective M/M/1 queues are also examined.
Asymptotic variance parameters for the boundary local times of reflected Brownian motion on a compact interval
Authors: Williams R. J.
Published: April 2006

A direct derivation is given of a formula for the normalized asymptotic variance parameters of the boundary local times of reflected Brownian motion (with drift) on a compact interval. This formula was previously obtained by Berger and Whitt using an M/M/1/C queue approximation to the reflected Brownian motion. The bivariate Laplace transform of the hitting time of a level and the boundary local time up to that hitting time, for a one-dimensional reflected Brownian motion with drift, is obtained as part of the derivation.