Network Calculus Lecture -- Pisa, July 7-11, 2003

Lecture Notes

• Online Book available here.
• "Optimal Smoothing for Guaranteed Service" (2000) Jean-Yves Le Boudec, Olivier Verscheure IEEE ACM Transactions on Networking: pdf.
• "Stochastic Analysis of Some Expedited Forwarding Networks" Proceedings of Infocom 2002, Milan Vojnovic and Jean-Yves Le Boudec: pdf.

Slides

Schedule

Day 1

Arrival Curves, Sub-Additivity, Leaky Buckets, GCRA. Max-Plus and Min-Plus Calculus. Min-Plus Convolution. Application to Integrated Services and MPLS.

Day 2

Service curves. Pay Bursts only once. Shapers. Conservation Properties. Shapers versus service curve elements. Application to Integrated Services. Packetizers.

Day 3

The Fixed Point method and Residuation theory. Optimal Smoothing. Smoothing versus shaping. Time reversal and deconvolution. Application to video playback. Guaranteed Rate schedulers and GPS.

Day 4

Aggregate Multiplexing and Instability. Delay Bounds for Differentiated Services. Packet Scale Rate Guarantee. Application to Expedited Forwarding.

Day 5

Stochastic loss bounds. Application to Differentiated Services. Burstiness Increase due to Aggregate Multiplexing. Route interference results. Application to MPLS. The ring is stable.

Homeworks