Assessment of common routing metrics for efficient RPL-based routing in large WSNs

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1 Assessment of common routing metrics for efficient RPL-based routing in large WSs LAMBROS SARAKIS, STAMATIS VOLIOTIS, DIMITRIOS BARGIOTAS, THEODORE ZAHARIADIS Department of Electrical Engineering Technological Educational Institute of Sterea Ellada Psachna Evias, 344 GREECE {sarakis, svoliotis, bargiotas, Abstract: - The IPv6 routing protocol for low-power and lossy networks (RPL) is based on routing metrics to build communication paths between a source and the destination node. In this regard, the selection of the routing metric determines the path cost with respect to some performance indicator. In this paper, we consider a number of common metrics derived from the lexical composition of hop-count, expected transmission count and network-layer forwarding reliability, and assess their performance against two performance indicators. The first one evaluates the energy cost indicated by the expected number of frame transmissions (including hop-byhop retransmissions over unreliable links) needed for the successful delivery of data from the source to the sink in the presence of lossy links and non-fully cooperative relays. The second performance indicator assesses the cost of the constructed paths in terms of the achieved end-to-end throughput. We use simulation to evaluate the impact of the topological distance between source and destination nodes and draw conclusions which can be used for selecting such metrics for energy- and throughput-efficient RPL-based routing in large wireless sensor networks. Key-Words: - Routing metric, lexical metric composition, energy cost, throughput, large WS, simulation 1 Introduction Routing in Wireless Sensor etworks (WSs) has received considerable attention during the last fifteen years [1 3]. In this context, the earlier research efforts led to the introduction of numerous protocols for data-centric, hierarchical, locationbased and Quality of Service (QoS)-aware routing [1]. The majority of these protocols were designed with the goal to optimize data/information dissemination inside the network and did not aim to support (in an efficient manner) interoperability with external networks. However, the need to integrate WSs with the Internet gave impetus to a new research direction, that of providing WSs (and in general networks of constrained devices) with IP functionality and IP-based routing. These challenges have been addressed by the IETF which specified IPv6 over IEEE networks [4] and the RPL (IPv6 Routing Protocol for Low-Power and Lossy etworks) protocol [5]. (Another emerging effort involves the adaptation of the Ad hoc On- Demand Distance Vector (AODV) routing protocol to constrained mobile ad-hoc networks [6].) RPL constructs Directed Acyclic Graphs (DAGs) to route traffic from network devices towards a central control point inside the network that is called DAG root. To build the DAG, the protocol specifies the rules based on which every node selects its parent (next hop towards the root) among a possibly large set of neighbor nodes. RPL is a distancevector protocol and is, thus, based on routing metrics to compute a weight (cost) for a path interconnecting an origin and a destination node. To cover the diverse requirements imposed by different applications running on constrained networks, a set of primary link and node routing metrics (the term primary is used to discriminate from composite metrics which will be discussed below), as well as static or dynamic constraints that are suitable for RPL have been specified in [7]. The node metrics include energy and hop count, while the link metrics include throughput, latency and reliability (the latter can be quantified by the Expected Transmission Count (ETX) or the Link Quality Level metrics). However, [7] does not preclude the use of other metrics or combinations of metrics. Examples of other routing metrics that can be used include [8] ETT (Expected Transmission Time), WCETT (Weighted Cumulative ETT), MIC (Metric of Interference and Channel-switching), RSSI ISB:

