Queueing Networks: A Fundamental Approach

✍ Scribed by Nico M. Van Dijk (auth.), Richard J. Boucherie, Nico M. van Dijk (eds.)

• Publisher: Springer US
• Year: 2011
• Tongue: English
• Leaves: 813
• Series: International Series in Operations Research & Management Science 154
• Edition: 1
• Category: Library

✦ Synopsis

This handbook aims to highlight fundamental, methodological and computational aspects of networks of queues to provide insights and to unify results that can be applied in a more general manner. The handbook is organized into five parts:

Part 1 considers exact analytical results such as of product form type. Topics include characterization of product forms by physical balance concepts and simple traffic flow equations, classes of service and queue disciplines that allow a product form, a unified description of product forms for discrete time queueing networks, insights for insensitivity, and aggregation and decomposition results that allow subnetworks to be aggregated into single nodes to reduce computational burden.

Part 2 looks at monotonicity and comparison results such as for computational simplification by either of two approaches: stochastic monotonicity and ordering results based on the ordering of the proces generators, and comparison results and explicit error bounds based on an underlying Markov reward structure leading to ordering of expectations of performance measures.

Part 3 presents diffusion and fluid results. It specifically looks at the fluid regime and the diffusion regime. Both of these are illustrated through fluid limits for the analysis of system stability, diffusion approximations for multi-server systems, and a system fed by Gaussian traffic.

Part 4 illustrates computational and approximate results through the classical MVA (mean value analysis) and QNA (queueing network analyzer) for computing mean and variance of performance measures such as queue lengths and sojourn times; numerical approximation of response time distributions; and approximate decomposition results for large open queueing networks.

Part 5 enlightens selected applications as loss networks originating from circuit switched telecommunications applications, capacity sharing originating from packet switching in data networks, and a hospital application that is of growing present day interest.

The book shows that the intertwined progress of theory and practice will remain to be most intriguing and will continue to be the basis of further developments in queueing networks.

✦ Table of Contents

Front Matter....Pages i-xxiii
On Practical Product Form Characterizations....Pages 1-83
Order Independent Queues....Pages 85-120
Insensitivity in Stochastic Models....Pages 121-140
Palm Calculus, Reallocatable GSMP and Insensitivity Structure....Pages 141-215
Networks with Customers, Signals, and Product Form Solution....Pages 217-267
Discrete Time Networks with Product Form Steady States....Pages 269-312
Decomposition and Aggregation in Queueing Networks....Pages 313-344
Stochastic Comparison of Queueing Networks....Pages 345-395
Error Bounds and Comparison Results: The Markov Reward Approach For Queueing Networks....Pages 397-459
Stability of Join-the-Shortest-Queue networks: Analysis by Fluid Limits....Pages 461-487
Methods in Diffusion Approximation for Multi-Server Systems: Sandwich, Uniform Attraction and State-Space Collapse....Pages 489-530
Queueing Networks with Gaussian Inputs....Pages 531-560
Mean Values Techniques....Pages 561-586
Response Time Distributions in Networks of Queues....Pages 587-641
Decomposition-Based Queueing Network Analysis with FiFiQueues....Pages 643-699
Loss Networks....Pages 701-728
A Queueing Analysis of Data Networks....Pages 729-765
Modeling a Hospital Queueing Network....Pages 767-798

✦ Subjects

Probability Theory and Stochastic Processes; Operations Research/Decision Theory; Mathematical Modeling and Industrial Mathematics; Computer Communication Networks; Operations Research, Mathematical Programming; Computer Systems Organiza