RPL Based on Triangle Module Operator for AMI Networks

Yanan Cao＊, Muqing Wu

Beijing Laboratory of Advanced Information Networks, Beijing University of Posts and Telecommunications, Beijing 100876, China

I. INTRODUCTION

AMI (advanced metering infrastructure) [1][2] is a kind of wireless sensor networks for two-way communication between smart meters and city utilities. It acts as control center to store, process, and manage meter data. For example, AMI can be used to manage real time data about power consumption of smart city [3] [4] utilities. Different from the general WSN (Wireless Sensor Network), AMI must support traf fic generated at a variety of sources(meters, data collectors, etc.) and the AMI network must ful fill the needs of different natures of traf fic while it may face constraints. Therefore, AMI networks [5] [6] [7] are composed of multiple constrained devices, including meters, distribution automation elements, and Home Area Network (HAN) devices. These devices are constrained with limited memory,processing power, and energy. They are interconnected by lossy links, and these lossy links are featured by low data rates, low packet successful delivery rates, low bandwidth, and instability. Furthermore, routing protocols are indispensable to the normal operation of AMI networks. Moreover, the routing protocol used in AMI network must guarantee low energy consumption, assure privacy and information security, as well as support self-organization and self-configuration characteristics. Therefore, Internet Engineering Task Force (IETF)has proposed an IPv6 routing protocol for low-power and lossy networks [8] (RPL),which is considered as an important routing protocol being used in AMI networks.

Although RPL gets some applications in AMI networks, it is still under improvement.Therefore, this paper proposes an improved algorithm of RPL based on triangle module operator (IAR-TMO) which can effectively improve the performance of AMI networks.IAR-TMO differs from the previous works and mainly includes the following three new aspects:

(1) According to the application requirements of AMI networks, IAR-TMO proposes membership functions of the following five typical routing metrics: end-to-end delay,number of hops, expected transmission count(ETX), remaining energy of node, and child node count (CNC).

(2) In order to comprehensively evaluate each candidate parent (neighbor), IAR-TMO uses triangle module operator to fuse the membership functions of routing metrics of every candidate parent.

(3) IAR-TMO selects preferred parents based on the triangle module operator. That is the node with maximum value of equation (7)will be selected as preferred parent.

The remainder of this paper is organized as follows: Section 2 introduces the most recently research works related to RPL used in AMI networks and triangle module operator.Section 3 details the new proposed IAR-TMO algorithm and its performance analysis. Section 4 presents the simulation results and analysis of IAR-TMO. Finally, Section 5 gives the conclusions and future research directions.

II. RELATED WORKS

In what follows, the main characteristics of RPL are given. Then, the problems of the most recent works which have been proposed to improve RPL are surveyed. Finally, triangle module operator is introduced

To improve the network performance of AMI networks, this paper proposed an improved algorithm of RPL based on triangle module operator.

2.1 Overview of RPL

RPL [7] [9] [10] is a distance-vector and source routing protocol standardized by IETF to support multiple applications such as AMI networks. As illustrated in figure 1,the network topology of RPL is maintained by Destination-Oriented Directed Acyclic Graph (DODAG). DODAG is a directed graph wherein all edges are oriented in such a way that no cycles exist. It is constructed based on objective function and internet control message protocol for the internet protocol version 6 (ICMPv6) [11] control messages (DODAG Information Object (DIO), Destination Advertisement Object (DAO), DODAG Information Solicitation (DIS), and Destination Advertisement Object Acknowledgement (DAO-ACK)).DIO carries information that allows nodes to discover a RPL Instance which consists of DODAGs, get relevant configuration parameters, select candidate parent set, etc. DAO is used to propagate destination information upward along DODAGs. DIS is used to solicit DIOs from RPL nodes. DAO-ACK is sent by DAO recipient in response to DAO. Objective function [12] [13] defines how to compute nodes’ rank which represents the node’s individual position relative to DODAG root.Meanwhile, according to different application requirements, RPL Instances can use different objective functions such as OF0 (Objective Function 0) [12], ETXOF (ETX Objective Function) [13], MRHOF (Minimum Rank with Hysteresis Objective Function) [14] and so on.

