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USC Computer Science Technical Reports, no. 831 (2004)
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USC Computer Science Technical Reports, no. 831 (2004)
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Data Acquisition in Multiple-sink Sensor Networks Abhimanyu Das a Debojyoti Dutta b abhimand@usc.edu ddutta@usc.edu a Dept. of Computer Science, University of Southern California, Los Angeles, CA, USA b Dept. of Biology, University of Southern California, Los Angeles, CA, USA I. Introduction Scalable, energy-efficient data acquisition in large sensor network deployments such as habitat moni- toring is an research important problem. In several papers [1, 2], sensor networks have been modeled as having a single sink (or base-station) that acts as the data recipient for a large number of sensors (data sources) deployed over a sensor field. The sensor net- work might use simple querying and data collection trees for hop-by-hop query dissemination and routing of sensor responses [1] back towards the sink. Since sensors are energy-constrained devices, we wish to minimize communication energy expenditure of these sensors. However, as the size of the sensor network grows, the distances between the sink (base-station) and the responding sensors become larger. Hence, the communication involved in query-flooding and data- acquisition between the sensors and the single sink can lead to high energy consumption, and possibly re- duce the lifetime of the sensors. Additionally, the sen- sors close to the sink can get rapidly exhausted as the amount of data to be extracted from these large sensor networks increases. Hence, we need to design energy- efficient data acquisition mechanisms that scale with the size of the network. A naive solution is to apriori partition the sensed area into several single-sink sensor networks. How- ever an optimal pre-partitioning of the sensor net- works to minimize sensor-sink communication-costs may be non-trivial. Additionally, with such static schemes, it would be hard to ensure robustness and energy-efficiency in the presence of sink failures or changes in network connectivity. In this paper, we explore an alternate solution, by simultaneously deploying multiple sinks within a sin- gle sensor network. Each sensor would then have an option of sending its data to any one of the sinks. In particular, it could choose to diffuse its data toward its closest sink, as dynamically determined by an appro- priate energy metric, in order to reduce communica- tion costs. This would entail lower hop-by-hop com- munication for data extraction, and hence, reduced en- ergy expenditure. These sinks would work simultane- ously to flood queries through the network, and col- lectively gather the corresponding sensed data from responding sensors. Problem: Given a sensor network with n sensor nodes and k sinks distributed in a field of area A, we pose the following questions: (1) Is there a sim- ple model for querying and data-collection protocols in the presence of multiple sinks, without adding ex- tra protocol overheads? (2) What are the average communication-energy savings for resolving a query in a multiple-sink sensor network, in comparison with that in a single sink scenario? We assume that the sinks do not have energy con- straints, with respect to computation and communi- cation operations. The sinks are also assumed to have dedicated energy-unconstrained connectivity to each other and to their remote server Additionally, in- network data aggregation in the presence of multiple sinks is not considered in this paper. In this paper, we introduce a simple abstraction for querying and data-acquisition in a multiple-sink sensor network. We propose a logical-graph model using a single virtual sink, created from the sensor- connectivity graph containing the multiple sinks. This is generic enough to allow for the seamless adaptation of existing routing and querying protocols designed for single-sink sensor networks to the multiple sink case. In particular, we prove that shortest path tree creation in our logical-graph model is equivalent to that in the original sensor-connectivity graph. Additionally, we analytically obtain the expected communication energy savings for data acquisition in the presence of multiple sinks. We consider both a uniform random sink placement as well as a deter- ministic grid-based sink placement. We validate our analysis through simulations on random multi-sink sensor network topologies. While our analysis is re- stricted to the one and two dimensional cases, we con- jecture that, in general, the expected energy savings in a d-dimensional sensor region due to a random place- ment of k sinks and n sensors is proportional to k 1 d . 