248 results
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2. AN ANALYSIS OF AIR FORCE EOQ DATA WITH AN APPLICATION TO REORDER POINT CALCULATION.
- Author
-
Mitchell, C. R., Rappold, R. A., and Faulkner, W. B.
- Subjects
PRODUCTION management (Manufacturing) ,PROJECT management ,INVENTORY control ,LEAD time (Supply chain management) ,SUPPLY chain management ,POISSON processes ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,SUPPLY & demand ,MATHEMATICAL optimization - Abstract
One of the important uses of an EOQ item's distribution of lead time demand is to set its reorder point. This paper shows that a realistic model of observed demand patterns can be chosen from the compound Poisson family of distributions. Actual historical data from several U.S. Air Force bases are analyzed using the geometric-Poisson and constant-Poisson distributions. The control discipline is order quantity, reorder point with continuous review. The service level is based on percent of demand supplied during lead time and is consistent with current USAF methodology. The reorder point is based on independent calculations and no attempt is made to jointly optimize the order quantity and reorder point. Lead time is assumed to be known and constant. [ABSTRACT FROM AUTHOR]
- Published
- 1983
- Full Text
- View/download PDF
3. ADAPTIVE FORECASTING MODELS BASED ON PREDICTIVE DISTRIBUTIONS.
- Author
-
Winkler, Robert L., Smiths, Wayne S., and Kulkarni, Ram B.
- Subjects
FORECASTING ,ECONOMIC forecasting ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,LINEAR programming ,MATHEMATICAL programming ,PAVEMENT maintenance & repair ,MANAGEMENT science ,MATHEMATICAL models - Abstract
The availability of data regarding variables of interest in forecasting problems is sometimes limited, but experts may possess a great deal of relevant information. The approach taken in this paper involves the development of adaptive forecasting models based on such information. Since the models and their parameters are difficult to consider intuitively, information from the experts is elicited in terms of predictive distributions of the variable to be forecasted. Various models can then be considered, and attempting to "fit" a model to the predictive distributions is analogous to attempting to fit a model to a set of observations. This general approach to forecasting is developed in this paper, and a specific model, a linear model with normally distributed errors, is considered in some detail. An actual application involving the forecasting of fatigue life of asphalt pavements illustrates the development of forecasting models from experts' predictive distributions. [ABSTRACT FROM AUTHOR]
- Published
- 1978
- Full Text
- View/download PDF
4. SCORING RULES FOR CONTINUOUS PROBABILITY DISTRIBUTIONS.
- Author
-
Matheson, James E. and Winkler, Robert L.
- Subjects
DECISION making ,DISTRIBUTION (Probability theory) ,SIMULATION methods & models ,STATISTICAL correlation ,MATHEMATICAL statistics ,STATISTICAL hypothesis testing ,PROBABILITY theory ,SCORING rubrics ,MATHEMATICAL models - Abstract
Personal, or subjective, probabilities are used as inputs to many inferential and decision-making models, and various procedures have been developed for the elicitation of such probabilities. Included among these elicitation procedures are scoring rules, which revolve the computation of a score based on the assessor's stated probabilities and on the event that actually occurs. The development of scoring rules has, in general, been restricted to the elicitation of discrete probability distributions. In this paper, families of scoring rules for the elicitation of continuous probability distributions are developed and discussed. [ABSTRACT FROM AUTHOR]
- Published
- 1976
- Full Text
- View/download PDF
5. A QUEUING SYSTEM WITH SERVICE-TIME DISTRIBUTION OF MIXED CHI-SQUARED TYPE.
- Author
-
Wishart, David M. G.
- Subjects
MARKOV processes ,QUEUING theory ,STATISTICAL correlation ,DISTRIBUTION (Probability theory) ,PRODUCTION scheduling ,PROBABILITY theory ,STOCHASTIC processes - Abstract
In this paper Kendall's technique of the embedded Markov chain
[5] is applied to a queuing system `with general independent input and a wide class of service-time distributions The matrix of transition probabilities is found to be formally identical `with that discussed in our earlier study,[9] which will be taken as read in the present paper Using the results of reference 9 we can write down the equilibrium distribution of waiting-times for customers in the more general system in terms of the roots of a transcendental equation An example is considered that arose in Bailey's study of hospital systems[1] [ABSTRACT FROM AUTHOR]- Published
- 1959
- Full Text
- View/download PDF
6. CHANCE-CONSTRAINED PROGRAMMING.
- Author
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Charnes, A. and Cooper, W.W.
- Subjects
STOCHASTIC programming ,LINEAR programming ,PROBABILITY measures ,DISTRIBUTION (Probability theory) ,MANUFACTURING processes ,HUMAN error ,DECISION making ,DECISION theory ,OPTIMAL designs (Statistics) ,RANDOM variables ,THEORY of constraints ,PROBABILITY theory - Abstract
A new conceptual and analytical vehicle for problems of temporal planning under uncertainty, involving determination of optimal (sequential) stochastic decision rules is defined and illustrated by means of a typical industrial example. The paper presents a method of attack which splits the problem into two non-linear (or linear) programming parts, (i) determining optimal probability distributions, (ii) approximating the optimal distributions as closely as possible by decision rules of prescribed form. [ABSTRACT FROM AUTHOR]
- Published
- 1959
- Full Text
- View/download PDF
7. An Algorithm for Fitting Heavy-Tailed Distributions via Generalized Hyperexponentials.
- Author
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Kaiqi Yu, Mei-Ling Huang, and Brill, Percy H.
- Subjects
DISTRIBUTION (Probability theory) ,COMPUTER algorithms ,PROBABILITY theory ,ESTIMATION theory ,LOGNORMAL distribution ,WEIBULL distribution ,PARETO analysis - Abstract
In this paper, we propose an algorithm to fit heavy-tailed (HT) distribution functions by generalized hyperexponential (GH) distribution functions. A discussion of the steps, usage, and accuracy of the GH algorithm is given. Several examples in this paper show that the proposed method can be applied to fit HT distributions with a completely monotone probability density function (pdf) very well, like the Pareto distribution and the Weibull distribution with the shape parameter less than one, as well as HT distributions whose pdf is not completely monotone, like the lognormal distribution. In addition, we provide an example that shows that the proposed method can be applied to density estimation of real data presenting a heavy tail. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
8. The Pht/Pht ∞ Queueing System: Part I--The Single Node.
- Author
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Nelson, Barry L. and Taaffe, Michael R.
