A Course on Queueing Models

QUEUES: BASIC CONCEPTS Introduction Queues: Features and Characteristics Graphical Methods Modelling Scope and Organization MARKOVIAN QUEUES Introduction A Simple Model: Steady-State Behaviour Birth-Death Models: Steady-State Behaviour Erlangian Models: Steady-State Behaviour Transient Behaviour Waiting Time and Little's Formula Busy Periods and Idle Periods 3 Networks of Queues - I Optimization Discussion REGENERATIVE NON-MARKOVIAN QUEUES - I Introduction Markovian Input Models Markovian Service-Time Models Bulk Queues Functional Relations: A Heuristic Approach Busy Periods Discrete-Time Queues Discussion COMPUTATIONAL METHODS - I Introduction Root Finding Methods The State Reduction Method Transient Behaviour: Numerical Approaches Discussion STATISTICAL INFERENCE AND SIMULATION Introduction Statistical Inference Solving Queueing Problems by Simulation A Practical Application Discussion REGENERATIVE NON-MARKOVIAN QUEUES - II Introduction Non-Markovian Queues: Transient Solution Combinatorial Methods Functional Relations Discussion GENERAL QUEUES Introduction Waiting Time and Idle Time: An Analytic Method Bounds for the Average Waiting Time A Heavy Traffic Approximation Diffusion Approximation Waiting Time and Idle Time: A Probabilistic Method Duality Discussion COMPUTATIONAL METHODS - II Introduction The Matrix-Geometric Solution The Block Elimination Method The Fourier Series Method for Inverting Transforms Discussion DISCRETE-TIME QUEUES: TRANSIENT SOLUTIONS Introduction Combinatorial Methods: Lattice Path Approach Recurrence Relations Algebraic Methods Discussion MISCELLANEOUS TOPICS Introduction Priority Queues Queues with Infinite Servers Design and Control of Queues Networks of Queues II Discussion APPENDICES INDEX Each chapter includes exercises and references.