82 Mobile Computing and Communications Review, Volume 9, Number 3 II. Related Work In this paper, we highlight only a few representative papers that are most relevant to our work. To the best of our knowledge, we are not aware of any re- lated work that has analytically modeled a multiple- sink sensor network and estimated the expected en- ergy savings with multiple sinks In [3], Muthukrishnan et. al. showed that if sen- sor networks are modeled using Random Geometric Graphs, and if the distance between two points u, v is given by D(u,v) and the transmission radius is r,then the number of hops needed to transmit a unit of data is given by 2D(u,v) r . We leverage this result to derive the energy savings analysis in our paper. The work that is most closely related to this paper is by Dubois-Ferriere et. al. [4]. In their paper, the authors divide the domain into Voronoi clusters and designate a sink for each cluster to perform data ac- quisition from sensors in that cluster. The authors validate their idea using a mote based implementa- tion and a grid based deployment. Our paper differs from this work in several aspects. First, we present a generic virtual graph based model that can handle Voronoi scoping as a special case. Second, our work is based on analytical models. III. Logical Graph Model In our model, we map a random geometric graph cor- responding to a multiple-sink sensor network into a logically equivalent single-sink counterpart. Thus, for purposes of data-acquisition or querying protocols in this new logical graph, we can view all the sinks as a single logical vertex. A sensor is therefore no longer aware of the existence of multiple sinks, since the routing and connectivity information for the various sinks is now advertised as originating from a single logical sink. More formally, we consider a multiple-sink sen- sor network modeled as an undirected graph G = (V,E) with a subset S of V that are sink-nodes, and edge weights w(i,j) on all edges (i,j) ∈ E.We then convert this graph G into another logical graph G =(V ,E ) where V = V − S +{s }. s can be viewed as a single logical vertex representing all the sinks. Thus, we have E = {(u,v)|(u,v) ∈ E and u,v / ∈ S}∪{(u,s )|∃s ∈ S,(u,s) ∈ E}. We also have a new edge weight function w (i,j) where w (i,j)= w(i,j) if i,j / ∈ S and w (i,s )= min ∀s∈S w(i,s) ifj/ ∈ S. Essentially, we construct a new graph where all the sinks are now considered to be a single logical sink and edges connecting a particular sensor to any sink in G are replaced by an edge from the sensor to the logical sink in G , with its new weight being the mini- mum distance of the sensor from any of the sinks. The weights here can be chosen appropriately based on the objective function to be optimized as a part of the data acquisition (e.g. it could be the communication cost or the error-rate of the link). Now we can adapt var- ious forms of querying or data-collection strategies, that are normally used in the single-sink networks, by using the logical graph G as its input (instead of G). For example, we can run the Shortest Path Tree and the Minimum Spanning Tree protocols for the multi- ple sink case, using existing algorithms that normally work in a single sink scenario. Weprove the following theorem and a corollary for adapting a shortest path tree creation algorithm. Theorem 1 Given a multi-sink sensor graph G, and a non-negative edge-weight function, and the corre- sponding logical graph G with a single logical sink s as described above, a path P, is the shortest path from any sensor m to its closest sink (say s m )in G if and only if P = P−{s m } +{s } is the shortest path from the sensor m to the logical sink s in G .If w and w are the weight functions for G and G ,then w(P)= w (P ). Corollary 1 Using the logical graph model, any dis- tributed Shortest-Path-Tree algorithm that can calcu- late the shortest path tree from a sensor to the sink in a single-sink sensor network, can also calculate the shortest path tree from a sensor to its closest sink, in the multiple-sink sensor network. IV. Analysis We now estimate analytically, the average energy