The statistical nature of traffic and its impact on the realisability of QoS guarantees

1. Tequila Workshop Jan 2001 The statistical nature of traffic and its impact on the realisability of QoS guarantees Jim Roberts, France Telecom R&D (james.roberts@francetelecom.com)

2. Quality of service: a commodity? • Example SLS: • Scope: N/N • Flow identification: EF-valued DSCP, set of destination prefixes • Traffic conformance: token bucket (r,b) • Excess treatment: drop • Service schedule: Oct 3, 9:00 - 11:00 • Performance parameters: 0% loss • The role of traffic engineering: • What is the relation between (r,b) and user traffic characteristics ? • How can the network guarantee 0% loss ? • How much does this service cost ? • Maybe these questions don’t have a satisfactory answer... • depending on the statistical nature of traffic and the realisability of QoS guarantees

3. Outline • What is “Quality of Service” ? • Characterising IP traffic • Performance for stream applications • Performance for elastic applications • QoS and pricing

4. QoS and reservation • users express their demand in terms of aggregates • different classes (EF, AF1-4, ...) • different scopes : point to point,..., point to world, (world to point?) • e.g., 2 Mb/s “class 1” from A to B, 5 Mb/s “class 3” from A to C or D,... • network filters traffic at ingress • packets are “in” or “out” ... or “nearly in” • e.g., token bucket, sliding window,... • network “reserves” bandwidth • admission control / traffic engineering • using policy servers, signalling,... • resource provisioning • relies on “adequate provisioning” • e.g., service differentiation through different overbooking factors

5. Doubts about aggregates • traffic characterization • can a user choose its filter parameters? • how can the network reserve enough resources? • what about the small user? • end-to-end performance • what absolute quality of service? • what relative quality of service? • pricing • pricing for value... • ...or pricing for cost?

6. QoS and end-to-end performance • transparency for streaming applications • audio and video: interactive or playback • QoS  low packet loss and delay • scope for differentiation: real time/non-real time, hi-fi / lo-fi,... • response time for elastic applications • Web, e-mail, file transfer, MP3,... • QoS  high throughput • scope for differentiation: interactive/background, large flows/small flows,... • QoS is a statistical phenomenon • probabilities, averages,... • ...depending on available capacity • ...and traffic demand • QoS is often binary • “good enough”... • ...or “too bad” !

7. Outline • What is Quality of Service? • Characterising IP traffic • Performance for stream applications • Performance for elastic applications • QoS and pricing

8. Internet traffic is self-similar • a self-similar process • variability at all time scales • due to: • infinite variance of flow size • TCP induced burstiness Ethernet traffic, Bellcore 1989

9. Internet traffic is self-similar • a self-similar process • variability at all time scales • due to: • infinite variance of flow size • TCP induced burstiness • a practical consequence • difficult to characterise a traffic aggregate 10 s Ethernet traffic, Bellcore 1989

10. Traffic on a US backbone link (Thomson et al, 1997) • traffic intensity is predictable ... • ... and stationary in the busy hour

11. Traffic on a French backbone link • traffic intensity is predictable ... • ... and stationary in the busy hour tue wed thu fri sat sun mon 12h 18h 00h 06h

12. IP flows • a flow = one instance of a given application • a "continuous flow" of packets • basically two kinds of flow, stream and elastic • stream flows • audio and video, real time and playback • rate and duration are intrinsic characteristics • highly variable rate and duration • Poisson arrival process (?) • elastic flows • digital documents ( Web pages, files, ...) • rate and duration are measures of performance • highly variable size • Poisson arrivals (?) • 95% of packets are in elastic flows

13. Modelling traffic demand • stream traffic demand • arrival rate x bit rate x duration • elastic traffic demand • arrival rate x size • a stationary process in the "busy hour" • e.g., Poisson flow arrivals, independent flow size traffic demand Mbit/s busy hour time of day

14. Outline • What is Quality of Service? • Characterising IP traffic • Performance for stream applications • Performance for elastic applications • QoS and pricing

15. Open loop control for stream traffic • buffered of bufferless multiplexing ? • jitter control ? • admission control or adaptive applications ? • reservation or implicit admission control ? • scope for service differentiation ? user-network interface user-network interface network-network interface

