Jacek Oko, Janusz Klink Institute of Telecommunication and Acoustics

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: +48(71) 320 25 37, fax: +48(71) 320 30 70 e-mail: jacek.oko@pwr.wroc.pl janusz.klink@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 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

5. Different accesses to the services Permanent access (xDSL, CATV, etc.) / usually broadband Switched access (POTS, ISDN) / usually narrowband

6. 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

7. 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 theInternet, 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

8. Average number of Internet sessions opened during the day

9. 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) Legendrepolynomial

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

12. Holding times • Detailed analysis of call holding times suggeststo 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

13. 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

14. 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:

15. Distribution (b)(description of all the other holding times) (2) Approximation by the followingdensity 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) Connections use 64 kbit/s unrestricted, 8 kHz structured ISDN service

16. 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

17. Thank you