Book contents
- Frontmatter
- Contents
- Notation
- Introduction
- Part I The Single Queue
- Part II Approximations of the Single Queue
- 4 The G/G/1 Queue
- 5 The Basic Probability Functional Limit Theorems
- 6 Scaling of G/G/1 and G/G/∞
- 7 Diffusions and Brownian Processes
- Part III Queueing Networks
- Part IV Fluid Models of Multi-Class Queueing
- Part V Diffusion Scaled Balanced Heavy Traffic
- Part VI Many-Server Systems
- References
- Index
6 - Scaling of G/G/1 and G/G/∞
from Part II - Approximations of the Single Queue
Published online by Cambridge University Press: 01 October 2021
Book contents
- Frontmatter
- Contents
- Notation
- Introduction
- Part I The Single Queue
- Part II Approximations of the Single Queue
- 4 The G/G/1 Queue
- 5 The Basic Probability Functional Limit Theorems
- 6 Scaling of G/G/1 and G/G/∞
- 7 Diffusions and Brownian Processes
- Part III Queueing Networks
- Part IV Fluid Models of Multi-Class Queueing
- Part V Diffusion Scaled Balanced Heavy Traffic
- Part VI Many-Server Systems
- References
- Index
Summary
We discuss fluid and diffusion approximations to the GI/GI/1 queue by scaling time and space. We also introduce the GI/GI/1 queueing system and study it under many-server scaling. The three types of scaling, fluid, diffusion, and many-server, form the backbone for Parts IV, V, andVI of the book, where we use them to study networks of queues. These approximations allow us to obtain a much better idea of how queues evolve over time than can be obtained from an exact discrete state Markov description.
- Type
- Chapter
- Information
- Scheduling and Control of Queueing Networks , pp. 83 - 101Publisher: Cambridge University PressPrint publication year: 2021