2 (Received Signal Strength Indication) and energyrelated metrics (like BAMER and GAMER [9]). In the development of routing metrics like the ones just presented, cooperation of the network nodes is usually taken for granted. However, full cooperation of nodes in WSs cannot be always assumed, especially in hostile environments or in cases where nodes may act selfishly in order to save resources. For example, in the case of network layer attacks [1], a malicious (i.e., non-fully cooperative) node may refuse to forward all or part of the received traffic towards the destination. To defend against routing attacks in WSs, an efficient approach is to let the network nodes establish trust relationships based on their expectation (trust) that their neighbors will sincerely cooperate on particular tasks (e.g. data forwarding) [11]. In other words, the routing protocol considers the trustworthiness of neighboring nodes as a metric for the selection of the routing path or the forwarding node. In contrast to the node or link metrics, this type of trustworthiness defines a network-layer routing metric. Two primary metrics can be combined in a lexical manner to produce composite metrics (there is also a second type of composition called additive composition which, however, is not relevant to the study presented in this paper). In this case, the primary metrics are prioritized and the candidate paths are first evaluated using the metric with the highest priority. If this procedure delivers more than one candidate paths (these paths will have equal weights; the weight values will depend on the first routing metric used) these paths will be evaluated against the metric with the lowest priority (second metric) and the lightest among these paths will be selected. For the formal definition and the properties of the composition of routing metrics, the interested reader is referred to [12]. In this paper, we consider a number of simple composite metrics that can be used in WS routing based on RPL, and assess their performance against two indicators of the quality of the constructed paths (performance metrics). The first performance metric evaluates the energy cost indicated by the expected number of frame transmissions (including hop-byhop retransmissions over unreliable links) needed for the successful delivery of data from the source to the sink. This metric was addressed in our previous works [13] and [14], where a routing metric, called TXPFI, was used to minimize this energy cost metric and deliver energy-efficient routing in RPLbased WSs. (This energy cost performance metric has been also studied in [9]) The second performance metric assesses the quality of the constructed paths in terms of the achieved end-toend (application-layer) throughput. For both metrics, we notably study the impact of the topological distance between source and destination nodes and we draw conclusions that can be used for selecting such routing metrics in large WSs. The routing metrics used in this paper are derived from the lexical composition of three primary routing metrics: Hop-Count (HC), ETX and forwarding reliability. In particular, the HC is a primary routing metric that is used to report the number of traversed nodes along the path. By minimizing the number of traversed nodes, the overall number of transmissions is expected to be minimized leading to the consideration that also the overall energy consumption and the packet latency are reduced. However, this is true only under the assumption of equally loaded and equally lossy links, which in general does not hold. The ETX on each link expresses the number of link layer transmissions (including retransmissions) required for the successful delivery of a message to the next-hop neighbor. Even if link layer losses are recovered by retransmission mechanisms, selecting lossy links results in high energy consumption and should be avoided. The successful delivery of a link layer frame is decided based on the reception of link layer acknowledgment. Based on ETX, the lossy links are distinguished irrespective of the cause of loss, e.g. physical layer causes or contention at the MAC layer. The last metric (following the terminology in [12], we call it Packet Forward Indication PFI) assesses the forwarding reliability of the constructed path taking into account the potential presence of malicious nodes. Since PFI can detect and minimize losses at the network layer caused by misbehaving nodes, it may be considered as a type of trust-related primary routing metric. PFI is evaluated as follows: each node, after transmitting a packet to a neighbor, enters the promiscuous mode and waits to listen whether the selected neighbor has actually forwarded its packet, thus building trust knowledge [15 17]. The remainder of the paper is organized as follows. In section 2 we formulate our problem, while in section 3 we provide the analysis of the performance metrics assessing energy cost and throughput. Section 4 presents simulation results evaluating the performance of the considered composite metrics in terms of energy cost and throughput. Finally, conclusions are provided in Section 5. ISB:

3 2 Problem Formulation The motivation for this work stems from observations presented in [13,14] on the performance of lexical combinations of the HC, ETX and PFI metrics with respect to an energy consumption metric that captures the number of link-layer (L2) frame transmissions needed for the successful delivery of a packet from the WS source to the destination (we elaborate on this metric in sub-section 3.1). Those composite metrics, by not being specifically designed to minimize this energy cost, performed worse than the metric that was explicitly designed for this purpose. However, the results showed that the lexical combination of ETX and PFI clearly outperformed the other lexical metrics in a variety of simulation settings and, notably, delivered close-to-optimal results in settings with a relatively small number of hops (e.g., 5) between the source and the destination nodes. Based on these observations, we formulate our problem as follows: given a representative set of routing metrics derived from the lexical combinations of the (commonly used) primary metrics HC, ETX and PFI, a) how is the metrics performance with respect to energy cost related with the metrics performance with respect to throughput, and b) are the conclusions drawn from the comparison of the performance of the metrics for small network topologies still valid for large networks? 3 Performance Metric Analysis In this section we present the analysis of the performance metrics evaluating the energy cost and the achieved end-to-end throughput. 3.1 Analysis of the performance metric assessing energy cost The goal of any routing protocol is to establish a communication path between the source and the destination nodes. Figure 1 shows such a path interconnecting the source and the destination nodes (s and d, respectively) through relay nodes (traffic forwarders f i, i = 1 ) and + 1 lossy links. A relay node i forwards a received packet to the next node with probability p i f. The forwarding probability has been used to model the behavior of a node which drops packets due to congestion or deliberately does not always cooperate in the packet forwarding process (for example, it may represent a network attacker or a node acting selfishly in order to save energy resources that would be otherwise spent for the packet forwarding). Every link between two nodes is characterized by an ETX value, ETX i, which represents the average number of L2 frame transmissions (including retransmissions) that are needed for the delivery of a packet to the destination end of the link. s Fig. 1. A path interconnecting a source and a sink node. Regarding the model for the communication between the source and sink nodes, it is assumed that these nodes rely on an end-to-end (e.g. TCPlike) transport mechanism ensuring that data packets are delivered to the sink. According to this mechanism, if a packet is dropped at a network node before reaching the sink, the packet will be retransmitted by the source node (this retransmission is different form L2 frame retransmission taking place because of the lossy nature of the link). It is further assumed that the reception of a packet by the sink node is signaled back to the source through an acknowledgement message transmitted over a reverse loss-free communication path. Based on the modeling approach just described, the formula for the expected number of frame transmissions (including hop-by-hop retransmissions over unreliable links) needed for the successful delivery of one packet from the source to the sink reads [13] ECM p f 1 f 1 = ETX 1 + p f 1 ETX p f i ETX +1. (1) f p i Since in WSs data transmission involves, in general, greater power consumption than data reception or processing, (1) can be used for a performance metric assessing energy cost in such networks. In the following, we will refer to this metric as Energy Cost Metric (EMC). Larger values of ECM correspond to worse performance since they involve more energy consumption for the delivery of a packet from the source to the destination. The minimum value of ECM is 1 and is obtained when the source and the sink are zero hops away and communicate through a non-lossy link. p f 2 f 2 p f ETX 1 ETX 2 ETX+1... f d ISB:

