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Accepted 17 September 2010Available online 29 September 2010

Keywords:Data gatheringWireless sensor networks

energy resources. We employ a hierarchical topology and routing structure with multiple

control trafc; and in industrial settings to track invento-ries and the state of other resources [37]. Recently, data-gathering WSNs nd increasingly widespread applicationsin ecological and environmental monitoring [13,14,29].

performing computations on-board in a sensor [36].In general, the lifetime of a sensor network can be

dened as the time frame between two successive sensordeployments, i.e., a deployment cycle. A deployment cycleconsists of successive periods of xed time length for whichtopology and/or routing decisions are made. Thus, prolong-ing the network lifetime corresponds to obtaining themaximum number of successive periods that the data

1570-8705/$ - see front matter 2010 Elsevier B.V. All rights reserved.

Corresponding author. Tel.: +1 979 845 9573.E-mail address: uster@tamu.edu (H. ster).

Ad Hoc Networks 9 (2011) 835851

Contents lists available at ScienceDirect

Ad Hoc Ne

.e lsdoi:10.1016/j.adhoc.2010.09.010Wireless sensors are used to sense a wide range ofnatural or articial phenomena including temperature,pressure, humidity, light, motion, weight, noise, etc. Wire-less sensor networks (WSNs) can be employed for datagathering purposes in inhospitable environments and dif-cult-to-reach terrains, such as forests, urban or rural battle-elds, and borderlines; in wild habitats and oceans tomonitor and observe natural phenomena; in disaster pre-vention and relief; in urban environments to monitor and

efcient design and operation of WSNs are topology control,which refers to the determination of an underlying networktopology and routing, which refers to the determinationdata transfer paths over this network. The relationship be-tween these problems is emphasized byWSN-specic attri-butes energy efciency and computation-communicationtrade-off. Energy efciency is important because each sen-sor is equipped with an on-board nonrenewable powerunit. The communication-computation trade-off refers tothe fact that communication consumes more energy thanNetwork design modelsAlgorithms

1. Introductionsinks and devise a topology control scheme via usable energy fraction at the sensors.We develop and examine three different mathematical models whose solutions prescribeclusterhead and sink locations and data routing from sensors to sinks in a period of adeployment cycle. We develop a heuristic solution algorithm which provides very smalloptimality gaps for the models. The approach utilizes two types of solution representa-tions, a combination of multiple neighborhoods, and objective value-based cut inequalitiesfor improving the evaluation of candidate solutions. We present extensive numerical testresults and analysis of the models and the solution approach. We determine that our pro-posed model, which minimizes average energy usage and the range of remaining energydistribution at the sensors, captures important characteristics of topology control and rout-ing integration in WSN design and exhibits signicantly better performance than ourbenchmark models and a well-known protocol HEED in extending network lifetime.

2010 Elsevier B.V. All rights reserved.

Two fundamental and related problems for effective andArticle history:Received 30 January 2010Received in revised form 30 July 2010

This study considers an integrated topology control and routing problem in wireless sensornetworks (WSNs), which are employed to gather data via use of sensors with limitedIntegrated topology control and roufor prolonged network lifetime

Halit ster , Hui LinDepartment of Industrial and Systems Engineering, Texas A&M University, Co

a r t i c l e i n f o a b s t r a c t

journal homepage: wwwg in wireless sensor networks

tation, TX 77843-3131, United States

tworks

evier .com/locate /adhoc

redundancy mentioned above. We assume that the

836 H. ster, H. Lin / Ad Hoc Networks 9 (2011) 835851generated at the sensors can reach the user. In our case, theend of a deployment cycle is reached when it is not possi-ble to obtain a feasible solution to the problem of transmit-ting data generated at the sensors to the user.

In this paper, we develop power-aware mathematicalmodels and solution approaches for the integrated topologycontrol and data routing problems to prolong the lifetime ofa WSN. To this end, we consider three models that differmainly in terms of their objective functions. The objectivesinclude minimization of (1) total or average energy usage inthe system, (2) maximum energy used at a sensor node, and(3) a weighted sum of the range of end-of-period remainingenergy distribution at the sensors and the average energyused in the system.

