Insensitivity in IP network performance

1. IPAM Workshop 18-19 March 2002 Insensitivity in IP network performance Jim Roberts (et al.) (james.roberts@francetelecom.com)

2. Traffic theory: the fundamental three-way relationship • traffic engineering relies on understanding the relationship between demand, capacity and performance demand • volume • characteristics capacity performance • bandwidth • how it is shared • response time • loss, delay

3. Outline • characterizing demand • statistical bandwidth sharing • performance of elastic traffic • integrating streaming traffic • extensions for an integrated network

4. Characterizing traffic demand • systematic traffic variations • hour of the day, day of the week,... • subject to statistical variations and growth trends • stochastic variations • model traffic as a stationary stochastic process • at the intensity of a representative demand • prefer a characterization at flow level (not packets or aggregates) • "appliflow": a set of packets from one instance of an application • two kinds of flow: streaming and elastic 50 Mb/s 50 Mb/s 0 Mb/s 0 Mb/s one day one week

5. Streaming and elastic traffic • elastic traffic is closed-loop controlled • digital documents ( Web pages, files, ...) • rate and duration are measures of performance • QoS  adequate throughput (response time)

6. Streaming and elastic traffic • elastic traffic is closed-loop controlled • digital documents ( Web pages, files, ...) • rate and duration are measures of performance • QoS  adequate throughput (response time) • streaming traffic is open-loop controlled • audio and video, real time and playback • rate and duration are intrinsic characteristics • QoS  negligible loss, delay, jitter

7. think times start of session flow arrivals end of session A generic traffic model • a session consists of a succession of flows separated by "think times" • flows are streaming or elastic • think times begin at the end of each flow • sessions are mutually independent

8. think times start of session flow arrivals end of session A generic traffic model • a session consists of a succession of flows separated by "think times" • flows are streaming or elastic • think times begin at the end of each flow • sessions are mutually independent • assume each flow is transmitted as an entity • eg, multiple TCP connections of one Web page constitute one flow

9. think times start of session flow arrivals end of session A generic traffic model • a session consists of a succession of flows separated by "think times" • flows are streaming or elastic • think times begin at the end of each flow • sessions are mutually independent • assume each flow is transmitted as an entity • eg, multiple TCP connections of one Web page constitute one flow • sessions occur as a homogeneous Poisson process • an Internet "invariant": [Floyd and Paxson, 2001]

10. Outline • characterizing demand • statistical bandwidth sharing • performance of elastic traffic • integrating streaming traffic • extensions for an integrated network

11. Statistical bandwidth sharing • reactive control (TCP, scheduling) shares bottleneck bandwidth... ...unequally • depending on RTT, protocol implementation, etc. • there are no persistent flows in the Internet • utility is not a function of instantaneous rate • performance is measured by response time for finite flows • response time depends more on the traffic process than on the static sharing algorithm

12. Performance of an isolated bottleneck • consider an isolated bottleneck of capacity C bits/s • shared by many users independently accessing many servers • performance is measured by • flow response time... • ...or realized throughput (= size / response time) users servers C bits/s

13. Performance of an isolated bottleneck • consider an isolated bottleneck of capacity C bits/s • shared by many users independently accessing many servers • performance is measured by • flow response time... • ...or realized throughput (= size / response time) • assume (for now) Poisson flow arrivals • arrival rate l • consider a fluid model • assuming packet level dynamics realize bandwidth sharing objectives users servers C bits/s

14. external rate limits, max_ratei(t) A fluid model of statistical bandwidth sharing • the number of flows in progress is a stochastic process • N(t) = number of flows in progress at time t • ratei(t) = rate of flow i • ratei(t) max_ratei(t) (due to other throughput limits) users servers C bits/s

15. A fluid model of statistical bandwidth sharing • the number of flows in progress is a stochastic process • N(t) = number of flows in progress at time t • ratei(t) = rate of flow i • ratei(t) max_ratei(t) (due to other throughput limits) • assume instant max-min fair sharing... • rate of flow i, ratei(t) = min {max_ratei (t), fairshare} • where fairshare is such that Sratei(t)= min {Smax_ratei (t), C} users servers C bits/s external rate limits, max_ratei(t)

16. A fluid model of statistical bandwidth sharing • the number of flows in progress is a stochastic process • N(t) = number of flows in progress at time t • ratei(t) = rate of flow i • ratei(t) max_ratei(t) (due to other throughput limits) • assume instant max-min fair sharing... • rate of flow i, ratei(t) = min {max_ratei (t), fairshare} • where fairshare is such that Sratei(t)= min {Smax_ratei (t), C} • ... realized approximately by TCP... • ...or more accurately by Fair Queuing users servers C bits/s external rate limits, max_ratei(t)

17. 1 Three link bandwidth sharing models • 1. a fair sharing bottleneck • external limits are ineffective: max_ratei (t)  C, ratei(t) = C/N(t) • e.g., an access link • 2. a fair sharing bottleneck with common constant rate limit • flow bandwidth cannot exceed r: max_ratei (t)  r,ratei(t) = min {r,C/N(t)} • e.g., r represents the modem rate • 3. a transparent backbone link • max_ratei(t) << C and link is unsaturated: S max_ratei(t) < C, ratei(t) = max_ratei (t) users servers external rate limits max_ratei(t)