2.2 Problems description

For RPL used in AMI networks, there have been several studies to enhance networks performances through different objective function. But there still exist some problems.

OF0, the default objective function, does not consider any routing metric proposed in[15]. It makes node selects the neighbor with minimum rank as its preferred parent. But the traf fic flows routed through preferred parents attempt to perform nothing load balancing.

MRHOF considers path cost as routing metric. It makes node selects the neighbor with minimum rank (path cost) as its preferred parent. If the smallest cost is less than the cost of the preferred parent by less than a threshold, the node does not change the current preferred parent. Otherwise, it selects the lowest cost node as its new preferred parent. However, MRHOF can only support additive routing metrics like ETX and cannot satisfy the application requirements of AMI networks.

In [16], authors used additive or lexical methods to combine two or three routing metrics when deciding routes. In additive method,the node’s rank is computed based on composition function. The composition function is the sum of the two or three selected metrics with their relative weights. The weight can be changed to emphasis different routing metrics.While in lexical method, node chooses its neighbor with the lowest or greatest value of the first selected metric, then if the first values are equal, the node will choose the one with the lowest or greatest value of the second selected metric. However, the additive method has no clear analysis about weight distribution theory. And the lexical method usually only makes the first routing metric works, because the second routing metric works only with the condition that the first routing metric values of neighbors are equal. And this condition is rarely met.

Fig. 1. RPL-based AMI network with 3 DODAGs in 2 instances.

In [17], authors proposed a QoS aware objective function based on fuzzy logic (OF-FL)which considers end-to-end delay, hop count,link quality, and node energy when selecting preferred parents. But in [17], authors considered nothing about child node count, and the membership functions of routing metrics has no mathematical theoretical analysis.

In [18], authors balanced the consumed energy between nodes through expected lifetime(ELT). But the simulation results about average end-to-end delay and packet delivery ratio do not show a good performance.

In a word, the recent improvements algorithms of RPL used in AMI networks still existing defects. Therefore, IAR-TMO, an improved algorithm of RPL based on triangle module operator, is proposed. Through using triangle module operator to fuse membership functions of several routing metrics, IARTMO can select the optimal candidate parent as preferred parent and improve the performance of AMI networks effectively.

2.3 Triangle module operator and membership function

Membership function [19] [20] can be defined as follows: if there is a number F(x) (F(x)∈[0, 1]) corresponding to any element x in the domain U (the study scope), then F is called a fuzzy set based on U, and F(x) is called the membership of x. when x changes in U, F(x) is the membership function of x. The closer the membership F(x) is to 1, the higher the degree that x belongs to F. The closer the F(x) is to 0,the lower the degree that x belongs to F. The membership function F(x) (F(x)∈[0, 1]) represents the degree that x belongs to F.

Moreover, in order to obtain the comprehensive evaluation results of one system,triangle module operator [21] can be used to fuse multiple membership functions of several factors which are related to this system and achieve strengthening and reconciliation of these factors. That is the evaluation result is not absolutely positive or negative, but rather a fuzzy set. Therefore, by using these technologies, IAR-TMO can effectively fuse multiple membership functions of routing metrics to comprehensively evaluate candidate parents.Then, IAR-TMO can select the optimal candidate parent as preferred parent and improve AMI network performance.

The definition of triangle module operator is as follows: the mapping T:[0, 1]2→[0, 1] is triangle module operator, if the following four conditions are true for ? a, b, c, d ∈[0,1]:

(1) T(0, 0)=0, T(1, 1)=1;

(2) T(a, b)≤T(c, d), if a≤c, b≤d;

(3) T(a, b)=T(b, a);

(4) T(T(a, b), c)=T(a, T(b, c).