- Subjects
QUEUING theory ,PRODUCTION scheduling ,STOCHASTIC processes ,MANAGEMENT science ,DISTRIBUTION (Probability theory) ,PROBABILITY theory - Abstract
We develop a numerically exact method for evaluating the time-dependent mean, variance, and higher- order moments of the number of entities in a Ph
t /Pht /∞ queueing system. We also develop a numerically exact method for evaluating the distribution function and moments of the virtual sojourn time for any time t; in our setting, the virtual sojourn time is equivalent to the service time for virtual entities arriving to the system at that time t. We include several examples using software that we have developed and have put in downloadable form in the Online Supplement to this paper on the journal's website. [ABSTRACT FROM AUTHOR]- Published
- 2004
- Full Text
- View/download PDF
9. Validation of Trace-Driven Simulation Models: Bootstrap Tests.
- Author
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Kleijnen, Jack P. C., Cheng, Russell C. H., and Bettonvil, Bert
- Subjects
SIMULATION methods & models ,STATISTICAL bootstrapping ,STATISTICAL sampling ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,MONTE Carlo method ,MANAGEMENT science ,MATHEMATICAL models ,QUEUING theory - Abstract
Trace-driven (or correlated inspection) simulation means that the simulated and the real systems have some common inputs (say, historical arrival times) so that the two systems' outputs are cross-correlated. To validate such a simulation, this paper focuses on the difference between the average simulated and real responses. To evaluate this validation statistic, the paper develops a novel bootstrap technique--based on replicated runs. This validation statistic and the bootstrap technique are evaluated in extensive Monte Carlo experiments with specific single-server queues. These experiments show acceptable Type-I and Type-II error probabilities. [ABSTRACT FROM AUTHOR]
- Published
- 2001
- Full Text
- View/download PDF
10. Sequential Stopping Rules for Fixed-Sample Acceptance Tests.
- Author
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Chang, R. C. and Ehrenfeld, S.
- Subjects
DISTRIBUTION (Probability theory) ,BAYESIAN analysis ,PRODUCT acceptance ,CHEBYSHEV approximation ,PROBABILITY theory ,DECISION making ,BERNOULLI hypothesis (Risk) ,STOCHASTIC processes - Abstract
This paper discusses optimal stopping rules for fixed-sample acceptance tests where the observations with time delays are obtained sequentially. It studies two cases, one with a known prior distribution and the other one without a prior distribution, discusses Bayes-optimal and minimax stopping rules, and considers a stopping rule using the maximum likelihood estimate of θ, the probability of a single success. An example is given assuming that the prior distribution is a beta distribution. It is shown that the Bayes-optimal stopping rule thus obtained approaches the stopping rule using the maximum likelihood estimate when the beta parameters, α and β, approach zero. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
11. ON THE EVALUATION OF COMPOUND OPTIONS.
- Author
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Selby, Michael J.P. and Hodges, Stewart D.
- Subjects
OPTIONS (Finance) ,CONTINGENT valuation ,VALUATION ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,ECONOMIC models ,ALGORITHMS ,MATHEMATICAL formulas ,MATHEMATICAL models ,PROBLEM solving ,INTEGRALS - Abstract
Compound option valuation formulae give rise to the summation of a series of multinormal distribution functions. This paper presents an identity on sums of nested multinormal distributions of arbitrary dimension. We show that this identity generalizes some well-known low order identities for the multinormal distribution. We present three applications of the new identity to contingent claims valuation problems. The first and second applications show that by reducing significantly the number of integrals to be evaluated, faster and more accurate algorithms can be developed for implementing the Geske-Johnson American put valuation formula and the Roll-Geske-Whaley American call formula; the third gives new economic insights into the valuation of disaggregated coupon bonds. [ABSTRACT FROM AUTHOR]
- Published
- 1987
- Full Text
- View/download PDF
12. Modeling Distribution Problems with Time Windows. Part II: Two Customer Types.
- Author
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Daganzo, Carlos F.
- Subjects
DISTRIBUTION (Probability theory) ,PHYSICAL distribution of goods ,PRODUCTION scheduling ,TRANSPORTATION ,PROBABILITY theory ,TIME series analysis ,CONSUMERS ,VEHICLES - Abstract
This paper extends the results of a previous study concerning distribution with time windows. It is recognized that customers who do not need to be allocated to a time window should receive different service than the rest. Three strategies were studied to accomplish that: stratified service, discriminating service, and staggered and discriminating service. Of these, the last strategy yields the lowest local distribution distance per customer, a distance which can be less than hall that for the strategy explained in the previous paper (joint service). Stratified service, however, can yield a lower line-haul distance per customer than staggered and discriminating service. In a specific case, a numerical comparison between stratified service and staggered and discriminating service should determine the overall best choice. This choice notwithstanding, the best strategy involves overlapping vehicle tours. The conventional wisdom of dividing customers into non-overlapping clusters for vehicle muting does not seem attractive for distribution problems with time windows. [ABSTRACT FROM AUTHOR]
- Published
- 1987
- Full Text
- View/download PDF
13. RANDOM BINARY SEARCH: A RANDOMIZING ALGORITHM FOR GLOBAL OPTIMIZATION IN R.
- Author
-
Zemel, Eitan
- Subjects
ALGORITHMS ,MATHEMATICAL optimization ,STOCHASTIC processes ,ITERATIVE methods (Mathematics) ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,STATISTICAL sampling ,MATHEMATICS ,OPERATIONS research - Abstract
Randomizing (stochastic) global optimization algorithms can be viewed as sampling procedures, where at each iteration a local optimum is sampled from the set of local optima. The effectiveness of such an algorithm depends crucially on the sampling distribution, i.e., on the probabilities of sampling the various local optima. There exists a very large body of research on stochastic global optimization. However, very little is known about the sampling distribution itself and, in particular, on the specific way in which it depends on the function being optimized, on the region in which the search takes place, and on the optimization routine. In this paper we set out to examine these issues in some detail and present some first results in this direction. The case analyzed in this paper is the optimization of a one-dimensional function using a randomizing version of binary search. We give an effective (computable in quadratic time) formula for the sampling distribution and obtain various interesting properties of this distribution which are relevant to the behavior of the algorithm in practice. We also discuss some issues related to adaptive search. [ABSTRACT FROM AUTHOR]
- Published
- 1986
- Full Text
- View/download PDF
14. A DIFFUSION APPROXIMATION FOR AN M/G/m QUEUE WITH GROUP ARRIVALS.
- Author
-
Kimura, Toshikazu and Ohsone, Tadashi
- Subjects
APPROXIMATION theory ,QUEUING theory ,PROBABILITY theory ,FUNCTIONAL analysis ,MANAGEMENT science ,PRODUCTION scheduling ,DISTRIBUTION (Probability theory) ,CLIENT/SERVER computing ,STAGNATION (Economics) ,CUSTOMER services ,INVENTORY management systems ,DATA transmission systems - Abstract
This paper deals with the M/G/m queueing system with group arrivals. Using a diffusion approximation, we present approximate formulae for the steady-state distribution of the number of customers in the system. From this distribution, approximate formulae for some queueing characteristics such as the delay probability and the mean queue length are derived. In order to check the accuracy of the approximate formulae, they are numerically tested on some special cases. [ABSTRACT FROM AUTHOR]
- Published
- 1984
- Full Text
- View/download PDF
15. DISCRETE APPROXIMATIONS OF PROBABILITY DISTRIBUTIONS.
- Author
-
Miller III, Allen C. and Rice, Thomas R.
