- Research Article
- Open Access
Determining Localized Tree Construction Schemes Based on Sensor Network Lifetime
© Jae-Joon Lee et al. 2010
- Received: 27 October 2009
- Accepted: 1 July 2010
- Published: 19 July 2010
The communication energy consumption in a data-gathering tree depends on the number of descendants to the node of concern as well as the link quality between communicating nodes. In this paper, we examine the network lifetime of several localized tree construction schemes by incorporating the communication overhead due to imperfect link quality. Our study is conducted based on empirical data obtained from a real-world deployment, which is further supported by mathematical analysis. For the case of a sparse node density, a large network size and a low link threshold, we show that the link-quality-based scheme provides the longer network lifetime than the minimum hop routing schemes. We present a lower bound on the number of nodes per hop and the link quality threshold of the radio range, which work together to result in a superior localized scheme for longer network lifetime.
- Network Lifetime
- Node Density
- Link Quality
- Balance Scheme
- Communication Load
For data-gathering path construction, nodes have to determine the next node to forward the data to the sink with a parent selection strategy. A localized tree construction scheme allows each node to select a parent node using its one-hop neighboring node information. Thus, the purpose of localized schemes is to reduce the communication overhead for the construction of a data-gathering path, which is desirable for energy-constrained wireless networks. Even though there have been studies on wireless network lifetime [1–6], and a few studies on localized tree construction , the effect of localized tree construction scheme on the network lifetime has not been extensively examined. Here, we examine localized tree construction schemes with different parent selection strategies and analyze their impact on the network lifetime in conjunction with diverse network conditions such as node density, network size, and link quality between communicating nodes.
The routing path selection in conjunction with link quality have been examined in several studies. De Couto et al. present a path selection metric, which is called expected transmission (ETX) count. This metric is used to select the minimum number of transmissions required for successful delivery to a destination among different paths by incorporating the quality of each link on the path in . Draves et al. provide comparison among path selection schemes based on link quality metrics and minimum hop counts through detailed experiment in . They find that the expected transmission (ETX) count scheme provides higher throughput than minimum hop count scheme when a DSR routing protocol  is used with stationary nodes. Woo et al.  examine the effect of link quality on different routing strategies in terms of hop distribution, path reliability, success rate from a source to the sink, and path stability. In their work, the minimum expected transmission scheme results in the highest end-to-end success rate. Seada et al.  present the analysis of forwarding strategies by incorporating link quality and calculate the energy efficiency in geographic routing. They show that the product of a packet reception rate and a distance metric provides the most energy efficient geographic forwarding path. In addition to the above work, several studies including [13, 14] examine the link quality effect on connectivity.
In this paper, we examine several localized tree construction schemes and point out the trade-off between link-quality-based schemes and minimum-hop-routing-based schemes in terms of network lifetime. If we use high quality links to reduce the number of retransmissions, the number of descendants to be processed in the data-gathering tree will increase, which results in the increase of energy consumption for communication due to more data. On the other hand, if we decrease the amount of forwarded data by distributing workload to more nodes, selected link's quality may not be the best and retransmissions can increase. Our study is conducted as follows. First, we examine the empirical data obtained from a real-world sensor deployment to capture the effects of different tree construction schemes on energy consumption. Then, to obtain the insight into the above trade-off and derive criteria to reach longer network lifetime, the energy consumption of each scheme is analyzed and compared. Finally, the global optimum is presented and compared with the analytical results of different tree construction schemes.
Our study shows that when the network size is small and the node density is high with a high link threshold (i.e., minimum packet reception rate that determines one-hop direct link or not between two nodes), minimum hop routing schemes achieve longer network lifetime than the scheme whose selection is based only on the link quality. However, with the opposite network conditions, the link-quality-based scheme can achieve longer network lifetime. We present lower bound on the number of nodes in a hop as a function network size, transmission energy portion, and radio range link quality, which guarantees that the load-balanced scheme achieves longer lifetime than the link-quality-based scheme. In addition, we present lower bound on link threshold as a function of node density, which guarantees the longer lifetime of the load-balanced scheme regardless of other network conditions such as the network size and the transmission energy portion. When the link threshold is less than , the load-balanced scheme does not guarantee longer lifetime than the link-quality-based scheme in 1D linear topology and 2D grid topology.
