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An Information-theoretic Approach to Network Measurement and Monitoring Yong Liu, Don Towsley, Tao Ye, Jean Bolot 1 Outline motivation background flow-based network model full packet trace compression marginal/joint coarser granularity netflow and SNMP future work 2 Motivation network monitoring: sensing a network traffic engineering, anomaly detection, … single point v.s. distributed different granularities full traffic trace: packet headers flow level record: timing, volume summary statistics: byte/packet counts challenges growing scales: high speed link, large topology constrained resources: processing, storage, transmission 30G headers/hour at UMass gateway solutions sampling: temporal/spatial compression: marginal/distributed 3 Questions how much can we compress monitoring traces? how much information is captured by different monitoring granularity? packet trace/NetFlow/SNMP how much joint information is there in multiple monitors? joint compression trace aggregation monitor placement 4 Our Contribution flow-based network models explore temporal/spatial correlation in network traces projection to different granularity information theoretic framework entropy: bound/guideline on trace compression quantitative approach for more general problems validation against measurement from operational network 5 Entropy & Compression Shannon entropy of discrete r.v. compression of i.i.d. symbols (length M) by coding coding: expected code length: info. theoretic bound on compression ratio: Shannon/Huffman coding assign short codeword to frequent outcome achieve the H(X) bound 6 Entropy & Correlation joint entropy entropy rate of stochastic process exploit temporal correlation Lempel-Ziv Coding: (LZ77, gzip, winzip) asymptotically achieve the bound for stationary process joint entropy rate of correlated processes 7 exploit spatial correlation Slepian-Wolf Coding: (distributed compression) encode each process individually, achieve joint entropy rate in limit Network Trace Compression naïve way: treat as byte stream, compress by generic tools gzip compress UMass traces by a factor of 2 network traces are highly structured data multiple fields per packet • diversity in information richness • correlation among fields multiple packets per flow • • packets within a flow share information temporal correlation • • most fields unchanged within the network spatial correlation multiple monitors traversed by a flow network models explore correlation structure quantify information content of network traces serves as lower bounds/guidelines for compression algorithms 8 Packet Header Trace 0 16 time stamp (sec.) Timing time stamp (sub-sec.) vers. HLen ToS IPID IP Header 31 TTL total length flags protocol fragment offset header checksum source IP address destination IP address source port destination port data sequence number acknowledgment number TCP Header Hlen TCP flags checksum 9 window size urgent pointer Header Field Entropy 0 16 time stamp (sec.) Timing time stamp (sub-sec.) vers. HLen ToS IPID IP Header 31 TTL total length flags protocol time fragment offset header checksum source IP address destination IP address source port destination port data sequence number acknowledgment number TCP Header Hlen TCP flags checksum 10 window size urgent pointer flow id Single Point Packet Trace T0 F0 T1 F1 T3 Tm F0 F0 Tn Fn packet inter-arrival: # bits per packet: temporal correlation introduced by flows packets from same flow closely spaced in time they share header information flow based trace: T0 F0 flow record: F0 K T3 Tm T0 flow flow arrival ID size time 11 F0 packet inter-arrival F0 Network Models flow-based model flow arrivals follow Poisson with rate flows are classified to independent flow classes according to routing (the set of routers traversed) flow i is described by: • flow inter-arrival time: • flow ID: • flow length: • packet inter-arrival time within the flow: packet arrival stochastic process: 12 Entropy in Flow Record # bits per flow: # bits per second: marginal compression ratio determined by flow length (pkts.) and variability in pkt. inter-arrival. 13 Single Point Compression: Results C1-in C2-in BB1-out BB2-out router Trace H (total) Model Ratio Compression Algorithm C1-in 706.3772 0.2002 0.6425 BB1-out 736.1722 0.2139 0.6574 BB2-out 689.9066 0.2186 0.6657 Compression ratio lower bound calculated by entropy much lower than real compression algorithm Real compression algorithm difference Records IPID, packet size, TCP/UDP fields Fixed packet buffer for each flow => many flow records for long flows 14 Distributed Network Monitoring single flow recorded by multiple monitors spatial correlation: traces collected at distributed monitors are correlated marginal node view: #bits/sec to represent flows seen by one node, bound on single point compression network system view: #bits/sec to represent flows cross the network, bound on joint compression joint compression ratio: quantify gain of joint compression 15 Baseline Joint Entropy Model “perfect” network fixed routes/constant link delay/no packet loss flow classes based on routes flows arrive with rate: # of monitors traversed: #bits per flow record: info. rate at node v: network view info. rate: joint compression ratio: dependence on # of monitors travered 16 Joint Compression: Results C1-in C2-in 17 BB1-out BB2-out router Set of Traces Joint Compression Ratio {C1-in, BB1-out, C2-in, BB2-out} 0.5 {C1-in, BB1-out} 0.8649 {C1-in, BB2-out} 0.8702 {C2-in, BB1-out} 0.7125 {C2-in, BB2-out} 0.6679 Coarser Granularity Models NetFlow model similar to flow model: joint compression result similar to full trace SNMP model any link SNMP rate process is sum of rate processes of all flow classes passing through that link traffic rates of flow classes are independent Gaussian entropy can be calculated by covariance of these processes information loss due to summation small joint information between monitors difficult to recover rates of flow classes from SNMP data 18 Joint Compression Ratio of Different Granularity C1-in C2-in 19 BB1-out BB2-out router Set of Traces SNMP NetFlow Packet Trace {C1-in, BB1-out} 1.0021 0.8597 0.8649 {C1-in, BB2-out} 0.9997 0.8782 0.8702 Conclusion information theoretic bound on marginal compression ratio -- ~ 20% (time+flow id, even lower if include other low entropy fields) marginal compression ratio high (not very compressible) in SNMP, lower in NetFlow, and the lowest in full trace joint coding is much more useful/nessassary in full trace case than in SNMP “More entropy for your buck” 20 Future Work network impairments how many more bits for delay/loss/route change model netflow with sampling distributed compression algorithms lossless v.s. lossy compression entropy based monitor placement maximize information under constraints 21 Thanks! 22