18. offered traffic ls C Example: a fair sharing bottleneck (case 1) • an M/G/1 processor sharing queue • Poisson arrival ratel • mean flow size s • load r = ls/C (assume r < 1) max_ratei(t) > C ratei(t) = C/N(t)

19. max_ratei(t) > C ratei(t) = C/N(t) Example: a fair sharing bottleneck (case 1) • an M/G/1 processor sharing queue • Poisson arrival ratel • mean flow size s • load r = ls/C (assume r < 1) • stationary distribution of number of flows in progress • p(n) = Pr [N(t) = n] • p(n) = rn (1 – r) offered traffic ls C

20. max_ratei(t) > C ratei(t) = C/N(t) Example: a fair sharing bottleneck (case 1) • an M/G/1 processor sharing queue • Poisson arrival ratel • mean flow size s • load r = ls/C (assume r < 1) • stationary distribution of number of flows in progress • p(n) = Pr [N(t) = n] • p(n) = rn (1 – r) • expected response time of flows of size s • mean throughput = s/R(s) = C(1 – r) offered traffic ls C

21. throughput of "mice": Pr[th'put=C/n]  p(n) throughput of "elephants":  mean = C(1 - r) C(1-r) ns simulation of TCP bandwidth sharing 1 Mbit/s Pareto size distribution Poisson flow arrivals load 0.5 1000 800 600 Throughput (Kbit/s) 400 200 0 0 500 1000 1500 2000 Size (Kbytes)

22. C max_rate load, r 0 1 Impact of max_rate: mean throughput as a function of load E[throughput] () fair sharing:  = C(1 – r) fair sharing with rate limit:  min {max_rate, C(1 – r)}

23. Accounting for non-Poisson flow arrivals • a stochastic network representation (cf. BCMP 1975, Kelly 1979) • sessions are customers arriving from the outside • the link is a processor sharing station • think-time is an infinite server station • ... Poisson session arrivals flows end of session link think-time

24. Poisson session arrivals flows end of session link think-time Accounting for non-Poisson flow arrivals • ... • a network of "symmetric queues" (e.g., PS, infinite server): • customers successively visit the stations a certain number of times before leaving the network • customers change "class" after each visit - class determines service time distribution, next station and class in that station • customers arrive as a Poisson process • ...

25. Accounting for non-Poisson flow arrivals • ... • performance of the stochastic network: • a product form occupancy distribution, insensitive to service time distributions • ... Poisson session arrivals flows end of session link think-time

26. Accounting for non-Poisson flow arrivals • ... • bandwidth sharing performance is as if flow arrivals were Poisson • same distribution of flows in progress, same expected response time Poisson session arrivals flows end of session link think-time

27. Accounting for non-Poisson flow arrivals • ... • bandwidth sharing performance is as if flow arrivals were Poisson • same distribution of flows in progress, same expected response time • class: a versatile tool to account for correlation in flow arrivals • different kinds of session • distibution of number of flows per session,... Poisson session arrivals flows end of session link think-time

28. Accounting for non-Poisson flow arrivals • ... • bandwidth sharing performance is as if flow arrivals were Poisson • same distribution of flows in progress, same expected response time • class: a versatile tool to account for correlation in flow arrivals • different kinds of session • distibution of number of flows per session,... • a general performance result for any mix of elastic applications Poisson session arrivals flows end of session link think-time

29. premium class best effort class C 0 0 C A Accounting for unfair sharing • slight impact of unequal per flow shares • e.g., green flows get 10 times as much bandwidth as red flows • approximate insensitivity throughput

30. 1 station per route session arrivals end of session think time Extension for statistical bandwidth sharing in networks • insensitivity in PS stochastic networks with state dependent service rates • theory of Whittle networks (cf. Serfoso, 1999)... • ...applied to statistical bandwidth sharing (Bonald and Massoulié, 2001; Bonald and Proutière, 2002)

31. number of flows throughput Underload and overload: the meaning of congestion • in normal load (i.e., r < 1): • performance is insensitive to all details of session structure • response time is mainly determined by external bottlenecks (i.e, max_rate << C) • but overloads can (and do) occur (i.e., r > 1): • due to bad planning, traffic surges, outages,... • the queuing models are then unstable, i.e., E[response time] 

32. number of flows throughput Underload and overload: the meaning of congestion • in normal load (i.e., r < 1): • performance is insensitive to all details of session structure • response time is mainly determined by external bottlenecks (i.e, max_rate << C) • but overloads can (and do) occur (i.e., r > 1): • due to bad planning, traffic surges, outages,... • the queuing models are then unstable, i.e., E[response time]  • to preserve stability: flow based admission control!

