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Traffic management 2007. 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.

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An example
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

What this requires
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

What if
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.

Traffic management
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


  • Economic principles

  • Traffic models

  • Traffic classes

  • Time scales - Mechanisms

Basics utility function
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


  • 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

Social welfare
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


  • 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

Some economic principles
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

Principles applied
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

The two camps
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!


  • Economic principles

  • Traffic models (+ our research)

  • Traffic classes

  • Time scales - Mechanisms

Traffic models
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

Telephone traffic models
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

Internet traffic modeling
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

Internet traffic models features
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

Fractal dimension 1
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

Fractal dimension 2
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)

The koch snowflake
The Koch Snowflake

  • D = log (4) / log (3) = 1.26

Fractal images
Fractal images

  • Fractal images can be very beautiful. Here are some of them, enjoy them!

  • Fractal is rather an art than a science.

Self similarity 1
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

Self similarity 2
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!

Self similarity 3
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

Self similar feature of traffic
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

Presence of self similar features in measured network traffic
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]

Self similar models
Self-similar models traffic

  • 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

Network delay on farima models with non gaussian distribution
Network delay on FARIMA models trafficwith non-Gaussian distribution

N n cell switch with input and output queueing
N*N Cell Switch trafficwith Input and Output Queueing

Farima p d q model and application
FARIMA( trafficp,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

The definition of chaos
The definition of chaos traffic

  • 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.

Chaos vs randomness
Chaos vs. Randomness traffic

Do not confuse chaotic with random:


  • irreproducible and unpredictable


  • 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

Nonlinear instabilities in tcp red priya ranjan eyad h abed and richard j la infocom 2002
Nonlinear Instabilities in TCP-RED trafficPriya 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.

Fig 5 bifurcation diagram of average and instantaneous queue length w r t w max 0 1
Fig.5. trafficBifurcationdiagram of average and instantaneous queue length w.r.t. w, max = 0.1

Study on the chaotic nature of wireless traffic
Study on the chaotic nature of wireless traffic 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.

Svm based models for predicting wlan traffic
SVM-Based Models for Predicting WLAN Traffic 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

Related works
Related Works traffic

  • 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

One step ahead prediction
One-step-ahead prediction traffic

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