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
4 - The G/G/1 Queue
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 present the ingenious scheme devised by Loynes to show that G/G/1 with stationary arrival and service processes is stable when the traffic intensity rho < 1, and transient if rho > 1. Under the stronger assumption that interarrivals and services are i.i.d., we explore the connection of the GI/GI/1 queue with the general random walk and obtain an insightful upper bound on waiting time.
- Type
- Chapter
- Information
- Scheduling and Control of Queueing Networks , pp. 61 - 70Publisher: Cambridge University PressPrint publication year: 2021