33. Outline • characterizing demand • statistical bandwidth sharing • performance of elastic traffic • integrating streaming traffic • extensions for an integrated network

34. L/p packets bursts arrival rate Fluid queueing models for streaming traffic • assume flows "on" at rate p, or "off" • by shaping to rate p (e.g., isolated packet of size L = burst of length L/p)

35. L/p packets bursts bufferless buffered arrival rate Fluid queueing models for streaming traffic • assume flows "on" at rate p, or "off" • by shaping to rate p (e.g., isolated packet of size L = burst of length L/p) • bufferless or buffered multiplexing? • Pr [arrival rate > service rate] < e • Pr [buffer overflow] < e

36. buffer size 0 0 log Pr [overflow] Sensitivity of buffered multiplexing performance • for a superposition of N independent on/off sources service rate input rate

37. buffer size 0 0 longer burst length shorter log Pr [overflow] Sensitivity of buffered multiplexing performance • for a superposition of N independent on/off sources • performance depends on: • mean lengths service rate input rate

38. more variable burst length less variable Sensitivity of buffered multiplexing performance • for a superposition of N independent on/off sources • performance depends on: • mean lengths • distributions buffer size 0 0 log Pr [overflow] service rate input rate

39. long range dependence burst length short range dependence Sensitivity of buffered multiplexing performance • for a superposition of N independent on/off sources • performance depends on: • mean lengths • distributions • correlation buffer size 0 0 log Pr [overflow] service rate input rate

40. Sensitivity of buffered multiplexing performance • for a superposition of N independent on/off sources • performance depends on: • mean lengths • distributions • correlation • sensitivity precludes precise control • prefer bufferless multiplexing buffer size 0 0 long range dependence burst length short range dependence log Pr [overflow] service rate input rate

41. service rate Bufferless multiplexing (alias rate envelope multiplexing) • ensure negligible probability of rate overload • Pr[input rate > service rate] <  • by provisioning • accounting for session/flow process and rate fluctuations within each flow • and using admission control to preserve transparency • measurement-based admission control (e.g. Gibbens et al., 1995) input rate

42. Insensitive performance of bufferless multiplexing • assuming Poisson session arrivals and peak rate p: • traffic offered = a bit/s, capacity = C bit/s bursts Poisson session arrivals end of session link silence/ think-time

43. Insensitive performance of bufferless multiplexing • assuming Poisson session arrivals and peak rate p: • traffic offered = a bit/s, capacity = C bit/s • i.e., loss depends only on load (a/C) and link/peak rate ratio (C/p) • for any mix of streaming applications bursts Poisson session arrivals end of session link silence/ think-time

44. Efficiency of bufferless multiplexing • small amplitude of rate variations ... • peak rate << link rate (eg, 1%) • e.g., C/p = 100  Pr [overflow] < 10-6 for a/C < 0.6 • ... or low utilisation • overall mean rate << link rate

45. Efficiency of bufferless multiplexing • small amplitude of rate variations ... • peak rate << link rate (eg, 1%) • e.g., C/p = 100  Pr [overflow] < 10-6 for a/C < 0.6 • ... 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

46. Integrating streaming and elastic flows • scheduling required to meet QoS requirements • priority to streaming flows • fair sharing of residual capacity by elastic flows (TCP or FQ?)

47. Integrating streaming and elastic flows • scheduling required to meet QoS requirements • priority to streaming flows • fair sharing of residual capacity by elastic flows (TCP or FQ?) • realizing a performance synergy • very low loss for streaming data • efficient use of residual bandwidth by elastic flows

48. Integrating streaming and elastic flows • scheduling required to meet QoS requirements • priority to streaming flows • fair sharing of residual capacity by elastic flows (TCP or FQ?) • realizing a performance synergy • very low loss for streaming data • efficient use of residual bandwidth by elastic flows • complex performance analysis • a PS queue with varying capacity (cf. Delcoigne, Proutière, Régnié, 2002) • exhibits local instability and sensitivity (in heavy traffic with high stream peak rate)... • ... but a quasi-stationary analysis is accurate when admission control is used

49. Conclusion: • we need to account for the statistical nature of traffic • a Poisson session arrival process • fair sharing for insensitive elastic flow performance • slight impact of unfairness (cf. Bonald and Massoulié, 2001) • fair sharing in a network (cf. Bonald and Proutière, 2002) • bufferless multiplexing for insensitive streaming performance • choosing a common maximum peak rate (C/p > 100 for efficiency) • packet scale performance (jitter accumulation)? • synergistic integration of streaming and elastic traffic • quasi-insensitivity with admission control (cf. Delcoigne et al., 2002, Benameur et al., 2001)

50. Conclusion: • we need to account for the statistical nature of traffic • a Poisson session arrival process • fair sharing for insensitive elastic flow performance • slight impact of unfairness (cf. Bonald and Massoulié, 2001) • fair sharing in a network (cf. Bonald and Proutière, 2002) • bufferless multiplexing for insensitive streaming performance • choosing a common maximum peak rate (C/p > 100 for efficiency) • packet scale performance (jitter accumulation)? • synergistic integration of streaming and elastic traffic • quasi-insensitivity with admission control (cf. Delcoigne et al., 2002, Benameur et al., 2001) • required congestion control mechanisms • implicit measurement-based admission control • shaping and priority queuing and reliance on TCP... • ... or per-flow fair queuing for all?