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Deadline-aware scheduling of cooperative relayers in TDMA-based wireless industrial networks

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Abstract

In this paper we consider a scenario in which a set of source nodes wishes to transmit real-time data packets periodically to a central controller over lossy wireless links, while using a TDMA-based medium access control protocol. Furthermore, a number of relay nodes are present which can help the source nodes with packet retransmissions. The key question we consider in this paper is how to schedule the TDMA slots for retransmissions while taking advantage of the relay nodes, so that the average number of packets missing their deadlines is minimized. We provide a problem formulation for the general deadline-aware TDMA relay scheduling problem. Since the design space of the general problem is large, we also present one particular class of restricted TDMA relay scheduling problems. We suggest and numerically investigate a range of algorithms and heuristics, both optimal and suboptimal, of the restricted scheduling problem, which represent different trade-offs between achievable performance and computational complexity. Specifically, we introduce two different Markov Decision Process (MDP) based formulations for schedule computation of the restricted TDMA relay scheduling problem. One MDP formulation gives an optimal schedule, another (approximate) formulation gives a sub-optimal schedule which, however, comes very close to the optimal performance at much more modest computational and memory costs.

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Notes

  1. More precisely, there are (M + K)T different choices for \(\sigma(\cdot)\). If for one such realization there are R relay slots scheduled, then there are M R different choices for \(\omega(\cdot)\). Assuming that for each source packet there is only one slot scheduled to the source itself, the number of source slots is \(\sum_{i=1}^M \frac{T}{T_i}\) and thus the number of relay slots is \(R = T \left(1 - \sum_{i=1}^M \frac{1}{T_i}\right)\). There are then M R ways to assign relayers to the relay slots and for each such assignment there are M R ways to select preferred sources. Thus the overall number of combinations to inspect is M 2R. For M = 5 and R = 10 this becomes a number with 14 digits, for M = 10 and R = 100 this becomes 201 digits. However, when the task periods T i satisfy certain relationships, schedule computation might become much simpler, see [4].

  2. Clearly, when the number of relayers is large, then the computational effort for this becomes prohibitive. It then makes sense to restrict to a subset of all relayers, so that the chosen relayers have reasonably “good” positions and to rule out relayers that likely will not have a role in the optimal allocation anyway.

  3. In our numerical implementation (presented in Sect. 6) we do not compute ϕ i (s) for arbitrarily large values of s, since this would quickly become computationally infeasible. Instead, we use a modified ϕ i (s) in which there is a threshold s 0 such that for s ≤ s 0 the value ϕ i (s) is computed as described above, whereas for s > s 0 we assume ϕ i (s) = ϕ i (s 0). For many practical setups a threshold s 0 = 6 or s 0 = 7 appears to be sufficient, we have used s 0 = 7 for the numerical evaluations of this paper.

  4. Please note that the symbols used in this section are identical to the ones used in reference [17], since these fit well to MDP terminology. They partially overlap with symbols used in the remaining paper, but no confusion should arise.

  5. It is worth noting here that due to our assumptions on the channel matrix C we can consider the relayer as being randomly placed. It is reasonable to expect that the results can be improved further when it is allowed to place relayers at “good” positions, see for example [5].

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Acknowledgments

This work was partially supported by the Department of Computer Science and Software Engineering at the University of Canterbury with a travel grant for Elisabeth Uhlemann. E. Uhlemann is partly funded by the Swedish Governmental Agency for Innovation Systems, Vinnova, through the VINNMER program, www.vinnova.se

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Authors and Affiliations

  1. Department of Computer Science and Software Engineering, University of Canterbury, Christchurch, New Zealand

    Andreas Willig

  2. Halmstad University, Halmstad, Sweden

    Elisabeth Uhlemann

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  1. Andreas Willig
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  2. Elisabeth Uhlemann
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Correspondence to Andreas Willig.

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Willig, A., Uhlemann, E. Deadline-aware scheduling of cooperative relayers in TDMA-based wireless industrial networks. Wireless Netw 20, 73–88 (2014). https://doi.org/10.1007/s11276-013-0593-x

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