How much energy saving does topology control offer for wireless sensor networks? a practical study

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1 How much energy saving does topology control offer for wireless sensor networks? a practical study Ajit Warrier, Sangjoon Park, Jeongki Min and Injong Rhee Department of Computer Science North Carolina State University Raleigh, NC, USA Abstract Topology control is an important feature for energy saving, and many topology control protocols have been proposed. Yet, little work has been done on quantitatively measuring practical performance gains that topology control achieves in a real sensor network. This is because many existing protocols either are too complex or make too impractical assumptions for a practical implementation and analysis. A rule of thumb or a practical upper-bound on the energy saving gains achievable by topology control would assist engineers in estimating the overall energy budget of a real sensor system. This paper proposes a new topology control protocol simple enough to permit a straightforward stochastic analysis and also a real implementation in Mica2. This protocol is currently deployed in our testbed network of 42 Mica2 nodes. Our contribution is not on the novelty of this protocol but on a practical performance bound we can study using this protocol. The stochastic analysis reveals that topology control can achieve a power gain proportional to network density divided by a factor of eight to ten. Our experiment result from the real testbed tests confirms this finding. We also find a tradeoff in terms of throughput loss due to reduced density by topology control which amounts to about 50% throughput loss. These performance figures represent rough rules of thumb on energy efficiency achievable even by a very simple, unoptimized protocol. Key words: Topology Control, Wireless Sensor Networks, Cluster address: acwarrie,sjpark2,jkmin,rhee@ncsu.edu (Ajit Warrier, Sangjoon Park, Jeongki Min and Injong Rhee). Preprint submitted to Elsevier Science 1 October 2006

2 1 Introduction Topology control is a power saving technique for a densely populated wireless network that reduces the number of nodes participating in forwarding and routing packets generated by the other nodes without diminishing network connectivity and coverage. This technique is very useful in wireless sensor networks because they are typically deployed densely, thus offering much redundancy in network coverage and connectivity. Moreover, most sensor network applications have a restricted form of communication patterns always involving the sink as an end-point (mostly from sensing nodes toward the sink). In such applications, as long as a there is a routing path between a node and the sink, the node is considered to be connected. Thus, connectivity can be maintained in these networks with much fewer routing nodes than in the general wireless networks with more diverse communication patterns. Topology control contributes to power saving mainly in two ways in sensor networks: (1) it allows non-routing nodes (or sensing nodes ) to maintain lower duty cycle because they don t have to receive packets for the routing purpose and (2) routing nodes can act as data aggregation points as all the packets are forwarded through these nodes. The former serves to reduce idle listening and overhearing since sensing nodes can simply turn off their radio most times while performing sensing. The latter serves to reduce the amount of traffic on the routing backbone. While these benefits are qualitatively promising, existing research [1 3] lacks in quantifying these benefits experimentally and analytically in real network settings. This lack of experimental work is, we believe, in general because most existing topology control protocols for sensor networks are difficult to implement in practice, either due to the complexity of the algorithms themselves, or due to the nature of the assumptions made therein, with respect to radio link connectivity, radio transmission power, processing power, or availability of global topology information or location information. Up to now, the experimental work by Younis and Fahmy [4] is the only work that demonstrates application of topology control on data aggregation in a real sensor network. Even this work relies on some assumption of network connectivity that may not generally hold in realistic sensor network settings (more details in Section 2). In this paper, we focus on quantifying the benefits of topology control on reducing idle listening and overhearing. Our approach is practical. We develop a simple, yet practical topology control protocol simple to be analytically tractable and practical to implement in real sensor networks. We do not claim any optimality of our protocol in achieving energy efficiency and furthermore the novelty of the protocol because some components of the protocol are similar to those of existing protocols. Notwithstanding these, our contribution lies in defining a rule of thumb or practical performance upper bound on the en- 2

3 ergy efficiency realizable by use of topology control through differential duty cycling. This rule of thumb defines a tradeoff between the cost and benefit of topology control. The cost is incurred because topology control is not necessarily capacity preserving although it maintains connectivity, it may lose throughput or latency, for instance, because the reduced number of routing nodes may ultimately result in reduced choices of feasible data paths that can concurrently carry data to the sink in the network or alternative paths in case of congestion or link losses in some part of the network. Thus, this rule of thumb can assist application designers in deciding to adopt topology control for improved energy efficiency. In this paper, we find through experiments on a network of 42 sensor Mica2 nodes, deployed over an area of size 400 x 300 sq. ft., that while topology control on such a network results in about 50% loss in throughput, we gain in energy saving by about two to three times, thereby achieving about times energy efficiency measured in terms of bits per joule. Our analysis based on a Poisson point topology model and a unit disk communication model also suggests that energy saving increases linearly with network density so that the lifetime of the network can be extended up to a ratio of the network density (measured by the number of nodes in one hop communication range) over a factor of eight to ten. This result closely follows our experimental result because in our network testbed the density of the network varies from 6 to 15 and we achieve about two-three times the energy saving compared to a naive duty cycling MAC without topology control. Note that these models are not used in the protocol operations, but in the stochastic performance analysis. Thus although the modeling assumptions may not be completely realistic, we confirm through experimental results that the result of the analysis is good enough for a rule of thumb. The remainder of the paper is organized as follows. Section 2 has discussion on related work, Section 3 describes our topology protocol, Section 4 analyzes the performance of the protocol, Section 5 reports our experiments and their results and Section 6 contains our conclusion. 2 Related work In topology control schemes like GAF [1] and SPAN [5], the goal is to leverage the network spatial redundancy to create a backbone of nodes responsible for communication, while the rest of the nodes sleep. GAF achieves this by the use of location information. Nodes are grouped together into virtual grids and only selected nodes participate in communication while the rest of the network sleeps. Acquiring location information in sensor nodes would require GPS-like hardware, or complex localization algorithms. 3

