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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
  • 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
farima p d q model and application
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
the definition of chaos
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.
chaos vs randomness
Chaos vs. Randomness

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-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.
study on the chaotic nature of wireless traffic
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.
svm based models for predicting wlan traffic
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
related works
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
one step ahead prediction
One-step-ahead prediction
  • Show the one-step-ahead prediction performance for various prediction methods