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Describing of parameters of traffic generated by

user 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: +48(71) 320 25 37, fax: +48(71) 320 30 70

e-mail: jacek.oko@pwr.wroc.pl

janusz.klink@pwr.wroc.plWroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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Plan of presentation

Introduction Definition of multimedia services Provision of (selected) services over ISDN Mathematical description of traffic generated

by „some services” Conclusion

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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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

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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Multimedia service*... From the end user’s 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 Provider’s 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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ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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Different accesses to the services

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

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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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

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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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

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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Average number of Internet sessions opened during the day

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0

500

1000

1500

2000

2500

3000

3500

4000

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

Time [h]

Nu

mb

er o

f ca

lls

Weekday Weekend

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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)

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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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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,0

,10,exp1

1

otherwise

xxcx i

k

ii

k

g

,, Rydyyxx

kk gF

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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Call intensity for dial-up connections, used as an access to the Internet

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

Wroclaw University of Technology, POLAND

Nor

mal

ised

num

ber

of s

ampl

es

Time (normalised value)

Determined dimension k=5

Coefficients:

=(0,3108; -0,1476; -0,1396; 0,1629;

-0,1453)

c=1,08208

Coefficients have been calculated basing on the highest credibility method and practical considerations (increase of dimension complicates model and decreases ability of its application)

f x x x Rkg

,

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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

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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

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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

The stripes has been described by discrete distribution The characteristic fractions: p0=13,43e-02, p120=1,00e-02, p300=2,00e-02, p1200=3,00e-02 where p=1-p0 … -p1200

An auxiliary random variable „W”, with discrete distribution, has been introduced:

Pr(W=0)=13,43e-02/(1-p) Pr(W=120)=1,00e-02/(1-p) Pr(W=300)=2,00e-02/(1-p) Pr(W=1200)=3,00e-02/(1-p),

where Pr(W=x) means event probability, that holding time amounts„x” seconds

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p0,

p120,...

p1200

1

1-p

p

Other

observations (a)

(b)

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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, b>0

As a good model, distribution function given by the following formula has been assumed:

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,,0

,0,1,

othervise

xaxx eF

b

ba

F x x x Rk

a bF F ,,

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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Distribution (b)(description of all the other holding times) (2)

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

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Approximation by the following density function:

Determined dimension k=5

Coefficients:

=(-0,0131; -0,0021; 0,0861; -0,0609; 0,1640)

c=1,01860

Parameters a and b are:a=0,0173, b=0,5449

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)

f x x x x Rk

a b a bg F f

, ,,

Time [s]

No

rmal

ised

num

be

r o

f sam

ples

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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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

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004

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Thank you

Wroclaw University of Technology, POLAND

ITS, 15th Biennal Conference, Berlin, Sept. 5-7, 2004