4 3.2 Analysis of the performance metric assessing throughput Assuming that the source and the destination nodes communicate through a mechanism which ensures reliability through the use of acknowledgements (implemented either at the transport layer or as part of the application) and that every information item sent by the source is included in a single packet (as is the case for periodic measurements of some e.g. environmental quantity), the rate at which a saturated source (i.e., a source that has always data to send) can transmit information is 1 packet every Round Trip Time (RTT). This rate is achieved when the time-out value used in the sender (for deciding whether the last transmitted packet should be sent again) equals the RTT. If the communication link between the sender and the receiver is lossy, the useful throughput (i.e., goodput) is approximated by p f i Goodput = RTT, where 1 is the end-to-end packet loss probability. The RTT is comprised of the one-way delay at the forward and the one-way delay at the reverse path. Following a common assumption that the links are symmetric and ignoring components of delay such as processing at the intermediate nodes, delay for medium access and delays due to possible congestion, we may define the following metric (Throughput Metric TM) as a representative indicator of the path s useful throughput p i f f TM = p i +1. (2) ETX i Equation (2) can be used to derive an approximation of the (useful) throughput when the one-way delay is dominated by the time spent for L2 frame transmissions (and retransmissions) over the links of the path. For two different metrics used for the calculation of paths between given source and sink nodes, the metric that delivers the path with the larger value of TM outperforms the other metric. The maximum value of TM is 1 and is obtained under the same conditions the ECM obtains its minimum value. In section 4, the TM (as well as the ECM) will be used to assess the throughput of the paths calculated by composite routing metrics derived from the lexical combination of a) ETX and PFI (Lex(ETX,PFI)), b) PFI and ETX (Lex(PFI,ETX), and c) HC and PFI (Lex(HC,PFI)). Each of these metrics selects paths according to different rules and, thus, affects the value of the TM performance indicator in different ways. The Lex(ETX,PFI) achieves paths with minimum ETX and, thus, it will mainly affect the denominator of (2). The Lex(PFI,ETX), on the other hand, calculates paths of maximum reliability and, thus, it will have a major impact on the numerator of (2). The Lex(HC,PFI) operates closer to the Lex(ETX,PFI) and it is anticipated that its performance will be more related to that of Lex(ETX,PFI) than to that of Lex(PFI,ETX). The following question then arises: what would be the baseline performance achieved by a simple routing metric which does not take into account either the reliability of the path or the transmission count? To calculate such a baseline performance we consider the HC primary routing metric as the sole metric used in the routing protocol. The metric calculates paths of minimum number of traversed nodes (and also of traversed links) and in case more than one such paths exist the selection among the candidates is done at random. In this case, we proceed to calculate the baseline performance as follows. For a source having a minimum topological distance from a destination ( in the following analysis is the number of traversed links) the selected path will consist of 1 relay nodes. We assume that the percentage of malicious relay nodes is p mal and that the forwarding probability of each i malicious node i is a random variable (r.v.) F m obtaining values in an interval [a i, b i ], a i, b i < 1. Then the (total) expectation of the r.v. F i, which is introduced to represent the forwarding probability of a relay node (irrespectively of whether the node is malicious or not), is given by E[F i ] = E[F i i is malicious] P{i is malicious} + E[F i i is not malicious] P{i is not malicious}. Since E[F i i is malicious] = E[F m i ] and E[F i i is not malicious] = 1, we get E[F i ] = 1 p mal (1 E[F m i ]). Then, assuming that the F m i are independent and identically distributed (i.i.d.) r.vs with expected value m Fm, we have ISB:

5 1 E [ F i ] = E[F i ] 1 = [1 p mal (1 m Fm )] 1. Similarly to the forwarding probability, the ETX of the link l, l = 1, is represented by a r.v. denoted by X l. The r.vs X l and F i are independent, and, thus, the expected value of the r.v. TM rv representing the throughput cost is given by E[TM rv ] = E [ 1 Fi X i 1 ] = E[ F i 1 ] E[ X i Assuming that the X l are i.i.d. r.vs with expected value m X, the following lower bound on the value of the throughput metric TM is obtained (using Jensen s inequality) and this value is used as the baseline performance E[TM rv ] TM baseline = [1 p mal(1 m Fm )] 1 m X. (3) 4 Performance Evaluation We use a custom simulation tool to evaluate the performance of the 3 lexical combinations of HC, PFI and ETX with respect to the performance metrics calculated from (1) and (2) in network settings which involve a distance-vector protocol (like RPL), lossy links and malicious nodes. The tool computes for the composite routing metrics the paths that would be used to forward