Describing of parameters of traffic generated by user of multimedia services offered by telco operators

1
Describing of parameters of traffic generated
byuser of multimedia servicesoffered by telco
operators

• Jacek Oko, Janusz Klink
• Institute of Telecommunication and Acoustics
• Wroclaw University of Technology
• Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, POLAND
• phone [phone], fax [phone]
• e-mail jacek.oko_at_pwr.wroc.pl
• janusz.klink_at_pwr.wroc.pl

2
Plan of presentation

• Introduction
• Definition of multimedia services
• Provision of (selected) services over ISDN
• Mathematical description of traffic generated by
  some services
• Conclusion

3
Introduction

• Meaning of the title
• Describing of parameters of traffic... the
  aim of the work
• ... multimedia services... definition on the
  next slide
• ... offered by telco operators means services
  which can be accessed via telecommunication
  (telephone) lines

4
Multimedia service...

• From the end users point of view
• ... is the combination of telecommunication
  capabilities required to support a particular
  multimedia application. (it is usually considered
  to be independent of the network(s) providing
  these capabilities)
• From the Network Providers point of view
• ... is a combination or set of combinations of
  two or more media components (e.g. audio, video,
  graphics, etc.) within a particular network
  environment in such a way as to produce a new
  telecommunication service (it is considered to be
  fully dependent on the specific capabilities of
  the networks utilized)
• ) According to ITU-T F.700 Recommendation

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Different accesses to the services

• Permanent access (xDSL, CATV, etc.) / usually
  broadband
• Switched access (POTS, ISDN) / usually
  narrowband

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Switched access... Why ISDN?

• Because it ...
• is or could be available almost everywhere
• guarantees high level of reliability and data
  security
• offers interfaces (bandwidths) for users having
  different needs
• PRI (2048 kbps) - for business subscribers
• BRI (144 kbps) - for residential subscribers
• Selection of specific type of access results
  first of all from user bandwidth requirements
  i.e. amount of data to transfer and / or
  acceptable transfer delay
• offers a variety of services

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Modeling of traffic generated by Internet access
dial-up connections

• Subject of research
• Behaviors of subscribers, using 64
  kbit/sunrestricted, 8 kHz structured ISDN
  service for connecting to the Internet, has been
  observed
• Internet sessions has been established using
  dial-up connections, but subscribers have paid
  monthly fee for the access (not for the time of
  connection or amount of data transferred)
• The analysis encompassed the following
  parameters
• - call intensity
• - holding time
• Data has being collected for several months, from
  Monday to Sunday, then the average week has
  been estimated

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Average number of Internet sessions opened during
the day
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Method of traffic analysis

• Attempt at finding, after data collection, a good
  mathematical model, for the distributions
  describing call intensity and call holding times
  for Internet sessions
• Problem
• the histograms didn't fit any common known and
  used distributions
• Some of them suggested that exponential functions
  could be useful in these descriptions
• Solution
• modeling these distributions using not simple
  exponential functions,
• but sequences of exponential families
• (method mentioned in the paper)

10
Distribution function for exponential families

• Distribution function of such exponential
  families could be given by the following formula
  
• Density function from exponential family of k
  dimension
• ? (?1, . . . . ., ?k) ? Rk - coefficients
• ?i - is a normalized in L2((0,1),dx) Legendre
  polynomial

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Call intensity for dial-up connections, used as
an access to the Internet
Determined dimension k5 Coefficients ?(
0,3108 -0,1476 -0,1396 0,1629 -0,1453)
c1,08208 Coefficients ? have been
calculated basing on the highest credibility
method and practical considerations (increase of
dimension complicates model and decreases ability
of its application)

• As a good model for the call intensity
  distribution, a model with density function given
  by the following formula has been assumed

• Connections using 64 kbit/s unrestricted, 8 kHz
  structured ISDN service

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Holding times

• Detailed analysis of call holding times suggests
  to describe it by exponential distribution
• however...
• the distribution is disturbed by some stripes,
  representing characteristic holding times (0s,
  120s, 300s etc.)
• it may be caused by user applications, which
  releases the calls after a specific time of user
  (or application) inactivity (no data transfer),
  or by operator after defined holding time (e.g.
  10 hours)
• so...
• it suggests division of the model into two parts
• distribution (a) describing the disturbances
  caused by characteristic holding times
• distribution (b) describing all the other call
  holding times

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Distribution (a)(description of the
disturbances...)

• The stripes has been described by discrete
  distribution
• The characteristic fractions
• p013,43e-02, p1201,00e-02, p3002,00e-02,
  p12003,00e-02
• where p1-p0 -p1200
• An auxiliary random variable W, with discrete
  distribution,
• has been introduced
• Pr(W0)13,43e-02/(1-p)
• Pr(W120)1,00e-02/(1-p)
• Pr(W300)2,00e-02/(1-p)
• Pr(W1200)3,00e-02/(1-p),
• where Pr(Wx) means event probability, that
  holding time amounts
• x seconds

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Distribution (b)(description of all the other
holding times) (1)

• Distribution of all the other call holding times
  reminds Weibull distribution
• Fa,b(x) is a Weibull distribution with parameters
  a, bgt0
• As a good model, distribution function given by
  the following formula has been assumed

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Distribution (b)(description of all the other
holding times) (2)
Approximation by the following density
function Determined dimension
k5 Coefficients ?(-0,0131 -0,0021 0,0861
-0,0609 0,1640) c1,01860 Parameters a and b
area0,0173, b0,5449 Coefficients ? and
parameters a and b have been calculated
basing on the highest credibility method and
practical considerations (increase of dimension
complicates model and decreases ability of its
application)

• Connections use 64 kbit/s unrestricted, 8 kHz
  structured ISDN service

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Conclusion

• Ability of traffic description is the key issue
  in solving of todays traffic engineering problems
• With the extension of assortment of services
  (including multimedia), these problems have
  become much more complicated than in POTS era
• The paper presents metod of traffic parameters
  description, on the basis of selected ISDN
  services, using the curves from exponential
  families
• The traffic describes behaviours of subscribers
  connecting to the Internet via telephone switched
  digital line (ISDN)
• This method can be extended for modeling other
  kinds of traffic (other services, etc.)
• It can also be used for traffic generation and
  building of traffic sources for simulations
  purposes

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• Thank you