Performance Metrics for Resilient Networks

1. Performance Metrics for Resilient Networks Michael Menth, Jens Milbrandt, Rüdiger Martin, Frank Lehrieder, Florian Höhn This work was in cooperation with Infosim GmbH & CoKG and supported by the Bavarian Ministry of Economic Affairs

2. Outline • Motivation • Unavailability of the network for end-to-end (e2e) aggregates • Calculation • Illustration of results • Overload probability for links • Calculation • Illustration of results • Summary & outlook

3. Availability of the network Link failures Node failures Link overload Redirected traffic due to failures More traffic due to increased user activity (hot spots) More traffic due to interdomain rerouting Tool for the assessment of network resilience Network availability Overload probability Why is it useful? Early discovery of risks Support of intentional overprovisioning Evaluation of potential upgrade strategies New routing More bandwidth, new links or nodes New customers or SLAs Motivation

4. Key Ideas • Network elements can fail • Failure probability • Independent failures • Correlated failures modelled by virtual element • Traffic matrices can vary • Example: additional interdomain traffic, hot spots • Traffic matrix probability • Independent of network failures • Definition: scenario = set of network failures and traffic matrix • Scenarios determine unavailability / overload • Derive scenario probability • Take all scenarios for the analysis with probability larger than pmin • Definition: set of considered scenarios S

5. Calculation of Network (Un)Availability • Problem: multiple failures can compromise connectivity • Loss of connectivity for e2e aggregate between node v and w in special scenario s? • Disconnected(v,w,s)  {0, 1} • Analysis of routing in scenario s • Conditional probability for loss of connectivity • Estimate for unavailability: not all possible scenarios respected in S • Upper and lower bounds available

6. European Nobel Test Network

7. Network Unavailability for Madrid‘s Aggregates of Madrid‘s Aggregates

8. Average Network Unavailability for Routers

9. Network Unavailability for Overall Traffic C

10. Calculation of „Link Overload“ • Problem: redirected and extra traffic leads to overload • Link utilization ρ(l,s) of link l in special scenario s? • Analysis of routing and traffic matrix in special scenario s • Probability to have utilization U(l) larger than x on link l • Complementary cumulative distribution function (CCDF) • Calculate ρ(l,s) for all considered scenarios sS • Sum all probabilities p(s) of scenario with ρ(l,s)>x • Comments • Intelligent data structures and efficient algorithms required • Only estimate, but upper and lower bounds available

11. pmin=10-8 Impact of Probability Limit pmax for Failure Scenarios pmin=10-6

12. Which Link is Most at Risk?

13. Link Rankings • Utilization threshold uc • Utilization percentile q • Appropriate weighted integral based on utilization distribution

14. Graphical Presentation

15. Summary & Conclusion • Tool for assessment of network resilience • Network availability • „Overload“ probability • Useful for planning and operation of networks • Achievements • Fast algorithms (Java) • Visualization of • Unavailabilty • „Overload“ • Outlook: interdomain resilience