We adopt a hierarchical data ow structure in whichdata generated at the sensors are rst routed to the sensorsdesignated as clusterheads (CHs). Each sensor is assignedto at least one CH which reduces the total data size thatit receives from sensors via aggregation. Each CH routesdata to a sink either through other CHs, which act onlyas relays without aggregation, or directly. Such a structureis benecial in terms of energy efciency in three ways:(1) Since the sensors in close proximity of each other arelikely to be in the same cluster and may generate very sim-ilar data, data aggregation at CHs helps to reduce redun-dancy and energy consumption in communication. (2)Hierarchical structure distributes the energy usage to mul-tiple sensors on multi-hop paths, thus eliminating thequick expiration of the sensors away from the sinks. (3)Since energy dissipation in communication is proportionalto the square of the distance, compared to direct commu-nication, the total energy dissipation due to communica-tion is less on a multi-hop route [31].

Our contributions in this paper can be summarized asfollows.

1. We devise three mathematical models for integratedtopology and routing decisions for data-gatheringWSNs. The objectives, minimization of total (or aver-age) energy usage in the network and minimization ofthe maximum energy usage at a sensor, are commonlyconsidered in devising communication protocols (e.g.,[15,16,25,27,28,38]). However, this has not been donefrom an integrated mathematical modelling perspectiveas in our case. We consider these two models as bench-mark models for our third proposed model, which min-imizes the total energy and the range of remainingenergy distribution in the network.

2. In devising our models, we consider the use of multiplesinks. This is helpful for energy efciency since multiplesinks create an opportunity for better proximity to sen-sors, thus saving energy in communication. It is possi-ble to route the data so that the energy drainage inthe network is more evenly distributed to the sensorsby changing the locations of the sinks and the CHs ineach period. Xue et al. [39] also consider multiple sinks,however, with known locations as opposed to our casewhere the locations are also determined.

3. We suggest a new approach to achieve topology controlvia limiting the usable energy at a sensor as a fraction ofits total available energy. We show that how this usableaggregation ratio increases with increasing sensordeployment density. In previous studies with dataaggregation (e.g., [15,16,19,42]), we observe thataggregation of data into a single signal at each CH,i.e., regardless of the amount of data received, is com-mon which is applicable in such cases as monitoringmaximum temperature in the sensor eld.

5. Since the models dictate large discrete optimization for-mulations, obtaining exact solutions are highly imprac-tical using exact optimization methods such as abranch-and-cut algorithm. Thus, we develop a heuristicsolution algorithm which provides very small optimal-ity gaps for the models. The approach utilizes two typesof solution representations, a combination of multipleneighborhoods, and objective value-based cut inequali-ties for improving the evaluation of candidate solutions.Computational evidence demonstrates that our pro-posed third model performs signicantly better thanboth benchmark models. Furthermore, we comparethe performance of the proposed model to a well-known protocol HEED [42] and show that our proposedmodel performs signicantly better in terms of networklifetime.

The rest of this paper is organized as follows. After aliterature review in Section 2, we introduce the notation,problem denition and the optimization models in Sec-tion 3. In Section 4, we develop algorithmic approachesfor solving our mathematical models. In Section 5, weprovide computational results illustrating the perfor-mance of our algorithms, impact of usable energy fractionon network lifetime, and a comparison of the models insingle-and multi-period settings as well as a detailedanalysis based on energy characteristics and network life-times. Finally, in Section 6, we present a summary andconclusions.

2. Related literature

In the WSN literature, extensive effort has been in-vested in developing energy efcient protocols and routingparadigms to maintain a requested WSN topology. In thissection, we provide an overview of the topology controland routing studies, and point out most relevant studiesto our work.

Topology control is mainly achieved by the adjustmentof sensors transmission ranges, which is related to thepower level settings at the sensors [30,31]. Topologyenergy determined is important and difcult in our twobenchmark models. On the other hand, the solution inthe proposed third model is insensitive to this charac-teristic as the control of energy distribution is implicitlyaccounted in the objective.

4. We consider cases where an overall v