4 SPAN, on the other hand tries to achieve this by periodically broadcasting connectivity information. SPAN is highly suitable for sparse-medium density mobile wireless environments where node connectivity may change often, but it is not well suited to the wireless sensor network environment due to the following reasons. First, the primary goal of SPAN is to save energy while preserving capacity. In sensor networks, on the other hand, the primary goal of topology control is to reduce energy consumption as much as possible while maintaining some acceptable capacity. In the kind of sensor network deployments seen till now [6], nodes have been static with extremely low data rates, indicating that the network capacity is not fully utilized. Second, SPAN is designed for ad-hoc wireless networks where some fraction of nodes may be mobile. In such networks, high density is often due to accident, and not by design. For instance, in a campus wide mesh network, local hot spots with high node density could be created for a short period of time due to classes being held during that time period. In order to take advantage from such rapidly changing topologies, SPAN needs to run the topology control algorithm continuously, requiring exchange of topology control messages. The number of such messages generated increases as the observed local density increases, requiring surrounding nodes to stay up most of the time, negating the benefits of topology control. Hence, the energy savings paradoxically do not improve with increasing network density. This problem has been noted in the original paper [5]. Due to the development of cheap sensor devices, it is feasible to deploy wireless sensor networks with high density for robustness to node failures and enhanced sensing coverage. Hence, a topology control control algorithm for sensor networks should take advantage of high density, whenever possible. Cluster-based routing algorithms have been extensively studied over the years. Generally, nodes in a network are divided into multiple overlapped clusters. Mario et al.[7] propose two clustering formation algorithms that are based on lowest-id and highest-connectivity for a mobile networking environment. The lowest-id based algorithm is shown to give better throughput in a mobile environment. Chiang et al.[8] propose a routing scheme for clustered mobile wireless network. They introduce the least cluster change (LCC) clustering algorithm to reduce the overhead of cluster head change caused by node mobility. They show that LCC performs better than both lowest-id based and highest-connected based algorithm. Jiang et al.[9] propose a protocol called cluster-based routing protocol (CBRP) and they use a variation of the lowest- ID cluster formation algorithm Heinzelman et al.[10] propose a cluster formation algorithm called LEACH. K cluster heads are randomly elected and the remaining nodes select the closest cluster head as their cluster head. In LEACH, the cluster heads are selected randomly without knowledge of their neighbors so the size of the cluster area and the number of member nodes of each cluster are non-uniform. In LEACH, they assume that all nodes can control the transmission power to reach the 4

5 sink, and cluster heads can directly communicate with the sink. Soheil et al.[2] propose an optimal balanced k-clustering scheme such that each cluster is balanced (in terms of the number of sensor nodes) and the total distance between sensor nodes and their cluster heads is minimized. Given the constraints that each cluster head can handle only a certain number of communication channels, this scheme does not allow each member node to choose the closest cluster head. Younis et al.[3] propose a protocol called Hybrid Energy-Efficient Distributed clustering (HEED) that periodically selects the cluster heads according to a combination of their residual energy and intra-cluster communication cost. Unlike LEACH, HEED provides well-balanced cluster heads and typically smaller sized clusters. They use two radio transmission power levels, one for intra cluster communication and the other for inter cluster communication. HEED assumes that cluster heads can always communicate with each other and form a connected graph realizing this assumption in practical deployments could be tricky. 3 Design of a Simple Clustering Scheme for Low Power Sensor Networks To summarize the related work in the previous section, a practical topology control scheme for wireless sensor networks should have the following characteristics. First, it should not rely on any assumption about connectivity between nodes [3,10], radio power or availability of global topology or position information [1]. Second, given the scarce resources available to nodes in sensor networks, the scheme should not be resource intensive. If the scheme requires extensive message passing between nodes, for example, any benefit from spatial redundancy achieved by high density may be canceled by the accompanying high overhead [5]. Third, the scheme should be simple enough for practical implementation on currently available sensor nodes. Fourth, the scheme should be analytically tractable, and should give the system designer some idea of the potential energy savings achievable given a certain network density. In this section we look at one such topology control scheme. Our clustering algorithm consists of a setup phase, where a high energy backbone of nodes called cluster heads and gateways is created and a data transmission phase during which all nodes report event data to the sink using the backbone. The nodes which are not part of the backbone maintain a very low duty cycle potentially they could completely shut down their radio, while still maintaining their sensing operations, and only switch it on when they sense an event to report. This gives significant energy savings, since the radio draws 5

