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doi:10.1016/j.peva.2005.10.003 
Copyright © 2005 Elsevier Ltd All rights reserved.
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Luciano Lenzinia, 
, Linda Martorinia, , Enzo Mingozzia, and Giovanni Stea
, a,
Received 13 September 2004;
Abstract
Aggregate scheduling has been proposed as a solution for achieving scalability in large-size networks. However, in order to enable the provisioning of real-time services, such as video delivery or voice conversations, in aggregate scheduling networks, end-to-end delay bounds for single flows are required. In this paper, we derive per-flow end-to-end delay bounds in aggregate scheduling networks in which per-egress (or sink-tree) aggregation is in place, and flows traffic is aggregated according to a FIFO policy. The derivation process is based on Network Calculus, which is suitably extended to this purpose. We show that the bound is tight by deriving the scenario in which it is attained. A tight delay bound can be employed for a variety of purposes: for example, devising optimal aggregation criteria and rate provisioning policies based on pre-specified flow delay bounds.
Keywords: Delay bounds; Quality of Service; Sink-tree networks; Network Calculus; FIFO multiplexing
Article Outline
- 1. Introduction
- 2. Network Calculus background
- 3. System model
- 4. Analysis
- 4.1. End-to-end service curve for the tagged flow
- 4.2. Computation of the delay bound
- 4.3. Analysis of the delay bound expression
- 4.4. Optimal end-to-end service curve for flow 1
- 4.5. Generalization to sink-tree networks of arbitrary topology
- 5. Numerical examples
- 5.1. Balanced tree topology
- 5.2. Comparison between aggregate scheduling and per-flow scheduling
- 5.3. Delay-constrained bandwidth provisioning
- 6. Related work
- 7. Conclusions and future work
- Appendix A. Appendix
- A.1. Proof of the properties of pseudoaffine curves
- A.2. Proof of Property 4.9
- A.3. Proof of Lemma A.1
- A.4. Proof of Theorem 4.14
- A.5. Table of symbols
- References
- Vitae
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