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INVERTING GENERATING FUNCTIONS WITH INCREASED NUMERICAL PRECISION-A COMPUTATIONAL EXPERIENCE

Journal of Systems Science and Systems Engineering 2011年第4期20卷 475-494页

作者： Nam K. kim Mohan L. CHAUDHRY Bong K. YOON kilhwan kim Department of Industrial Engineering Chonnam National University Department of Mathematics and Computer Science Royal Military College of Canada Defense Management College Korea National Defense University Internet Research Lab. Electronics and Telecommunications Research Institute

In this paper, we consider the numerical inversion of a variety of generating functions （GFs） that arise in the area of engineering and non-engineering fields. Three classes of GFs are taken into account in a comprehensive manner： classes of probability generating functions （PGFs） that are given in rational and non-rational forms, and a class of GFs that are not PGFs. Among others, those PGFs that are not explicitly given but contain a number of unknowns are largely considered as they are often encountered in many interesting applied problems. For the numerical inversion of GFs, we use the methods of the discrete （fast） Fourier transform and the Taylor series expansion. Through these methods, we show that it is remarkably easy to obtain the desired sequence to any given accuracy, so long as enough numerical precision is used in computations. Since high precision is readily available in current software packages and programming languages, one can now lift, with little effort, the so-called Laplacian curtain that veils the sequence of interest. To demonstrate, we take a series of representative examples： the PGF of the number of customers in the discrete-time Geo^X/Geo/c queue, the same in the continuous-time M^X/D/c queue, and the GFs arising in the discrete-time renewal process.

关键词： Queuing applied probability numerical inversion generating function

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A Complete and Simple Solution to a Discrete-Time Finite-Capacity BMAP/D/c Queue

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Applied Mathematics 2012年第12期3卷 2169-2173页

作者： Nam K. kim Mohan L. Chaudhry Bong K. Yoon kilhwan kim Defense Management College Korea National Defense University Seoul South Korea Department of Industrial Engineering Chonnam National University Gwangju South Korea Department of Management Engineering Sangmyung University Cheonan South Korea Department of Mathematics and Computer Science Royal Military College of Canada Kingston Canada

We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.

关键词： Discrete-Time Queue Batch Markovian Arrival Process Deterministic Service Time Multiple Server

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