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Theoretical Aspects of Distributed Computing in Sensor Networks pp 553–588Cite as

Prolong the Lifetime of Wireless Sensor Networks Through Mobility: A General Optimization Framework

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Abstract

Though mobility is rarely considered in traditional wireless sensor networks (WSNs), actively exploiting mobility to improve the performance of WSNs has been increasingly recognized as an important aspect of designing WSNs. This chapter focuses on exploiting mobility to improve the network lifetime of a WSN. We present a general optimization framework that is able to capture several aspects of maximizing network lifetime (MNL) involving mobile entities. Based on this framework, we conduct an in-depth analysis on each of these aspects and also describe algorithms that can be used to solve the resulting optimization problems. We also present certain numerical results where engineering insights can be acquired.

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Notes

  1. 1.

    In this chapter, the words sensor node and node are used interchangeably.

  2. 2.

    These are the entities that collect data from WSNs; sometimes they are also termed base stations.

  3. 3.

    The physical features of the radio of node i are usually specified by a tuple \((P_i,R,\mu)\); here P i is the transmission power, R is the data rate, μ is the threshold (specified by the required bit error rate (BER) of a given modulation scheme that produces the rate R) such that a link \((i,j)\) may operate on rate R iff \(P_i\cdot\eta_{i,j} \ge \mu\), where \(\eta_{i,j}\) represents the fading, shadowing, and path loss effects between nodes i and j. Our model can be considered as a more generalized form of the aforementioned model, as \(e^\mathrm{T}_i = \dfrac{P_i}{R} \ge \dfrac{\mu}{R\eta_{i,j}} = c(i,j)\) is indeed the criterion to indicate the existence of link \((i,j)\). Note that, under our model, \(e^\mathrm{T}_i\) may have a unit of, for example, Joules/Bit.

  4. 4.

    This assumption is reasonable because each sensor node should be equipped with an energy source that is at least enough for the node to forward data for all nodes in one time unit. Otherwise if a node \(i:E_{i}/\left(e_{i}^\mathrm{T}+\mathrm{I}_{j\ne i}\cdot e^\mathrm{R}\right){<}\sum_{i}\lambda_{i}\) is deployed close to a static sink (assuming a randomly deployed WSN), the network lifetime can be even less than one time unit. In addition, it can be proved that an approximation ratio of \((1-\varepsilon)^{-3}\) is still achievable without this assumption.

  5. 5.

    The original work by Shi and Hou [30] is only designed for a single mobile sink. In this section, we extend their approach by combining it with MNL_ALGO presented in Sect. 18.2.4 to deal with multiple mobile sinks.

  6. 6.

    A byproduct of this change is that the cost assignment c is not needed anymore, as any link \((i,j)\) is feasible given a sufficiently high transmission energy \(e^\mathrm{T}_{i,j}\).

  7. 7.

    By aggregation, we refer to any transformation that summarizes or compresses the data acquired and received by a certain node and hence reduce the volume of the data to be sent out, e.g., [25].

  8. 8.

    As an example, the decision problem related to MNL (on-graph) is the following:

    • Instance: A set of nodes \(\mathcal{N}\), a cost assignment \(\mathbf{c}:c(i,j)=e, \forall i,j\in\mathcal{N}\), a set \(\mathcal{S}\) of sinks with \(|\mathcal{S}|{<}|\mathcal{N}|\), and for each \(i\in\mathcal{N}\), a transmission energy \(e_i^{\mathrm{T}}\), a receiving energy e R, an energy reserve E i , a rate λ i , and a positive real number t.

    • Question: Is there a sink layout schedule \(\{(\mathit{sl}_{k},t_{k})\}\) (\(\mathit{sl}_{k}\) is a vector of \([\delta^{k}_{is}]\) where \(\delta^{k}_{is}:\mathcal{N}\times\mathcal{S}\rightarrow\{0,1\}\) and \(\sum_{i}\sum_{s}\delta^{k}_{is}=|\mathcal{S}|\)) such that the lifetime \(T=\sum_{k}t_{k}\) is at least t?

    This problem can be shown as NP-hard by, for example, a polynomial-time reduction from the Dominating Set on a unit disk graph [22].

  9. 9.

    Although Shi et al. [31] have proposed an approximation algorithm for BSP, using a technique similar to the one presented in Sect. 18.3.2.1 that algorithm is only pesudo-polynomial in time, as the time complexity is actually exponential in the number of base stations.

  10. 10.

    This is a special case of our general formulation, which assigns a uniform data rate to the source nodes and a zero rate to others.

  11. 11.

    The “many-to-one” data aggregation implies that, no matter how many unit of flows converge at an intermediate node, node only send one unit flow out. These are cases where special aggregation functions such as Average, Max, or Min are used.

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Authors and Affiliations

  1. School of Computer Engineering, Nanyang Technological University (NTU), Singapore, Singapore

    Jun Luo

  2. School of Computer Engineering, Nanyang Technological University (NTU), Nanyang Avenue, Singapore, Singapore

    Liu Xiang

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  1. Jun Luo
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Correspondence to Jun Luo .

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Editors and Affiliations

  1. Computer Technology Institute, N. Kazantzaki Street 1, Rion, Patras, 265 04, Greece

    Sotiris Nikoletseas

  2. Centre Universitaire d'Informatique, Université de Genève, rte de Drize 7, Carouge, 1227, Switzerland

    José D.P. Rolim

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Luo, J., Xiang, L. (2011). Prolong the Lifetime of Wireless Sensor Networks Through Mobility: A General Optimization Framework. In: Nikoletseas, S., Rolim, J. (eds) Theoretical Aspects of Distributed Computing in Sensor Networks. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14849-1_18

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  • DOI: https://doi.org/10.1007/978-3-642-14849-1_18

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