Continuous data aggregation and capacity in probabilistic wireless sensor networks

https://doi.org/10.1016/j.jpdc.2013.02.005Get rights and content

Highlights

  • A network partition method is designed and analyzed.

  • We design an optimal snapshot data aggregation algorithm for probabilistic WSNs.

  • We design an optimal continuous data aggregation algorithm.

  • Extensive simulations are conducted to validate the proposed algorithms.

Abstract

Due to the existence of many probabilistic lossy links in Wireless Sensor Networks (WSNs) (Liu et al., 2010)  [25], it is not practical to study the network capacity issue under the Deterministic Network Model (DNM). A more realistic one is actually the Probabilistic Network Model (PNM). Therefore, we study the Snapshot Data Aggregation (SDA) problem, the Continuous Data Aggregation (CDA) problem, and their achievable capacities for probabilistic WSNs under both the independent and identically distributed (i.i.d.) node distribution model and the Poisson point distribution model in this paper. First, we partition a network into cells and use two vectors to further partition these cells into equivalent color classes. Subsequently, based on the partitioned cells and equivalent color classes, we propose a Cell-based Aggregation Scheduling (CAS) algorithm for the SDA problem in probabilistic WSNs. Theoretical analysis of CAS and the upper bound capacity of the SDA problem show that the achievable capacities of CAS are all order optimal in the worst case, the average case, and the best case. For the CDA problem in probabilistic WSNs, we propose a Level-based Aggregation Scheduling (LAS) algorithm. LAS gathers the aggregation values of continuous snapshots by forming a data aggregation/transmission pipeline on the segments and scheduling all the cell-levels in a cell-level class concurrently. By theoretical analysis of LAS and the upper bound capacity of the CDA problem, we prove that LAS also successfully achieves order optimal capacities in all the cases. The extensive simulation results further validate the effectiveness of CAS and LAS.

Introduction

Wireless Sensor Networks (WSNs) are mainly used for gathering data from the physical world to a sink (base station). During a data gathering process, if the raw data of all the sensors are transmitted to the sink without any data aggregation, we call this data collection   [28], [6], [19], [17], [16]. If the raw data can be aggregated and only an aggregation value is transmitted to the sink, we call this data aggregation   [32], [8]. Furthermore, the union of all the data from all the sensors at a particular time instant is called a snapshot   [8]. The problem of collecting the aggregated value of one snapshot is called Snapshot Data Aggregation (SDA). The problem of collecting the aggregated value of each snapshot of multiple continuous snapshots is called Continuous Data Aggregation (CDA). To evaluate network performance, network capacity, which can reflect the achievable data gathering rate, is usually used  [8], [1], [2], [6], [12], [23], [29], [34]. For instance, unicast capacity,multicast capacity, broadcast capacity, and data collection capacity are used to denote the network capacities of unicast, multicast, broadcast, and data collection, respectively. For SDA and CDA, we use the ratio between the amount of data being aggregated and the time used to transmit the aggregated values of these data to the sink, referred to as SDA capacity and CDA capacity respectively, to measure their achievable network capacity.1

After the first work  [13] in this area, many works emerged to study the network capacity issue under the Protocol Interference Model (PrIM)  [8], [6] and/or the Physical Interference Model (PhIM)  [22] for a variety of network scenarios, e.g. multicast capacity  [23], unicast capacity  [27], broadcast capacity  [24], and data collection capacity  [6], [26]. However, for data aggregation (especially CDA), which is a different communication mode, only a few works consider it  [8]. Moreover, to the best of our knowledge, all of the above mentioned works are based on the ideal Deterministic Network Model (DNM), where any pair of nodes in a network is either connected or disconnected. If two nodes are connected, i.e. there is a deterministic link between them, then a successful data transmission can be guaranteed as long as there is no collision. Otherwise, if two nodes are disconnected, the direct communication between them is assumed to be impossible. However, in real applications, this DNM assumption is too ideal and not practical due to the “transitional region phenomenon”  [25], [40]. With the transitional region phenomenon, a large number of network links (probably more than 90%  [25]) become unreliable, named lossy links   [25]. Even without collisions, data transmission over a lossy link is successfully conducted with a certain probability, rather than being completely guaranteed. Therefore, a more practical network model for WSNs is the Probabilistic Network Model (PNM)  [25], in which data communication over a link is successful with a certain probability rather than always being successful or always fail. For convenience, the WSNs considered under the DNM/PNM are calleddeterministic/probabilistic WSNs.