6 an order of magnitude higher energy than the sensing board [11]. Nodes in the backbone maintain a relatively higher duty cycle, since they need to forward packets from the non-backbone nodes to the sink. One of our contributions is the analysis (in Section 4.5) of how the differential duty cycles maintained at backbone and non-backbone nodes affect the overall performance of the network. During the setup phase, a node runs the following operations in sequence: Time Synchronization, Neighbor Discovery, Cluster Selection, Gateway Selection and Routing, as shown in Figure 1. This setup phase needs to be repeated regularly during the lifetime of the network to ensure uniform energy dissipation across all nodes in the network. We define one such complete sequence of the setup phase and data transmission phase to be a cluster iteration. We discuss how to tune the periodicity of such cluster iterations in a later section. The time and energy spent in this phase is the constant overhead accompanying our scheme, and we report representative values for each on a 42 node Mica2 network in Section 5. We will now describe each phase in detail. Time Neighbor Sync. Discovery Cluster Selection Gateway Selection Routing Data Tx Setup Phase Fig. 1. Topology Control Operations 3.1 Time Synchronization Phase Nodes in the system need to maintain time synchronization, so that they start the clustering, and subsequent re-clustering phases together. Since the time between two clustering phases is expected to be significantly long, coarse time-synchronization schemes with synchronization errors of the order of a few seconds or even minutes is more than enough. In the implementation, we use a localized time synchronization algorithm [12,13]. Due to lack of space, we explain the algorithm briefly. During every time synchronization period, nodes exchange time stamps with their neighbors. At the end of the time synchronization phase, each node sets its own clock to the average of the clocks of its neighbors. After a few rounds, the average time of all nodes converges to a unique value, as proved in [13]. As we shall see in the Section 4, maintaining a time synchronization phase every 17 hours affords us a time synchronization error of up to 10 seconds. 6

7 3.2 Neighbor Discovery Phase During this phase, nodes periodically broadcast neighbor discovery beacons. A node receiving such beacon messages uses them to generate link quality estimates to its neighbors. This information is useful later during the cluster and gateway selection phases. 3.3 Cluster Selection Phase During this phase, a fraction of nodes in the network are selected as cluster heads. Non-cluster head nodes adjacent to a cluster head become members of the cluster head. The algorithm proceeds in rounds as follows: 1. Cluster head candidate selection: At the beginning of a round, a covered node is a node which has become either a cluster head or a member node in one of the previous rounds. At the beginning of round i, an uncovered node becomes a cluster head candidate with probability k i p 0. As we shall see in Section 4, the system parameters k and p 0 decide the number of cluster heads generated at the end of the clustering phase, as well as the number of rounds required for the whole network to become covered. 2. Cluster head advertisement : When a node j becomes a cluster head candidate, it starts a timer and broadcasts a Cluster head Advertisement (CA) message after the timer expires. The timer expiry period is inversely proportional to the residual energy of the node; if the node has more residual energy, the timer expires earlier. Once a node becomes a cluster head in round i, it continues sending its advertisement messages in subsequent rounds, so that nodes with high link loss still receive such advertisements. 3. Cluster head advertisement message reception: When an uncovered node k receives a CA message from another node j, it becomes a member of node j. If it was a candidate cluster head in the same round, waiting on its CA message timer, it suppresses its timer. 4. Cluster head decision: At the end of N ROUND rounds, a member node which has received CA messages from cluster heads CH 1, CH 2,...CH n, selects one of them as its own cluster head. The member node makes its decision based on the link quality estimates to these n cluster heads, which it obtained during the neighbor discovery phase. The member node informs its chosen cluster head with a Member Advertisement (MA) message. It also overhears its neighbors MA messages and updates its neighbor table with the information about the clusters they belong to. 7

8 A 1100 C B D E F G I H J 0 1 K L 0 1 M Fig. 2. Routing paths of cluster heads towards the sink (node A). Cluster Head A C C D Cluster Cluster Head B Head A Cluster Head B Gateway Node (A) Gateway Nodes (B) Fig. 3. Two classes of gateways Type A gateways are directly within radio range of two or more cluster heads, Type B gateways are within radio range of a member node of a different cluster. 3.4 Gateway Selection Phase Note that at the end of the cluster selection phase, the selected cluster heads may not be enough to create a routing tree from each cluster head to the sink. A few more nodes may need to be selected for connectivity. We refer to such nodes as gateway nodes. Figure 2 shows the routing paths created by a routing protocol for each cluster head toward the sink node (node A). Nodes A, E, F, J, K and M are the cluster heads selected during the cluster selection phase. Nodes B, C, D, G, H, I and L are gateway nodes which act as a communication link between two adjacent clusters. From the figure, we can see that the gateway nodes can be classified into two types depending on the way they connect two adjacent clusters. We show these two types in Figure 3 (A) and (B), which we shall henceforth term as type A and type B respectively. In the first case (Figure 3 (A)), two adjacent clusters share some member nodes in common, while in the second case (Figure 3 (B)), the two adjacent clusters do not have member nodes in common, however, some member nodes belonging to either cluster are adjacent to each other. Note that these two types are not mutually exclusive, a gateway could act as type A between two clusters, while at the same time connecting other clusters 8