For the convenience of practical application, triangle module operator can be extended to multi-dimension. For example IAR-TMO uses five-dimensional triangle module operator.

III. IAR-TMO

In this section, the abovementioned three new aspects (as introduced in I) of IAR-TMO are described in detail.

3.1 Architecture of IAR-TMO

IAR-TMO, the improved algorithm of RPL,mainly includes the following four steps:

(1) Selecting routing metrics which will be evaluated in the selection of preferred parents.

(2) Determining membership functions of these selected routing metrics.

(3) Determining triangle module operator to fuse membership functions of these selected routing metrics.

(4) Selecting preferred parents according to the fusion result of triangle module operator.

In the following, the specific contents of IAR-TMO are introduced based on the abovementioned four steps.

3.2 Selecting routing metrics

In what follows, five typical routing metrics are proposed to be considered in IAR-TMO.

(1) Child Node Count (CNC)

CNC [22] [23] represents the child nodes number of neighbors (candidate parents), used to optimize the parent selection and the unbalanced networks. Thus, the candidate parent with minimum child node count will be selected as preferred parent.

(2) End-to-End delay (EED)

This is an additive metric and represents the sum of link latency. If a path from the node through a candidate parent to root has minimum end-to-end delay, then this candidate parent will be selected as preferred parent.

(3) Node Energy (NE)

NE represents the residual energy of node.In order to extend network lifetime, NE should be used to avoid selecting neighbors with low residual energy as preferred parents.

(4) Hop Count (HC)

HC represents the number of hops between candidate parent and root. And the candidate parent with minimum HC will be selected as preferred parent.

(5) Expected Number of Retransmissions(ETX)

ETX is the expected number of transmissions required to successfully transmit and acknowledge a packet on the link. And the candidate parent with minimum ETX will be selected as preferred parent.

The reasons why selecting the above five routing metrics are as follows: each network has its own unique characteristics. Thus the selection of metrics must capture the fundamental characteristics of each network. For example, the basic concerns in ad hoc networks are link reliability and node mobility.While in IP networks, bandwidth and latency are of great importance. In AMI networks,the resource constraints of nodes demand for energy conservation, link stability and traffic load balance. Therefore, in AMI networks,NE, ETX and CNC should be considered for energy conservation, link stability and traffic load balance. Moreover, for some real-time applications of AMI networks, EED and HC also should be considered. Since that some shortest paths may experience larger EED and higher energy consumption due to congestion or other reasons. Thus combing HC and EED will be more effective for some real-time ap-plications in AMI networks. In general, each metric has an important impact on routing selection. Therefore, in order to select the optimal routes, all the above routing metrics should be considered by IAR-TMO.

3.3 Membership functions of routing metrics

IAR-TMO uses assignment method to determine membership functions of the abovementioned five routing metrics. And their membership functions are as follows.

(1) CNC membership function

This paper uses Gaussian membership function as membership function of CNC. As shown in equation (1), CNC(i) and N represent the CNC of the candidate parent node i and the total number of nodes in the network respectively.

Here, c and σ are constant parameters that can determine the location and shape of the Gaussian membership function and c=0,σ2=0.125. Meanwhile, the smaller the CNC, the greater the probability that the neighbor becomes preferred parent, otherwise the probability of becoming preferred parent is smaller, as shown in figure 2.

(2) EED membership function

Nodes compute EED by adding two sections: (1) the EED of the link from a node to a neighbor (candidate parent), (2) the value of EED in DIO sent by that neighbor. This paper uses Gaussian membership function as membership function of EED. As shown in equation (2), EED(i) and EEDmaxrepresent the EED of the path from a node through the candidate parent node i to root and the maximum EED of the path from this node through a candidate parent (among all the candidate parents) to root respectively.