As mentioned before, for the network capacity issues (including uni/multi/broadcast, data collection/aggregation capacities), most of the existing works are based on the ideal DNM rather than the more practical PNM. This motivates us to study the achievable network capacity of WSNs under the realistic PNM, i.e. for probabilistic WSNs. Specifically, in this paper, we investigate the achievable network capacities of SDA and CDA under the PNM. When studying the SDA and CDA capacities, inspired by the network partition method in  [20], we first partition the network into cells and derive the lower and upper bounds of the number of sensors within each cell. Afterwards, we use two vectors to further partition all the cells into different equivalent color classes. In terms of the equivalent color classes, we design a Cell-based Aggregation Scheduling (CAS) algorithm for SDA, and a Level-based Aggregation Scheduling (LAS) algorithm for CDA. Furthermore, we prove that both CAS and LAS are order optimal by analyzing their achievable network capacities. Particularly, the main contributions of this paper are summarized as follows:

  • Inspired by the network partition method in  [20], we first partition a WSN into cells and use two vectors to further partition these cells into equivalent color classes. According to the obtained cells and equivalent color classes, we design a two-phase Cell-based Aggregation Scheduling (CAS) algorithm for the SDA problem in probabilistic WSNs. In the first phase, all the non-local aggregation nodes transmit their data packets to the local aggregation node in the same cell. In the second phase, all the local aggregation nodes transmit the local aggregation values along the constructed data aggregation tree to the sink. Theoretical analysis shows that the achievable capacities of CAS are all Ω(poenlogn2ωW) in the worst case, in the average case, and in the best case, where po is the promising transmission threshold probability (Section  3), n is the number of sensor nodes in the considered WSN, ω is a constant value, and W is the bandwidth of the wireless channel. Moreover, we study the upper bound capacity of the SDA problem, which is O(poenlogn3W). This implies that CAS has successfully achieved order optimal capacities in all the cases.

  • We propose a Level-based Aggregation Scheduling (LAS) algorithm for the CDA problem in probabilistic WSNs. LAS gathers the aggregation values of continuous snapshots by forming a data aggregation/transmission pipeline on the segments and scheduling the cell-levels in a cell-level class concurrently. Theoretical analysis of LAS shows that its achievable network capacity is {Ω(epoN13.4ωnlognW),ifN=O(nlogn);Ω(po13.4ω2nlognW),ifN=Ω(nlogn)

  • in the worst case, {Ω(poN2eωnlognW),ifN=O(nlogn);Ω(po2eω2nlognW),ifN=Ω(nlogn)

  • in the average case, and {Ω(eepoNωnlognW),ifN=O(nlogn);Ω(epoω2nlognW),ifN=Ω(nlogn)

  • in the best case, where N is the number of snapshots in a continuous data aggregation task. We also investigate the upper bound capacity of the CDA problem, which is {O(2eepoN3nlognW),ifN=O(nlogn);O(2epo9nlognW),ifN=Ω(nlogn).

  • This implies that LAS has already achieved optimal capacities in order in every case.

  • To be more general, we further theoretically analyze the capacity performance of CAS and LAS under the Poisson point distribution model. The analysis shows that CAS and LAS can also achieve order optimal capacities under the Poisson distribution model.

  • We also conduct extensive simulations to validate the performances of CAS and LAS in probabilistic WSNs. Evaluation results indicate that CAS and LAS can improve the SDA and CDA capacities, as well as network lifetime, of probabilistic WSNs significantly, compared with the latest SDA and CDA methods for deterministic WSNs, respectively.

The rest of this paper is organized as follows: in Section  2, we summarize the related works and make remarks for the difference between our work and existing works. In Section  3, we give the PNM and make some assumptions. In Section  4, we discuss the network partition method, which is crucial for the following data aggregation scheduling algorithms. The Cell-based Aggregation Scheduling (CAS) algorithm for SDA is proposed and analyzed in Section  5. In Section  6, we design the Level-based Aggregation Scheduling (LAS) algorithm for CDA, and we also derive the achievable capacity of LAS theoretically. To make our work more general, we also analyze the capacity performance of CAS and LAS under the non-i.i.d. node distribution model in Section  7, which turns out to be order optimal either. In Section  8, the simulations are conducted to validate the performances of CAS and LAS, and we conclude this paper and point out possible future research directions in Section  9.

Section snippets

Capacity analysis for wireless networks

Following the first work in this area  [13] by Gupta and Kumar, many works emerged to study the network capacity issue. The authors of  [6] derived the upper and lower capacity bounds of data collection under the PrIM for deterministic WSNs. In another similar work  [8], the authors obtained the data collection and aggregation capacity bounds in a general deterministic WSN under the PrIM. In  [23], the authors investigated the multicast capacity for large scale deterministic wireless ad hoc

Network model

In this paper, we consider a probabilistic WSN consisting of n sensors, denoted by s1,s2,,sn respectively, and one sink deployed in a square area with size A=cn (i.e., the node density of this WSN is 1c), where c is a constant. All the sensor nodes know their location information. Furthermore, we assume all the sensors are independent and identically distributed (i.i.d.) and without loss of generality, the sink is located at the top-right corner of the square.2

Network partition

In this section, we study how to partition a WSN, which is essential for our following scheduling algorithms. Inspired by  [20], first, we partition the network into cells by horizontal and vertical lines. Subsequently, we partition these cells into equivalent color classes by two vectors. Moreover, we derive some useful results for these cells and equivalent color classes.

Snapshot data aggregation

In this section, we consider the SDA problem, propose a Cell-based Aggregation Scheduling (CAS) algorithm for SDA, and analyze the achievable network capacity of CAS. Furthermore, we also derive the upper bound network capacity of the SDA problem, which shows our proposed CAS is order optimal.

