We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial ... more We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative-binomial experiment having the same p.
We investigate the one-dimensional telegraph random process in the presence of an elastic boundar... more We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or negative). When the particle hits the origin, it is either absorbed, with probability α, or reflected upwards, with probability 1 − α. In the case of exponentially distributed random times between consecutive changes of direction, we obtain the distribution of the renewal cycles and of the absorption time at the origin. This investigation is performed both in the case of motion starting from the origin and non-zero initial state. We also study the probability law of the process within a renewal cycle.
Professor emeritus Lajos Takács passed away on December 4, 2015, in Cleveland Heights, Ohio. He i... more Professor emeritus Lajos Takács passed away on December 4, 2015, in Cleveland Heights, Ohio. He is survived by his wife Dalma, their two daughters Judith and Susan, and their families. Lajos Takács will be remembered as a brilliant mathematician, a groundbreaking contributor to the theory of stochastic processes, a world-leading queueing theorist, and a very kind person. We provide here a short biography and a discussion of his main contributions to queueing and fluctuation theory.
We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the... more We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the largest value of t (the Frobenius number g(a1,. .. , a d)) such that d k=1 m k a k = t has no solution in nonnegative integers m1,. .. , m d. We introduce a method to compute upper bounds for g(a1, a2, a3), which seem to grow considerably slower than previously known bounds. Our computations are based on a formula for the restricted partition function, which involves Dedekind-Rademacher sums, and the reciprocity law for these sums.
The paper is focused on the problem of estimating the probability p of individual contaminated sa... more The paper is focused on the problem of estimating the probability p of individual contaminated sample, under group testing. The precision of the estimator is given by the probability of proportional closeness, a concept defined in the Introduction. Twostage and sequential sampling procedures are characterized. An adaptive procedure is examined.
We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the... more We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the largest value of t (the Frobenius number) such that d k=1 m k a k = t has no solution in nonnegative integers m1,. .. , m d. Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by √ a1a2a3 5/4 − a1 − a2 − a3.
, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection w... more , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the TI-ade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Natalie Johnson; manufacturing supervised by Robert Paella.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Summary In a recent paper [7] the authors studied the optimal control policy of the following que... more Summary In a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.
Under purely sequential sampling schemes, a theory is developed for the exact determination of th... more Under purely sequential sampling schemes, a theory is developed for the exact determination of the distributions of two classes of stopping variables (rules) in order to handle point estimation problems for the parametric functionals in an exponential distribution. Explicit formulae are derived for the expected value and risks of sequential estimators of the mean, failure rate, and reliability function of an exponential distribution. These are utilized to compare performances of several competing estimators of the mean and the failure rate. Recommended by Ben Boukai
The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arriva... more The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arrival rate λ0 of customers shifts at unknown epoch, τ, to a known value, λ1. The service intensity of the system starts at μ0 and can be increased at most N times to μ1 < μ2 < · · · < μN. The cost structure consists of the cost changing μi to μj (i + 1 ≦ j ≦ N); of maintaining service at rate μ (per unit of time) and of holding customers at the station (per unit of time). Adaptation policies are constrained by the fact that μ can be only increased. A Bayes solution is derived, under the prior assumption that τ has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future.
We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial ... more We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative-binomial experiment having the same p.
We investigate the one-dimensional telegraph random process in the presence of an elastic boundar... more We investigate the one-dimensional telegraph random process in the presence of an elastic boundary at the origin. This process describes a finite-velocity random motion that alternates between two possible directions of motion (positive or negative). When the particle hits the origin, it is either absorbed, with probability α, or reflected upwards, with probability 1 − α. In the case of exponentially distributed random times between consecutive changes of direction, we obtain the distribution of the renewal cycles and of the absorption time at the origin. This investigation is performed both in the case of motion starting from the origin and non-zero initial state. We also study the probability law of the process within a renewal cycle.
Professor emeritus Lajos Takács passed away on December 4, 2015, in Cleveland Heights, Ohio. He i... more Professor emeritus Lajos Takács passed away on December 4, 2015, in Cleveland Heights, Ohio. He is survived by his wife Dalma, their two daughters Judith and Susan, and their families. Lajos Takács will be remembered as a brilliant mathematician, a groundbreaking contributor to the theory of stochastic processes, a world-leading queueing theorist, and a very kind person. We provide here a short biography and a discussion of his main contributions to queueing and fluctuation theory.
We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the... more We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the largest value of t (the Frobenius number g(a1,. .. , a d)) such that d k=1 m k a k = t has no solution in nonnegative integers m1,. .. , m d. We introduce a method to compute upper bounds for g(a1, a2, a3), which seem to grow considerably slower than previously known bounds. Our computations are based on a formula for the restricted partition function, which involves Dedekind-Rademacher sums, and the reciprocity law for these sums.
The paper is focused on the problem of estimating the probability p of individual contaminated sa... more The paper is focused on the problem of estimating the probability p of individual contaminated sample, under group testing. The precision of the estimator is given by the probability of proportional closeness, a concept defined in the Introduction. Twostage and sequential sampling procedures are characterized. An adaptive procedure is examined.
We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the... more We study the Frobenius problem: given relatively prime positive integers a1,. .. , a d , find the largest value of t (the Frobenius number) such that d k=1 m k a k = t has no solution in nonnegative integers m1,. .. , m d. Based on empirical data, we conjecture that except for some special cases the Frobenius number can be bounded from above by √ a1a2a3 5/4 − a1 − a2 − a3.
, except for brief excerpts in connection with reviews or scholarly analysis. Use in connection w... more , except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc., in this publication, even if the former are not especially identified, is not to be taken as a sign that such names, as understood by the TI-ade Marks and Merchandise Marks Act, may accordingly be used freely by anyone. Production managed by Natalie Johnson; manufacturing supervised by Robert Paella.
DOI to the publisher's website. • The final author version and the galley proof are versions of t... more DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers. Link to publication General rights Copyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright owners and it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the purpose of private study or research. • You may not further distribute the material or use it for any profit-making activity or commercial gain • You may freely distribute the URL identifying the publication in the public portal. If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement:
Summary In a recent paper [7] the authors studied the optimal control policy of the following que... more Summary In a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.
Under purely sequential sampling schemes, a theory is developed for the exact determination of th... more Under purely sequential sampling schemes, a theory is developed for the exact determination of the distributions of two classes of stopping variables (rules) in order to handle point estimation problems for the parametric functionals in an exponential distribution. Explicit formulae are derived for the expected value and risks of sequential estimators of the mean, failure rate, and reliability function of an exponential distribution. These are utilized to compare performances of several competing estimators of the mean and the failure rate. Recommended by Ben Boukai
The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arriva... more The paper studies the problem of optimal adaptation of an M/M/1 queueing station, when the arrival rate λ0 of customers shifts at unknown epoch, τ, to a known value, λ1. The service intensity of the system starts at μ0 and can be increased at most N times to μ1 < μ2 < · · · < μN. The cost structure consists of the cost changing μi to μj (i + 1 ≦ j ≦ N); of maintaining service at rate μ (per unit of time) and of holding customers at the station (per unit of time). Adaptation policies are constrained by the fact that μ can be only increased. A Bayes solution is derived, under the prior assumption that τ has an exponential distribution. This solution minimizes the total expected discounted cost for the entire future.
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