9 as type B. Since gateway nodes are required to forward data packets between clusters, they have to maintain a high duty cycle just like cluster heads. To reduce energy consumption, it is imperative to keep the number of such gateway nodes to be as low as possible while still keeping the network connected. We adopt the following gateway selection algorithm similar to the cluster head selection algorithm described above: 1. Candidate gateway selection A node receiving more than one CA message during the cluster selection phase, becomes a candidate gateway node, e.g. in Figure 3 (A), member node C will hear CA messages from both cluster head A and B. Additionally, a node which observes that its neighbors belong to different clusters also becomes a candidate gateway node, e.g. in Figure 3 (B), member node C observes that D belongs to cluster B and becomes a candidate gateway. Member node D also becomes a candidate gateway by the same argument. All candidate gateways start a timer whose expiry period is proportional to the cardinality of its connectivity set, which is defined as the set of cluster heads they potentially connect together. 2. Gateway advertisement When the timer expires, the candidate gateway node becomes a gateway node, and broadcasts a Gateway Advertisement (GA) message, which includes the connectivity set of the node, as well as the neighbors of the other cluster that it needs to connect to, to obtain its connectivity set, e.g. in Figure 3 (B), member node C will have cluster heads A,B in its connectivity set and it will also mention neighbor D since it requires D to have cluster head B in its connectivity set. 3. Gateway advertisement reception If a candidate gateway i receives an advertisement from another candidate gateway j, it checks if the connectivity set of i is a subset of that of j and the loss rates to the connectivity set is better than itself, in which case it suppresses its own timer. However, if it is mentioned as a neighbor node in the GA message, then it will become a gateway node itself, e.g. in Figure 3 (B), the GA message from C will mention D as a neighbor node. Hence D on receiving the message will also become a gateway node. 3.5 Routing Phase At the end of the gateway selection phase, a routing algorithm computes routes to the sink on the overlay consisting of only the selected cluster head and gateway nodes. Note that gateway nodes not on a routing path from a cluster head to the sink may relegate themselves back into member nodes. If a reactive routing protocol (e.g. DSR [14]) is used to pre-compute routes for all cluster heads to the sink, then each node in the network is aware of whether it 9

10 is on a routing path to the sink. If the routing protocol is pro-active in nature (e.g. Mint [15], DSDV [16]), such knowledge can be obtained by making each cluster head send a small control ping packet toward the sink to which the sink replies. Gateway nodes which do not receive such ping packets during the routing phase may relegate themselves back to the status of member nodes. 3.6 Data Transmission Phase At the end of the routing phase, nodes are ready to begin data transmission (if needed). Cluster heads and gateway nodes maintain a duty cycle of X% while member nodes adopt a duty cycle period which is a small fraction δ of X. As we shall see in Section 4.5, δ allows the system designer the functionality of a control-knob controlling the amount of energy savings obtained by the use of topology control. Member nodes always transmit event packets to their cluster head, while cluster heads then utilize the overlay created by cluster heads and gateway nodes to forward these packets towards the sink, using the routes computed in the Routing Phase. 4 Stochastic Analysis of Clustering In this section we analyze the clustering scheme presented in Section 3, our goal is to study how the network density and initial bootstrap parameters affect the energy dissipation rate and consequently the lifetime of the network. 4.1 Analytical Model Proceeding in a manner similar to [17], we model the sensor network as nodes distributed in a A A area, following the spatial homogeneous Poisson Point Process [18] distribution with intensity λ. Hence, by the definition of the Poisson Point Process, the total number of nodes in the network (denoted by N) would be: N = λa 2 We assume that all nodes transmit with the same radio power, and hence have the same radio range R. Consider one such sensor node. The number of sensor nodes within radio range of this node (including itself) will be given by: 10

11 N R = λπr 2 Note that we use the expected number of nodes (N and N R ) for ease of analysis. 4.2 Expected Number of Rounds for Network Coverage The algorithm in Section 3 proceeds in rounds. Let the initial probability of being a cluster head in round 0 be denoted as p 0. In a subsequent round i, a node becomes a cluster head with probability k i p 0. If it hears a cluster head announcement message from its neighbors, it becomes a member node. We define P cov (i) to be the probability that a node becomes covered in round i it hears a cluster head announcement message, and hence becomes a member node, or it becomes a cluster head with probability k i p 0. Hence, in a round i, the fraction of nodes still uncovered would be given by: i 1 P uncov (i) = 1 P cov (s) s=0 Hence, in round i, the number of nodes within radio range of a node which are still uncovered, and hence still trying to be a cluster head is: N uncov (i) = P uncov (i)(n R 1) A node in round i which is yet uncovered may become covered if: (1) It decides to be a cluster head in round i, with probability k i p 0, or (2) It does not become a cluster head in round i with probability (1 k i p 0 ), but at least one of its N uncov (i) uncovered neighbors becomes a cluster head, with probability P nbr ch (i). P nbr ch (i) = 1 (1 k i p 0 ) Nuncov(i) Note that in the algorithm specified in Section 3, a node about to become a cluster head in a round, may suppress its own cluster head announcement message if it hears a cluster head announcement message from one of its neighbors in the same round, and may choose to become a member node instead. This is not modeled in this analysis, to simplify the analysis. Hence, P cov (i) can be written as: 11