- Subjects
APPROXIMATION theory ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,GAUSSIAN quadrature formulas ,GAUSSIAN distribution ,DECISION making ,MATHEMATICAL models of decision making ,MATHEMATICAL models ,STATISTICAL correlation ,DECISION theory ,MANAGEMENT science ,NUMERICAL analysis - Abstract
Practical limits on the size of most probabilistic models require that probability distributions be approximated by a few representative values and associated probabilities. This paper demonstrates that methods commonly used to determine discrete approximations of probability distributions systematically underestimate the moments of the original distribution. A new procedure based on gaussian quadrature is developed in this paper. It can be used to decrease the error in the approximation to any desired level. [ABSTRACT FROM AUTHOR]
- Published
- 1983
- Full Text
- View/download PDF
16. THE VALUE OF DATA FOR A QUADRATIC DECISION PROBLEM.
- Author
-
Rice, Thomas Richard
- Subjects
DECISION making ,APPROXIMATION theory ,DATA ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,QUADRATIC equations ,EXPECTED returns ,MANAGEMENT science ,MATHEMATICAL models ,MATHEMATICAL analysis - Abstract
A question that recurs in the decision analysis literature is: What is the value of additional data gathering? We use a very general definition of data that includes subjective probability distributions provided by experts, calculations from models, and traditional experimental data. General expressions for the expected value of data have little practical use because they involve probability distributions whose arguments are themselves probability distributions. The traditional approach to alleviate the problem of dimensionality is to introduce arbitrary parameterization of the data. This paper shows that for an interesting class of decision problems, arbitrary parameterization is not necessary. For the class of decision problems in which the value function over outcomes is a quadratic function of the state and decision variables, the value of data depends on the state variables only through the prior covariances of the posterior means. To use this result in the calculation of the approximate value of data for practical problems, it is necessary to simplify the value function. The paper suggests simplifying the value function by expanding it in a Taylor series with respect to the state and decision variables. The resulting expressions for the approximate value of information should be useful and inexpensive to evaluate for practical decision problems. [ABSTRACT FROM AUTHOR]
- Published
- 1978
- Full Text
- View/download PDF
17. DETERMINING REORDER POINTS WHEN DEMAND IS LUMPY.
- Author
-
Ward, J.B.
- Subjects
INVENTORY control ,INVENTORIES ,SUPPLY & demand ,ECONOMIC demand ,DISTRIBUTION (Probability theory) ,POISSON processes ,MATHEMATICAL optimization ,SUPPLY chain management ,BUSINESS logistics ,SALES forecasting ,PROBABILITY theory - Abstract
Lumpy or sporadic demand patterns with highly skewed distributions are common in parts and supplies types of stockholdings, and much of available inventory control methodology is not appropriate for such items. This paper presents a simple, easily used regression model to calculate order points for lumpy items from knowledge of demand parameters and the desired service level. It is derived from the particular compound Poisson distribution commonly called 'stuttering Poisson.' Results are derived and presented in the following framework, though application is not limited to these conditions. The control discipline is the order quantity, order point (Q, R) approach with continuous review. Lead time is assumed to be known and constant. An assigned service level is assumed based on fraction of demand supplied without backorder. Joint optimization of Q and R is not addressed, but rather order point is based on an independently calculated order quantity. Forecasting methods are not addressed, but the mean and variance of lead time demand forecasts are assumed available. [ABSTRACT FROM AUTHOR]
- Published
- 1978
- Full Text
- View/download PDF
18. WAITING TIME DISTRIBUTION IN A POISSON QUEUE WITH A GENERAL BULK SERVICE RULE.
- Author
-
Medhi, J.
- Subjects
SCHEDULING ,QUEUING theory ,POISSON processes ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,STOCHASTIC processes ,MANAGEMENT science ,OPERATIONS research ,LOADING & unloading - Abstract
This paper relates to a queueing system with Poisson input and exponential service time, service taking place in batches under a 'general bulk service rule'. (A batch will contain no fewer than 'a' and no more than 'b' units.) The object of this paper is to study the waiting time distribution of such a bulk service system under steady state and also to indicate how the moments of the distribution can be obtained. [ABSTRACT FROM AUTHOR]
- Published
- 1975
- Full Text
- View/download PDF
19. Stochastic Duels with Damage.
- Author
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Nagabhushanam, A. and Jain, G. C.
- Subjects
AMMUNITION ,EXPLOSIVES ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,STOCHASTIC processes ,ESTIMATION theory - Abstract
This paper considers the duel between two contestants with unlimited ammunition supplies, each one firing at the other. It assumes that the damage resulting from a round of fire is measurable and has a probability distribution. The cumulative damage function depends both on time and on number of rounds fired. For given rates of fire, damage functions, and other parameters, the paper calculates the probabilities that a given side will win. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
20. COMPUTING THE EXPECTED END-PRODUCT SERVICE TIME USING STOCHASTIC ITEM DELAYS.
- Author
-
Rose, Marshall
- Subjects
DISTRIBUTION (Probability theory) ,PROBABILITY theory ,STOCHASTIC processes ,ESTIMATION theory ,PRODUCT lines ,PRODUCT management - Abstract
This paper derives an expression for the expected completion time of a repair project, such as the servicing of end products, when the servicing is composed of a sequence of repair activities on parts of the end product. These parts are subject to repair with a specified probability and, at first, it is assumed that the completion time of each activity is constant. Subsequently, this assumption is relaxed so that an arbitrary probability distribution can be specified for the activity completion times. The concluding parts of the paper show how to compute the expected end-product service time for a particular class of activity-time probability distributions. [ABSTRACT FROM AUTHOR]
- Published
- 1971
- Full Text
- View/download PDF
21. BAYESIAN DETERMINATION OF THE REORDER POINT OF A SLOW MOVING ITEM.
- Author
-
Silver, Edward A.
