Characterizing Link and Path Reliability in Large-Scale Wireless Sensor Networks Turgay Korkmaz Department of Computer Science University of Texas at San Antonio
[email protected]
Abstract—Reliable data transfer (RDT) is one of the key issues in wireless sensor networks (WSNs) and can be achieved by using link-level re-transmissions and multipath routing. Another key issue is the scalability of WSNs. In this paper, we try to better understand and characterize/quantify the relationships between reliability and scalability, and identify possible design options for the future RDT protocols in large-scale WSNs. With this in mind, we first conducted actual experiments to characterize link reliability measures in an actual sensor network setting. We then used these measures and analyze how commonly used RDT mechanisms impact overall path reliability. In general, our analysis shows that the combination of link-level re-transmissions and multi-path routing is a viable solution in small-scale WSNs. However, due to the increased length of paths between sensor nodes and sinks in large-scale WSNs, it becomes costly to sustain the overall reliability at an acceptable level. Therefore, the future RDT protocols should focus on minimizing the path lengths using hierarchical structures in large-scale WSNs. It is also necessary to couple RDT protocols with routing protocols that can take link reliability measures into account.
Keywords: Wireless sensor networks; Reliable data transport; Reliability modeling; TinyOS; I. I NTRODUCTION Wireless sensor networks (WSNs) are essential to the success of several different real-world applications interacting with the environment [1], [2]. In many of these applications, sensor nodes (a) monitor their environment, (b) collect and/or aggregate sensor data, and (c) send the collected and/or aggregated data to base stations (or actuator nodes). If the sensor nodes are not within the communication range of the final destination, then the other sensor nodes act as relay nodes (routers) and forward the messages from the originating sensor nodes to the final destination through a path or multiple paths. This research is supported by DoD Infrastructure Support Program for HBCU/MI, Grant: 54477-CI-ISP (UNCLASSIFIED).
Kamil Sarac Department of Computer Science University of Texas at Dallas
[email protected]
The success of many WSN applications (particularly mission-critical ones) depends on the reliable and efficient transmission of the sensory data from the original sources to the final destination(s) [3], [4], [5]. Accordingly, the research community has been paying significant attention to the design and implementation of reliable data transport (RDT) protocols in WSNs, as we review in Section II. In addition to reliability, it is necessary to consider the scalability of RDT protocols because many WSNs are envisioned to be very large to cover larger areas. Thus, before designing yet-another RDT protocol, we need to first better understand and characterize the relationships between reliability and scalability, and identify possible design options for the future RDT protocols and large-scale WSNs. In this paper, we focus on most commonly used two key RDT mechanisms (namely, link-level retransmissions and multiple paths) and analyze how these mechanisms perform when underlying network gets larger and larger. To carry out our analysis based on realistic data, we first conducted an experimental study where we measure and statistically characterize the reliability of wireless links in an actual one-hop WSN. Assuming that the wireless links in a multi-hop WSN would have similar link reliability characteristics at best, we analytically determine and characterize the overall reliability of the underlying paths in a large-scale WSN.1 In general, our analysis shows that the combination of link-level re-transmissions and multi-path routing is a viable solution as long as the average path length (the number of hops) is small. However, when the average path length increases, it becomes costly to sustain the overall path reliability at an acceptable level. Therefore, 1
Note that due to extra interference and hidden node problems in a multi-hop WSN, the wireless link reliability could be worse and further reduce the overall path reliability. So, our analysis are actually showing the best possible case for the RDT protocols in large-scale networks.
