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1Lect04.ppt S-38.145 - Introduction to Teletraffic Theory - Spring 2003
4. Traffic measurements and modelling
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4. Traffic measurements and modelling
Contents
Traffic measurements
Traffic variations
Traditional modelling of telephone traffic
Traditional modelling of data traffic
Novel models for data traffic
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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Traffic measurements (2)
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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4. Traffic measurements and modelling
Traffic measurements (3)
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Contents
Traffic measurements
Traffic variations
Traditional modelling of telephone traffic
Traditional modelling of data traffic
Novel models for data traffic
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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Contents
Traffic measurements
Traffic variations
Traditional modelling of telephone traffic
Traditional modelling of data traffic
Novel models for data traffic
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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Call arrival process (2)
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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4. Traffic measurements and modelling
Call arrival process (3)
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Contents
Traffic measurements
Traffic variations
Traditional modelling of telephone traffic
Traditional modelling of data traffic
Novel models for data traffic
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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Traffic process at the packet level (2)
time
time
C
Link occupation (averaged)
Link occupation (continuous)
C
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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Modelling data traffic on flow level (2)
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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4. Traffic measurements and modelling
Modelling data traffic on flow level (3)
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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4. Traffic measurements and modelling
Modelling of ATM traffic (1)
Three different time scales:
Call level
Burst level
Cell level
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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
Contents
Traffic measurements
Traffic variations
Traditional modelling of telephone traffic
Traditional modelling of data traffic
Novel models for data traffic
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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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4. Traffic measurements and modelling
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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