Here,. And the smaller the EED, the greater the probability that the neighbor becomes preferred parent, otherwise the probability of becoming preferred parent is smaller, as shown in figure 2.

(3) NE membership function

As shown in equation (3), Enow(i) and Emaxrepresent the current energy and the maximum initial energy of the candidate parent node i respectively. This paper uses arctangent membership function as membership function of NE, as shown in equation (4).

Here, λ=20,α=0.4. And the greater the NE, the greater the probability that the neighbor becomes preferred parent, otherwise the probability of becoming preferred parent is smaller, as shown in figure 2.

(4) HC membership function

This paper uses descending semi-Cauchy distribution membership function as membership function of HC. As shown in equation(5), HC(i) and HCmaxrepresent the HC from the candidate parent node i to root and the maximum HC among all the candidate parents to root respectively.

Here, α=70, a=0.02 and β=2. And the smaller the HC, the greater the probability that the neighbor becomes preferred parent, otherwise the probability of becoming preferred parent is smaller, as shown in figure 2.

(5) ETX membership function

Nodes compute ETX by adding two sections: (1) the ETX for the link from a node to a neighbor, (2) the value of ETX in DIO sent by that neighbor. This paper uses descending semi-normal distribution membership function as membership function of ETX. As shown in equation (6), ETX(i) and ETXmaxrepresent the ETX of the path from a node through the candidate parent node i to root and the maximum ETX of the path from this node through a candidate parent (among all the candidate parents)to root respectively.

Here, a=0.01,k=15. And the smaller the ETX, the greater the probability that the neighbor becomes preferred parent, otherwise the probability of becoming preferred parent is smaller, as shown in figure 2.

3.4 Triangle module operator

As shown in equation (7), IAR-TMO uses five-dimensional triangle module operator.Equation (7) satisfies the definition of triangle module operator and can be used to fuse the membership functions of routing metrics to comprehensively evaluate candidate parents.

In equation (7), i represents the i-th candidate parent. gj( i) ( j = 1,2,3,4,5) is the membership function of each routing metric of candidate parent i and j=5 represents the number of evaluated routing metrics. Moreover, equation (7) satisfies the following characteristics:

(1) Shrinking dimension mapping f: [0,1]5→[0, 1];

Here, the proof of each characteristic is omitted and just give the proof of characteristic (3).

Proof characteristic （3）:According to equation (7), equation (8) can be obtained.

In equation (8):

Fig. 2. Membership function curve.

Therefore, characteristic (3) is true.

3.5 Selecting preferred parents

Through using triangle module operator, the selected probabilities of the advantage nodes can be enhanced and the weak nodes can be weakened. Meanwhile, the contradictions may appear in CNC, EED, NE, HC and ETX among candidate parents can also be reconciled and can balance the selection criteria of preferred parent. For example, if CNC, EED,NE, HC and ETX of a candidate parent are all in good conditions (the membership function values of CNC, EED, NE, HC and ETX are all greater than 0.5), the probability that this candidate parent selected as preferred parent will be increased, vice versa. And if there are contradictions between CNC, EED, NE, HC and ETX of a candidate parent (the membership function values of CNC, EED, NE, HC and ETX some are greater than 0.5 and some are less than 0.5), then the probability of this candidate parent selected as preferred parent is determined by their neutral value. Therefore, IAR-TMO can comprehensively evaluate these routing metrics and select the optimal routes to improve the network performance of AMI networks.

In other words, IAR-TMO takes the fusion result of equation (7) as the final judgment,and selects the candidate parent with maximum value of equation (7) as preferred parent.That is if a node has n candidate parents, this node can obtain n values according to equation (7). And the candidate parent with the maximum value of equation (7) will be selected as preferred parent. But except as indicated below:

(1) If the value of equation (7) of the current preferred parent is less than the maximum value by less than parent switch threshold, the node may continue to use the current preferred parent.

(2) If the value of equation (7) of a candidate parent is greater than 1 or less than 0, this node should be excluded from candidate parent set.