- Subjects
INVENTORY control ,BAYESIAN analysis ,INVENTORIES ,INDUSTRIAL procurement ,PROBABILITY theory ,DISTRIBUTION (Probability theory) ,OPERATIONS research - Abstract
Consider an inventory item for which the procurement (or production setup) lead time is nonzero. One of the commonly used methods of determining the reorder point of such an item is to specify the probability of a stockout or a desired service level (fraction of demand that is to be instantaneously satisfied) and then select the reorder level that will provide such service. However, such an approach has assumed that the probability distribution of demand during the lead time is exactly known. In many inventory situations this assumption is not justified, particularly in the case of a slow moving item with limited available sales history. For such a situation this paper explores the use of a Bayesian approach to selecting a reorder point. [ABSTRACT FROM AUTHOR]
- Published
- 1965
- Full Text
- View/download PDF
22. OPTIMUM AMMUNITION PROPERTIES FOR SALVOS.
- Author
-
Walsh, John E.
- Subjects
AMMUNITION ,OPERATIONS research ,EXPLOSIVES ,PROBABILITY theory ,REALISM ,DISTRIBUTION (Probability theory) - Abstract
Calculation of the probability of kill from firing a salvo of ammunition rounds often is a very complicated and time-consuming problem Thus there is a tendency to sacrifice realism to obtain greater mathematical simplicity There are, however, some worthwhile salvo-firing problems where realism and mathematical simplicity are both attainable Let the salvo size, the lethality properties of the ammunition, the shape and vulnerability properties of the target, and the probability properties of the salvo-aiming system against this target all be arbitrary but given Consider determination of the maximum salvo kill-probability value obtainable through use of the optimum hit-location probability distribution for the ammunition rounds Evaluation of this maximum salvo kill probability, and of the corresponding optimum round-hit-location probability distribution, is the problem analyzed in this paper Although this problem is solved for a very general class of situations, the computations required are not extensive The results derived also can be used to indicate the effects on salvo kill probability of salvo size, target shape and vulnerability distribution, target maneuver, fire-control-system properties, etc [ABSTRACT FROM AUTHOR]
- Published
- 1956
- Full Text
- View/download PDF
23. THE USE OF DISTRIBUTION FUNCTIONS TO REPRESENT UTILITY FUNCTIONS.
- Author
-
Berhold, Marvin H.
- Subjects
DECISION making ,DISTRIBUTION (Probability theory) ,UTILITY functions ,GAUSSIAN distribution ,PROBABILITY theory ,CHARACTERISTIC functions ,EXPECTED utility ,MATHEMATICAL models ,UNCERTAINTY - Abstract
This paper considers the decision maker whose evaluation and consequent choice of actions is accomplished through the use of the expected utility hypothesis. In cases where the utility function is increasing with upper and lower bounds then the utility function can be characterized by a distribution function, and we can take advantage of the various properties of such functions as well as existing results with respect to such functions. Using these properties and results we can determine the certainty equivalents as a function of the parameters of the distribution function (utility function) and the parameters of the probability distribution on the uncertain payoff. The following cases are considered: (1) Gaussian distribution function and Gaussian probability distribution, (2) Exponential distribution function and exponential distribution and (3) Exponential distribution function and Gaussian probability distribution. [ABSTRACT FROM AUTHOR]
- Published
- 1973
- Full Text
- View/download PDF
24. SOME SPECIAL P-MODELS IN CHANCE-CONSTRAINED PROGRAMMING.
- Author
-
Charnes, A. and Kirby, M.J.L.
- Subjects
CONSTRAINT programming ,COMPUTER programming ,PROBABILITY measures ,DISTRIBUTION (Probability theory) ,MATHEMATICAL programming ,MANAGEMENT education ,PROBABILITY theory ,MATHEMATICAL optimization ,MATHEMATICAL models ,EDUCATION - Abstract
This paper establishes sufficient conditions for decision rules to be optimal for two n-period P-models of chance-constrained programming. The models considered are the triangular model with total probability constraints and the block triangular model with conditional probability constraints. It is shown that, for both these models, a sufficient condition for optimality is that the decision rule be the optimal piecewise linear rule. Proofs of theorems are based on results contained in earlier papers by the authors, on n-period E-models of chance-constrained programming. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
25. An Asymptotic Test of Optimality Conditions in Multiresponse Simulation Optimization.
- Author
-
Angün, Ebru and Kleijnen, Jack
- Subjects
MATHEMATICAL optimization ,EXPERIMENTAL design ,NUMERICAL analysis ,PROBABILITY theory ,DISTRIBUTION (Probability theory) ,SIMULATION methods & models - Abstract
This paper derives a novel, asymptotic statistical test of the Karush-Kuhn-Tucker first-order necessary optimality conditions in random simulation models with multiple responses. This test combines a simple form of the delta method and a generalized version of Wald's statistic. The test is applied to both a toy problem and an (s, S) inventory-optimization problem with a service-level constraint; its numerical results are encouraging. [ABSTRACT FROM AUTHOR]
- Published
- 2012
- Full Text
- View/download PDF
26. An Exact Solution Approach for Portfolio Optimization Problems Under Stochastic and Integer Constraints.
- Author
-
Bonami, P . and Lejeune, M. A.
- Subjects
PORTFOLIO management (Investments) ,MATHEMATICAL optimization ,STOCHASTIC processes ,MATHEMATICAL programming ,DISTRIBUTION (Probability theory) ,PROBABILITY theory - Abstract
In this paper, we study extensions of the classical Markowitz mean-variance portfolio optimization model. First, we consider that the expected asset returns are stochastic by introducing a probabilistic constraint, which imposes that the expected return of the constructed portfolio must exceed a prescribed return threshold with a high confidence level. We study the deterministic equivalents of these models. In particular, we define under which types of probability distributions the deterministic equivalents are second-order cone programs and give closed-form formulations. Second, we account for real- world trading constraints (such as the need to diversify the investments in a number of industrial sectors, the nonprofitability of holding small positions, and the constraint of buying stocks by lots) modeled with integer variables. To solve the resulting problems, we propose an exact solution approach in which the uncertainty in the estimate of the expected returns and the integer trading restrictions are simultaneously considered. The proposed algorithmic approach rests on a nonlinear branch- and-bound algorithm that features two new branching rules. The first one is a static rule, called idiosyncratic risk branching, while the second one is dynamic and is called portfolio risk branching. The two branching rules are implemented and tested using the open-source Bonmin framework. The comparison of the computational results obtained with state-of-the-art MINLP solvers (MINLP_BB and CPLEX) and with our approach shows the effectiveness of the latter, which permits to solve to optimality problems with up to 200 assets in a reasonable amount of time. The practicality of the approach is illustrated through its use for the construction of four fund-of-funds now available on the major trading markets. [ABSTRACT FROM AUTHOR]
- Published
- 2009
- Full Text
- View/download PDF
27. Games with Incomplete Information Played by "Bayesian" Players, I-III.
- Author
-
Harsanyi, John C.
