1 Slides by Yong Liu 1, Deep Medhi 2, and Michał Pióro 3 1 Polytechnic University, New York, USA 2 University of Missouri-Kansas City, USA 3 Warsaw University of Technology, Poland & Lund University, Sweden October 2007 Routing, Flow, and Capacity Design in Communication and Computer Networks Chapter 11: Multi-hour & Multi-Period Design

2 Outline  Multi-Hour Network Modeling & Design  uncapacitated  capacitated  robust routing  Multi-Time Period Design

3 Time-of-Day Effect  Traffic demand varies during hours of a day  Variations not synchronized

4 Illustration: 3-node network  Traffic Data

5 Design for Non-split flows  Optimal capacity  Optimal allocation in different hours

6 Multi-Hour Dimensioning  how much capacities needed to handle demands at all times?  rearrange routing when demand changes  modular link dimensioning

7 Multi-Hour Dimensioning  unsplittable flows  non-rerangable routing

8 Multi-Hour Routing  link capacity fixed  recalculate routing for each time t  problem separable, optimal routing at each t

9 Extension: robust routing under with multiple Traffic Matrices (TM)  multiple Traffic Matrices  dynamic traffic: demands between routing update period  estimation error: possible traffic demands  Robust routing: single set of routes achieving good performance under all possible TMs  routing reconfiguration too expensive  routing: link-path, node-link, destination based, link weight based  performance measure good average performance bounded worst-case performance trade-off between two  References  “On Optimal Routing with Multiple Traffic Matrices”,  “Optimal Routing with Multiple Traffic Matrices: Tradeoff between Average Case and Worst Case Performance”, ftp://gaia.cs.umass.edu/pub/Zhang05_tradeofftr.pdf

10 Multi-Time Period Design  When routes are to be planned/designed over multiple time periods  There may be installation cost and maintenance cost

11 Multi-time period Capacity Planning

12 How to handle disconnect?  How to allow ‘disconnect’ at a future time, set  This would mean  But, ensure that decrease is only on paths that have positive allocation in a previous period; thus, need   Above replaces non-negative requirement on flows

13 Relation of spare capacity from this period to satisfy capacity requirement in the next period

14 Continuing …  After some rearrangement, we arrive at  See next model

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