cost savings for a query resolution in the presence of mul- tiple sinks. We assume that every sensor has an equal probability of responding to a given query. The total energy expenditure for a query resolution consists of two parts: the query flooding part, and the data col- lection part. Since the cost of query flooding is in- dependent of the number of sinks in the network, we therefore only estimate the expected energy expendi- ture for a query response. In our analysis, we also assume that the bulk of the sensors’ energy consumption for data acquisition is due to their transmission costs, and hence, we use this transmission cost (proportional to d 2 ,where d is the transmission distance) as a metric when creating Mobile Computing and Communications Review, Volume 9, Number 3 83 routing paths for data acquisition. Additionally, our analysis of the energy savings in this section, is nor- malized for a unit sensor-to-sink transmission. Weassume that k sinks are uniformly randomly dis- tributed in a sensor region S of area A. It is not hard to show [5] that for a uniform sensor grid and k sensors, the average energy costs scale as 1 k , 1 √ k for one and two dimensions respectively. We will only present re- sults for the random sink and sensor placement over here. The n sensors themselves are also uniformly randomly distributed in region S. First we consider a one dimensional sensor region and then move on to the two dimensional case. One-DimensionalCase: Firstconsider a1Dunit line, where the k sinks as well as the n sensors are uni- formly randomly distributed on the line. Given this model, we estimate the average energy consumption per query response as a function of k.Wehavethe following theorem (proved in [5]): Theorem 2 Given a uniform random distribution of n sensors and k sinks on a straight line, and the sen- sor communication radius r satisfies the asymptotic connectivity threshold, the average energy costs in- curred per query response is asymptotically inversely proportional to O(k). TwoDimensional Case: In the 2D case, the nsensors and the k sinks are uniformly randomly distributed on a unit square. We obtain the expected distance of a random sensor from its closest sink: Lemma 1 Given a random placement of k sensors and n sinks in a unit square, the expected distance D avg of a random sensor node from its closest sink is given by D avg = 1 1/8 0.5 a=0 0.5 b=a D(a,b)da.db, where, D(a,b) is given by D(a,b)= a r=0 8kr 2 (1− 4r 2 ) k−1 dr + b r=a kr(4r+2a)(1− 2r(a + b)) k−1 dr + 1−b r=b kr(2r + a + b)(1− (r + a)(r + b)) k−1 dr + 1−a r=1−b kr(1− (r + a)) k−1 dr. Here, the distance between two locations (x,y) and (a,b) is defined as D((x,y),(a,b)) = max(|x− a|,|y− b|). Proof Sketch: Let us divide the square into eight identical triangles.Define the origin to be at the lower leftmost corner of the square. Consider any sensor X located at (a,b) chosen from the triangle region T, such that (0r]. The expected distance of the closest sink from sensor X (as a function of its location [a,b]) is therefore given by D(a,b)= 1−a r=0 rP(r)dr. The expected distance of the closest sink from any random sensor in the unit square, D avg , is therefore obtained by integrating D(a,b) over all sensor placements (a,b) in triangle T and dividing it by its area, 1 8 . Thus, we have D avg = 1 1/8 0.5 a=0 0.5 b=a D(a,b)da.db While this expression does not have a closed form so- lution, D avg can be obtained numerically. Once we have the expected distance between a ran- dom sensor and its closest sink, we now make use of a result in Muthukrishnan et. al. [3], to prove (for details, see [5]) the following lemma: Lemma 2 Given a random placement of k sensors and n sinks in a unit square region S, the maximum transmission radius r satisfying the asymptotic con- nectivity threshold, the expected energy consumption , E avg , is proportional to D avg .r,where D avg is as defined before. While E avg in the above lemma does not have a closed form solution, we can numerically observe that E avg seems to fall off inversely proportional to k β , where k is the number of sinks, and 0.4<β < 0.5. V. Simulation Results Wevalidate our analytical results through simulations, using a uniformly random sensor and sink place- ment. We simulate both one-dimensional and two- dimensional scenarios by placing 200 sensors and a variable number sinks uniformly at random on a unit 84 Mobile Computing and Communications Review, Volume 9, Number 