traffic management and modeling

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1Lect04.ppt S-38.145 - Introduction to Teletraffic Theory - Spring 2003

4. Traffic measurements and modelling


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Contents

Traffic measurements

Traffic variations

Traditional modelling of telephone traffic

Traditional modelling of data traffic

Novel models for data traffic


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Traffic measurements (1)

Traffic measurements are needed for network design and traffic management

a basis for dimensioning

traffic modelling

traffic predictions

implementation of dynamic traffic control

measurement based connection admission control

dynamic routing

congestion detection and control

performance evaluation of a network or its components

evaluation of quality of service but also for getting accounting information

More and more information about traffic is needed because of new services and networks

new users, new ways to use, new tariffs (as for existing services and

networks) tougher competition


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Traffic measurements in telephone networks

traffic on different links

traffic process (carried traffic intensity = number of occupied channels)

call arrival process (interarrival times)

call holding times

traffic on different trunk network nodes distribution of incoming traffic from different directions

distribution of outgoing traffic in different directions

traffic on different access network nodes

distribution according to the type of traffic source

e.g. residential vs. business subscribers

use of different services


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Traffic measurements in data networks (Internet/LAN) traffic on different links (or network nodes)

traffic process (carried traffic intensity in bits per second)

packet level (e.g. IP)

packet arrival process (interarrival times)

packet lengths

packet loss ratio

connection level (e.g. TCP applications: ftp / http / email / telnet etc.)

connection arrival process

connection holding times

total amount of information transferred end-to-end traffic measurements

delay and its variation (jitter) experienced by packets

average throughput of a connection


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Analysis of traffic measurements

Traditional statistical methods:

parameter estimation

traffic intensity

traffic variability (short term variance, coefficient of variation)

traffic peakedness

estimation of traffic auto-correlation

New approach:

scalability analysis

self-similarity

multifractal characterization


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Contents


Traffic variations





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Traffic variations in different time scales (1)

Predictive variations

Trend (years)

traffic growth: due to

existing services (new users, new ways to use, new tariffs)

new services

Regular year profile (months) Regular week profile (days)

Regular day profile (hours)

including busy hour

Variations caused by predictive (regular and irregular) external events

regular: e.g. Christmas day

irregular: e.g. World Championships, televoting

Note: different profiles for different types of user groups


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Traffic variations in different time scales (2)

Non-predictive variations

Short term stochastic variations (seconds - minutes)

related to the independence of users

random call arrivals

random call holding times

Long term stochastic variations (hours - ...) random deviations around the profiles

each day, week, month, etc. is different

Variations caused by non-predictive external events

e.g. earthquakes, hurricanes


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Busy hour (1)

An estimate of the traffic load is needed for dimensioning

however, it is not meaningful to use the highest possible peak value

In telephone networks, standard way is to use so called busy hourtraffic for dimensioning

This is unambiguous only for a single day (lets call it daily peak hour)

For dimensioning, however, we have to look at not only a single day butmany more (why?)

At least three different definitions for busy hour (covering several days)have been proposed:

Average Daily Peak Hour (ADPH)

Time Consistent Busy Hour (TCBH)

Fixed Daily Measurement Hour (FDMH)

Busy hour the continuous 1-hour period for which the traffic volume is greatest


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Let

N= number of days during which measurements are done (e.g. N= 10)

an() = measured avg. traffic volume during an interval of day n

max an() = daily peak hour traffic volume of day n

Busy hour traffic a using different methods:

Obviously (why?),

Busy hour (2)

= = N

n nN aa

1

1ADPH )(max

= = N

n nN aa

1

1TCBH )(max

= = N

n nN aa

1 fixed1

FDMH )(

11ADPHTCBHFDMH aaa


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Contents


Traffic variations





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Traffic Calls

Modelling of telephone traffic

In telephone networks:

Traffic model (for a single link) should specify

the type of the call arrival process (at what times a new call attempts to

enter the system)

the distribution of call holding times (how long does a single call last)

These together specify

the traffic process that tells the number of ongoing calls= number of occupied channels= instantaneous intensity of the traffic carried (in erlangs)