- Subjects
MANAGEMENT games ,GAME theory ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,BAYESIAN analysis ,THEORY of distributions (Functional analysis) ,LOTTERIES ,MANAGEMENT science ,GAMES of strategy (Mathematics) - Abstract
The paper develops a new theory for the analysis of games with incomplete information where the players are uncertain about some important parameters of the game situation, such as the payoff functions, the strategies available to various players, the information other players have about the game, etc. However, each player has a subjective probability distribution over the alternative possibilities. In most of the paper it is assumed that these probability distributions entertained by the different players are mutually "consistent," in the sense that they can be regarded as conditional probability distributions derived from a certain "basic probability distribution" over the parameters unknown to the various players. But later the theory is extended also to cases where the different players' subjective probability distributions fail to satisfy this consistency assumption. In cases where the consistency assumption holds, the original game can be replaced by a game where nature first conducts a lottery in accordance with the basic probability distribution, and the outcome of this lottery will decide which particular subgame will be played, i.e., what the actual values of the relevant parameters will be in the game. Yet, each player will receive only partial information about the outcome of the lottery, and about the values of these parameters. However, every player will know the "basic probability distribution" governing the lottery. Thus, technically, the resulting game will be a game with complete information. It is called the Bayes-equivalent of the original game. Part I of the paper describes the basic model and discusses various intuitive interpretations for the latter. Part II shows that the Nash equilibrium points of the Bayes-equivalent game yield "Bayesian equilibrium points" for the original game. Finally, Part III considers the main properties of the "basic probability distribution." [ABSTRACT FROM AUTHOR]
- Published
- 2004
- Full Text
- View/download PDF
28. The [Pht/Pht/∞]K Queueing System: Part II--The Multiclass Network.
- Author
-
Nelson, Barry L. and Taaffe, Michael R.
- Subjects
QUEUING theory ,PRODUCTION scheduling ,STOCHASTIC processes ,DISTRIBUTION (Probability theory) ,MANAGEMENT science ,PROBABILITY theory - Abstract
We demonstrate a numerically exact method for evaluating the time-dependent mean, variance, and higher- order moments of the number of entities in the multiclass [Ph
t /Pht /∞]K queueing network system, as well as at the individual network nodes. We allow for multiple, independent, time-dependent entity classes and develop time-dependent performance measures by entity class at the nodal and network levels. We also demonstrate a numerically exact method for evaluating the distribution function and moments of virtual sojourn time through the network for virtual entities, by entity class, arriving to the system at time t. We include an example using software that we have developed and have put in downloadable form in the Online Supplement to this paper on the journal's website. [ABSTRACT FROM AUTHOR]- Published
- 2004
- Full Text
- View/download PDF
29. A Second Order Stochastic Network Equilibrium Model,I: Theoretical Foundation.
- Author
-
Watling, David
- Subjects
STOCHASTIC orders ,STOCHASTIC processes ,PROBABILITY theory ,TRAVEL costs ,TRANSPORTATION ,LOCOMOTION ,DISTRIBUTION (Probability theory) ,EQUILIBRIUM - Abstract
Existing models of stochastic network equilibrium route choice in transport networks are able to represent exogenously specified variations in drivers' actual or perceived travel costs, but assume throughout that flows are deterministic. In this paper, a new notion of equilibrium is presented based on stochastic flow variables, in which the impact of variable flows on the variability in travel costs is endogenously handled. Firstly, a very general notion of equilibrium is deduced as a fixed point condition on the joint probability distribution of network flows. Then, an approximation to this condition is derived, which operates by equilibrating moments of order n and below of the joint flow probability distribution, and is termed a Generalized Stochastic User Equilibrium of order n, being denoted GSUE(n). The GSUE(1) model is seen to be a conventional Stochastic User Equilibrium. The paper goes on to focus on the second order model, GSUE(2). Conditions are presented to guarantee the existence of GSUE(2) solutions. Conditions are deduced to guarantee (a) uniqueness of solutions in networks with a single interzonal movement, and (b) proximity of solutions in networks with multiple interzonal movements. Finally, a simple example is presented. [ABSTRACT FROM AUTHOR]
- Published
- 2002
- Full Text
- View/download PDF
30. CRITIQUE OF: "RANKING PROCEDURES AND SUBJECTIVE PROBABILITY DISTRIBUTIONS"
- Author
-
Green, Paul E.
- Subjects
CRITICISM ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,BUSINESS planning ,MATHEMATICAL statistics ,STRATEGIC planning ,MANAGEMENT education ,UNCERTAINTY reduction theory (Communication) ,LEGAL judgments ,EDUCATION - Abstract
Lee Smith's paper is interesting as much for the questions he raises as for the answer he proposes. Those of us who have tried to elicit subjective probability distributions in the context of corporate systems can sympathize with his position that no "objective" way has yet been proposed. It is no wonder that the procedures which he cites as precursors to his proposal are ad hoc and, shall we say, "flexible." The main issue, however, is whether the procedure advocated in his paper overcomes the limitations of previous devices. Related questions concern: (a) the compatability of probabilistic thinking with the culture of line managemerit; and (b) the accuracy of the elicited judgments, using the "best" of methods. [ABSTRACT FROM AUTHOR]
- Published
- 1967
- Full Text
- View/download PDF
31. The nonpreemptive priority MAP/G/1 queue.
- Author
-
Takine, Tetsuya
- Subjects
MARKOV spectrum ,STATIONARY processes ,QUEUING theory ,STOCHASTIC processes ,PROBABILITY theory ,DISTRIBUTION (Probability theory) ,STIELTJES transform ,MATHEMATICAL transformations - Abstract
This paper considers the nonpreemptive priority queue with MAP (Markovian Arrival Process) arrivals. Since MAP is weakly dense in the class of stationary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distributed according to a general distribution function that may differ among priority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length distribution of each class. Further, we provide the delay cycle analysis of the waiting time distribution of each class and characterize its Laplace-Stieltjes transform. [ABSTRACT FROM AUTHOR]
- Published
- 1999
- Full Text
- View/download PDF
32. D/G/1 QUEUES WITH VACATIONS.
- Author
-
Servi, L. D.
