1. Trajectory Sampling for Direct Traffic Oberservation N.G. Duffield and Matthias Grossglauser IEEE/ACM Transactions on Networking, Vol. 9, No. 3 June 2001

2. Problem: Which (spatial) path does traffic take? Circuit switched networks (e.g. telephone): Per-call state is maintained =>trivial IP networks: Don’t maintain per- flow information ?

3. Why is this interesting? Quality of Service depends on traffic management Traffic control Timescale: seconds no human intervention Traffic engineering Timescale: minutes - months Resource allocation Pricing Failover strategies

4. Options Indirect measurement Uses information on Network model Network state Direct measurement Direct observation of traffic at multiple points in the network

5. Problems with indirect measurement Behavior of network elements depends on vendor-specific design choices Deliberate sources of randomness to avoid collision Events outside domain (route advertising by neighboring domains) Interactions may be too complex to predict

6. Direct measurement: Sampling of packets Sample packets that traverse each link Subset of packets used as representative Problem: How do we get the actual path?

7. Key idea of the paper Use a deterministic hash function over the packet’s content to determine subset of packets Use the same hash function throughout the domain Use second hash function to label packets

8. Theory Measurement domain represented as a directed graph Packets enter at ingress node exit at egress node Invariance function Packet content without changing fields, e.g. time-to-live field which is decremented each hop

9. Sampling Hash Function Decides whether or not a given packet should be sampled Deterministic function of the invariant packet content Same function on each link Results in L-bit binary number

10. Identification Hash Function Entire packet content could be used Aim: limit traffic to measurement collection system Results in m-bit binary number Additional information may be included Length of packet Source, destination

11. Invariant content Header: three categories of fields Variable fields (not included) E.g., TTL, header checksum, etc. Low entropy fields (not included) Content changes little between packets E.g., version, header length, protocol High entropy fields (included) Source and destination IP, etc. Part of remainder of packet

12. Ambiguities (f-h)

13. Dealing with ambiguities Probability that trajectory can be disambiguated depends on network topology and traffic => renormalization of results necessary Safer to discard all duplicate labels (greater loss of samples)

14. Specification of Hash Functions Ordered bits of invariant part of packet content x are considered as binary integers:  (x) Sampling hash function h(  (x)) =  (x) mod A Identification hash function g(  (x)) =  (x) mod B with A, B positive integers

15. Identical Packets Automatically ambiguous => lead to biased estimators Question: How much packet content is needed to avoid collisions? Answer: 40 bytes lead to collision probability smaller than 10 -3

16. Implementation of hashing 40 byte “numbers” are represented by vector of 16 bit words z = (z k,z k-1,…,z 0 ) =  i=0 k z i 2 16i Use 32 bit long division Iteratively compute (z k,z k-1,…,z 0 ) mod A = (z k-1 + 2 16 (z k mod A),…,z 0 ) mod A

17. Sampling independent of packet content? Note: IP address of source and destination are included in the invariant content! Chi-squared test 40 byte packet prefix => 95% confidence level 20 byte packet prefix results in strong dependence

18. Optimal Sampling Tradeoff More unambiguous samples => more accuracy More samples => more measurement traffic Optimize for given measurement traffic mn (m bits per sample, n samples) Small m increases collisions Large m means smaller n

19. (Question to the authors Doesn’t the measurement traffic itself get sampled and thereby add another source of error? … may be part of their future work statement)

20. Example Service provider wants to determine what fraction of packets on a certain backbone link belongs to a certain customer Compare customer packets observed both on backbone and on access link Total number of packets observed on backbone Real and estimated fractions largely within error bars

21. Implementation issues Can trajectory sampling be part of next generation of high-speed interfaces? Authors claim “yes”: Compute both hash functions in parallel Processor cost negligible compared with cost of interface cards Processor speed doubles every 18 months, maximum trunk speed every 21 months

22. Other Common Approaches Aggregation-based approaches e.g., sum of packets traversing a link Sampling-based approaches sample subset of observations

23. Aggregation-based Approaches Link measurements (direct) Traffic statistics (# of bytes / # of packets transferred / dropped) Measurements reported periodically Flow aggregation (indirect) Flow: sequence of packets with common field in header Relies on emulation of routing protocol

24. Sampling-based Approaches Active end-to-end probes (direct) Hosts send probe packets to one or more other hosts Packet loss rate Round-trip delay End-to-end path characteristics Variation: collect and exchange measurements of multicast session

25. Related Work Measure end-to-end performance of individual flows ATM cells sampled at ingress and egress points Determine QoS for a single connection, e.g., delay and loss rate

26. Extensions and Other Applications Distributed denial of service attacks Attackers use packet spoofing Filtering A configurable packet filter may allow trajectory sampling for a subset of packets Probe Packets Packet content may be constructed to ensure sampling

27. Conclusions Simple processing No Router state required Packets directly observed