II. R ELATED W ORK Reliable data transfer (RDT) protocols usually send a packet or a group of packets and set a timer to wait until appropriate ACKs come [6]. If there is no ACK and timer goes off, then RDT protocols re-transmit the lost packets. RDT protocols may operate on an endto-end or hop-by-hop basis. Due to high bit error rate of wireless links, end-to-end RDT is not efficient in wireless networks [7]; thus, hop-by-hop or link-level re-transmissions are commonly used in wireless RDT protcols [8]. Authors in [9] combined MAC and transport layer NACK-based schemes to provide multi segment reliability. Some researchers has focused on reliable transmission from sink to sensor nodes [10], [11]. Clearly, link-level re-transmissions improve the reliability of individual links and thus the overall reliability of a path. In addition to re-transmissions, we can also use multipath routing to further improve the overall reliability by forwarding packets along many (possibly disjoint) paths [12]. The scheme in [13] forwards multiple copies of the same packet over randomly chosen routes. Some other schemes identify multiple paths but only use one as the primary route while the other alternatives are used in case of problems in the primary path [14], [15]. In general, determining and maintaining multiple paths
could be costly in a large-scale WSN. The combination of link-level re-transmissions and multi-path routing may provide a balanced mechanism. In this paper, we analyze and try to quantify the impact of these two mechanisms on the overall path reliability in large-scale WSNs. III. C HARACTERIZING L INK R ELIABILITY Using TinyOS 1.x [16] and nesC on Crossbow IRIS motes [17], we created a one-hop WSN where sensor nodes programmed to randomly generate a message per second on average and send it to the base station over the underlying 2.4 GHz IEEE 802.15.4 wireless MAC protocol. We located 10 sensor nodes around the base station within the radius of 20 meters and use the maximum default power so that all the nodes were actually within the communication range of each other. We also used channel 26 which is non-overlapping with 802.11. Our goal in this setup was to minimize the packet losses due to collisions, interferences, hidden node problems, and congestion so that we can obtain the best possible case for RDT protocols. In a multi-hop WSN setup, these factors may further deteriorate link reliability and the overall path reliability. We run the same setup several times at different environments and monitored each wireless link for 10 minutes. In each case, we counted the number of messages that are sent and received. We then took the ratio of the number of received messages to the number of the sent ones as the reliability of a wireless link. For each link, we also computed the average of the readily available RSSI (Received Signal Strength Indicator) values for the successfully received messages. Figure 1 shows the relationship between average RSSI and link reliability. In essence, it is expected that the 1 0.9 0.8 0.7 Link Reliability
when planning large-scale WSN applications, we need to first focus on minimizing the hop counts between sensor nodes and sinks through various mechanisms such as a hierarchical structure with special sink nodes, multiple and mobile sinks. We also need to actively monitor link reliability measures and take them into account by coupling RDT protocols with routing mechanisms. Otherwise, it is impossible to deploy and successfully operate a large-scale WSN. The rest of this paper is organized as follows. We present related work in Section II. We try to characterize the link reliability data collected through actual measurements in Section III. Based on these data, we then analyze tradeoffs and how multiple re-transmissions and multi paths impact the overall reliability. Specifically, we will first consider the base case SxSP (single linklevel transmission over single path) in Section IV. We then consider MxSP (multiple link-level re-transmissions over single path) in Section V and SxMP (single linklevel transmission over multiple paths) in Section VI. We then consider the middle ground, namely MxMP (multiple link-level re-transmissions over multiple paths) in Section VII. Finally, we conclude this paper and discuss some future work in Section VIII.
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underlying link will be more reliable as the RSSI increases. Clearly, our experiments show that there is a positive correlation (which is 0.5206) between RSSI and reliability. However, this is not a strong correlation. For many links, particularly when the RSSI is small, we see all the possible link reliability values. This suggest that we cannot simply rely on RSSI values as the link reliability measures. We need to monitor each link to determine its reliability measure. We now try to get a general idea about the distribution of link reliability measures that we collected. For this, we first determine the histogram of link reliability measures, as shown in Figure 2. Using disttool in matlab,
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Experimental Data: Histogram of Link Reliability.