16. Buffered multiplexing performance • a buffer to absorb rate overload • admission control to ensure Pr[buffer overflow]<e • but performance depends on complex traffic characteristics • e.g., self-similarity •  QoS of buffered multiplexing is uncontrollable • NB. token bucket is a virtual queue • difficult choice of r and b parameters? •  no satisfactory descriptor for variable rate flows or aggregates buffer size 0 0 more variable less variable log Pr[saturation]

17. time “Bufferless” multiplexing: alias rate envelope multiplexing • admission control to ensure Pr [Lt>C] < e • performance depends only on stationary rate distribution • loss rate  E [(Lt -C)+] / E [Lt] • performance is insensitive to self-similarity (and other correlation) • “negligible jitter” for flows shaped at the ingress (cf. INFOCOM 2001) output rate C combined input rate Lt

18. Efficiency of bufferless multiplexing • low loss imposes small amplitude of rate variations ... • peak rate << link rate (eg, 1%) • ... or low utilisation • overall mean rate << link rate • we may have both in an integrated network • priority to streaming traffic • residue shared by elastic flows

19. Implicit admission control • accept new flow only if transparency preserved • given flow peak rate • and estimated available bandwidth • reject new flow if necessary • by discarding first packets (probes) • uncritical decision threshold if streaming traffic is light • in an integrated network

20. Differentiation for stream traffic • different delays? • priority queues, WFQ, ... • but what guarantees? • different loss? • different utilisation (WFQ, ...) • "spatial queue priority" • partial buffer sharing, push out • or negligible loss and delay for all • elastic-stream integration ... • ... and low stream utilisation delay delay loss loss loss delay

21. utilization (r=a/m) for E(m,a) = 0.01 r 0.8 0.6 0.4 0.2 m 0 20 40 60 80 100 Provisioning for negligible blocking • "classical" teletraffic theory; assume • Poisson arrivals, rate l • constant rate per flow r • mean duration 1/m •  mean demand, A = l/m r bits/s • blocking probability for capacity C • B = E(C/r,A/r) • E(m,a) is Erlang's formula: • E(m,a)= •  scale economies • generalizations exist: • for different rates • for variable rates

22. Outline • What is Quality of Service? • Characterising IP traffic • Performance for stream applications • Performance for elastic applications • QoS and pricing

23. Closed loop control for elastic traffic • impact of packet scale on flow scale response time? • performance of statistical bandwidth sharing ? • need for admission control ? • scope for service differentiation ? user-network interface user-network interface network-network interface

24. Bandwidth and packet loss rate • a multi-fractal arrival process • but loss and bandwidth related by TCP (cf. Padhye et al.) • thus, p = p(B): i.e., loss rate depends on bandwidth share congestion avoidance loss rate p B(p)

25. Bandwidth sharing • reactive control (TCP, scheduling) shares bottleneck bandwidth unequally • depending on RTT, protocol implementation, etc. • and differentiated services parameters • optimal sharing in a network: objectives and algorithms... • max-min fairness, proportional fairness, maximal utility,... • ... but response time depends more on traffic process than the static sharing algorithm! Example: a linear network route 0 route 1 route L

26. Flow level performance of a bottleneck link link capacity C • assume perfect fair shares • link rate C, n elastic flows  • each flow served at rate C/n • assume Poisson flow arrivals • an M/G/1 processor sharing queue • load, r = arrival rate x size / C • performance insensitive to size distribution • Pr [n transfers] = rn(1-r) • E [response time] = size / C(1-r) • instability if r > 1 • i.e., unbounded response time • stabilized by aborted transfers... • ... or by admission control fair shares  a processor sharing queue throughput C r 0 0 1

27. transfer flows Poisson session arrivals processor sharing think time infinite server Generalizations of PS model • non-Poisson arrivals • Poisson sessions • general session structure • discriminatory processor sharing • weight fi for class i flows • service rate fi • rate limitations (same for all flows) • maximum rate per flow (eg, access rate) • minimum rate per flow (by admission control)

28. Admission control can be useful

29. Admission control can be useful

30. Admission control can be useful ... ... to prevent disasters at sea !

31. Admission control can also be useful for IP flows • improve efficiency of TCP • reduce retransmissions overhead ... • ... by maintaining throughput • implicit admission control • discard packets of new flows • when available capacity is low • prevent instability • due to overload (r > 1)... • ...and retransmissions • avoid aborted transfers • user impatience • "broken connections" • a means for service differentiation...

