Hisashi Kobayashi

Queuing networks with multiple closed chains: theory and computational algorithms

In this paper a recent result of Baskett, Chandy, Muntz, and Palacios is generalized to the case in which customer transitions are characterized by more than one closed Markov chain. Generating functions are used to derive closed-form solutions to stability, normalization constant, and marginal distributions. For such a system with N servers and L chains the solutions are considerably more complicated than those for systems with one subchain only. It is shown how open and closed subchains interact with each other in such systems. Efficient algorithms are then derived from our generating function representation.

Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions

The practical value of queueing theory in engineering applications such as in computer modeling has been limited, since the interest in mathematical tractability has almost always led to an oversimplified model. The diffusion process approximation is an attempt to break away from the vogue in queueing theory.nThe present paper introduces a vector-valued normal process and its diffusion equation in order to obtain an approximate solution to the joint distribution of queue lengths in a general network of queues. In this model, queueing processes of various service stations which interact with each other are approximated by a vector-valued Wiener process with some appropriate boundary conditions. Some numerical examples are presented and compared with Monte Carlo simulation results. A companion paper, Part II, discusses transient solutions via the diffusion approximation.

Queueing Models for Computer Communications System Analysis

Modeling and performance prediction are becoming increasingly important issues in the design and operation of computer communications systems. Complexities in their configuration and sophistications in resource sharing found in todays computer communications demand our intensive effort to enhance the modeling capability. The present paper is intended to review the state of affairs of analytic methods, queueing analysis techniques in particular, which are essential to modeling of computer communication systems. First we review basic properties of exponential queueing systems, and then give an overview of recent progress made in the areas of queueing network models and discrete-time queueing systems. A unified treatment of buffer storage overflow problems will be discussed as an application example, in which we call attention to the analogy between buffer behavior and waiting time in the GI/G/1 queue. Another application deals with the analysis of various multiplexing techniques and network configuration. An extensive reference list of the subject fields is also provided.

Correlative level coding and maximum-likelihood decoding

Modems for digital communication often adopt the so-called correlative level coding or the partial-response signaling, which attains a desired spectral shaping by introducing controlled intersymbol interference terms. In this paper, a correlative level encoder is treated as a linear finite-state machine and an application of the maximum-likelihood decoding (MLD) algorithm, which was originally proposed by Viterbi in decoding convolutional codes, is discussed. Asymptotic expressions for the probability of decoding error are obtained for a class of correlative level coding systems, and the results are confirmed by computer simulations. It is shown that a substantial performance gain is attainable by this probabilistic decoding method.

A Survey of Coding Schemes for Transmission or Recording of Digital Data

In this survey we shall review coding techniques and results which pertain to such problems as reduction of dc wandering, suppression of intersymbol interference, and inclusion of selfclocking capability. These problems are of engineering interest in the transmission or recording of digital data. The topics to be discussed include: 1) dc free codes such as bipolar signals and feedback balanced codes, 2) correlative level codes and optimal decoding methods, 3) Fibonacci codes and run-length constraint codes, and 4) state-oriented codes.

Application of the Diffusion Approximation to Queueing Networks II: Nonequilibrium Distributions and Applications to Computer Modeling

Quite often explicit information about the behavior of a queue over a fairly short period is wanted. This requires solving the nonequilibrium solution of the queue-length distribution, which is usually quite difficult mathematically. The first half of Part II shows how the diffusion process approximation can be used to answer this question. A transient solution is obtained for a cyclic queueing model using the technique of eigenfunction expansion. The second half of Part II applies the earlier results of Part I to modeling and performance problems of a typical multiprogrammed computer system. Such performance measures as utilization, throughput, response time and its distribution, etc., are discussed in some detail.

An Approximate Method for Design and Analysis of an ALOHA System

We develop here an approximate method for the design and performance prediction of a multiaccess communication system which employs the ALOHA packet-switching technique. Our model is based on the use of a diffusion process approximation of an ALOHAlike system (with or without time-slotting). A simple closed-form solution for the variable Q(t) , a variant of the number of backlog messages at time t , is given in terms of a few system and user parameters. Final results are expressed in terms of ordinary performance measures such as throughput and average delay. Several numerical examples are given to demonstrate the usefulness of the approximation technique developed.

Image data compression by predictive coding I: prediction algorithms

This paper deals with predictive coding techniques for efficient transmission or storage of two-level (black and white) digital images. Part I discusses algorithms for prediction. A predictor transforms the two-dimensional dependence in the original data into a form which can be handled by coding techniques for one-dimensional data. The implementation and performance of a fixed predictor, an adaptive predictor with finite memory, and an adaptive linear predictor are discussed. Results of experiments performed on various types of scanned images are also presented. Part II deals with techniques for encoding the prediction error pattern to achieve compression of data.

On Decoding of Correlative Level Coding Systems with Ambiguity Zone Detection

Decoding of a correlative level coding or partialresponse signaling system is discussed in an algebraic framework. A correction scheme in which the quantizer Output includes ambiguity levels is proposed. The implementation and algorithm of error correction is discussed in some detail. An optimum design of the quantizer based on Chows earlier work is discussed. Both analytical and simulation results on the performance of the proposed decoding scheme are presented. An asymptotic expression for the decoding error rate is derived in closed form as a function of the channel signal-to-noise ratio. This is also compared with the conventional bit-by-bit detection method and the maximumlikelihood decoding method recently studied.

Image data compression by predictive coding II: encoding algorithms

This paper deals with predictive codihg techniques for efficient transmission or storage of two-level (black and white) digital images. Part I discussed algorithms for prediction. Part II deals with coding techniques for encoding the prediction error pattern. First, we survey some schemes fore ncoding if the error pattern is assumed to be memoryless. Then a method is developed for encoding certain run-length distributions. Finally, some experimental results for sample documents are presented.