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Optimal size-based opportunistic scheduler for wireless systems

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Abstract

Modern wireless cellular systems are able to utilize the opportunistic scheduling gain originating from the variability in the users’ channel conditions. By favoring users with good instantaneous channel conditions, the service capacity of the system can be increased with the number of users. On the other hand, for service systems with fixed service capacity, the system performance can be optimized by utilizing the size information. Combining the advantages of size-based scheduling with opportunistic scheduling gain has proven to be a challenging task. In this paper, we consider scheduling of data traffic (finite-size elastic flows) in wireless cellular systems. Assuming that the channel conditions for different users are independent and identically distributed, we show how to optimally combine opportunistic and size-based scheduling in the transient setting with all flows available at time 0. More specifically, by utilizing the time scale separation assumption, we develop a recursive algorithm that produces the optimal long-run service rate vectors within the corresponding capacity regions. We also prove that the optimal operating policy applies the SRPT-FM principle, i.e., the shortest flow is served with the highest rate of the optimal rate vector, the second shortest with the second highest rate, etc. Moreover, we determine explicitly how to implement the optimal rate vectors in the actual time slot level opportunistic scheduler. In addition to the transient setting, we explore the dynamic case with randomly arriving flows under illustrative channel scenarios by simulations. Interestingly, the scheduling policy that is optimal for the transient setting can be improved in the dynamic case under high traffic load by applying a rate-based priority scheduler that breaks the ties based on the SRPT principle.

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Notes

  1. In fact, by adjusting the corresponding flow sizes, we could, as well, have assumed that, for each user i, there is a constant a i such that processes a i R i (t) are independent and identically distributed, cf. [7, 17].

  2. In the present paper it is natural to define operating policies ϕ as a sequence of rate vectors (c 1,…,c n ) due to the time scale separation assumption made in Sect. 3. For more generic capacity regions, the optimal control in continuous time would, of course, be a relevant question.

  3. An example is given in [2, p. 189] demonstrating that the result is not necessarily true for more generic capacity regions.

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Acknowledgements

This research has been partially supported by the HEWINETS (Dynamic Heterogeneous Wireless Access Networks) project, funded by Ericsson, Cassidian Systems and TEKES.

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Authors and Affiliations

  1. Aalto University School of Electrical Engineering, Helsinki, Finland

    Samuli Aalto, Aleksi Penttinen, Pasi Lassila & Prajwal Osti

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  1. Samuli Aalto
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  2. Aleksi Penttinen
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  3. Pasi Lassila
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  4. Prajwal Osti
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Correspondence to Pasi Lassila.

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Aalto, S., Penttinen, A., Lassila, P. et al. Optimal size-based opportunistic scheduler for wireless systems. Queueing Syst 72, 5–30 (2012). https://doi.org/10.1007/s11134-012-9285-y

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