1. Modelling and channel borrowing in mobile communications networks Richard J. Boucherie University of Twente Faculty of Mathematical Sciences University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 30

2. Aim : dynamic channel allocation Initial capacity C channels Not sufficient for required QoS (blocking probabilities) Traffic jam peak requires T > C channels How do we provide capacity?  University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 29 C channels Borrowing but from which neighbour? Interaction road traffic and teletraffic (shape of traffic jam,...)

3. Plan : issues relevant to solve problem 1Telecommunications model for QoS Single cell : Erlang loss model - equilibrium exact results - transient : Modified Offered Load Network : Handovers - equilibrium approximate results - transient : MOL 2Highway traffic model Fluid model for unidirectional road 3Relation road traffic and teletraffic Implementation MOL approximation to characterise required capacity 4Self optimising network On-line capacity borrowing on the basis of shape traffic jam University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 28

4. GSM : terminology Base stations, mobile terminals, subscribers, … Call = microwave connection (base - mobile) Limited bandwidth Channels: FDMA / TDMA : Frequency / Time Division Multiple Access ~ 100 frequencies of 200 kHz (carriers) 7 or 8 channels per frequency Calls use single channel call arrival process call length mobility of calls Call blocking probabilities University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 27

5. Basic model: single cell Assign all frequencies to single base station Establish connection upon request Base station C=100 x 7,5 = 750 channels With mean time 2 mins/hour, 30.000 subscribers  blocking probability E(1000,750) = 25 % 3.5 milj. Subscribers (KPN Mobile, medio 2000) 180 mins / year  blocking probability 1% busy hour  100 % University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 26

6. Blocking probability: Erlang loss formula (1917) Telecommunications model: single cell Poisson arrivals rate  call length L mean  number of channels C University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 25 blocked call GSM and UMTS (single cell model) C

7. Erlang loss queue Markov chain (birth-death process) for exponential call length State space S={0,1,…,C} Markov chain birth rate q(n,n+1)=  death rate q(n,n-1)=n/  Equilibrium distribution Blocking probability determined by offered load  =   University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 24 Insenstive!

8. Proof: (exponential case)    n n+1 n/  (n+1)/  equilibrium distribution solution global balance detailed balance insert distribution and rates, and normalize Markov chain (birth-death process) for exponential call length State space S={0,1,…,C} Markov chain N=(N(t), t  0) birth rate q(n,n+1)=  death rate q(n,n-1)=n/  Equilibrium distribution Blocking probability determined by offered load  =   University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 23

9. Erlang loss queue: offered load University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 22 unlimited capacity C=  Time dependent arrival process Modified Offered Load approximation Capacity C Offered load

10. Telecommunication model: single cell So know we know how to compute blocking probabilities in a single cell with static users (assuming that the network consists of a single cell) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 21 C channels

11. Telecommunications network model GSM - divide channels (F/TDMA) over cells University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 20 Capacity = number of available channels - fixed channel assignment (FCA) - dynamic channel assignment (DCA) - cells not regular - interference constraints - capacity known in advance

12. Telecommunications network model multiple cells i=1,…,D Poisson arrivals rate  ( i ) call length mean  ( i ) number of channels C( i ) number of calls in cell i n( i ) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 19 Basic network n(i)  C(i) Layered network: n(i)  C(i)+C(0) n(i)+n(j)  C(i)+C(j)+C(0) n(i)+n(j)+n(k)  C(i)+C(j)+C(k)+C(0) i j k State space C(0)

13. Telecommunications network model Markov chain (loss network) for exponential call length State space Markov chain  (i) birth rate q(n,n+e(i))=  (i) death rate q(n,n-e(i))=n(i)/  (i) n(i)/  (i) Equilibrium distribution offered load  (i)=  (i)  (i) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 18 Loss network

14. Telecommunications network model Equilibrium distribution Blocking or loss probabilities Computation: - recursive methods, inversion Laplace transforms (exact) - asymptotic methods (normal approx, large deviations) - Monte Carlo summation University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 17

15. Telecommunications network model Typical capacity allocation problems Dimensioning problem: For given offered load  (i), there are C(i) channels required at cell i for loss probability < 1% Find colouring with C(i) colours at edge i Call admission problem: For given colouring, find load such that loss <1 % When load changes then a new colouring is required University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 16