12 P cov (i)=p uncov (i 1) [k i p 0 + (1 k i p 0 )P nbr ch (i)] The total number of rounds taken for all nodes to be covered is given by: N ROUNDS = MIN{s : i=s 1 i=0 P cov (i) 1} 4.3 Expected Number of Cluster Heads We now derive the expression for the expected number of cluster heads generated at the end of the clustering phase. A node would become a cluster head in round i with probability: P CH (i) =P unconv (i)k i p 0 The total probability that a node becomes a cluster head in N ROUNDS rounds is: N ROUNDS 1 P CH = P CH (i) i=0 Hence the expected number of cluster heads generated in N ROUNDS rounds is: N E[#CH] = [P CH 1] i=1 =NP CH N ROUNDS 1 =N k i i 1 p 0 {1 P cov (t)} i=0 t=0 By substituting the recursive expression for P cov (t), we may get the expected number of cluster heads. As we shall see in later sections, the expected number of cluster heads is a dominant factor in the energy consumption rate of the system. For a given network of density λ and nodes with transmission range R, E[#CH] depends on the initial probability p 0 and the multiplicative constant k. 12

13 Analytical Vs. Simulated Values of Pch Analytical - Po =.032, k = 2 Simulated, No Suppression - Po =.032, k = 2 Simulated, With Suppression - Po =.032, k = 2 Cluster Head Selection Probability - Pch Network Density Fig. 4. Analytical Vs Simulated Values for P CH We simulate our clustering to verify the correctness of the analysis. The simulation does not model contention or message losses due to radio collisions. We generate 10 instantiations of Poisson Point Process graphs of density ranging from λ =.0002 to λ =.002 with the radio transmission range R set to 90m in a square of size 500x500m. This results in topologies with each node having on average 5 to 50 nodes as single-hop neighbors. We then run our clustering algorithm on each graph and report the the average and standard deviations. Figure 4 shows the value of P CH as observed in the experiment with p 0 =.032 and k = 2. Note that both cases with and without suppression are plotted. While we observe that the analytical model predicts the value of P CH with sufficient accuracy, it is interesting that the case with suppression does not significantly reduce the number of cluster heads. We attribute this to that although on one hand the number of cluster heads may be reduced by suppression, each suppressed cluster head actually results in reduced coverage, hence lengthening the clustering phase and compensating the gain achieved by the reduced number of cluster heads. Another interesting observation is that a significant fraction of the network is chosen as cluster heads for networks of low density, which affects the degree of energy savings obtained by clustering. The system designer may use the above analysis to decide when to rely on clustering based on the density of his network. Impact of Multiplier (k) k = 1.2 k = 2 k = 6 k = 9 Cluster Head Selection Probability - Pch Network Density Fig. 5. Impact of k on P CH 13

14 4.3.1 Parameter Selection Figure 5 shows the impact of k on the value of P CH for a system with p 0 = k influences the speed of the clustering phase. With k less than 1.5, the network takes as many as 38 rounds to complete the clustering phase while k = 2 takes only 6 rounds. However, increasing k beyond 2 does not impact P CH, hence we choose to set k = 2 for the rest of the paper Impact of Initial Bootstrap Probability (Po) Cluster Head Selection Probability - Pch Po =.032 Po =.064 Po =.128 Po =.256 Po = Network Density Fig. 6. Impact of p 0 on P CH The parameter p 0 influences the number of cluster heads generated. Figure 6 shows the impact of the selection of p 0 on the value of P CH, for a system with k = 2. With decreasing p 0, the value of P CH also decreases. However, from the figure we can see that we do not observe much reduction for p 0 <.032. Hence we choose to set p 0 to be for the rest of the paper. 4.4 Expected Number of Gateways and Member Nodes As described in Section 3, after the clustering and gateway selection phases, a routing protocol generates a routing tree composed only of cluster heads and gateway nodes. Gateway nodes act as the connecting link between the cluster heads of two or more clusters. It is difficult to estimate the exact number of gateways required for connectivity. However, we can derive the upper bound on the number of gateways required. The worst case occurs when all the required gateways are of type B. In this case, the routing tree is composed of cluster heads, with two gateway nodes connecting two adjacent clusters. Hence, the number of gateway nodes would be twice the number of edges in the routing tree. Since a tree of n vertices has n 1 edges, the upper bound on the number of gateway nodes is given by: E[#GW] = 2 (E[#CH] 1) 2NP CH 14

15 By a similar argument, consider the case when all the required gateways are of type A. In this case, the routing tree is composed of cluster heads, with one gateway node connecting two adjacent clusters. Hence, the number of gateway nodes would be equal to the number of edges in the routing tree: E[#GW] = (E[#CH] 1) NP CH In the real environment, we conjecture that the number of required gateways would be much lower than this upper bound, since there would be a mix of type A and type B gateways in the network. To verify our worst case bound and to observe how many gateways are created on average, we perform simulations with p 0 = and k = 2, the results of which are shown in Figure 7. We plot the following cases (1) Analytical upper bound (2P CH ) (2) All gateways of type A (P CH ) and (3) Average fraction of network consisting of gateways obtained by simulation. The result supports our conjecture that for general networks, the number of required gateways is much lower than the analytical upper bound and is closer to the bound when all gateways are assumed to be of type A (= P CH ). Fraction of Network Selected as Gateways - Simulated Vs Analytical Upper Bound Analytical Upper Bound - All Gateways of Type B All Gateways of Type A Simulation Fraction of Network Selected as Gateways Network Density Fig. 7. Fraction of the network selected as gateways for the following cases: (1) the analytical upper bound (assuming all gateway are of type B) (2) assuming all gateways are of type A and (3) average obtained by simulation Finally, the expected number of member nodes(e[#mn]) is given by: E[#MN] N E[#CH] E[#GW] = N(1 3P CH ) 4.5 Analysis of Energy Consumption Consider a sensor network that is idle most of time and sees activity only for short bursts of time. In such networks, the energy dissipation rate is domi- 15