traffic from the source to the sink node. We are particularly interested to apply the metrics discussed in this paper to the RPL protocol; for this purpose, the simulator implements a suitable variation of the distributed Bellman-Ford algorithm to take account of the composite metrics. In all simulations, the network consists of 4 nodes placed on a 2x2 grid topology. Each node located at the periphery of the grid has five one-hop neighbors except from the nodes located at the corners which have three neighbors. All the rest (inner) nodes have eight neighbors. Following the modeling approach presented in section 3 the links between nodes may be unreliable (in this case they have an ETX value greater than 1) and the routing paths may include malicious forwarders. In every simulation run, the network involves one destination node placed at a corner of the grid and one source node placed at the main diagonal of ]. the grid at various topological distances (number of hops) from the source. The rest of the nodes act as forwarders. The forwarders include both malicious and non-malicious nodes. The forwarding probabilities of the malicious nodes are obtained by getting samples from a uniform distribution in [.7, 1] and then setting the forwarding probability to the quantized probability value that is closer to the sample (we have specified five probability intervals with equal length, which gives a total of five discrete forwarding probability values). The ETX value of every link is obtained by sampling the uniform distribution in [1,4], and applying a quantization to the sample similar to the one just described (for ETX we specified six intervals of equal length, which gives a maximum ETX of 3.75). The quantizations are done in order to allow composite metrics that use the PFI or the ETX as first-priority metrics in a lexical combination to make also use of the second metric. (If the probability or the ETX values were not quantized, the probability of finding two or more paths of equal PFI or ETX values, in a network with many malicious nodes and long paths, would be very small.) The performance of the Lex(ETX,PFI), Lex(PFI,ETX) and Lex(HC,PFI) with respect to the ECM, for various distances (measured in minimum number of hops) between source and destination nodes and different levels of penetration of the malicious nodes, are shown in Fig. 2. The results (for each depicted point, the value is the average over 1 simulation runs) show that as the distance between the communicating nodes increases the energy cost increases and tends to follow an exponential increase for all metrics for distances larger than 8 hops (Fig. 2b). For relatively small distances (i.e., 2 and 5 hops) the Lex(ETX,PFI) and Lex(HC,PFI) metrics show comparable performance and clearly outperform Lex(PFI,ETX). This is mainly due to the fact that the selection of the most reliable path (achieved by Lex(PFI,ETX)), especially in cases where clear paths do exist (as is the case for 5% and 75% of malicious nodes), results in significant path stretching (increase of the number of hops) which negatively impacts the path s overall ETX and thus the energy cost metric ECM. ISB:

6 Average ECM Average ECM Average ECM Lex(PFI,ETX) 5 hops Lex(HC,PFI) 5 hops Lex(ETX,PFI) 5 hops Lex(PFI,ETX) 2 hops Lex(HC,PFI) 2 hops Lex(ETX,PFI) 2 hops Malicious odes (%) (a) Lex(ETX,PFI) 11 hops Lex(HC,PFI) 11 hops Lex(PFI,ETX) 11 hops Lex(ETX,PFI) 8 hops Lex(PFI,ETX) 8 hops Lex(HC,PFI) 8 hops Malicious odes (%) (b) Lex(ETX,PFI) 17 hops Lex(HC,PFI) 17 hops Lex(ETX,PFI) 14 hops Lex(HC,PFI) 14 hops Lex(PFI,ETX) 17 hops Lex(PFI,ETX) 14 hops Malicious odes (%) (c) Fig. 2. Average Energy Cost Metric (ECM) for different topological distances between source and destination and different percentage of malicious nodes. Smaller values correspond to better performance. For a distance of 8 hops the performance of all composite metrics addressed in this study is similar. However, as the distance increases beyond 8 hops (which would be reasonable for large WSs), the difference in performance becomes more clear, especially for a large percentage of malicious forwarders. In such cases, some of the conclusions drawn previously for small distances (i.e., small networks) are not valid and the composite metric that gives priority to reliability (i.e., the Lex(PFI,ETX) metric) achieves constantly better performance than the metrics that strive to minimize the number of hops or the total ETX of the path (Fig. 2c). Furthermore, the rate of ECM increase for Lex(PFI,ETX) is lower than that of the other metrics and, notably, Lex(PFI,ETX) for 17 hops even outperforms Lex(ETX,PFI) and Lex(HC,PFI) for 14 hops (Fig. 2c). A first