16. Telecommunications network model University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 15 equilibrium distribution Truncation of infinite capacity case Infinite capacity Poisson distribution remains valid for time-dependent load  (i,t) Modified Offered Load approximation Depends only on load  (i)=  ( i )  ( i )  (i )  (i,t)  = C 

17. i j  (i) p(i,j)  (i) p(i,0) Telecommunications network model University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 14 handovers Infinite capacity Poisson distribution for time-dependent load  (i,t) exponential holding times Poisson arrivals rate  ( i ) time in cell mean  ( i ) call termination rate  ( i ) p( i,0 ) handover rate  ( i ) p( i,j ) Offered load,t 0  (i,t) Modified Offered Load approximation

18. University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 13 Poisson arrivals rate  ( i+1,t+1 )=  ( i, t ) time in cell mean  ( i ) call termination probaility p( i,0 )=0.8 resp. 0.2 handover probability p( i,i+1 )=1-p( i,0 ) load cell 1 cell 3

19. Telecommunication model: network So know we know how to compute blocking probabilities in a network with users moving among the cells (assuming that users move according to a Markov chain) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 12 C channels

20. Highway traffic model University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 11 Travelling with speed v  (x,t) Cell 0 Cell 1 Cell 2 Density of traffic  (x,t) speed of traffic v(x,t) System of differential equations (fluid model) Location x time t

21. Relation road traffic and teletraffic University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 10 Travelling with speed v  (x,t) Cell 0 Cell 1 Cell 2 Density of traffic  (x,t) density of calls in cell i  (i,t) Location x time t Mean call length  (extends over the cells!) arrival rate per unit traffic mass 

22. Relation road traffic and teletraffic University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 9 Travelling with speed v  (x,t) Cell 0 Cell 1 Cell 2 Density of traffic  (x,t) density of calls in cell i  (i,t) Theorem: Offered Load model where Depends on call length only through its mean Location x time t

23. Self optimising network (GSM - FCA) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 8 Travelling with speed v  (x,t) Cell 0 Cell 1 Cell 2 Cell 0 Cell 1 Cell 2 C C(0,t) C(2,t) C(1,t) Modified Offered Load approximation: Under FCA distribution factorises over the cells blocking probability in cell i To guarantee QoS: solve C(i,t) such that E < 1% C C(i,t) C C C But where do we get the capacity

24. Self optimising network (GSM - FCA) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 7 Travelling with speed v  (x,t) Cell 0 Cell 1 Cell 2 Cell 0 Cell 1 Cell 2 C C(0,t) C(2,t) C(1,t) Borrowing from the left neighbour: Let be the capacity that cell s+1 borrows from cell s at time t. The family of functions is borrowing from the left if at most 2 cells are borrowing at each time, and Borrowing from the right neighbour: similar

25. Self optimising network (GSM - FCA) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 6 Travelling with speed v  (x,t) Cell 0 Cell 1 Cell 2 Cell 0 Cell 1 Cell 2 C C(0,t) C(2,t) C(1,t) We can completely characterise on the basis of C(i,t) i.e. on the basis of the road traffic information  (x,t) borrow from the left if  (x,t) steeper on the left right if  (x,t) steeper on the right road traffic prediction 10 mins ahead of time sufficient for channel re-allocation

26. Self optimising network (GSM - FCA) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 5 Diagonal traffic jam moving along road with constant speed Estimated blocking probabilities in cell 1 over time reach 1.87% above 1% for considerable time 

27. Self optimising network (GSM - FCA) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 4 Demand for capacity in cell 1 for blocking probabilities of 1% and 1.2% obtained from MOL approximation C(1,t)

28. Self optimising network (GSM - FCA) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 3 borrowing from right borrowing from left Estimated blocking probabilities

29. Self optimising network (GSM - FCA) University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 2 Estimation from discrete event simulation

30. We have realised: dynamic channel allocation Initial capacity C channels Not sufficient for required QoS (blocking probabilities) Traffic jam peak requires T > C channels How do we provide capacity?  University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 29 C channels Borrowing but from which neighbour? Interaction road traffic and teletraffic (shape of traffic jam,...)

31. Concluding remarks QoS constraints require sufficient capacity estimation of QoS (blocking probabilities) borrowing based on road traffic information shape of traffic density determines strategy feasible solution: 10 mins ahead of time prediction sufficient for modern networks University of Twente - Stochastic Operations Research Stochastic network analysis for the design of self optimising cellular mobile communications networks 1

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