The localized data-gathering tree construction schemes with different parent selection criteria are described in Section 2. We examine the effect of these schemes on energy consumption and network lifetime by incorporating a link quality metric and the communication load distribution based on the empirical data in Section 3 as well as analysis in Section 4. Criteria for superiority of a localized scheme in terms of network lifetime are analyzed in Section 5. The comparison with the global optimal strategy is presented in Section 6. Finally, concluding remarks and future research directions are presented in Section 7.
where is the expected number of transmission required for successful transmission over a link between nodes and . Qualitatively speaking, a low ETX link can require less energy consumption due to redundant retransmission than a higher ETX link. However, the quantitative effect of a link-quality-based path selection scheme on energy consumption and/or network lifetime has not been fully investigated before.
Besides link quality, the number of hops (called the hop count) to the destination is widely used for routing path selection. Each link can be counted as one hop. Then, the routing path with the minimum number of hop counts to the sink is the shortest path. The minimum hop routing (MHR) path can be constructed using the currently known hop level of neighboring nodes. In order to know its minimum hop level, the sink node sends the broadcasting message to all nodes initially once. In the MHR, each node selects a neighbor node in the upper hop level, which provides the minimum number of hops to the sink. Detailed discussion of energy consumption in the MHR can be found in . Rigorously speaking, the link quality and the radio range will also affect energy consumption in addition to the hop counts. Here, we incorporate the link quality into the energy consumption analysis of MHR schemes. By using the ETX link quality metric and the hop count to the sink, we will examine the following four localized tree construction schemes.
The lowest ETX parent selection scheme, where a node selects a neighbor node that provides the lowest ETX link between each other and is closer to the sink. This scheme does not necessarily select a node in the upper hop level and accordingly the minimum hop (shortest path) routing may not be achieved.
The random parent selection scheme with the MHR, where a node randomly chooses a parent among neighbor nodes in the upper hop level, which provides the minimum hop routing to the sink.
The lowest ETX parent selection scheme with the MHR, where a node chooses its neighbor node in the upper hop level that provides the lowest ETX.
The balanced parent selection scheme with the MHR, where a node selects the neighbor node in the upper hop level that has the fewest number of children as a parent in the data-gathering tree.
The first scheme does not utilize the hop count but the link quality metric only while the other three schemes take the hop count into consideration for parent selection as well. These localized schemes are examined by real empirical data and analysis in the following sections.
In this section, with the empirical data in a real deployment, we examine four localized tree construction schemes to understand their impact on the communication load and discuss their differences. The data are from the experiments conducted by the UCLA/CENS group , where the PRR of each node from all other nodes is given. A set of 55 nodes was deployed in the ceiling of the lab in their indoor experiment.
With this PRR information, we examine the connectivity between adjacent hop levels and the communication overhead distribution among nodes. Without respect to a target node, any other node that has a PRR for bidirectional links higher than the link threshold is called its neighboring node. In other words, every pair of neighboring nodes can directly communicate with each other if the successful packet transmission and reception rates are above the link threshold. Communication to all the other nodes may require multihop forwarding through neighboring nodes. The link threshold can be adjusted, which will change the hop level of nodes from the sink. The use of this threshold makes routing more reliable. As the link threshold increases, a constructed tree with more hop levels can provide higher throughput due to higher successful transmission rate of the link than a simple minimum hop count routing.
3.1. Data-Gathering Topology Maps
As shown in Figure 2(a), the lowest ETX parent selection without hop count consideration results in longer hop levels. The longest hop level is 7. Since each node uses the lowest ETX parent selection, the distance between the parent and the children nodes tends to be close and the number of hop levels increases. All possible direct links between adjacent hop level nodes by the random parent selection scheme with MHR are presented in Figure 2(b). Each node randomly selects one among nodes that are connected with a direct link as its parent node. As the distance from the sink increases, the first-hop nodes have more direct links to the second-hop level nodes. With the link threshold 0.9, the MHR scheme significantly reduces the hop count as compared with the lowest ETX scheme in Figure 2(a). Figure 2(c) shows the connectivity graph of the lowest ETX parent selection with MHR. Since each node selects the lowest ETX neighboring nodes in the upper hop level, the selected parent nodes tend to be located at the edge of the hop level, closer to the second-hop level nodes. For the balanced scheme shown in Figure 2(d), data forwarding paths to the sink are almost evenly spread among the first-hop level nodes.