- Subjects
QUEUING theory ,PRODUCTION scheduling ,OPERATIONS research ,PROBABILITY theory ,DISTRIBUTION (Probability theory) - Abstract
Many data switching systems have processors with arrival streams of regularly spaced tasks (e.g., individual bytes) requiring attention (e.g., directing the bytes to the appropriate outgoing line). In many of these systems the processor might also be required to handle other jobs (small maintenance routines or secondary tasks that await service in one or more other queues) as well. From the point of view of the primary queue of tasks, the processor ceases its service and takes a vacation. The performance of such a system is determined in part by the processor service schedule. In this paper, we define and analyze a model for investigating the waiting time probability distribution at the primary queue in terms of the primary task arrival rate, the service time distribution for the primary tasks, the probability distribution of the vacation duration, and the processor's service schedule. In addition, we discuss two characteristics of systems of this type that may have important design implications: (i) the steady-state waiting time probability distribution might be dependent upon the initial state of the system; and (ii) the waiting time might not decrease if the service time of the system decreases. [ABSTRACT FROM AUTHOR]
- Published
- 1986
- Full Text
- View/download PDF
33. Distribution-Free Approximations for Chance Constraints.
- Author
-
Allen, F. M., Braswell, R. N., and Rao, P. V.
- Subjects
APPROXIMATION theory ,CLUSTER analysis (Statistics) ,DISTRIBUTION (Probability theory) ,MATHEMATICAL statistics ,PROBABILITY theory ,RANDOM variables ,MULTIVARIATE analysis ,STATISTICAL sampling - Abstract
This paper concerns developing methods for approximating a chance-constrained set when any information concerning the random variables must be derived from actual samples. Such a situation has not been presented in the literature. When existing chance-constrained programming techniques are used, it is not possible to relate the accuracy of sample-based assumptions to actual constraint satisfaction. The methods presented here employ the concept of a distribution-free tolerance region to construct various sets whose elements have the common property of satisfying the chance constraint with a preassigned level of confidence. The sample size required to meet the desired confidence is readily available in tabular or graphical form. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
34. The Expected Number of Visits to State k before a Total System Failure of a Complex System with Repair Maintenance.
- Author
-
Nakagawa, Toshlo
- Subjects
STOCHASTIC analysis ,STOCHASTIC processes ,SYSTEM failures ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,MARKOV processes ,MATHEMATICAL optimization ,BINOMIAL distribution - Abstract
This paper investigates the stochastic behavior before a total system failure for a standby redundant system with repair maintenance. It derives the expected number of visits to state k before a total system failure and other measures explicitly by considering 'taboo' probabilities for an imbedded Markov chain generated by the system. The transition probabilities and the first-passage distributions are also discussed. Numerical examples are presented. [ABSTRACT FROM AUTHOR]
- Published
- 1974
- Full Text
- View/download PDF
35. Generalized Traffic Equilibrium with Probabilistic Travel Times and Perceptions.
- Author
-
Mirchandani, Pitu and Soroush, Hossein
- Subjects
TOURISM ,TRAFFIC engineering ,TRANSPORTATION ,TRAVEL time (Traffic engineering) ,TRAFFIC surveys ,EQUILIBRIUM ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,UTILITY functions - Abstract
The paper studies the problem of predicting traffic equilibrium (TE) in a transportation network within the framework of decision making among discrete choices in a probabilistic and uncertain environment. Conventional approaches to predict TE typically assume that travel times are deterministic and perceived accurately by the travelers; and some new TE models have considered probabilistic travel times or inaccurate perceptions but not both. In our generalized model, which we refer to as GTESP, the travel time on each route is random and each traveler perceives, possibly inaccurately, a travel time probability distribution for each route which may vary from traveler to traveler Each traveler uses a disutility function of travel time to evaluate each route and chooses that route which minimizes his expected disutility. GTESP is difficult to solve for general nonlinear disutility functions. However, special cases—in particular when arc travel times are statistically independent and the disutility functions to evaluate route travel times are linear, exponential, or quadratic—are solvable, at least approximately. GTESP is general in the sense that most existing TE models can be shown to be special or limiting cases of GTESP. Furthermore, this paper demonstrates, with illustrative examples, that GTESP appears to capture travelers' risk-taking behavior more realistically than existing TE models. [ABSTRACT FROM AUTHOR]
- Published
- 1987
- Full Text
- View/download PDF
36. ON THE COOKIE-CUTTER GAME: SEARCH AND EVASION ON A DISC.
- Author
-
Danskin, John M.
- Subjects
PROBABILITY theory ,COOKIE cutters ,DISTRIBUTION (Probability theory) ,TRIGONOMETRIC functions ,EQUATIONS ,UNIFORM distribution (Probability theory) - Abstract
In the cookie-cutter game, there is a trapping circle, of radius 1, in which an evader hides. A searcher has a "cookie-cutter", a disk of radius r < 1. If, when he places the cookie-cutter on the trapping circle, the evader is within it, the evader is caught and the searcher wins. Otherwise the evader wins. If r = √2/2, the problem is trivial. The evader should choose a point from the uniform distribution on the outer circumference of the trapping circle, and the searcher a point from the uniform distribution on the circle of radius r* = (1 - r²)
1/2 concentric to that circle; this choice gives him maximum coverage of the outer circumference. For the case r ≧ 1/2, an easy and elegant solution was given by Gale and Glassey in 1974. Both players should go to the center with probability 1/7. The minimizer should go to the outer circumference, and the maximizer to r* = √3/2, both with probability 6/7. For other r the problem is difficult. This paper proves that there are no solutions based on finitely many radii if r < r0 ... 0.476, where r0 solves a cubic equation, finds two-point solutions on [r0 , r1 ], where r1 ... 0.515 solves a trigonometric equation, and proves qualitative facts for r ∈ (r1 , √2/2). [ABSTRACT FROM AUTHOR]- Published
- 1990
- Full Text
- View/download PDF
37. AN ALGORITHM TO CALCULATE THE RETURN DISTRIBUTION OF PORTFOLIOS WITH OPTION POSITIONS.
- Author
-
Bookstaber, Richard and Clarke, Roger
- Subjects
PORTFOLIO management (Investments) ,FINANCIAL management ,INVESTMENT analysis ,ASSET management ,SECURITIES ,STOCKS (Finance) ,ALGORITHMS ,SIMULATION methods & models ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,APPROXIMATION theory ,RATE of return - Abstract
The use of options in altering the return distribution of stock portfolios has found increasing interest among investment managers. The potential of options in forming portfolio return distributions that are more consistent with investor preferences has been well developed, but determining the actual effect of options on portfolio returns remains a complex and unsolved problem. The purpose of this paper is to describe an algorithm for determining the return distribution that will result when option positions are taken on stocks in a portfolio. The distribution is determined for a finite time horizon, and does not rely on the assumption of continuous portfolio revisions. Simulation tests on the algorithm are also discussed. The algorithm is then used to illustrate the effect that several simple and well-known options strategies will have on portfolio return characteristics. This algorithm will be of practical value, giving a technique for generating and analyzing the expanded opportunity set that exists by using options in portfolio management. [ABSTRACT FROM AUTHOR]