we considered various distributions and their PDFs, and determined that our histogram looks like Beta distribution. Thus, we selected the family of Beta distribution as the best possible model for our data and computed its parameters as 𝛼 = 1.4381 and 𝛽 = 0.6342 with the 95%confidence level of [1.2208 1.6554] and [0.5196 0.7489], respectively. To quickly demonstrate how well the Beta distribution models our empirical data, we compared the theoretical and empirical PDFs and CDFs. As shown in Figure 3, they closely match. Since our goal is to get a general idea about link reliability, we are contented with these graphical methods. In the future, we plan to consider more empirical data and use well-known goodness-of-fit tests [18]. As the above figure shows, the single link reliability measures close to 1 are more likely than those close to 0. So, in case of single-hop WSNs (e.g., star topology), the underlying applications may be satisfied with the reliability they get. However, in case of multi-hop WSNs, this will not be the case since the reliability of a multihop path will significantly decrease as the number of
hops increases. In the following sections, we look at how link-level re-transmissions and multi-path routing may improve the overall reliability. IV. S X SP Assuming that the link reliability measures are independent, we can compute the reliability of a path as the product of the link reliability measures along that path and formally define it as follows: 𝑟(𝑝) = Π(𝑖,𝑗)∈𝑝 𝑟(𝑖, 𝑗)
(1)
where 𝑟(𝑖, 𝑗) is the reliability measure of link (𝑖, 𝑗). As we discussed in previous section, 𝑟(𝑖, 𝑗) can be modeled as a random variable having Beta distribution. Accordingly, the distribution of path reliability will be the product of Beta random variables. The exact densities of the product of independent Beta random variables are studied in the literature [19], [20]. However, the resulting non-closed form formulas are too complicated for our purpose. Instead, we consider the following numerical approach to get a general idea about the distribution of path reliability.
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We first generate 10,000 paths for different hop counts. We then randomly generate the link reliability measures from the experimentally determined distribution of Beta(𝛼 = 1.4381, 𝛽 = 0.6342). Finally, we compute the path reliability by using (1). Based on that data, we determined the PDFs and CDFs of path reliability for different number of hop counts as shown in Figure 4. In case of two hops, the path reliability becomes almost
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on just the mean values of path reliability measures in the following sections. 1
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Fig. 4. PDF and CDF of Path Reliability when Link Reliability ∼ Beta(𝛼 = 1.4381, 𝛽 = 0.6342).
uniform in the range [0 1]. However, as the number of hops increases, the path reliability density becomes a significantly decaying function, indicating that the path reliability measures close to 0 are more likely than those close to 1. This can be seen better in Figure 5 which shows the box plot for path reliability data as well as mean and median values. Clearly, as the number of hops increases, the path reliability measures for almost all paths are getting significantly lower than any acceptable level. This suggests that a WSN involving more than one or two hops will not be practical unless some mechanisms are put in place to improve the link and/or path reliability. We analyze such mechanisms and focus
V. M X SP In this scenario, we assume that the underlying WSN routing protocol maintains a single path from every sensor node to the base station and try to improve the reliability of every link along the single path by retransmitting messages several times over each link. Using the same experimental data collected in Section III, we first show how the link reliability can be improved by using re-transmissions. Accordingly, we ⌉ as the group ID for each packet. first assign ⌈ 𝑃 𝑎𝑐𝑘𝑒𝑡𝐼𝐷 𝐾 This makes sure that we will have at most 𝐾 packets in each group, and a group can be seen as a message that is re-transmitted 𝐾 times. So, if there is at least one packet from a group, we call this group a successfully received group (or message). We then divide the number of successfully received groups by the total number of groups so that we can determine the link reliability with 𝐾 re-transmissions. Figure 6 shows the link reliability under the different values of 𝐾 .
