An approximate solution to a jit-based ordering system

In this paper we consider a multi-stage multi-product production, inventory and transportation system including lot production processes and develop a goal programming model for a pull type ordering system based on the concept of a Just-In-Time(JIT) production system. We also present a pragmatic approach which reduces the required computational time for the formulated mixed integer goal programming problem using a mathematical programming modeling language. The proposed solution procedure is realized utilizing the post-optimal analysis which can be performed by the modeling language.     

A cheap approximate solution to everett-type rational approximation problems

M. G. Everett posed a non-standard problem of rational approximation of the exponential. Kaufman and Taylor developed a special method for this problem. In this note is given an easier approach.     

A tandem queueing system with priorities

A system ofN unlimited queues andN time-discrete servers in series, is investigated. The input consists ofN stochastic processes where requests which have been generated according to thei-th process leave the system after they have received serivice by servers 1, 2, ...,i. The holding-time distributions can be calculated by means of an equivalence theorem which holds under certain conditions for the service times.     

A Mathematica program for the approximate analytical solution to a nonlinear undamped Duffing equation by a new approximate approach

According to Mickens [R.E. Mickens, Comments on a Generalized Galerkin's method for non-linear oscillators, J. Sound Vib. 118 (1987) 563], the general HB (harmonic balance) method is an approximation to the convergent Fourier series representation of the periodic solution of a nonlinear oscillator and not an approximation to an expansion in terms of a small parameter. Consequently, for a nonlinear undamped Duffing equation with a driving force Bcos(ωx), to find a periodic solution when the fundamental frequency is identical to ω, the corresponding Fourier series can be written as

     

An approximate solution for a system with a symmetric matrix

In this paper, a large system with a symmetric and essentially (2,2)-band matrix is reformulated as the product of two banded matrices for the purpose of obtaining a solution of a linear system more efficiently. An error term for the approximate solution is justified in the spirit of the work by Yan and Chung [1].     

A general solution for multichannel queueing systems with ordered entry

This paper presents a general solution of multichannel ordered entry queueing systems with heterogeneous servers and storage. It is assumed that the arrivals follow a Poisson distribution and the service times are exponentially distributed (M/M/n queueing system). A computer program was developed to solve this queueing system numerically. Measures of the system's performance as well as the steady-state probabilities are evaluated.     

A system for approximate tree matching

Ordered, labeled trees are trees in which each node has a label and the left-to-right order of its children (if it has any) is fixed. Such trees have many applications in vision, pattern recognition, molecular biology, programming compilation, and natural language processing. Many of the applications involve comparing trees or retrieving/extracting information from a repository of trees. Examples include classification of unknown patterns, analysis of newly sequenced RNA structures, semantic taxonomy for dictionary definitions, generation of interpreters for nonprocedural programming languages, and automatic error recovery and correction for programming languages. Previous systems use exact matching (or generalized regular expression matching) for tree comparison. This paper presents a system, called approximate-tree-by-example (ATBE), which allows inexact matching of trees. The ATBE system interacts with the user through a simple but powerful query language; graphical devices are provided to facilitate inputing the queries. The paper describes the architecture of ATBE, illustrates its use and describes some aspects of ATBE implementation. We also discuss the underlying algorithms and provide some sample applications     

Existence and uniqueness of nonnegative solution of M/GB/1 queueing model

In this paper, we set up M/G^B/1 queueing model as an abstract Cauchy problem and prove the existence of a unique positive solution using the theory of strongly continuous semigroups of operators.     

A discrete-time retrial queueing system with recurrent customers

We consider a discrete-time single-server retrial queue with general service times and two classes of customers: transit and a fixed number of recurrent customers. After service completion, recurrent customers always return to the orbit and transit customers leave the systems forever. In this work we study the influence of recurrent customers. This structure appears in many applications on computer and communication networks, but also has theoretical interest. The explicit expressions of generating functions of the stationary distribution of the Markov chain are given. We also provide the main reliability indexes and numerical examples with the use of discrete Fourier transform inversion.     

On approximating the generalized occupancy of the G/M/K queueing system

The G/M/K is one of very few multiserver queueing systems for which analytical results exist. In 1951 Kendall [4] showed how to compute the steady-state probabilities of a G/M/K queueing system. Later, Takacs [6] suggested an iterative procedure for the evaluation of a needed component in Kendall's scheme; namely, the generalized occupancy ω^*. However, Takàcs' algorithm requires the computation of a general integral for each of its interations.In this paper we propose a simple and explicit approximation for the generalized occupancy of the G/M/K system. Several numerical results are also included.     

Optimal control of admission to a queueing system

Congestion in a queueing system can sometimes be controlled by restricting arrivals, either by "closing a gate" or by charging an entrance fee or toll. We review both static (open-loop) and dynamic (closed-loop) models for control of admission to a queueing system. The main emphases are on the difference between socially optimal and individually optimal (equilibrium) controls and on the use of dynamic-programming inductive analysis to show that an optimal control is monotonic or characterized by one or more "critical numbers." We discuss the potential for use of these models in the analysis of computer/ communication systems and compare the results to certain others in the literature.     

LS-SVM approximate solution to linear time varying descriptor systems

This paper discusses a numerical method based on Least Squares Support Vector Machines (LS-SVMs) for solving linear time varying initial and boundary value problems in Differential Algebraic Equations (DAEs). The method generates a closed form (model-based) approximate solution. The results of numerical experiments on different systems with index from $0$ to $3$, are presented and compared with analytic solutions to confirm the validity and applicability of the proposed method.     

Approximate solution to multichain queueing networks with state dependent service rates

An approximation scheme for solving non-product form queueing networks with multiple chains and state dependent service rates is described. Estimates of the steady state probability distribution are obtained using less computational requirements than the standard solution techniques.The approximation scheme is based on a property called chain conditional balance, which leads to a decomposition of the global balance equations into smaller sets of equations. A technique for combining conditional distributions is examined and used to combine the solutions of conditional balance equations into the final estimates. Expressions for the storage and computational requirements of the approximation algorithm are given and an example is provided.An error analysis is described in which the approximation is tested on a large number of randomly generated queueing networks. The experimental results indicate that the approximation yields good estimates of the steady state distribution, as well as several important performance measures of these networks.     

A single-server queueing system with waiting and relative priority

Cybernetics and Systems Analysis -     

A closed-form solution on a level-dependent Markovian arrival process with queueing application

Abstract This paper reports a closed-form solution of the arrival events for a particular level-dependent Markovian arrival process (MAP). We apply the Baker–Hausdorff Lemma to the matrix expression of the number of arrival events in (0, t]. The successful derivation depends on the fact that the matrices representing the MAP have a specific structure. We report the results of numerical experiments indicating that the closed-form solution is less time-consuming than the uniformization technique for large values of t. As an application, we consider a finite-capacity, multi-server queueing model with impatient customers for possible use in automatic call distribution (ACD) systems. Our primary interest lies in performance measures related to customer waiting time, and we demonstrate how the closed-form solution is applicable to performance analysis.