- Published
- 1983
- Full Text
- View/download PDF
38. EFFECTIVE SCORING RULES FOR PROBABILISTIC FORECASTS.
- Author
-
Friedman, Daniel
- Subjects
ECONOMIC forecasting ,FORECASTING ,PREDICTION models ,MATHEMATICAL models of decision making ,FOREIGN exchange rates ,DISTRIBUTION (Probability theory) ,DELPHI method ,PROBABILITY theory ,MATHEMATICAL models ,MATHEMATICAL analysis ,MATRICES (Mathematics) ,MATHEMATICAL functions - Abstract
This paper studies the use of a scoring rule for the elicitation of forecasts in the form of probability distributions and for the subsequent evaluation of such forecasts. Given a metric (distance function) on a space of probability distributions, a scoring rule is said to be effective if the forecaster's expected score is a strictly decreasing function of the distance between the elicited and "tree" distributions. Two simple, well-known rules (the spherical and the quadratic) are shown to be effective with respect to suitable metrics. Examples and a practical application (in Foreign Exchange rate forecasting) are also provided. [ABSTRACT FROM AUTHOR]
- Published
- 1983
- Full Text
- View/download PDF
39. AN AXIOMATIC APPROACH TO EXPERT RESOLUTION.
- Author
-
Morris, Peter A.
- Subjects
PROBABILITY theory ,AXIOMS ,AXIOMATIC set theory ,BAYESIAN analysis ,DECISION making ,SPECIALISTS ,STATISTICAL decision making ,PROBLEM solving ,DISTRIBUTION (Probability theory) ,MANAGEMENT science - Abstract
This paper proposes a set of axioms for combining expert probability assessments. The axioms provide a framework for understanding previous results, and are used to derive a new method for combining event probabilities from different sources into a single estimate. [ABSTRACT FROM AUTHOR]
- Published
- 1983
- Full Text
- View/download PDF
40. SAMPLE VS. POPULATION MEAN-VARIANCE EFFICIENT PORTFOLIOS.
- Author
-
Levy, Haim and Kroll, Yoram
- Subjects
RATE of return ,ANALYSIS of variance ,PORTFOLIO management (Investments) ,ESTIMATION theory ,OPTIONS (Finance) ,ERROR analysis in mathematics ,STATISTICAL sampling ,STATISTICAL correlation ,SCIENTIFIC observation ,DEPENDENCE (Statistics) ,DISTRIBUTION (Probability theory) ,PROBABILITY theory - Abstract
It is common to use historical data in calculating the rates of return of risky options, and these data are used to calculate the mean and the variance, which are employed in the (MV) preference ranking. In this paper we study the effect of possible sampling error on the portfolio ranking. It is shown that in order to keep the error at a reasonable level (5 percent), one needs 50-100 observations, a number that is rarely used in the (MV) comparison of portfolios. The results are almost independent of the correlation between the portfolios. [ABSTRACT FROM AUTHOR]
- Published
- 1980
- Full Text
- View/download PDF
41. PLANNING AND DYNAMIC CONTROL OF PROJECTS UNDER UNCERTAINTY.
- Author
-
Burt, John M.
- Subjects
PROJECT management ,NETWORK analysis (Planning) ,RESOURCE allocation ,MATHEMATICAL optimization ,DYNAMIC programming ,HEURISTIC programming ,DECISION making ,MATHEMATICAL programming ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,MANAGEMENT science ,INDUSTRIAL management - Abstract
This paper addresses the problem of planning and controlling (through resource allocation decisions) projects under conditions of uncertainty. Particular attention is given to the dynamic reallocation of resources over the duration of projects as information about actual activity times becomes known. The effect of resource allocations on an activity is represented by modifications in the probability function of the time to process that activity. Analytic procedures such as dynamic programming and distribution analysis, which might lead to optimal dynamic decision rules, are shown to be computationally intractable even for very small problems. For a set of project networks of relatively simple structure, the efficacy of several heuristic decision rules is tested via simulation. The results of these simulation studies indicate some general concepts that should be applicable to the management of larger, more realistic, projects. [ABSTRACT FROM AUTHOR]
- Published
- 1977
- Full Text
- View/download PDF
42. A NOTE ON THE RATIO OF TWO NORMALLY DISTRIBUTED VARIABLES.
- Author
-
Hayya, Jack, Armstrong, Donald, and Gressis, Nicolas
- Subjects
APPROXIMATION theory ,RATIO & proportion ,MATHEMATICAL variables ,DISTRIBUTION (Probability theory) ,RISK assessment ,MONTE Carlo method ,SIMULATION methods & models ,PROBABILITY theory ,MANAGEMENT science - Abstract
This note is a continuation of a previous paper on normal approximations of standard forms. The standard form treated here is the ratio of two normally distributed variables. It is found that a suitable transformation of this ratio is approximately normally distributed provided that the coefficient of variation of the denominator is less than 0.39. [ABSTRACT FROM AUTHOR]
- Published
- 1975
- Full Text
- View/download PDF
43. AN OPTIMAL INVENTORY MODEL FOR THE INTERMEDIATE ECHELON WHEN REPAIR IS POSSIBLE.
- Author
-
Haber, Sheldon E. and Sitgreaves, Rosedith
- Subjects
INVENTORY control ,DISTRIBUTION (Probability theory) ,REPAIRING ,MATHEMATICAL combinations ,PROBABILITY theory ,SENSITIVITY theory (Mathematics) ,FAILURE time data analysis ,STOCHASTIC processes ,EDUCATION ,ECONOMICS - Abstract
The basic contribution of the paper is the development of a probabilistic model for computing the optimal purchase, i.e., stockage quantity of an item at an intermediate echelon of supply when repair of the item is possible. For commonly assumed probability distributions of the failure and repair process, it is found that the optimal stockage quantity depends to a large extent on the failure rate and is relatively insensitive to the repair rate. The model is then applied to the problem of determining the extent to which repair is economical at the intermediate echelon. It is concluded that for systems where most items deemed repairable have a low failure rate, the effectiveness of the intermediate echelon may be larger when its primary function is storage rather than repair. [ABSTRACT FROM AUTHOR]
