Traffic management 2007

1. Traffic management2007

2. An example • Executive participating in a worldwide videoconference • Proceedings are videotaped and stored in an archive • Edited and placed on a Web site • Accessed later by others • During conference • Sends email to an assistant • Breaks off to answer a voice call

3. What this requires • For video • sustained bandwidth of at least 64 kbps • low loss rate • For voice • sustained bandwidth of at least 8 kbps • low loss rate • For interactive communication • low delay (< 100 ms one-way) • For playback • low delay jitter • For email and archiving • reliable bulk transport

4. What if… • A million executives were simultaneously accessing the network? • What capacity should each trunk have? • How should packets be routed? (Can we spread load over alternate paths?) • How can different traffic types get different services from the network? • How should each endpoint regulate its load? • How should we price the network? • These types of questions lie at the heart of network design and operation, and form the basis for traffic management.

5. Traffic management • Set of policies and mechanisms that allow a network to efficiently satisfy a diverse range of service requests • Tension is between diversity and efficiency • Traffic management = Connectivity + Quality of Service • Traffic management is necessary for providing Quality of Service (QoS) • Subsumes congestion control (congestion == loss of efficiency) • One of the most challenging open problems in networking

6. Outline • Economic principles • Traffic models • Traffic classes • Time scales - Mechanisms

7. Basics: utility function • Users are assumed to have a utility function that maps from a given quality of service to a level of satisfaction, or utility • Utility functions are private information • Cannot compare utility functions between users ? • Rational users take actions that maximize their utility • Can determine utility function by observing preferences

8. Example • Let u = S - a t • u = utility from file transfer • S = satisfaction when transfer infinitely fast (t=0) • t = transfer time • a = rate at which satisfaction decreases with time • As transfer time increases, utility decreases • If t > S/a, user is worse off! (reflects time wasted) -- timeout • Assumes linear decrease in utility • S and a can be experimentally determined

9. Social welfare • Suppose network manager knew the utility function of every user • Social Welfare is maximized when some combination of the utility functions (such as sum) is maximized • An economy (network) is efficientwhen increasing the utility of one user must necessarily decrease the utility of another -- conservation law • An economy (network) is envy-free if no user would trade places with another (better performance also costs more) ? • Goal: maximize social welfare • subject to efficiency, envy-freeness, and making a profit

10. Example • Assume: two users - A, B • Single switch, each user imposes load 0.4 (=ρ) • Same delay to both users: delay = d • A’s utility: 4 - d • B’s utility : 8 - 2d (wish less delay than A) • Conservation law(KL_Q_v2_117) • 0.4d + 0.4d = C => d = 1.25 C • social welfare (sum of utilities) = 12-3.75 C • If B’s delay reduced to 0.5C, then A’s delay = 2C • sum of utilities = 12 - 3C • Increase in social welfare (sum of utilities) need not benefit everyone • A loses utility, but may pay less for service

11. Some economic principles • Lowering delay of delay-sensitive traffic increased welfare • can increase welfare by matching service menu to user requirements • BUT need to know what users want (signaling) • A single network that provides heterogeneous QoS is better than separate networks for each QoS - Q theory • unused capacity is available to others • For typical utility functions, welfare increases more than linearly with increase in capacity ? • individual users see smaller overall fluctuations • can increase welfare by increasing capacity - Q theory, Large number law

12. Principles applied • A single wire that carries both voice and data is more efficient than separate wires for voice and data • IP Phone • ADSL • Moving from a 20% loaded10 Mbps Ethernet to a 20% loaded 100 Mbps Ethernet will still improve social welfare • increase capacity whenever possible • Better to give 5% of the traffic lower delay than all traffic low delay • should somehow mark and isolate low-delay traffic

13. The two camps • Can increase welfare either by • matching services to user requirements or • increasing capacity blindly • small and smart vs. big and dumb • Which is cheaper? no one is really sure! • It seems that smarter ought to be better • otherwise, to get low delays for some traffic, we need to give all traffic low delay, even if it doesn’t need it • But, perhaps, we can use the money spent on traffic management to increase welfare • We will study traffic management, assuming that it matters!