explanation we can give for this behavior is that the variability of the reliability of the candidate paths is proportionally larger than the variability of the paths ETX and since Lex(PFI,ETX) selects the path with maximum reliability (i.e. largest deviation from the average value) it delivers lower values of ECM, as the ETXs affect the numerators of the factors of (1) while the reliability affects the denominators of the factors of (1). The observations regarding the ECM are generally reflected to the observations stemming from the comparison of the metrics performance with respect to the TM. The performance according to TM is depicted in Fig. 3, where we have also included the baseline performance TM baseline obtained by utilizing the HC as the sole routing metric (the baseline performance is given by (3) and is illustrated with the Lower Bound LB legend in the figure). The results show that as the distance increases, the throughput achieved by each metric (which is proportional to TM) decreases. For a minimum distance of 2 hops, the Lex(PFI,ETX) metric achieves the lowest performance (this observation is in line with the observation from Fig. 2a), which, for large percentage of malicious nodes (approximately above 35%), is even lower from the baseline performance. However, for minimum distances of 5 hops and above the routing metric gradually achieves increasingly better performance compared to Lex(ETX,PFI) and Lex(HC,PFI). This observation holds even in cases the Lex(PFI,ETX) is used in settings which involve a topological distance between source and destination which is larger than that considered for the calculation of paths according to Lex(ETX,PFI) and Lex(HC,PFI). (For example, Fig. 3c illustrates that Lex(PFI,ETX) for a minimum distance of 17 hops achieves better throughput than Lex(ETX,PFI) or Lex(HC,PFI) for 14 hops.) ISB:

7 Average TM Lex(ETX,PFI) 2 hops Lex(HC,PFI) 2 hops Lex(ETX,PFI) 5 hops Lex(HC,PFI) 5 hops Lex(PFI,ETX) 2 hops LB for HC metric (2 hops) Lex(PFI,ETX) 5 hops LB for HC metric (5 hops) different percentage of malicious nodes. Larger values correspond to better performance. The Lex(ETX,PFI) and Lex(HC,PFI) achieve comparable performance in most of the settings, with Lex(ETX,PFI) achieving a slightly better throughput in cases of small penetration of malicious nodes. As a final remark, we note that in all cases the performance of Lex(HC,PFI) is almost indistinguishable from the baseline performance (based only on the use of the HC metric)..6 Average TM Average TM Lex(ETX,PFI) 8 hops Lex(HC,PFI) 8 hops Lex(ETX,PFI) 11 hops Lex(HC,PFI) 11 hops Malicious odes (%) (a) Malicious odes (%) (b) Lex(ETX,PFI) 14 hops Lex(HC,PFI) 14 hops Lex(ETX,PFI) 17 hops Lex(HC,PFI) 17 hops (c) Lex(PFI,ETX) 8 hops LB for HC metric (8 hops) Lex(PFI,ETX) 11 hops LB for HC metric (11 hops) Lex(PFI,ETX) 14 hops LB for HC metric (14 hops) Lex(PFI,ETX) 17 hops LB for HC metric (17 hops) Malicious odes (%) Fig. 3. Average Throughput Metric (TM) for different topological distances between source and destination and 5 Conclusion In WSs with lossy links and non-fully cooperative nodes, calculating routing paths of minimum energy cost and maximum end-to-end throughput is a challenging task. In this paper, we compared the performance of simple composite routing metrics that can be used in RPL-based routing in WSs against two performance indicators that assess energy cost indicated by the expected number of frame transmissions needed for the successful delivery of data from the source to the sink, and achieved end-to-end throughput. The simulation results showed that in WSs with lossy links, nonfully cooperative relays and small topological distances between the source and the destination, metrics that rely primarily on the number of traversed nodes or the link quality outperform the metric that computes paths mainly according to the forwarding reliability of the relay nodes. On the contrary, routing based primarily on the forwarding reliability achieves significantly better performance in WSs with distant sources. These conclusions can be used for selecting such metrics for energyand throughput-efficient RPL-based routing in WSs. Acknowledgment: This research has been cofinanced by the European Union (European Social Fund ESF) and Greek national funds through the Operational Program Education and Lifelong Learning of the ational Strategic Reference Framework (SRF) - Research Funding Program ARCHIMEDES III Investing in knowledge society through the European Social Fund, sub-project 8 TROLLS. References: [1] K. Akkaya, M. Younis, A survey on routing protocols for wireless sensor networks, ISB:

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