Abstract

Stability is one of the important issues for a TCP/AQM (Active Queue Management) system. In this paper, we study the local and global stability of TCP-newReno/RED under many flows regime. The existing results of the local stability are mostly for TCP-Reno, not for newReno. These results are obtained based on a small scale model with a few number of flows and thus cannot be blindly applied to a large system with many flows. Moreover, traditional approaches for the global stability based on Lyapunov functions is not suitable for a system with a large amount of flows due to its complexity. Motivated by this, we present a normalized discrete-time model to capture the essential dynamics of TCP-newReno/RED with many flows and obtain its local stability criterion. The normalized model allows us to proceed numerical iterations to analyze the global stability in an efficient manner. Our results show that by properly choosing some ‘free’ parameters, we can always ensure that a locally stable TCP-newReno/RED system is in fact globally stable. Our results become more accurate as the number of flows increases. Finally, we extend our normalized model to the case of heterogeneous RTTs.

Keywords: TCP; NewReno; Local stability; Global stability

Article Outline

1. Introduction

2. System model

2.1. Problem description

2.2. Normalized model

2.3. Model comparison

3. Local stability criterion

3.1. Linearizing system around equilibrium point

3.2. Local stability criterion

4. From local stability to global stability

4.1. Convergence from outside a box

4.2. Choosing free parameters to ensure global stability

4.3. Discussion

5. Extension to heterogeneous RTTs

5.1. Normalized model for heterogeneous RTTs

5.1.1. Normalized window dynamics

5.2. Equilibrium point for heterogeneous RTTs

5.3. Stability condition for heterogeneous RTTs

5.4. Decomposition of stability condition for heterogeneous RTTs

5.5. Discussion

6. Simulation results

6.1. Homogeneous RTTs

6.2. Heterogeneous RTTs

7. Conclusion

References

Vitae

An early version of this paper has appeared in the proceedings of IEEE ICC’05 [1].