Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites

Transcription

1 Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites Sara Alouf, Eitan Altman, Jérôme Galtier, Jean-François Lalande, Corinne Touati Mascotte project, I3S-INRIA Maestro project, INRIA France Telecom R&D Alcatel Space Industries Sophia-Antipolis, France 15 March 2005

2 Problem and model Allocate ressources for a satellite/terminals communication Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

3 Satellite: allocate the resources Problem and model divided in space: bandwidth divided in time: cycles Communication with terminal on the ground Terminals: Placed on spots (geographic zones) Split in zones Each zone requires specific demands Demands are timeslots: (frequency bandwidth, duration) Each zone transmits a number of times each type of demand Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

4 Spatially: 32 to 128 spots Terminals Divided in zones Figure 1: Geographical distribution Figure 2: Example with 2-zone spots Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

5 Gain computation and interferences Zone Gain I(.,Spot 1) I(.,Spot 2) I(.,Spot 3) Table 1: Gains and interferences table G(z) z active I(spot(z),z ) σ Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

6 Dividing the bandwith Spots are regularly placed: spatial reuse Dividing the frequency bandwidth by 3, we consider only one color Figure 3: Simplification of the problem with 3 colors No interferences: separating over 3 different bandwidths Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

7 Dividing the bandwith Spots are regularly placed: spatial reuse Dividing the frequency bandwidth by 3, we consider only one color Figure 4: Simplification of the problem with 3 colors One color: 8 spots to 32 spots Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

8 Defining demands Type Bandwidth Maximum number of Time Maximum number of carriers time slots per frame per spot bandwidth Properties: Type=(b,t) with b t = cte To be placed in a space (B, T ) = (36000, 52992) B is a multiple of bandwidth of type i : b i T is a multiple of time of type i : t i All t i s have integer multiplicity All b i s have integer multiplicity Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

9 Satisfaying demands To place timeslots on time frequency space n i times type type i Interference constraints Introduce the notion of family B F1, t1 zone i F2, t2 0 t Figure 5: Two types of demand Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

10 A set of active zones: Défining a family One active zone in a spot Interference criterion is respected Figure 6: Threshold σ of 0.30 Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

11 Families are typified Family (f i ) with one type type j : A set of active zones: Interferences criteria Transmit the type type j in the timeslot Mixed families: Order of multiplicity c Transmits c times the demands in: type j for a set of active zones type k for others active zones Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

12 Families are typified Family (f i ) with one type type j : A set of active zones: Interferences criteria Transmit the type type j in the timeslot Mixed families: Order of multiplicity c Transmits c times the demands in: type j for a set of active zones type k for others active zones Number of families with n spots and t types: without types: n 8 families! typified families: n 8 t n!! Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

13 Solving the problem Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

14 Generation of families spot éteint spot allumé Figure 7: Family 6/7 spot éteint spot allumé Figure 8: Family 5/7 Heuristics of generation: with a valid family with a non valid one (interference criterion not respected) Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

15 Heuristic with a valid family Generation of families Activate randomly a zone of an inactive spot If the threshold respected, we keep this zone Retry until a number of iterations is reached Heuristic with a non valid family While the threshold is not respected do: Deactivate a zone of an active spot Retry until the family becomes valid Try the first heuristic Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

16 Linear program for satisfaying demands Linear program: Variables: x Fi typified family Constraint: demands are satisfied Constraint: these families can be placed on space B T For example, F i For a spot s = (z, z1, z2) Fi T (s) = t j (type j is procuded on this spot) Fi A (z) = on (this zone is active) Fi A(z 1) = off Fi A(z 2) = off Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

17 Linear program for satisfaying demands i / j, z, / s = (z, z 1, z 2 ), Fi M x Fi d(z, t j ) Fi T (s) = t j et (z) = on F A i These families F i transmit type j demand Only one zone z is active Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

18 i / j, z, z / s = (z, z, z 2 ), Fi M x Fi d(z, t j ) + d(z, t j ) Fi T (s) = t j et ( Fi A (z) = on ou Fi A(z ) = on ) These families F i produce type j A zone z or z are active Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

19 Space constraint: i F M i x Fi T B δ B F1, t1 zone i F2, t2 0 t Figure 9: Allocating typified families on B T Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

20 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

21 Why the space constraint is sufficient? 0 x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

22 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

23 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

24 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

25 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

26 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

27 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

28 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

29 Why the space constraint is sufficient? x y Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

30 Why the space constraint is sufficient? x y Figure 10: Placement algorithm Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

31 Why the space constraint is sufficient? Result 1. If B is an integer, it is feasible to place in the time t b 1 frequency space x t i timeslots, for i 1,..., τ if: i {1...τ} x t i BT tb 1 t b τ + 1. In our experiments, we lose less than 1% of the bandwidth Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

32 Global algorithm process action Generate families with heuristics Master program Reaugment families if possible Generate new families by pruning Give families to slave program No Optimality? optimal with the current set of families Time slot placement on BxT Solve final integer linear program Store used typified families from solution Slave program Extract dual coefficient Assign types to families Solve the linear program Select useful families Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

33 Experiments Program realized with Java and Cplex CONCERT Generation of families (typified or not) Finding optimal integer solution is impossible: Fix a distance from the optimal solution (5%) Solve the float associated problem: Column generation: keep the good candidate columns Use this columns in a smaller ILP Separate the problem in a master/slave fashion Reduce the number of combinations of types Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

34 A resulting frequency-time allocation T Surface 0 Type t 1 Type t 1,2 2 Type t 1,3 8 Type t 1,4 32 Type t 2 Type t 2,3 Type t 2, Type t 3 Type t 3,4 4 B/2 Type t 4 Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

35 Optimal surface 3500 Aire optimale Aire Threshold Figure 11: Timeslots required for different possible thresholds Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

36 Families Threshold 80 Threshold 100 Threshold 150 Number of Timeslots Families Figure 12: Timeslots required for different initial set of families Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

37 Time Time for solving (s) Threshold 80 Threshold 100 Threshold 120 Threshold Families Figure 13: Solving time vs. the number of random families used Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

38 Conclusion New approach: Introducing typified families Master/Slave decomposition Column generation Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

39 Conclusion New approach: Introducing typified families Master/Slave decomposition Column generation Results Optimal solution for the 8-spot case 1% far from optimal for the 32-spot case Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

40 Conclusion New approach: Introducing typified families Master/Slave decomposition Column generation Results Optimal solution for the 8-spot case 1% far from optimal for the 32-spot case Futur work: Alcatel Space Industries is testing... Extending the model Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March

41 Thank you! Quasi-optimal bandwidth allocation for multi-spot MFTDMA satellites - March