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What deterministic algorithm is suitable for the following resource allocation/scheduling problem?

Consider a set of players: P1, P2, P3 and P4. Each player receives data from a cell tower (e.g. in a wireless network). The tower transmits data in 1 second blocks. There are 5 blocks. Each player can be scheduled to receive data in an arbitrary number of the blocks.

Now, the amount of data received in each block is a constant (C) divided by the number of other players scheduled in the same block (because the bandwidth must be shared). A greedy approach would allocate each player to each block but then the data received per block would be reduced.

How can we find an allocation of the players to time-blocks so that the amount of data delivered by the network is maximised? I have tried a number of heuristic methods on this problem (Genetic Algorithm, Sim Anneal) and they work well. However, Id like to solve for the optimum schedule.

pnuts
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T-800
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  • Could you give an example? I don't see why the throughput isn't constant. – David Eisenstat Nov 16 '15 at 12:25
  • How big is the real problem? – TimChippingtonDerrick Nov 16 '15 at 23:30
  • Thanks for your replies. The throughput isn't constant because it's given by Shannon's law: TP = (bandwidth / n)*log_2(1+SINR), where n is the number of players sharing a block and SINR is the Signal to Noise and Interference Ratio. Therefore, as n increases (more players are scheduled) TP decreases and vice versa. The tradeoff is that when a player is not scheduled in a block then it receives no data. The real problem is not much bigger than described: 40 blocks and around 20-30 players. There could be many cell towers but they are independent. – T-800 Nov 17 '15 at 13:21

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