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

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

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 Mars 2015

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

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

NETWORK MODEL 6 IDEFIX MEETING Mars 2015

Macro Cell NETWORK MODEL 7 IDEFIX MEETING Mars 2015

NETWORK MODEL 8 Macro Cell IDEFIX MEETING Mars 2015

ASSUMPTIONS 9 IDEFIX MEETING Mars 2015

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 Mars 2015

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 Mars 2015

MARKOVIAN MODEL 12 IDEFIX MEETING Mars 2015

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 Mars 2015

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 Mars 2015

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

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 Mars 2015

FIXED POINT APPROXIMATION 17 IDEFIX MEETING Mars 2015

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 Mars 2015

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

20 FIXED POINT APPROXIMATION 20 IDEFIX MEETING 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 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 Mars 2015

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

PERFORMANCE RESULTS 23 IDEFIX MEETING Mars 2015

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

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

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

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

CONCLUSION & FUTURE WORKS 28 IDEFIX MEETING Mars 2015

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

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

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

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