Continuous data aggregation

To address the CDA problem, we design a Level-based Aggregation Scheduling (LAS) algorithm in this section. Firstly, LAS partitions the data aggregation tree T (constructed in Section  5.1) into segments and cell-level classes. Subsequently, LAS forms a data aggregation pipeline on the segments by scheduling the data aggregations of a level class concurrently. Furthermore, we also analyze the achievable capacities of LAS in every case, as well as the upper bound capacity of the CDA problem,

Discussion: capacity of CAS and LAS under non-i.i.d. models

We assume the network distributed according to an i.i.d. model is convenient for algorithm design and analyzing the achievable data aggregation capacity of the proposed algorithms. However, this assumption may not hold in some situations. Therefore, in this section, we analyze the capacity performance of CAS and LAS under non-i.i.d. models. Specifically, we consider that all the sensor nodes are deployed according to a stationary Poisson point process in this section.

Similar as in Section  3,

Simulations

In this section, we validate the effectiveness of CAS and LAS via simulations. The simulations are conducted on a home-made simulator, which is implemented by VC++. Basically, the simulator consists of several modules involving the network generation module, the network time/synchronization control module, the network topology control module, the protocol module, etc. In all the simulations, we consider a WSN with one sink and all the sensors randomly distributed in a square area. The network

Conclusion and future work

Considering that there are no existing works studying the data aggregation problem in probabilistic WSNs, we investigate the SDA and CDA problems under the PNM in this work. First, we partition a WSN into cells and equivalent color classes. Then, based on the partitioned cells and equivalent color classes, we propose a data aggregation algorithm for the SDA problem, named Cell-based Aggregation Scheduling (CAS). The theoretical analysis of CAS shows that its achievable network capacities are

Shouling Ji is a Ph.D. candidate in the Department of Computer Science at Georgia State University. He received his B.S. (with Honors) and M.S. degrees in computer science from Heilongjiang University, Harbin, China, in 2007 and 2010, respectively. He received another M.S. degree in computer science from the Department of Computer Science at Georgia State University in Summer, 2011. His research interests include wireless sensor networks, cognitive radio networks, and social networks. He is now

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    Shouling Ji is a Ph.D. candidate in the Department of Computer Science at Georgia State University. He received his B.S. (with Honors) and M.S. degrees in computer science from Heilongjiang University, Harbin, China, in 2007 and 2010, respectively. He received another M.S. degree in computer science from the Department of Computer Science at Georgia State University in Summer, 2011. His research interests include wireless sensor networks, cognitive radio networks, and social networks. He is now a student member of ACM, IEEE, and IEEE COMSOC.

    Jing (Selena) He is currently an Assistant Professor in the Department of Computer Science at Kennesaw State University. She received her Ph.D. and M.S degrees from the Department of Computer Science at Georgia State University (GSU) emphasized in wireless networking. Before joining GSU, she received a B.S. degree in electronic engineering from Wuhan Institute of Technology, Wuhan, Hubei China. She received another M.S. degree in computer science concentrated in artificial intelligence from Utah State University. She also had experience in the IT industry. She worked with Electronic Arts in the Salt Lake Branch as a software engineer. Her research interests include wireless networking, network optimization, and social networks.

    Yi Pan is the Chair and a Full Professor of the Department of Computer Science at Georgia State University, Atlanta, Georgia, USA. Dr. Pan received his BE and ME in computer engineering from Tsinghua University, China, in 1982 and 1984, respectively, and his Ph.D. in computer science from the University of Pittsburgh, USA, in 1991. Dr. Pan’s research interests include parallel and distributed computing, optical networks, wireless networks, and bioinformatics. Dr. Pan has received many awards from agencies such as NSF, AFOSR, JSPS, IISF and Mellon Foundation. His recent research has been supported by NSF, NIH, NSFC, AFOSR, AFRL, JSPS, IISF and the states of Georgia and Ohio. He has served as a reviewer/panelist for many research foundations/agencies such as the US National Science Foundation, the Natural Sciences and Engineering Research Council of Canada, the US–Israel Binational Science Foundation, the Australian Research Council, the Swedish Research Council, and the Hong Kong Research Grants Council. Dr. Pan has served as an editor-in-chief or editorial board member for 15 journals including 6 IEEE Transactions and a guest editor for 10 special issues for 9 journals including 2 IEEE Transactions.

    Yingshu Li received her Ph.D. and M.S. degrees from the Department of Computer Science and Engineering at the University of Minnesota-Twin Cities. She received her B.S. degree from the Department of Computer Science and Engineering at Beijing Institute of Technology, China. Dr. Li is currently an Associate Professor in the Department of Computer Science at Georgia State University. Her research interests include wireless networking, cyber-physical systems, and phylogenetic analyses. Her research has been supported by the National Science Foundation (NSF) of US, the National Science Foundation of China (NSFC), the Electronics and Telecommunications Research Institute (ETRI) of South Korea, and GSU internal grants. Dr. Li is the recipient of an NSF CAREER Award.

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