Note:

Traffic volume refers tothe amount of carried traffic during some time interval

= integral of the instantaneous traffic intensity over this interval


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Traffic process

654321

6

543210

time

time

call arrival times

blocked call

channel-by-channeloccupation

nr of channelsoccupied

traffic volume

call holdingtime

channels

numberofcha

nnels


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Call arrival process (1)

Aggregated traffic (in trunk network)

Traditional model: Poisson process (with some intensity > 0)

In a short time interval of length , there are two possibilities:either a new call arrives (with probability )or nothing happens (with probability 1 )

Disjoint intervals are independent of each other As a result: call interarrival times are

independently and exponentially distributed with mean 1/

This is found to be a good model when user population is large (infinite)and users make independent decisions

Corresponding teletraffic models are loss models:

Erlang model (finite link capacity)

Poisson model (infinite link capapcity)


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Overflow traffic in trunk networkdue to hierarchical alternativerouting

Model:e.g. Interrupted Poissonprocess (IPP) or more generallyMarkov modulated PoissonProcess (MMPP)

In addition to the traffic processitself, there is a modulatingprocess that tells whether thearrivals of an ordinary Poisson

process will be realized or not Traffic stream consists of the

calls blocked in the direct link

b

ca

direct route: a - calternative route: a - b - c


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Traffic generated by an individual user (subscriber)

Traditional model: exponential on-off process

The user alternates between on and off states

When on, a call is going on

When off, the user is idle

The times spent in different states are assumed to be

independent and exponentially distributed (with state-dependent mean)

Traffic generated by a superposition of users in access network Finite number of individual users

modelled separately as above

making independent decision

Corresponding teletraffic models are loss models:

Engset model (insufficient link capacity)

Binomial model (sufficient link capacity)


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Call holding time (1)

Basic assumption:

call holding times are independent and identically distributed (IID)

Distribution of call holding times traditional model: exponential distribution

one parameter simple!

memoryless property: given that the holding time is at least (any)t,the probability that the call will end in a short time interval (t, t+)

depends just on (but not on t) exponential tail

more complicated models:

normal distribution (two parameters: mean and variance) log-normal distribution (two parameters)

hyper-exponential (with two parameters)

Weibull distribution (with two/three parameters)


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Call holding time (2)

Call holding time distribution is typically different for

business and residential calls (daytime vs. evening calls)

ordinary and data calls (fax, Internet access, etc.)


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Contents


Traffic variations





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Traditional modelling of data traffic on packet level

Traditional traffic model on packet level

new packets arrive according to a Poisson process

packet interarrival times independent and exponentially distributed

packet lengths are independent and exponentially distributed

packet transmission times (in links) independent and exponentiallydistributed

system model is a single server queueing model (M/M/1-FIFO)


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Traffic process at the packet level (1)

time

time

Packet arrival times

Buffer occupation (number of packets)

4321

0

C

Link occupation


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Traffic process at the packet level (2)

time

time

C

Link occupation (averaged)

Link occupation (continuous)

C


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Modelling data traffic on flow level (1)

A flow is a kind of an approximation of connection level traffic observed

on the packet level

Flow is a sequence of subsequent packets, which have the samesource and the same destination, and belong together on some criteria

in the simplest form, classifying flows would take into account only source

and destination information on a finer level of granularity, higher layer protocols could be used as

criteria in classifying (e.g. TCP, UDP, HTTP, FTP, )

subsequent flows are separated by a timer; subsequent packets can belong

to same flow only if their mutual distance in time is small enough

Note that the definition of flow is very flexible. How to classify flows inpractice is a completely another story

selection of granularity

selection of timer timeouts


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Classifying flows based on the nature of traffic

Streaming flows, which are characterized by reserved bandwidth and

lifetime

e.g. audio and video streams using UDP

Elastic flows, which are characterized by the size

E.g. document transfer (HTTP, FTP, ) using TCP Note that the used bandwidth and flow lifetime are determined

dynamically by state of the network


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Flow level model of elastic traffic

new flows are generated according to a Poisson process distribution of flow sizes may be selected freely, e.g. based on

measurements

If we are interested in a single link only, we could use a single serverprocessor sharing queuing system, where all the clients are

simultaneously receiving service, but sharing the service capacity (M/G/1-PS queuing model)

