Teletraffic Models, developed in the Institute of Mathematics and Informatics - BAS and in the College of Telecommunications and Post, under the frame of international cooperation Stoyan A. Poryazov 1, Emiliya T. Saranava 1,2 1 Institute of Mathematics and Informatics -BAS 2 College of Telecommunications and Post

Contents 1. Object of Investigation 2. Objectives and Necessity of the Research 3. International Current Projects and Partners 4. Conceptual Model and Notation System 5. Analytical Model 5.1. Main Assumptions 5.2. Equations 6. Computational Model 7. Model validity 8. Presentation Model 9. Numerical Experiments 10. Conclusions 11. Acknowledgments 12. References

1. Object of Investigation: Overall terminal and network teletraffic of a (virtual) circuit switching telecommunication system with: BPP (Bernoulli–Poisson–Pascal) input flow; repeated calls; limited number of homogeneous terminals; losses due to abandoned and interrupted dialing, blocked and interrupted switching, not available intent terminal, blocked and abandoned ringing and abandoned communication (like GSM and PSTN)

2.1. Objectives: Developing of methods for creation of useful (for research, designing and education) teletraffic models of overall (virtual) circuit switching telecommunication systems Necessity of the Research: 1. (Virtual) channel switching is a fundamental telecommunication principal and technology; 2. PSTN and GSM are widely used; 3. The Network and Terminal Teletraffic Theory is not developed enough, e.g. the following usual premises are illusions: 3.1. Call Holding Time is independent from the state of the system;

2.2. Necessity of the Research (cont.): 3.2. Occupation times for calling (A) and called (B) terminals differ a little; 3.3. Traffic intensities of A and B-terminals are almost equal. 4. The only way to liberate ourselves from the main old illusions is to develop and use Network and Terminal Traffic Models of the overall real communication systems. ________________________________________ In this paper one of possible approaches is demonstrated.

3. International Current Projects and Partners Involved: "New Models of Terminal Teletraffic in Circuit Switching Systems", RAN (Information Transmission Problems Institute, Moscow) EU Action COST 285 “Modelling and Simulation Tools for Research in Emerging Multi- service Telecommunications“ (12 countries) " Methods and Tools for Terminal Teletraffic Modelling in (Virtual) Channel Switching Systems". Beijing University of Posts&Telecom, China. (Liang Xiong-Jian) EU Action COST 290 "Traffic and QoS Management in Wireless Multimedia Networks" (24 countries).

4. Conceptual Model and Notation System

7. Model validity The model presented is verified through: mathematical analysis and confirmation tests of values of the main output variables; comparison with data from detailed simulation model, a development of [Todorov, Poryazov 1985]; qualitative behaviour comparison with measurements in real PSTN. Full validation of the model is not performed, due lack of suitable real teletraffic measurements data (Telecom Operator ?).

9. Numerical Experiments (1/4): Traffic intensities of the A-terminals (Ya) and B-terminals (Yb) as functions of the intensity of the overall terminal traffic (Yab). Ns = number of available internal switching lines. Nab = number of the terminals.

9. Numerical Experiments (2): Occupation time of the A-terminals (Ta), B-terminals (Tb) and all busy terminals (Tab) as functions of the intensity of the overall terminal traffic (Yab).

9. Numerical Experiments (3/4): Relative difference, in percents, between: (Ya-Yb); (Tb-Ta); (Tb-Tab), as functions of the overall terminal traffic (Yab).

9. Numerical Experiments (4/4): The offered to the switching system traffic (ofd.Ys) and its components – offered intensity of the calls flow (ofd.Fs), and mean holding time (Ts) of one switching line, as functions of the macrostate of the system (Yab) in two cases.

10. Conclusions (1/5) 1. Detailed conceptual and analytical models of an overall (virtual) circuit switching telecommunication system are created; 2. Results of numerical experiments presented, show considerable differences between correspondent time and traffic characteristics of A and B-terminals in the modeled system. The values of the relative difference between intensity of traffics of A and B-terminals ((Ya- Yb)/Ya) are in the interval from 10.7% to 100%, and between occupation times ((Tb-Ta)/Ta) – from 0.578% to 627.9%;

Conclusions (2/5) 3. The mean holding time of the B-terminals (Tb) is a constant in the overall allowed interval of the macrostate of the system Yab; The mean holding time of the A-terminals (Ta) is decreasing with increasing of Yab. The minimum of Ta is 13.76% of its maximum. ; 4. The mean holding time of one equivalent internal switching line (Ts) depends on Pbr (respectively on Yab) only, and is decreasing faster than Ta – its minimum is 3.96% of its maximum.

Conclusions (3/5) 5. Offered to the switching system traffic ofd.Ys is higher in the case of nonzero blocking, in comparison with the case of zero blocking (for one and the same Yab). This is because ofd.Fs has higher values at this Yab (when Pbs > 0), Ts is independent of Pbs (see Conclusion 4) and obviously ofd.Ys = ofd.Fs Ts (Little's formula). The relative difference between values of ofd.Fs, in both cases, may exceed 112%. 6. The fast decreasing of the holding time of one line (Ts) causes existing of a local maximum of Pbs and of the offered traffic (ofd.Ys) correspondingly, at extremely high load of the system.

Conclusions (4/5) 7. The predicted two phenomena in the studied communication systems (difference between the values of offered traffic in the cases with and without blocking and existing of a local maximum of Pbs) must be experimentally confirmed through measurements in real systems. 8. Described phenomena in terminal time and traffic characteristics are emerging on network level. Therefore, the only way to liberate ourselves from the main old illusions is to develop and use Network and Terminal Traffic Models of the overall real communication systems;

Conclusions (5/5) 9. In this paper one of possible approaches is demonstrated, which may allows developing the Network and Terminal Teletraffic Theory and helping in determination of many network characteristics at call and session levels, in performance evaluation of the present and next generation fixed and mobile networks. 10. This approach may be used directly for every (virtual) circuit switching telecommunication system (like GSM and PSTN) and may help considerably for ISDN, BISDN and most of core and access networks traffic modelling. For packet switching systems, like Internet, proposed approach may be used as a comparison base.

THANK YOU Dr. Stoyan A. Poryazov Tel: (+359 2) Fax: (+359 2) Ass. Prof. Emiliya T. Saranova Tel: (+359 2) ext. 251 Fax: (+359 2) (+359-2)