14. Outline • Economic principles • Traffic models (+ our research) • Traffic classes • Time scales - Mechanisms

15. Traffic models • To effectively manage traffic, need to have some idea of how users or aggregates of users behave => traffic model • e.g. average size of a file transfer • e.g. how long a user uses a modem • Models change with network usage • We can only guess about the future • Two types of models - hard to match both • from measurements • mathematical analysis - educated guesses

16. Telephone traffic models • How are calls placed? • call arrival model • studies show that time between calls is drawn from an exponential distribution • memoryless: the fact that a certain amount of time has passed since the last call gives no information of time to next call • call arrival process is therefore Poisson • How long are calls held? • usually modeled as exponential • however, measurement studies show it to be heavy tailed • means that a significant number of calls last a very long time

17. Internet traffic modeling • A few apps account for most of the traffic • WWW, FTP, telnet • A common approach is to model apps (this ignores distribution of destination!) • time between app invocations • connection duration • # bytes transferred • packet interarrival distribution • Little consensus on models - hard problem • Poisson models, Markov-modulated models • Self-similar models

18. Internet traffic models: features • LAN connections differ from WAN connections • Higher bandwidth (more bytes/call) • longer holding times • Many parameters are heavy-tailed --> Self-similarity • Examples: # bytes in call, call duration • means that a few calls are responsible for most of the traffic • these calls must be well-managed • can have long bursts • also means that evenaggregates with many calls not be smooth • New models appear all the time, to account for rapidly changing traffic mix

19. Fractal dimension (1) • A point has no dimensions • A line has one dimension - length • A plane has two dimensions - length and width, no depth • Space, a huge empty box, has three dimensions - length, width, and depth • Fractals can have fractional (or fractal) dimension • A fractal might have dimension of 1.6 or 2.4 • If you divide a line segment into N identical parts, each part will be scaled down by the ratio r = 1/N

20. Fractal dimension (2) • A two dimensional object, such as a square, can be divided into N self-similar parts, each part being scaled down by the factor r = 1/N(1/2) • If one divides a self-similar D-dimensional object into N smaller copies of itself, each copy will be scaled down by a factor r, where r = 1 / N(1/D) • given a self-similar object of N parts scaled down by the factor r, we can compute its fractal dimension (also called similarity dimension) from the above equation as • D = log (N) / log (1/r)

21. The Koch Snowflake • D = log (4) / log (3) = 1.26

22. Fractal images • Fractal images can be very beautiful. Here are some of them, enjoy them! • Fractal is rather an art than a science.

23. Self-similarity (1) • How long is the coast-line of Great Britain? • Using sticks of different size S to estimate the length L of a coastline

24. Self-similarity (2) • It turns out that as the scale of measurement decreases the estimated length increases without limit. • Thus, if the scale of the (hypothetical) measurements were to be infinitely small, then the estimated length would become infinitely large!

25. Self-similarity (3) • self-similarity • any portion of the curve, if blown up in scale, would appear identical to the whole curve (see a coast-line from an airplane) • Thus the transition from one scale to another can be represented as iterations of a scaling process • fractal ( by Mandelbrot ) • any curve or surface that is independent of scale • This property, referred to as self-similarity

27. Self-similar feature of traffic • Fractal characteristics • order of dimension = fractal • Self-similar feature • across wide range of time scales • Burstness • across wide range of time scales • Long-range dependence • autocorrelations that span many time scales • ACF (autocorrelation function) r(k) = limT∫-T~T XtXt+kdt • ACF does not decay exponentially as lag increases

28. Presence of self-similar features in measured network traffic • Ethernet [Bellcore Leland 1992] • Variable-Bit-Rate video traces [Bellcore 95] • WAN-TCP [Paxson], NSFNET [Klivan],CERNET [TJU] • Common Channel Signaling Network (CCSN) - SS7 - Terabyte range [Bellcore] • MAN-DQDB and LAN cluster [Cinotti] • FTP - a file server [Raatikainen] • Web [Crovella][TJU] • ATM-Bay Area Gigabit Testbed (BAGNet) [Siddevad] • WiFi [Stanford, UCSD, TJU]