We can summarize observations from these topology maps produced by four localized schemes as follows. If we exploit only link quality without using the hop count in the parent selection decision, the distance between the chosen link becomes relatively short and hop levels increases accordingly. When the MHR scheme is used, the link-quality-based selection results in an unbalanced topology where fewer nodes at the border of hop levels handle most data forwarding tasks from larger hop level nodes.
3.2. Link Quality and Communication Load
The amount of communication energy of a node during a data-gathering round is determined by the amount of data received from children nodes and transmitted to the parent node and their link quality (ETX). Basically, the amount of data received from a child node is the product of the link ETX from that child node and the amount of data that is transmitted by that child node. As discussed in other work such as [17, 18], since receiving of corrupted packet incurs energy consumption at the receiving node, retransmission of packets increases energy consumption not only at the transmitting node, but also at the receiving node.
where and denote the amplifier energy and the electronic energy, respectively, and is the radio range and is the path loss exponent similar to . By following the parameters given in , we set nJ/bit and pJ/bit/m2. Besides, when m and , . We use to denote the set of children nodes of and the set of parent nodes of . The localized selection scheme chooses one parent, and consists of data generated by the descendant nodes of node in addition to the data generated by node . Thus, consists of and data generated by node .
Overall, the number of descendants tends to increase along the distance in the random selection scheme. The lowest ETX parent selection scheme can provide higher throughput at a given time, but it results in an extremely unbalanced communication load. This causes much faster energy depletion of some nodes so as to result in a large gap of energy depletion time among first-hop level nodes. The balanced parent selection scheme provides a similar energy depletion time among nodes.
In this paper, the maximum energy consumption, denoted by , is defined to be the time before the death of the first node. The duration in which all nodes are functional is called the network lifetime. As discussed in , even if workloads are different among the first-hop nodes due to the use of different parent selection schemes with same hop levels, the energy depletion time of the last surviving node in the first hop would be the same. Thus, we focus on the time before the death of the first node.
In the last section, we examined the effect of different localized tree schemes on communication loads for one real deployment case. It was observed that the effect of link quality is not significant when MHR has a relatively large number of nodes in the first hop, since the communication load can be distributed and the energy consumption of a single node is reduced accordingly. However, it is not clear from this empirical data set whether a lower node density with a small number of nodes in the first hop produces the same result. In this section, we characterize how diverse network conditions (such as the node density and the network size) affect the energy consumption of each localized tree construction scheme in conjunction with the link threshold. Based on the analysis in this section, we examine whether a balanced scheme can always produce longer network lifetime than the link-quality-based scheme for any network conditions in the next section.
4.1. Energy Consumption of Localized Schemes
Summary of notation.
Total number of nodes (network size)
Number of nodes in one hop level with MHR in linear topology
Number of children of node
Number of descendants of node
Energy consumption of node per round
Distance between the nearest adjacent nodes
Radio range determined by link threshold
Distance between sink and the furthest node (network radius)
Number of nodes in a radio range
Expected transmission count (ETX)
between nodes and , and distance
Link threshold ETX and PRR
Some considerations in our analysis are explained below. While there could be fluctuation in link quality even in the static node deployment, energy depletion time can be analyzed through a long-term average of link quality for a given link length. In addition, as discussed in previous work [14, 20], temporal variation of link quality should be minimal for links with good quality. It is worthwhile to point out that the PRR is actually the result built upon all underlying layer interactions. Since our focus is the long-term effect of the routing layer on network lifetime, we use the PRR to represent the cumulative effect of all underlying layers (including the MAC layer). Investigation on energy consumption with MAC layer interactions is an interesting research topic, which has been studied in previous work, for example, [21, 22].
4.1.1. Lowest ETX Parent Selection
which is the maximum energy consumption by the lowest ETX parent selection scheme.
4.1.2. Random Parent Selection with MHR
Then, the maximum energy consumption by the random parent selection scheme in a data-gathering round can be computed via (2), which is the energy consumption of node during a data-gathering round.
4.1.3. Lowest ETX Parent Selection with MHR
4.1.4. Balanced Parent Selection with MHR
4.2. Comparison of Localized Tree Construction Schemes
The energy consumption result from the empirical data as presented in Figure 5 is consistent with that of the linear topology with a high link threshold, a high node density and a small network size. Under these conditions, the lowest ETX without MHR has the larger maximum energy consumption as compared to MHR-based tree construction schemes.