PS queuing discipline is an idealization of the fact TCP-flows reduce theirspeed when experiencing congestion (adaptive behaviour)

Flow level model of streaming traffic using UDP

new flows are generated according to a Poisson process

distribution of lifetimes may be selected freely, e.g. based onmeasurements

Reserved bandwidth fixed or random (independent of the state of thenetwork)

If modelling only UDP-traffic, simple blocking models could be used? (cf.

ATM traffic models on connection level)


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Modelling of ATM traffic (1)

Three different time scales:

Call level

Burst level

Cell level


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Modelling of ATM traffic (2)

Call level

traffic unit = connection

loss model (for CBR and VBR connections)

Burst level

traffic unit = burst of varying length (and possibly of varying rate)

(traditional) fluid buffer models: superposition of exponential ON-OFF sources

(Anick-Mitra-Sondhi model, (A-M-S))

burst arrivals according to Poisson process (Kosten model)

Cell level

traffic unit = fixed length cell

queueing models:

superposition of periodic sources (N*D/D/1)

cell arrivals according to Poisson process (M/D/1)


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Contents


Traffic variations





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Bellcore Ethernet measurements

Ethernet (LAN) measurements by Leland, Willinger, (89-92)

high-accuracy recording of hundreds of millions Ethernet packets including both the arrival time and the length

see: IEEE/ACM Trans. Networking, vol. 2, nr. 1, pp. 1-15, February 1994

Conclusions: Ethernet traffic seems to be extremely varying

presence of burstiness across an extremely wide range of time scales(from microseconds to milliseconds, seconds, minutes, hours, )

bad from the performance point of view

Ethernet traffic is statistically self-similar (fractal-like)

it looks the same in all time scales when zooming

a single parameter (the Hurst parameter) describes the fractal nature

good from the modelling point of view (parsimony!)

Traditional data traffic models (Poisson process, exponential distribution) donot capture these properties!


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Internet measurements

Internet (WAN) measurements by Paxson and Floyd (93-95)

both the connection and the packet level concerned

see: IEEE/ACM Trans. Networking vol. 3, nr. 3, pp. 226-244, June 1995

Connection level conclusions:

For interactive TELNET traffic (and other user-initiated sessions),

connection arrivals are well-modelled by a Poisson process(with hourly fixed rates)

But for connections within user-initiated sessions (FTP data, HTTP) andmachine-generated connections

connection arrivals are more bursty than in a Poisson process

suggests (and even correlated) Packet level conclusions

empirical distribution of TELNET packet interarrival times is

heavy-tailed (not exponential as traditionally modelled)


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New models for data traffic (1)

New distributions:

Subexponential distributions worse than exponential tail

e.g. log-normal, Weibull and Pareto distributions

Heavy-tailed distributions

power-law tail

e.g. Pareto distribution (with location parameter a and shape parameter

)

In the new models for data traffic, these distributions are used todescribe packet lengths and interarrival times

connection holding times and interarrival times

0,0,)/(}{ >>=> axxaxXP


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New models for data traffic (2)

New models for traffic processes:

processes exhibiting long range dependence (LRD)

self-similar processes

If a stochastic process is (asymptotically) self-similar with positivecorrelations, then it exhibits long range dependence (LRD)

e.g. fractional Brownian motion (FBM) suitable for describing aggregated traffic (in trunk network)

just three parameters (thus, parsimonious!)

one of them, so called Hurst parameter H, describes

the grade of long range dependence (when in the interval (,1))

Self-similarity and long range dependence can be caused by heavy-tailed distributions (see the following Example)


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1

Example

Consider an infinite system (M/G/) new customers arrive according to a Poisson process

service times independent and identically distributed

service time distribution heavy-tailed

service time has an infinite variance

e.g. Pareto distribution with shape parameter < 2 Then the traffic volume process is asymptotically self-similar and

containing long range dependence

traffic management and modeling

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