29. Self-similar models • Traditional models can only capture short-range dependence -- Poisson process, ARIMA(p,d,q) etc. • Computer networks exhibits self-similarity, i.e. long-range dependence. • Self-similar models • only describe the long-range dependence, can't be used to describe the short-range dependence • FGN (fractional Gaussian noise) • FDN (fractional differencing noise) = FARIMA(0,d,0) • FARIMA(p,d,q) (fractional autoregressive integrated moving average) model can describe both long-range and short-range dependence simultaneously

30. Network delay on FGN models

31. Network delay on FARIMA models

32. Network delay on FARIMA models with non-Gaussian distribution

33. N*N Cell Switch with Input and Output Queueing

34. Cell Loss Probability versus Input Buffer Size

35. FARIMA(p,d,q) model and application • FARIMA models • Generating FARIMA processes • Traffic modeling using FARIMA models • Traffic prediction using FARIMA models • Prediction-based bandwidth allocation • Prediction-based admission control

36. The definition of chaos • Definition: • Chaos is aperiodic time-asymptotic behaviour in a deterministicnon-linear dynamic system which exhibits sensitive dependence on initial conditions. • Sensitive dependence on initial conditions (Butterfly effect) ： • It refers to sensitive dependence on initial conditions. In nonlinear systems, making small changes in the initial input values will have dramatic effects on the final outcome of the system. • The result of the butterfly effect is unpredictability.

37. Chaos vs. Randomness Do not confuse chaotic with random: Random: • irreproducible and unpredictable Chaotic: • deterministic - same initial conditions lead to same final state…but the final state is very different for small changes to initial conditions • difficult or impossible to make long-term predictions

38. Nonlinear Instabilities in TCP-REDPriya Ranjan, Eyad H. Abed and Richard J. La INFOCOM 2002 • This work develops a discrete time feedback system model for a simplified TCP network with RED (Random Early Detection) control. • The model involves sampling the buffer occupancy variable at certain instants. • The non-linear dynamical model is used to analyze the TCP-RED operating point and its stability with respect to various RED controller and system parameters.

39. Fig.5. Bifurcationdiagram of average and instantaneous queue length w.r.t. w, max = 0.1

40. Study on the chaotic nature of wireless traffic • Thecorrelation dimensionof wireless traffic traces isnon-integer number. • The largest Lyapunov exponentof wireless traffic traces ispositive. • The principal components analysisshowed that the intrinsic information of the traffic isaccumulatedin thefirst and few lower-index components. • All those results indicated that the wireless traffic is a low dimensional chaotic system. • This gives us the good theoretical basis for the analysis and modeling of wireless traffic using Chaos Theory.

41. SVM-Based Models for Predicting WLAN Traffic • SVM (Support Vector Machine): a novel type of learning machine, Presented by V. Vapnik et. al. in 1995 • Advantages • Good generalization performance: SVM implements the Structural Risk Minimization Principle which seeks to minimize the upper bound of the generalization error rather than only minimize the training error • Absence of local minima: Training SVM is equivalent to solving a linearly constrained quadratic programming problem. Hence the solution of SVM is unique and globally optimal • Small amount of training samples: In SVM, the solution to the problem only depends on a subset of training data points, called support vectors

42. Related Works • SVM Applications • Pattern recognition, document classification, etc. • Time series prediction, Internet traffic prediction, call classification for AT&T’s natural dialog system, multi-user detection and signal recovery for a CDMA system, SVM-based bandwidth reservation in sectored cellular communications • Our work: • Applying SVM for wireless traffic prediction • One-step-ahead prediction • Multi-step ahead prediction • Comparing its performance with three baseline predictors

43. One-step-ahead prediction • Show the one-step-ahead prediction performance for various prediction methods