As shown in Figure 12, the balanced scheme with the MHR does not always achieve longer network lifetime than the lowest ETX scheme. This is because the balanced parent selection scheme may select a link of poor quality, which results in more data transmission over the link. Network lifetime is also related to the node density for a given network size. Thus, we would like to determine ( ) the number of nodes in a hop, which share the communication load from the nodes in the longer hop levels and ( ) the link threshold needed to guarantee longer network lifetime of the balanced scheme. First, we will investigate the criteria for linear topology based on the discussion in Section 4.1. Then, we will analyze the case of 2D topology.
5.1. Linear Topology Case
We see that this lower bound is a function of the network size, the portion of energy consumption for transmission ( ), and the link threshold. The effect of the network size and is minor since . As increases, the increase of that quickly saturates and the gap between small and large values is quite small. For the link threshold effect, decreases as the link threshold improves.
We can also obtain the link threshold that guarantees longer lifetime of the balanced scheme regardless of network size and that depends on the transmitter power.
The balanced scheme guarantees the longer lifetime regardless of other network conditions including the network size, the transmitter power, if the link threshold is greater or equal to .
Basically, lower bound of the link threshold is determined by node density in a hop. Since , , and , is always greater than and less than . Thus, is less than 1. In addition, is less or equal to . Thus, the right-hand side of (13), , is always less than regardless of other parameters.
A link threshold PRR above always guarantees the longer lifetime of the balanced parent selection scheme regardless of the network size or node density, or any other parameters.
This link threshold lower bound comes from the minimum number of nodes in a hop, , when nodes are evenly deployed in the linear topology.
5.2. 2D Topology Case
5.2.1. Energy Consumption of Lowest ETX Parent Selection
5.2.2. Energy Consumption of Balanced Parent Selection with MHR
The minimum value of this link threshold can be derived by following the procedure in proving Theorem 1 and Corollary 1. Since is greater than and is greater than 1, in the right-hand side of (17) is greater than 0 and less than 1. Thus, and the right-hand side of (17) is always less than . We can conclude that when the link threshold is greater or equal to , the balanced scheme with the MHR always achieves longer network lifetime than the lowest ETX parent selection scheme even in the 2D topology. In grid topology, since is greater or equal to , a link threshold with PRR above guarantees longer lifetime of the balanced parent selection scheme.
In this section, we compare the network lifetime performance of localized tree construction schemes and the centralized scheme that uses the global knowledge of the network including the quality of all links. We present a linear programming formulation, which is similar to that in . Here, the main difference is that we incorporate the link quality metric into the energy consumption model. The objective is to find the optimal flow for every directional links to maximize the network lifetime, , which corresponds to duration of time before death of first node.
In the above, the sink is represented by node and data generating and forwarding nodes are represented by nodes to . is the battery capacity of node . All flows on links and the generated data by each node is nonnegative.
Figure 15(b) shows the ratio of two localized schemes to the optimal lifetime. The network lifetime of the lowest ETX scheme linearly decreases to the normalized optimal value as the link threshold increases. For the balanced scheme, almost 90% of the optimal network lifetime is achieved when the link threshold is 0.7 or above.
Localized tree construction schemes with empirical data were examined and their performance was analyzed and compared. The link threshold and the node density are the main factors that affect the energy consumption of each localized scheme. In the dense node deployment with a high link threshold and a small network size, the MHR schemes reduce the energy consumption significantly when compared to schemes that use only the link quality for parent selection. However, for the opposite network conditions, the lowest ETX scheme can achieve longer network lifetime than MHR schemes. Criteria that guarantee longer network lifetime of the balanced parent selection scheme were derived for both linear topology and 2D topology.
In the future, we would like to examine a distributed topology establishment algorithm that incorporates link quality and load balancing to provide longer network lifetime under dynamic network conditions. In addition, we will examine the optimal link threshold that provides maximum lifetime. In the case of fixed node density deployments, the careful adjustment of link threshold will optimally balance communication overhead driven by imperfect link quality and communication load sharing by more nodes in a larger radio range.
This research was supported by the MKE, Korea, under the ITRC Support Program supervised by the NIPA (NIPA-2010-(C1090-1021-0011)).
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