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Whittle index approach to size-aware scheduling for time-varying channels with multiple states

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Abstract

We consider the optimal opportunistic scheduling problem for downlink data traffic in a wireless cell with time-varying channels. The scheduler itself operates at a very fast time scale of milliseconds, but the objective function is related to minimizing the holding costs at a much longer time scale, at the so-called flow level. The Whittle index approach is a powerful tool in this context, since it renders the flow-level optimization problem with heterogeneous users tractable. Until now, this approach has been applied to the opportunistic scheduling problem to generate non-anticipating index policies that may depend on the amount of attained service but do not utilize the exact size information. In this paper, we produce a size-aware (i.e., anticipating) index policy by applying the Whittle index approach in a novel way. By a numerical study based on simulations, we demonstrate that the resulting size-aware index policy systematically improves performance. As a side result, we show that the opportunistic scheduling problem is indexable when the file sizes follow the Pascal distribution, and we derive the corresponding Whittle index, which generalizes earlier results.

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Notes

  1. The length of the time slot in current wireless cellular systems is of the order of 1 ms.

  2. The generic term job refers to the file to be downloaded by some user.

  3. In fact, we could have used a constraint where 1 on the right-hand side of (1) is replaced by any \(N \in \{1,2,\ldots \}\) as, for example, in [13], which still would have resulted in exactly the same size-aware Whittle index.

  4. For the geometric job size distribution (i.e., \(J = 1\)), the index values \(\nu ^*_{i,\beta }(j,r_{i,1})\) and \(\nu ^*_{i,\beta }(j,r_{i,2})\) differ by a factor of \(\beta \) from those given in [5], which is due to a slight difference in the cost models: While we “pay” the holding cost \(c_i\) for job i even in the time slot where its service is completed, this is not the case in the cost model of [5].

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Acknowledgments

This research was partially supported by the TOP-Energy project funded by Academy of Finland (Grant No. 268992).

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Correspondence to Pasi Lassila.

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Aalto, S., Lassila, P. & Osti, P. Whittle index approach to size-aware scheduling for time-varying channels with multiple states. Queueing Syst 83, 195–225 (2016). https://doi.org/10.1007/s11134-016-9484-z

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