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Actually, we can analytically obtain the similar results as follows. Let 𝑟(𝑖, 𝑗) denote the reliability of link (𝑖, 𝑗) when 𝐾 = 1. Assuming that the re-transmissions are independent, then we can define the link reliability with 𝐾 re-transmissions as 𝑟𝐾 (𝑖, 𝑗) = 1 − (1 − 𝑟(𝑖, 𝑗))𝐾
(2)
Using this formula and the experimental link reliability measures obtained in Section III, we can analytically compute the link reliability measures for 𝐾 > 1 retransmissions. Figure 7 depicts the box plot of the resulting link reliability measures. These results are similar to the experimentally obtained ones in Figure 6. We can now rewrite (1) to compute the reliability of a single path when 𝐾 re-transmissions are done over each link as follows: 𝐾
𝑟(𝑝𝐾) = Π(𝑖,𝑗)∈𝑝 (1 − (1 − 𝑟(𝑖, 𝑗)) )
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As in Section IV, we can use a numerical approach to illustrate how MxSP behaves under different parameters. Specifically, we generate 10,000 paths with different number of hop counts for various values of 𝐾 . We
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then randomly generate the link reliability measures from the experimentally determined distribution of Beta(𝛼 = 1.4381, 𝛽 = 0.6342). Using (3), we numerically compute the average path reliability under the different values of 𝐾 and the different number of hop counts, as shown in Figure 8. Clearly, as 𝐾 increases, more and more 1 K=12
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Fig. 8. Reliability of single-path routing with multiple retransmissions.
links become highly reliable and thus the overall reliability improves. However, increasing the number of re-transmissions over a single path may increase the congestion level on that path and make the nodes along that path consume more energy. To balance the load, it would be better to distribute the traffic over multiple paths. In the next two sections, we consider multiple paths with single and multiple re-transmissions. VI. S X MP In this scenario, we assume that the underlying WSN routing protocols maintain 𝑀 paths from every sensor node to the base station and try to improve the reliability by forwarding messages over several paths while each message is transmitted once over a link. We will consider multiple re-transmission in the next section. To simplify our analysis, we assume that the multiple paths from a sensor to the base station are disjoint. Accordingly we can define the reliability of 𝑀 paths as 𝑟(𝑀 𝑝) = 1 − Π𝑀 (4) 𝑚=1 (1 − Π(𝑖,𝑗)∈𝑝𝑚 𝑟(𝑖, 𝑗)) As in Section IV, we can use a numerical approach to illustrate how SxMP behaves under different parameters. Specifically, we generate 10,000 paths with different number of hop counts for each value of 𝑀 . We then randomly generate the link reliability measures from the experimentally determined distribution of Beta(𝛼 = 1.4381, 𝛽 = 0.6342). Using (4), we numerically compute the average path reliability under the different values of 𝑀 and the different number of hop counts. Figure 9 shows the average path reliability. In general, the overall 1 M=1 M=2 M=3 M=4 M=5 M=6 M=7 M=8 M=9 M=10
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VII. M X MP In this scenario, we assume that the underlying WSN routing protocols maintain 𝑀 paths from every sensor node to the base station and uses 𝐾 re-transmissions over each link. This is the combination of MxSP and SxMP that we analyzed before. Again to simplify our analysis, we assume that 𝑀 paths are disjoint and 𝐾 re-transmissions are independent. Accordingly we can define the overall reliability as 𝐾 𝑟(𝑀 𝑝𝐾) = 1 − Π𝑀 𝑚=1 (1 − Π(𝑖,𝑗)∈𝑝𝑚 (1 − (1 − 𝑟(𝑖, 𝑗)) ) (5) As in Section IV, we can use a numerical approach to illustrate how MxMP behaves under different parameters. Specifically, we generate 10,000 paths with different number of hop counts under various values of 𝑀 and 𝐾 . We then randomly generate the link reliability measures from the experimentally determined distribution of Beta(𝛼 = 1.4381, 𝛽 = 0.6342). Using (5), we numerically compute the overall reliability under the different values of hop count, 𝑀 , and 𝐾 , as shown in Figure 10. In general, the combination of multiple paths with multiple re-transmissions provides a viable solution to reliability and scalability problem in large-scale WSN. Depending on the application objectives, different values for 𝐾 and 𝑀 can be selected to provide the same level of reliability. For example, if an application wants to provide better load balance or to minimize the energy usage per node, it can increase 𝑀 while decreasing 𝐾 . If the application wants to simplify the routing protocol, it can increase 𝐾 while decreasing 𝑀 .