32. 1 .8 .6 .4 .2 0 300 200 100 0 Blocking probability E [Response time]/size r = 1.5 r = 1.5 r = 0.9 r = 0.9 0 100 200 N 0 100 200 N Choosing an admission control threshold • N = the maximum number of flows admitted • negligible blocking when r<1, maintain quality when r>1 • M/G/1/N processor sharing system • bandwidth  C/N; bandwidth  C/N , for r>1 • Pr [blocking] = rN(1 - r)/(1 - rN+1)  (1 - 1/r) , for r>1 • uncritical choice of threshold • eg, 1% of link capacity (N=100)

33. throughput C backbone link (rate C) access rate access links (rate<<C) 0 0 r 1 Impact of access rate on backbone sharing • TCP throughput is limited by access rate... • modem, DSL, cable • ... and by server performance, TCP receive window, other links,... •  backbone link transparent unless saturated! • ie, unless r > 1 (or r > 0.9...)

34. Differentiation for elastic traffic throughput • different utilization • separate pipes • class based queuing • different per flow shares • WFQ • impact of RTT,... • discrimination in overload • impact of aborts (?) • or by admission control C access rate r 0 0 1 1st class 3rd class 2nd class throughput C access rate r 0 0 1

35. Integrating streaming and elastic traffic • priority to packets of streaming flows • low utilization  negligible loss and delay • using EF ? • elastic flows use all remaining capacity • better response times • per flow fair queuing (?) • to prevent overload • implicit admission control... • ...and adaptive routing • an identical admission criterion for streaming and elastic flows • available rate > R

36. 1 r1 = r2 = 1.2 .17 0 100 N2 Differentiation by accessibility • block class 1 when 100 flows in progress - block class 2 when N2 flows in progress • in underload: both classes have negligible blocking (B1» B2» 0) • in overload: discrimination is effective • if r1 < 1 < r1 + r2, B1» 0, B2» (r1+r2-1)/r2 • if 1 < r1, B1» (r1-1)/r1, B2» 1 1 1 B2 r1 = r2 = 0.4 r1 = r2 = 0.6 B2 .33 B1 B2B10 B1 0 0 N2 N2 0 0 100

37. Provisioning for negligible blocking for elastic flows • "elastic" teletraffic theory; assume • Poisson arrivals, rate l • mean size s • blocking probability for capacity C • utilization r= ls/C • m = admission control limit • B(r,m) =rm(1-r)/(1-rm+1) • impact of access rate • C/access rate = m • B(r,m) E(m,rm) utilization (r) for B = 0.01 r 0.8 E(m,rm) 0.6 0.4 0.2 m 0 20 40 60 80 100

38. Outline • What is Quality of Service? • Characterising IP traffic • Performance for stream applications • Performance for elastic applications • QoS and pricing

39. Service differentiation and pricing • different QoS requires different prices... • or users will always choose the best • ...but streaming and elastic applications are qualitatively different • choose streaming class for transparency • choose elastic class for throughput •  no need for streaming/elastic price differentiation • different prices exploit different "willingness to pay"... • bringing greater economic efficiency • ...but QoS is not stable or predictable • depends on route, time of day,.. • and on factors outside network control: access, server, other networks,... •  network QoS is not a sound basis for price discrimination

40. demand capacity $$$ time of day Pricing to pay for the network • fix a price per byte • to cover the cost of infrastructure and operation • estimate demand • at that price • provision network to handle that demand • with excellent quality of service optimal price  revenue = cost capacity demand $$$ time of day

41. Price differentiation • maximise value by exploiting different “willingness to pay” • business, professional, residential • price components • flat rate subscription • per byte charge ( 0) • time of day variations • price differences based on stable criteria • e.g., access rate, available services • pay for differentiated accessibility... • e.g., flat rate payment for guaranteed reliability • ...but not for congestion • i.e., pay more for worse quality !

42. C r 0 0 1 Conclusions • a statistical characterisation of demand • a stationary random process in the busy period • a flow level characterisation (streaming and elastic flows) • transparency for streaming flows • rate envelope ("bufferless") multiplexing • the "negligible jitter conjecture" • response time for elastic flows • a "processor sharing" flow scale model • instability in overload (i.e., E[demand]>capacity) • service differentiation • distinguish streaming and elastic classes • limited scope for within-class differentiation • flow admission control in case of overload • pricing • per byte + flat rate charges