16 nated by the duty cycles of individual nodes and not by their data rate. Let cluster heads and gateway nodes maintain a duty cycle X% and the rest of the network maintains duty cycle δx% where 0 δ 1. Hence the effective duty cycle of each node is given by: E eff = X(E[#GW] + E[#CH])/N + δx(e[#mn])/n = X(3P CH ) + δx(1 3P CH ) We can think of δ as a control knob to adjust the degree of power savings desired by the system designer. Note that δ = 1 corresponds to the case where all nodes maintain the same duty cycle. This is identical to the situation where each node runs a naive duty cycling MAC (e.g. B-MAC), and the nodes do not take any advantage of topology control. On the other hand, δ = 0 represents the other extreme where cluster member nodes are completely switched off, and only cluster heads maintain a duty cycle. To decouple this metric from the base duty cycle X, we hereby define the normalized power gain, E N, as follows: E N = X/E eff 1 = 3P CH + δ(1 3P CH ) δ = 0 δ = 0.2 δ = 0.4 δ = 0.6 δ = 0.8 δ = 1.0 Normalized Power Gain 3 Power Gain Network Density Fig. 8. The normalized power gain for various graph densities Intuitively, since the system lifetime is inversely proportional to the duty cycle of the network, the normalized power gain gives us the factor by which the system lifetime increases by the use of clustering with respect to naive duty cycling. The Figure 8 shows this numerical result of the normalized power gain plotted for various graph densities and values of δ after setting p 0 =.032 and k = 2. The curve for δ = 0 represents the maximum energy reduction that can be obtained by clustering, which increases linearly with the density of the graph. From the graph, as a thumb rule, we can say that the energy saving achievable by our topology control algorithm is proportional to the density of the network divided by a factor of eight to ten. 16

17 4.6 Re-Clustering Period Restrictions Since cluster heads dissipate energy faster than member nodes, it is important to run re-clustering periodically so that energy dissipation is balanced out among all nodes. We defined each such re-clustering as a cluster iteration in Section 3. We know that a node becomes a cluster head or gateway in one such iteration with probability 3P CH. Hence, the number of cluster iterations K required for a node to be a cluster head at least once follows the geometric distribution with parameter 3P CH : E[K] = 1 3P CH Clearly, as long as the number of cluster iterations till a node completely runs out of energy is an integral multiple of K, all nodes will get an equal opportunity to be a cluster head or gateway, and hence will dissipate energy at an equal rate. In the extreme case, a system performs exactly K cluster iterations during its entire lifetime. Let E OH be the total energy spent in the setup phase, which is essentially the amount of overhead incurred by the system per cluster iteration. Let T C be the time spent by the system in the data transmission phase of each cluster iteration, and let T OH be the time spent in the setup phase. Usually, T OH T C and hence we shall use T C and the term re-clustering period interchangeably. Let P RX be the power consumed by the node radio when performing idlelistening. Let E C be the battery capacity of a typical node in the network. From the viewpoint of a single node in the system, this corresponds to the following energy equation: E C = KE OH + (T C X)P RX + (K 1)(T C δx)p RX This comes from the fact that for K iterations, (1) a node incurs the overhead energy, (2) it becomes a cluster head for one cluster iteration, consuming T C XP RX energy, and (3) it is a member node for the remaining K 1 cluster iterations, consuming T C δxp RX energy. Hence, T C is given by: E C KE OH T C = P RX X (1 + (K 1)δ) 3P CH E C E OH P RX X (3P CH + (1 3P CH )δ) 17

18 350 Re-Clustering Period Re-Clustering Period (Hours) δ = 0 δ = 0.2 δ = 0.4 δ = 0.6 δ = Network Density Fig. 9. Impact of network density and δ on re-clustering period Figure 9 shows the impact of network density and the value of δ on the reclustering period T C for a clustering system with p 0 =.032, k = 2, and X = 50%. Under dense networks, the fraction of cluster heads being smaller, the number of cluster iterations required for all nodes to become cluster heads at least once increases. Hence we require more re-clusterings to balance the energy, consequently reducing the re-clustering period. It is important to note here that T C is the upper bound on the value of the reclustering period. In practice, the re-clustering period would be much shorter, to take into account time-synchronization requirements, routing failures and node failures. While routing and node failures are unpredictable, the maximum re-clustering period gives us the minimum bound on the length of the time synchronization phase (T S ). Since member nodes may completely switch off their radios (δ = 0) for maximum energy conservation, they may not participate in the exchange of time synchronization messages. Hence, the length of the time synchronization phase should be just enough to account for the maximum possible clock drift between two nodes. Given a clock drift of r clk, by [19]: T S 4 T C r clk 4.7 System Lifetime Given K and T C from above, the system lifetime would be given by: T L K T C 3P CH E C E OH = 3P CH P RX X (3P CH + (1 3P CH )δ) Figure 10 shows the results comparing the lifetime obtained by a simulated 18