A. MxMP with Target Link Reliability
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reliability improves as 𝑀 increases. However, the increase in the number of hop counts severely overcomes
So far we assumed that every link uses the same value of 𝐾 . Actually, instead of that, we may set a target reliability 𝑡(𝑖, 𝑗) for each link (𝑖, 𝑗) and let each link determine the required number of re-transmissions to reach that target reliability. To determine the required number of re-transmissions (i.e., 𝐾 ) for reaching that target reliability, we can use the following expression obtained from (2). 𝐾=
log(1 − 𝑡(𝑖, 𝑗)) log(1 − 𝑟(𝑖, 𝑗))
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Using the experimentally obtained link reliability measures in Section III and the above expression, we determined the required number of re-transmissions (i.e., 𝐾 ) for each link to reach various target link reliability values. Figure 11 shows the box plot of that data as well as the mean and median values. In general, since most of the links have high link reliability measures (recall Figure 2), they can easily be made highly reliable with a reasonable amount of re-transmissions. Actually, as also shown in Figure 6, most links become almost 100% reliable with a few re-transmissions. Nevertheless, some links that has very low reliability requires significant number of re-transmissions to reach an acceptable target reliability. In practice, such links should be identified and eliminated during path selection phase. Clearly, most individual links can be made highly reliable with multiple link-level re-transmissions. However, we still need to look at the overall path reliability. Suppose that every link (𝑖, 𝑗) has reached the target link reliability of 𝑡 using enough number of re-transmissions
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Fig. 11. Fig. 10. Reliability of multi-path routing with multiple retransmissions.
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as described before. We can then compute the reliability of 𝑀 path as follows: 𝑀 𝑃 𝑅 = 1 − (1 − 𝑡𝐻 )𝑀
(7)
where we assume that each of 𝑀 paths has 𝐻 hops. Figure 12 illustrates the footprint of (7) for different hop counts under the various values of 𝑀 and 𝑡. As the number of multiple paths increases, the overall reliability keeps increasing. In this case, even with the target link reliability of 0.99, we can make the overall reliability acceptable by using a few disjoint paths. If target link reliability is low, then we need to increase the number of disjoint paths. However, the underlying WSN may not have enough number of disjoint paths to get acceptable overall reliability. In such cases, it is necessary to increase the number of re-transmissions to improve the target link reliability measures while using less number of disjoint paths. VIII. C ONCLUSIONS
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We first conducted actual experiments to characterize link reliability measures in an actual WSN setting. As
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Analytical: Multi Path Reliability under different parame-
byproduct, we also determined the relationship between RSSI and link reliability. The correlation between RSSI and reliability is not strong enough to use the RSSI as a measure of link reliability. To measure link reliability, we need to directly monitor the link and determine the ratio of the received messages to the sent ones. Then we showed that link reliability measures have Beta distributions and one-hop links are mostly reliable. However, when we use these links in a multi-hop scenario, the overall reliability gets significantly poor as the path length increases. Using re-transmissions and multi-paths, we may improve the overall reliability for a moderate size WSN. However, for a very large WSN, new mechanisms are needed to minimize the hop count. In this regard, we must design a large-scale WSN using hierarchical routing protocols where we will have special sink nodes within the network so that we can limit the path lengths. Special sink nodes need to communicate with each other using a longer range wireless communication technology. As future work, we plan to investigate new RDT protocols and evaluate their performance in an actual multi-hop WSN. In addition, we investigate how to determine multiple (possible disjoint) paths that can maximize the overall reliability. R EFERENCES [1] H. Karl and A. Willig, Protocols and Architectures for Wireless Sensor Networks. Wiley, 2006. [2] I. Stojmenovic, Handbook of Sensor Networks: Algorithms and Architectures. Wiley-InterScience, 2005. [3] C. Lim, H. Luo, and C.-H. Choi, “RAIN: A reliable wireless network architecture,” in Proceedings of the 2006 14th IEEE International Conference on Network Protocols (ICNP ’06), 1215 Nov 2006, pp. 228 – 237.
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