Abstract

The issue of Quality of Service (QoS) performance analysis in packet-switched networks has drawn a lot of attention in the networking community. There is a lot of work including an elegant theory under the name of network calculus, which focuses on analysis of deterministic worst case QoS performance bounds. In the meantime, researchers have studied stochastic QoS performance for specific schedulers. However, most previous works on deterministic QoS analysis or stochastic QoS analysis have only considered a server that provides deterministic service, i.e. deterministically bounded rate service. Few have considered the behavior of a stochastic server that provides input flows with variable rate service, for example wireless links. In this paper, we propose a stochastic network calculus to analyze the end-to-end stochastic QoS performance of a system with stochastically bounded input traffic over a series of deterministic and stochastic servers. We also prove that a server serving an aggregate of flows can be regarded as a stochastic server for individual flows within the aggregate. Based on this, the proposed framework is further applied to analyze per-flow stochastic QoS performance under aggregate scheduling.

Keywords: Network calculus; Quality of service; Generalized stochastically bounded burstiness (gSBB); Stochastic service curve

Article Outline

1. Introduction

2. Related work

2.1. Deterministic traffic under deterministic server

2.2. Stochastic traffic under deterministic server

2.3. Deterministic traffic under stochastic server

2.4. Stochastic traffic under stochastic server

3. Network model

3.1. Traffic models

3.1.1. Exponentially bounded burstiness (EBB)

3.1.2. Stochastically bounded burstiness (SBB)

3.1.3. Generalized stochastically bounded burstiness (gSBB)

3.2. Server models

4. Stochastic bounds under deterministic server

4.1. Single node case

4.2. Multi-node case

5. Stochastic bounds under stochastic server

5.1. Single node case

5.2. Discussion

5.3. Multi-node case

5.4. Discussion

6. Per-flow stochastic bounds under aggregate scheduling

6.1. Aggregate scheduling with deterministic server

6.2. Aggregate scheduling with stochastic server

6.3. Discussion

7. Conclusion

Appendix A. Proofs of results

A.1. Proof of Theorem 2

A.2. Proof of Theorem 3

A.3. Proof of Theorem 4

A.4. Proof of Theorem 5

A.5. Proof of Lemma 2

A.6. Proof of Theorem 6

A.7. Proof of Theorem 7

A.8. Proof of Theorem 8

A.9. Proof of Theorem 10

A.10. Proof of Corollary 14

A.11. Proof of Theorem 11

References

Vitae