Mathematical Modeling and Computation of Real-Time Problems

An Interdisciplinary Approach

Rakhee Kulshrestha, Chandra Shekhar, Madhu Jain, Srinivas R. Chakravarthy, Rakhee Kulshrestha, Chandra Shekhar, Madhu Jain, Srinivas R. Chakravarthy

• Publisher: CRC Press
• Year: 2021
• Print ISBN: 9780367517434
• eBook ISBN: 9781000288674
• Edition: 1
• Topic: Mathematics
• Subtopic: Operations
• Index: Mathematics

This book covers an interdisciplinary approach for understanding mathematical modeling by offering a collection of models, solved problems related to the models, the methodologies employed, and the results using projects and case studies with insight into the operation of substantial real-time systems.

The book covers a broad scope in the areas of statistical science, probability, stochastic processes, fluid dynamics, supply chain, optimization, and applications. It discusses advanced topics and the latest research findings, uses an interdisciplinary approach for real-time systems, offers a platform for integrated research, and identifies the gaps in the field for further research.

The book is for researchers, students, and teachers that share a goal of learning advanced topics and the latest research in mathematical modeling.

Section I
Operations Research Models

1
A Comparative Study of Vacation Models Under Various Vacation Policies

A Simulation Approach

Srinivas R. Chakravarthy

Kettering University, Flint, MI, USA

CONTENTS

1.1 Introduction

1.1.1 Single-Server Systems

1.1.2 Multiserver Systems

1.2 Validation of the Simulation

1.3 Details on Input Data for Simulation

1.4 Comparison of Gated, G-Limited, and T-Limited Policies against the Classical Vacation (Single-Server System)

1.5 Integration of Classical, Gated, G-Limited, and T-Limited Policies and Comparing their Respective Times on Vacation (Single-Server System)

1.6 Comparison in the Context of Multiserver Systems

1.7 Comparison of Integrated Vacation Models under the Assumption of Setup Delay (Single-Server System)

1.8 Comparison of the Classical Vacation Models under the Assumption of Setup Delay (Multiserver System)

1.9 Concluding Remarks

References

1.1 INTRODUCTION

In classical queueing models, the server providing services is assumed to be available at all times even when there is no customer in the system. This idle time of the server is a wasted resource for the service provider and was one of the motivating factors for the introduction of the (pure or classical) vacation models in the 1970s (see, e.g., [1,2]). The term “vacation” can be interpreted in many ways depending on the context of the application. For example, the servers (or machines) may have to be rested, readjusted, or undergo preventive maintenance or be shared with other systems, among other things. Since then a number of variations in how the vacation starts and ends in the case of single- and multiple-sever systems have been introdu...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgements
• About the Editors
• Section I Operations Research Models
• Section II Soft Computing Models
• Section III Statistical Models
• Index