19 Network Lifetime - Simulated Vs Analytical Network Lifetime (hours) Analytical Lifetime - All Gateways of Type B Analytical Lifetime - All Gateways of Type A Simulation Network Density Fig. 10. Comparison of network lifetime for the following cases (1) analytical, assuming all gateways are of type A (2) analytical, assuming all gateways are of type B and (3) average obtained by simulation run with p 0 = and k = 2 for different network densities with the analytical upper bound. We calculate system lifetime numerically in the following manner. We use a re-clustering period of T c = 17 hours. Each node is equipped with a 3V battery of capacity of 2500mAh resulting in an E c = 27000J. We set the listening power drawn by the radio of each node to be P RX = 0.045mW. Cluster heads and gateways maintain a duty cycle of X = 5% and member nodes completely switch off their radios during the data transmission phase (δ = 0). Finally, we set E OH = 5J which was the average energy we observed being used during the setup phase for the real experiments (Section 5). For the simulation, we measure lifetime in the following manner. Each node is equipped with a battery with capacity E c = 27000J. At the end of every re-clustering period of duration T c = 17 hours, each node examines its residual battery capacity. If its battery has been completely depleted, it switches itself off, rendering itself unavailable for future re-clusterings. We continue the reclusterings with the remaining nodes till we reach a point where the network becomes disconnected, and report the time elapsed as the network lifetime. As before, we plot the following cases (1) Analytical lifetime assuming all gateways are of type A, using E[#GW] = NP CH (2) Analytical lifetime assuming all gateways are of type B, using E[#GW] = 2NP CH (3) Average simulated lifetime. As expected, the network lifetime stays within the analytical lifetimes for the two cases, indicating that the gateways in general networks are a mix of type A and type B. Interestingly, as the network density increases, the lifetime becomes closer to the analytical case when all gateways are of type A. This is because of the following. Under low network density, there exist several nodes which are critical to network connectivity. Hence, such nodes may end up being always selected as gateways because of their position in the network resulting in their energy being depleted faster. When the energy of such nodes is completely depleted, they will die, leaving the network disconnected. However, as the network density increases, it possesses sufficient spatial redundancy to allow the gateway selection to cycle between potential 19

20 nodes, balancing their energy and consequently increasing network lifetime. 5 Experimental Results We test our clustering algorithm on a testbed comprising of 42 Mica2 nodes, each placed in faculty offices and classrooms of our computer science building. Figure 11 shows the testbed and wireless communication links among nodes. In this testbed, the maximum one-hop neighborhood size of all nodes is 15. Links between the nodes have link loss rates up to 30-40% and some asymmetric links also exist ft ft. Fig. 11. Testbed Topology ft ft. Fig. 12. Routing Paths Created by Mint 5.1 Implementation Details We are interested in the performance of our clustering scheme with respect to a naive duty-cycling scheme which does not perform any form of topology control. We choose B-MAC [20] with Low Power Listening (LPL) for this purpose. Note that the choice of the MAC-layer protocol is orthogonal to 20

21 Application (Data Generation) Clustering Module Routing (Mint Route) Time Synchronization Module MAC (modified B MAC) Fig. 13. TinyOS Clustering Algorithm System Design our goal, which is to see how much energy efficiency can be obtained in real test environments using our clustering scheme. In fact, other MAC protocols which provide ultra-low duty cycling [19] could also be used for this purpose. Since the results we show (as well as the analysis in Section 4) are relative, we believe that the relative cost benefits should be independent of the protocol being used System Design The overall system design of our clustering algorithm as it is implemented in TinyOS is presented in Figure 13. The clustering module takes care of clustering and re-clustering. At the end of the cluster head selection phase, it shares information about the current status of a node (whether it has been selected as a cluster head or a member node) with the routing module, which is a modification of the Mint routing module in TinyOS. Together, these two modules decide whether the current node should act as a gateway during the gateway selection and routing phase. During the data transmission phase, the MAC layer applies a duty cycle on a node depending on its current status, which it obtains from the clustering module. Finally, the time synchronization module time-stamps each data packet as it leaves the system at the MAC Configuration of Member Nodes To get the maximum benefit of topology control, we completely switch off the member node radios (δ = 0), unless a node has a packet to send, in which case it wakes up, waits for the channel to become idle, transmits the packet and then switches the radio off again. While transmitting the packet, the member nodes need to maintain a preamble length long enough to wake up their respective cluster heads. 21