- Published
- 1975
- Full Text
- View/download PDF
44. Optimal Search with Uncertain Sweep Width.
- Author
-
Richardson, Henry R. and Belkin, Barry
- Subjects
DISTRIBUTION (Probability theory) ,MARGINAL distributions ,PROBABILITY theory ,OPERATIONS research ,MATHEMATICAL optimization ,MATHEMATICS - Abstract
This paper considers the problem of optimal search for a stationary target when the detection capability of the search sensor, as characterized by its sweep width, is fixed but not known in advance. Most of the results are confined to the assumption of a gamma prior sweep-width distribution and to the cases of normal and uniform prior target-location distributions. Explicit formulas are obtained for the optimal search plans, the probability of detection versus time, the expected time to detection, and the posterior marginal distributions for target location and sweep width. In the case of a normal prior target-location distribution, expected time to detection is compared for the optimal plan and search plans based on the assumption of a known value for sweep width; this includes a sensitivity analysis treating actual sweep width as a parameter. For a target of value, the search plan that maximizes expected net return is determined. This plan requires specification of a rule for terminating an unsuccessful search. Explicit results are given assuming a nonincreasing target value and a nondecreasing search-cost rate. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
45. Sequential Search for an Unknown Number of Objects of Nonuniform Size.
- Author
-
Cozzolino, John M.
- Subjects
DISTRIBUTION (Probability theory) ,PROBABILITY theory ,CHARACTERISTIC functions ,SEARCH theory ,OPERATIONS research ,SYSTEMS theory - Abstract
This paper deals with a search model for allocating effort when there are many target objects of differing sizes present in a search area. All target objects are initially present in the search area and remain at least until discovered; no new objects are generated during the search process. Targets are not moveable. The search process is characterized by the quantity of search effort. The model describes the distribution of the number and sizes of target objects present. The probability of discovery is assumed proportional to object size. The paper gives many results, including the probability distribution of the number and sizes of discovered objects, and the prior and posterior distributions of the number of objects remaining undiscovered. Then it gives the method of maximum likelihood estimation of the model parameters, and solves the sequential decision problem of when to terminate the search process. [ABSTRACT FROM AUTHOR]
- Published
- 1972
- Full Text
- View/download PDF
46. A MATRIX APPROACH TO NONSTATIONARY CHAINS.
- Author
-
Harary, Frank, Lipstein, Benjamin, and Styan, George P. H.
- Subjects
MARKOV processes ,MATRICES (Mathematics) ,MATRIX derivatives ,PROBABILITY theory ,MATHEMATICAL functions ,DISTRIBUTION (Probability theory) ,CHARACTERISTIC functions - Abstract
A finite discrete nonstationary Markov chain is completely characterized (after the initial probability distribution has taken effect) by its time sequence of transition probability matrices P
i . The ith causative matrix Ci is defined as the product Pi -1 (if it exists) times Pi+1 Thus, the causative matrices are analogous to derivatives in calculus as an indication of rate of change. The eigenvalues and eigenvectors of a constant causative matrix C have been found useful in their connection with the tendency of the chain to be convergent or divergent. Results for two-state chains are presented in some detail. A comprehensive bibliography of papers on non-stationary chains is included. [ABSTRACT FROM AUTHOR]- Published
- 1970
- Full Text
- View/download PDF
47. A MULTISERVER SYSTEM WITH PREEMPTIVE PRIORITIES.
- Author
-
Segal, M.
- Subjects
DISTRIBUTION (Probability theory) ,SYSTEMS theory ,OPERATIONS research ,PROBABILITY theory ,DECISION theory ,MATHEMATICAL programming - Abstract
This paper considers a multiserver system with preemptive priorities and derives recurrence relations for the moments of the lifetime distribution. [ABSTRACT FROM AUTHOR]
- Published
- 1970
- Full Text
- View/download PDF
48. A SINGLE-SERVER PRIORITY QUEUING SYSTEM WITH GENERAL HOLDING TIMES, POISSON INPUT, AND REVERSE-ORDER-OF-ARRIVAL QUEUING DISCIPLINE.
- Author
-
Durr, L.
- Subjects
DISTRIBUTION (Probability theory) ,CHARACTERISTIC functions ,PROBABILITY theory ,POISSON processes ,POINT processes ,DOUBLY stochastic Poisson processes - Abstract
This paper gives an explicit formula for the waiting-time distribution in a single-server system with general holding times subject to a Poisson input from any number of priority classes. In the general case, where the holdingtime distributions of the demands in each priority case are different, the Laplace-Stieltjes transform and the moments of the distribution are found. The queue discipline is last-come first-served in each priority class. The cases of preemptive resume and nonpreemptive priorities are considered. It is shown that the variance of the waiting-time distribution (whatever the holding-time distribution) is greater than the corresponding variance when the queue discipline is first-come first-served. [ABSTRACT FROM AUTHOR]
- Published
- 1969
- Full Text
- View/download PDF
49. THE REMAINING BUSY PERIOD FOR A SINGLE SERVER QUEUE WITH POISSON INPUT.
- Author
-
Erlander, Sven
- Subjects
POISSON processes ,QUEUING theory ,OPERATIONS research ,STOCHASTIC analysis ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,CONSUMER behavior - Abstract
Consider a single-server queuing process with Poisson input and general service time distribution. Define the remaining busy period x(t) as the time from a given instant t until the server becomes idle for the first time. Let ξ(t) be the number of customers in the system at time t. Let
x1 (t) be the remaining service time for the customer being served at time t. In this paper we shall study the stochastic law of the remaining service timex1 O) given that ξ(0)=i and ξ(t)-r. The result will then be applied to the problem of finding the joint distribution of the remaining busy periodx (t) and the number of customers served duringx (t) given that ξ(0) = i and ξ(t)=r. [ABSTRACT FROM AUTHOR]- Published
- 1965
- Full Text
- View/download PDF
50. ON SINGLE--SERVER BULK--QUEUING PROCESSES WITH BINOMIAL INPUT.
- Author
-
Bhat, U. Narayan
- Subjects
BINOMIAL distribution ,BULK queues ,QUEUING theory ,CONSUMERS ,DISTRIBUTION (Probability theory) ,PROBABILITY theory ,STATISTICS ,MATHEMATICS ,MATHEMATICAL models - Abstract
In this paper, treating time as a discrete variable, we study the transient behavior of a bulk-service queuing system in which the number of customers arriving within a fixed time interval follows a binomial probability distribution. The service times are assumed to be identically distributed and statistically independent. The busy period and queue length distributions have been obtained in terms of probability generating functions. [ABSTRACT FROM AUTHOR]
- Published
- 1964
- Full Text
- View/download PDF
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