1. IMPACT OF MOBILITY IN DENSE LTE-A NETWORKS WITH SMALL CELLS M. Bruno Baynat (Université Pierre et Marie Curie – LIP6) Mme. Raluca-Maria Indre (Orange Labs) M. Narcisse Nya (Université Pierre et Marie Curie – LIP6) M. Philippe Olivier (Orange Labs) M. Alain Simonian (Orange Labs) 1

2. PLAN  Context  Motivations  Goal  Network Model  Network assumptions  Modeling assumptions  Markovian Model  Fixed Point approximation  Performance results  Conclusion and future works 2 IDEFIX MEETING 26-27 Mars 2015

3. CONTEXT  Constant increase of data in mobile networks  Massive deployment of small cells  Increase the proportion of mobile users  Impact of this increase on the performance of LTE-A 3 IDEFIX MEETING 26-27 Mars 2015

4. MOTIVATIONS  Evaluate and quantify the impact of mobility on the performance of small cells 4 IDEFIX MEETING 26-27 Mars 2015

5. GOAL  Simple analitical models  Influence of mobile users on the performance of static users  Amount of generated handovers 5 IDEFIX MEETING 26-27 Mars 2015

6. NETWORK MODEL 6 IDEFIX MEETING 26-27 Mars 2015

7. Macro Cell NETWORK MODEL 7 IDEFIX MEETING 26-27 Mars 2015

8. NETWORK MODEL 8 Macro Cell IDEFIX MEETING 26-27 Mars 2015

9. ASSUMPTIONS 9 IDEFIX MEETING 26-27 Mars 2015

10. 10 NETWORK ASSUMPTIONS  Cell with constant capacity C  Two types of users  Static users  Mobile users  Equitable ressources sharing : Round-Robin  Each users download data of size Σ  Full transmission for static users  Mobile users remain in the cell for a limited time θ IDEFIX MEETING 26-27 Mars 2015

11. 11 MODELING ASSUMPTIONS  Requests for transmission is generated according to Poisson processes  Rate λ s for static users  Rate λ m for mobile users  Exponential distribution of service time  Exponential remaining sojourn time of an active mobile user θ  Exponential distribution of data to download Σ IDEFIX MEETING 26-27 Mars 2015

12. MARKOVIAN MODEL 12 IDEFIX MEETING 26-27 Mars 2015

13. MARKOVIAN MODEL 13 n s, n m 13 n s, n m +1 n s +1, n m n s -1, n m n s, n m -1 Inverse of mean sojourn time Arrival rate of static users’ requests Arrival rate of mobile users’ requests Service rate of the cell IDEFIX MEETING 26-27 Mars 2015

14. MARKOVIAN MODEL 14  The model is exact  Stability condition  Does not depend on the mobile users  Numerical resolution  Truncating both dimensions of state space  Gauss-Seidel or Least mean square IDEFIX MEETING 26-27 Mars 2015

15. MARKOVIAN MODEL 15 IDEFIX MEETING 26-27 Mars 2015 Mean time to transfer the average volume E(Σ)  Performance indicators of interest  Average throughput obtained by any user  Propotion of handover

16. MARKOVIAN MODEL 16  Limitations of the model :  Exponential distribution of mobile users sojourn time  Exponential distribution of data to transmit  Resolution complexity  Scalability IDEFIX MEETING 26-27 Mars 2015

17. FIXED POINT APPROXIMATION 17 IDEFIX MEETING 26-27 Mars 2015

18. 18 FIXED POINT APPROXIMATION 18 Capacity of the cell Average size of the downloaded file Average size downloaded by a mobile user ?  Two classes of users with different service rate  Multi-class Processor-Sharing queue with two classes of customers IDEFIX MEETING 26-27 Mars 2015

19. 19 FIXED POINT APPROXIMATION 19 IDEFIX MEETING 26-27 Mars 2015  Stability condition  Multi-class PS queue  Thus necessary that  For this system  is sufficient

20. 20 FIXED POINT APPROXIMATION 20 IDEFIX MEETING 26-27 Mars 2015  How to calculate ?  Depends on sojourn time and average throughput of the user  If the parameter is known  Standard results for the stationary multi-class processor sharing

21. 21 FIXED POINT APPROXIMATION 21  Knowing the distribution of Σ  Fixed point Throughput of the user given by the PS queue  If is known IDEFIX MEETING 26-27 Mars 2015

22. FIXED POINT APPROXIMATION  Performance indicators of interest  Average throughput obtained by any user  handover probability  Exponential distribution of and and 22

23. PERFORMANCE RESULTS 23 IDEFIX MEETING 26-27 Mars 2015

24. 24 PERFORMANCE RESULTS  Θ and Σ are both exponentially distributed  The Markovian model is exact IDEFIX MEETING 26-27 Mars 2015 Static users throughputMobile users throughput

25. 25 PERFORMANCE RESULTS  Θ and Σ are both exponentially distributed  The Markovian model is exact IDEFIX MEETING 26-27 Mars 2015

26. 26 PERFORMANCE RESULTS  Impact of sojourn time distribution IDEFIX MEETING 26-27 Mars 2015

27. 27 PERFORMANCE RESULTS  Impact of key parameters User throughput with differrent cell size User throughput with different speed IDEFIX MEETING 26-27 Mars 2015

28. CONCLUSION & FUTURE WORKS 28 IDEFIX MEETING 26-27 Mars 2015

29. 29 CONCLUSION AND FUTURE WORKS IDEFIX MEETING 26-27 Mars 2015  Markovian model  Exponential distribution of θ and Σ  Resolution complexity  Not extensible  Exact

30. 30 CONCLUSION AND FUTURE WORKS IDEFIX MEETING 26-27 Mars 2015  Fixed point approximation  Approximate model   Very simple  Easily extensible

31. 31 CONCLUSION AND FUTURE WORKS IDEFIX MEETING 26-27 Mars 2015  Future Works  Macro-cell with several coding zones  Several neighboring cells

32. THANK YOU FOR YOUR ATTENTION