Author: International Business Machines Corporation. Research Division
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Gerald S. Shedler
Publisher: Elsevier
ISBN: 0080925723
Category : Mathematics
Languages : en
Pages : 412

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Book Description
Simulation is a controlled statistical sampling technique that can be used to study complex stochastic systems when analytic and/or numerical techniques do not suffice. The focus of this book is on simulations of discrete-event stochastic systems; namely, simulations in which stochastic state transitions occur only at an increasing sequence of random times. The discussion emphasizes simulations on a finite or countably infinite state space.* Develops probabilistic methods for simulation of discrete-event stochastic systems* Emphasizes stochastic modeling and estimation procedures based on limit theorems for regenerative stochastic processes* Includes engineering applications of discrete-even simulation to computer, communication, manufacturing, and transportation systems* Focuses on simulations with an underlying stochastic process that can specified as a generalized semi-Markov process* Unique approach to simulation, with heavy emphasis on stochastic modeling* Includes engineering applications for computer, communication, manufacturing, and transportation systems

Author: International Business Machines Corporation. Research Division
Publisher:
ISBN:
Category :
Languages : en
Pages : 30

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Book Description
Discrete-event simulations are often non-Markovian in the sense that the underlying stochastic process of the simulation cannot be modeled as a Markov chain with countable state space. We discuss regenerative simulation methods for non-Markovian systems whose underlying stochastic process can be represented as a generalized semi-Markov process. Applications to modeling and simulation of ring and bus networks are given. Keywords include: Regenerative simulation; Generalized semi-Markov processes; Non-Markovian systems; Recurrence and regeneration; Ring and bus networks.

Author: Lawrence Duane Fossett
Publisher:
ISBN:
Category : Digital computer simulation
Languages : en
Pages : 200

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Book Description
One approach to modeling queueing networks and other complex stochastic systems which has received some attention in the literature is the generalized semi-Markov process (GSMP). This idea is an example of the supplementary variables approach to non-Markovian systems. This approach supplements the natural description of the system by variables which contain information about the past history of the system. In this way, a model of a non-Markovian system can be made Markovian. For GSMPs the supplementary variables are clocks which record the amount of time until the occurrence of various events which could influenece the system. Our approach to this problem is to find closely related regenerative processes on which to base the central limit theorem for the process under study. New results in the theory of Markov chains on a general state space make it clear how these regenerative processes can be constructed.

Author: International Business Machines Corporation. Research Division
Publisher:
ISBN:
Category : Central limit theorem
Languages : en
Pages : 32

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Abstract: "The usual model for the underlying process of a discrete-event stochastic system is the generalized semi-Markov process (GSMP). A GSMP is defined in terms of a general state space Markov chain that describes the process at successive state-transition times. We provide conditions on the clock-setting distributions and state-transition probabilities of a finite state GSMP under which this underlying chain is [phi]-irreducible and satisfies a drift criterion for stability due to Meyn and Tweedie. If the GSMP also has a 'single state' in which exactly one event is scheduled to occur, then this state is hit infinitely often with probability 1 and the time between successive hits has finite second moment. It follows that the standard regenerative method can be used to obtain strongly consistent point estimates and asymptotic confidence intervals for time-average limits of the process. We also show that, under our conditions, point estimates and confidence intervals for time- average limits can be obtained using methods based on standardized time series. In particular, the method of batch means (with the number of batches fixed) is applicable. Our results rest on a new functional central limit theorem for GSMP's together with results of Glynn and Iglehart. The standardized time series methods apply even when the GSMP does not have a single state or indeed any type of regenerative structure."

Author: Peter W. Glynn
Publisher:
ISBN:
Category :
Languages : en
Pages : 79

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Book Description
A wide variety of stochastic systems may be viewed as Markov chains taking on values in a general state space. An example is the class of generalized semi-Markov processes, which are commonly obtained in network queueing problems via the technique of supplementary variables. A simulator is often interested in obtaining steady state properties of such a system. Some recent developments in Markov chain theory by Athreya, Ney, and Nummelin allow one to embed a certain subclass of these processes in a regenerative environment. We study some consequences of this embedding and develop statistical estimation procedures for the general problem that bear close resemblance to the regenerative method of simulation analysis for finite state Markov chains. (Author).

Author: International Business Machines Corporation. Research Division
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 31

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Author: Georg Ch. Pflug
Publisher: Springer Science & Business Media
ISBN: 1461314496
Category : Business & Economics
Languages : en
Pages : 384

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Book Description
Stochastic models are everywhere. In manufacturing, queuing models are used for modeling production processes, realistic inventory models are stochastic in nature. Stochastic models are considered in transportation and communication. Marketing models use stochastic descriptions of the demands and buyer's behaviors. In finance, market prices and exchange rates are assumed to be certain stochastic processes, and insurance claims appear at random times with random amounts. To each decision problem, a cost function is associated. Costs may be direct or indirect, like loss of time, quality deterioration, loss in production or dissatisfaction of customers. In decision making under uncertainty, the goal is to minimize the expected costs. However, in practically all realistic models, the calculation of the expected costs is impossible due to the model complexity. Simulation is the only practicable way of getting insight into such models. Thus, the problem of optimal decisions can be seen as getting simulation and optimization effectively combined. The field is quite new and yet the number of publications is enormous. This book does not even try to touch all work done in this area. Instead, many concepts are presented and treated with mathematical rigor and necessary conditions for the correctness of various approaches are stated. Optimization of Stochastic Models: The Interface Between Simulation and Optimization is suitable as a text for a graduate level course on Stochastic Models or as a secondary text for a graduate level course in Operations Research.

Author: Dmitrii Silvestrov
Publisher: Springer Nature
ISBN: 3030923991
Category : Mathematics
Languages : en
Pages : 420

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Book Description
This book is the second volume of a two-volume monograph devoted to the study of limit and ergodic theorems for regularly and singularly perturbed Markov chains, semi-Markov processes, and multi-alternating regenerative processes with semi-Markov modulation. The second volume presents a complete classification of ergodic theorems for alternating regenerative processes, including more than twenty-five such theorems. The text addresses new asymptotic recurrent algorithms of phase space reduction for multi-alternating regenerative processes modulating by regularly and singularly perturbed finite semi-Markov processes. It also features a new study of super-long, long, and short time ergodic theorems for these processes. The book also contains a comprehensive bibliography of major works in the field. It provides an effective reference for both graduate students as well as theoretical and applied researchers studying stochastic processes and their applications.

Author: International Business Machines Corporation. Research Division
Publisher:
ISBN:
Category : Markov processes
Languages : en
Pages : 27

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Book Description
A generalized semi-Markov process provides a stochastic process model for a discrete-event simulation. This representation is particularly useful for non-Markovian systems where it is nontrivial to obtain recurrence properties of the underlying stochastic processes. The authors develop geometric trials arguments which can be used to obtain results on recurrence and regeneration in this setting. Such properties are needed to establish estimation procedures based on regenerative processes. Applications to modeling and simulation of ring and bus networks are discussed. (Author).