22 Table 1 The default settings for Mica2 experiments TinyOS experiment parameter Default Initial cluster probability (p 0 ).032 Constant multiplier (k) 2 Cluster head and gateway duty cycle (X) Varied Member node duty cycle (δ = 0) 0 Transmission power (full power) 10 dbm Communication bandwidth (CC1000 Radio) 19.2 Kbps Preamble size Varied Payload size 36 bytes Radio transmission power consumption 60mW Radio receiving power consumption 45mW Channel sampling power consumption 5.75mW Configuration of Cluster Heads and Gateways Cluster heads, when receiving packets from their member nodes, forward the packets toward the sink through intermediate cluster heads and gateways Routing We use the Mint [15] routing protocol to create the routes among the cluster heads and gateways. Figure 12 shows a snapshot of the routes created on top of the nodes on the testbed for one particular experiment, with node 22 (left middle section of the building) selected as the sink node. The black nodes are the cluster heads while the grey nodes are the gateways. In this run, 11 nodes in total are selected as cluster heads and gateways which accounts for about 25% of the nodes in the network. On average we observed about 25-30% of nodes being selected as cluster heads or gateways on our testbed and hence according to our analysis in Section 4.5, we expect to achieve roughly 3 times the energy efficiency of B-MAC on this testbed. 5.2 Experimental Method We run comprehensive experiments using our clustering scheme and B-MAC to get the full performance profile of both schemes. Our experimental method is as follows: In the case of clustering, we use p 0 = and k = 2. Once data transmission phase starts, all nodes in the network begin sending packets with probability α% every second. We run two experiments, a low rate experiment where α is varied from.1 to 1, and a high rate experiment where α is varied from 10 to 100. Hence in our testbed of 42 nodes, this corresponds to an aggregate packet rate to the sink to be.04 to 0.4 packets per second for the low rate experiment, and 4 to 40 packets per second for the high data rate experiment. 22

23 Table 2 Clustering Setup Overhead Cost Phase Average Average Time Energy Time Synchronization 10s 0.235J Neighbor Discovery 20s 0.469J Cluster Selection 60s 1.288J Gateway Selection 20s 0.429J Routing 120s 2.583J Total 230s 5.004J Throughput -- Clustering - Low Rate Throughput -- Clustering - High Rate 0.2 Clustering B-MAC Duty Cycling 3.5 Clustering B-MAC Duty Cycling Throughput(Kbps) 0.1 Throughput(Kbps) Send Rate Send Rate (A) (B) Fig. 14. Throughput Comparison for the low rate (A) and the high rate (B) clustering experiment The low rate experiment emulates the general scenario where most nodes in the network is idle whereas the high rate experiment emulates brief periods of activity where many nodes may begin transmission simultaneously resulting in high aggregate throughput to the sink. The cluster head and gateway duty cycles are varied between 45% down to 2%, but we report results only for 10%, 5% and 2% since the other duty cycles yield sub-optimal performance. The complete list of default parameters used in our experimental evaluation is shown in Table Overhead The overhead of our protocol consists of the time and energy required for the setup phase in each cluster iteration which are reported in Table 2. There are a couple of interesting observations to be made. Firstly, about the half of the overhead is due to routing. Clustering takes up about another half of the remaining overhead. Secondly, although we maintain a time synchronization phase of T S = 10s, it is not necessary to limit time synchronization messages to this phase alone. Nodes may continue exchanging time synchronization messages until the routing phase ends. Given T S = 10s, we use a re-clustering period of T C T S /(4r clk ) 17 hours. 23

24 (A) (B) Fig. 15. Energy Efficiency for the Low Rate Clustering Experiment (A) (B) Fig. 16. Energy Efficiency for the High Rate Clustering Experiment 5.4 Throughput Figure 14 shows the best throughput observed over all duty cycles for each sending rate in the low and high rate experiments. In both cases, B-MAC with low duty cycle achieves higher throughput than clustering. This is because of two reasons. Firstly, note that clustering essentially limits the selectivity available to routing since only a fraction of the existing nodes are available. Hence, routes on top of such overlays may be sub-optimal. Secondly, the reduced number of paths available to the sink also consequently reduces the available network capacity. But surprisingly, the reduced throughput does not in turn degrade the energy efficiency of the network. In fact, as we shall see in the next section, clustering makes up for the reduced throughput by improving energy saving, thus resulting in improved energy saving per transmitted bits (i.e., energy efficiency). 24

25 5.5 Energy Efficiency We define energy efficiency for the purpose of this experiment to be the throughput received at the sink per unit of energy consumed by the system. We measure energy at each node based on the number of packet transmissions, receptions and channel samplings by the radio. The default values for the power used for these operations for the CC1000 [21] radio are reported in Table 1. Figure 15 shows the performance of clustering and duty-cycling for the low rate experiment. As expected, we observe, in general, a 2-3 times performance improvement in the energy efficiency of clustering as compared to duty-cycling. Note that this is despite the fact that in terms of throughput, B-MAC dutycycling actually performs slightly better than clustering for the low rate experiment. Figure 16 shows the energy efficiency of clustering and duty-cycling for the high rate experiment. The performance improvement here is 2 times compared with the 3 times which we got in the low rate case. This is due to the better throughput achieved under B-MAC duty-cycling as observed in the previous section. Hence, even under brief periods of activity when the network experiences high data rates, clustering would be able to support better energy efficiency, albeit with lower throughput. 6 Conclusion We designed and analyzed a topology control scheme, simple enough for practical implementation as well as amenable to mathematical analysis. Our analysis offers a general rule of thumb to determine the amount of energy saving possible under a network of given density namely, that the energy saving gain is roughly equal to the density of the network divided by a factor of four to eight (where we define density to be the average number of one hop neighbors). We report the results of our implementation on top of a 42 node Mica2 testbed, and show that topology control achieves roughly up to 1.5 to 2 times energy efficiency gain in our testbed which is in accordance with our analysis given that the density of our testbed is about 6 to 15. We also find that use of topology control reduces the achievable throughput of our testbed by up to 50%. The source code for simulation and experiments can be found at www4.ncsu.edu/ acwarrie/topologycontrol.html. 25