3 024 6 810 Number of Sinks 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Normalized average distance between a sensor and its closest sink Simulation Analytical 024 6 810 Number of Sinks 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 Normalized average energy to reach closest sink Simulation Analytical 0 5 10 15 20 Number of Sinks 0 0.2 0.4 0.6 0.8 1 Normalised Average Energy to Reach Closest Sink Analytical Result beta=0.5 beta=0.4 (i) Average distance (ii) Average Energy (iii) Compare analytical value of E avg with k β Figure 1: Comparison of analytical values from our model and simulations depicting the normalized average distance/energy between sensors and its nearest sink for a 2D-unit square. (iii) shows plots the normalized average energy for the 2D-case from our analytical model and k −β where β =0.4,0.5. line as well as on a unit square. Due to space con- straints, we only present the two-dimensional results here. We run a Distance Vector protocol in the sensor network using the logical graph model, to find optimal cost paths fromsensors totheir closest sinks. Fromthe simulations, we estimate the normalized communica- tion costs of asingle query response, and compare that to our analytical predictions, using our random graph model. Weobserve in Figure 1(i), (ii) that our analyti- cal modelhas high accuracy in predicting theexpected sensor-sink communication energy consumed. From our simulation results, we make two sim- ple observations that match our analytical predictions. First, for one-dimensional scenarios(not shown here), the expected communication energy spent falls off in- versely proportional to the number of sinks, k. Sec- ond, in the two dimensional case, the communica- tion energy expenditure seems to be inversely pro- portional to k β ,where k is the number of sinks and 0.4 <β < 0.5. Note that k is much closer to 0.5 as shown in Figure 1 (iii). We conjecture that the ex- pected energy savings in a d-dimensional sensor re- gion due to deployment of k sinks is proportional to k 1 d. VI. Conclusions and Future Work In this paper, we studied the energy savings incurred in data acquisition from multiple-sink sensor net- works. We first proposed a logical graph model wherein a single virtual sink replaces the various physical sinks in the multi-sink network. This allows us to easily adapt, with minimal protocol overheads, algorithms designed for a single sink sensor network to that with multiple sinks. In particular, we show the above result for shortest path tree construction. We then obtained analytical results to characterize the en- ergy savings by using multiple sinks on both a deter- ministic sensor grid along with uniform sink place- ment as well as uniformly random sensor and sink placement. Ouranalytical results were validated using simulations. We conjectured and empirically showed that the expected energy savings in a d-dimensional sensor region due to a random placement of k sinks is proportional to k 1 d. Interesting future work includes practical protocol design for different optimization functions in multi- sink sensor networks using our logical graph model. Another open area is to consider trade-offs in the pres- ence of in-network data aggregation. More details can be found at http://netweb.usc.edu/ ddutta/research/sensor. References [1] C. Intanagonwiwat, R. Govindan, and D. Es- trin, “Directed Diffusion: A Scalable and Ro- bust Communication Paradigm for Sensor Net- works,” in ACM Mobicom, 2000. [2] B. Krishnamachari, D. Estrin, and S. Wicker, “Impact of data aggregation in wireless sensor networks,” in International Workshop of Dis- tributed Event Based Systems (DEBS), Vienna, Austria, July 2002. [3] S. Muthukrishnan and G. Pandurangan, “The Bin-Covering Technique for Thresholding Ran- dom Geometric Graph Properties,” Tech. Rep. 2003-39, DIMACS Tech Report, 2003. [4] H. Dubois-Ferriere and D. Estrin, “Efficient and Practical Query Scoping in Sensor Networks,” Tech. Rep. 2004-39, CENS/UCLA Tech Report, 2004. [5] A. Das and D. Dutta, “Data Acquisition in Multiple-sink Sensor Networks,” Tech. Rep. USC-CS-TR-04-013, USC, July 2004. Mobile Computing and Communications Review, Volume 9, Number 3 85
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Abhimanyu Das, Debojyoti Dutta. "Data acquisition in multiple-sink sensor networks." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 831 (2004).
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