(3) If the values of equation (7) of several candidate parents are equal and are the maximum, another routing metric such as RSSI(Received Signal Strength Indicator) may be used to select preferred parent among them.

(4) If the current preferred parent is one of the candidate parents with the value of equation (7) are maximum, the node should continue to use this current preferred parent.

IV. PERFORMANCE EVALUATION

To demonstrate IAR-TMO can improve AMI network performances quantitatively, we simulate it through OPNET and conduct a series of simulations to compare the performance of IAR-TMO, ETXOF and OF-FL in different aspects.

4.1 Simulation statistic metrics

(1) Average packet loss ratio

As shown in equation (9), the average packet loss ratio represents the ratio of the total number of lost packets by root to the total number of sent packets by routers.

Here, Nreceiviedand Nsendrepresent the total number of packets successfully received by root and the total number of packets sent by routers respectively.

(2) Average end-to-end delay

Average end-to-end delay is the average time required from starting packet transmission to its reception by root. As shown in equation (10).

Here, Tkis the average time required from starting the k-th packet transmission to its reception by root. Nsuccessis the total number of packets that successfully received by root.

(3) Network lifetime

Average remaining energy and average alive node number can estimate network lifetime effectively. Average remaining energy represents the average remaining energy of nodes. And average alive node number represents the average alive node number in AMI networks.

(4) Average hop count

Average hop count represents the average number of hops between routers and root.

(5) Average parents changed times

Average parents changed times represents the average number of times nodes changing their preferred parents which indicates the stability of network topology. With low parents changed times, the network topology can be stable but the performances of selected routes cannot be ensured. On the contrary, the performance of selected routes can be ensured but the network topology will be unstable.

4.2 Simulation Settings

RPL nodes are randomly distributed in 1000m×1000m network scenario. The arrival of data packets follows Poisson distribution.The initial energy of nodes is a random value between 0.75J and 1J, and the node is considered dead when its energy is less than 5%.The related key simulation parameters [8] are listed in table I.

In table I, E(k,d) [24] is calculated as follows:

Parameters used in E(k, d) are illustrated in table II. Eelecis the energy consumption of transmitting and receiving 1bit data. εampand εfsare the energy consumption of the transmission amplifier sending 1bit data respectively.d0is the threshold of free space model and multi-path attenuation model. And d is the communication distance between two nodes.

Table I. Key simulation parameters.

Table II. Parameters of E(k, d).

4.3 Simulation results and analysis

(1) Average packet loss ratio

Figure 3. shows the average packet loss ratio of IAR-TMO, OF-FL and ETXOF in different node density. It shows that with low node density, the average packet loss ratio is low. Otherwise, the average packet loss ratio is high. Moreover, the average packet loss ratio of IAR-TMO is much lower than that of OF-FL and ETXOF at different node density.Because when selecting preferred parents,ETXOF only considers ETX and OF-FL considers nothing about CNC which make the selected preferred parents may have too many CNC or low energy. But IAR-TMO simultaneously evaluates CNC, EED, NE, HC and ETX and fuses their membership functions based on triangle module operator. Then node selects preferred parent based on this triangle module operator. That is, IAR-TMO selects preferred parent based on equation (7) and the candidate parent with maximum value of equation (7)will be selected as preferred parent. Therefore,IAR-TMO can reduce the packet loss ratio and improve the network reliability significantly.

(2) Average end-to-end delay

The average end-to-end delays of IARTMO, OF-FL and ETXOF with different node density are shown in figure 4. It shows that the average end-to-end delay increases with the increase of node density. And, the average end-to-end delay of IAR-TMO is much lower than that of OF-FL and ETXOF at different node density. It indicates that IAR-TMO can significantly improve the real-time property of AMI networks through using triangle module operator to evaluate different aspects of routing metrics.

(3) Network lifetime

Average remaining energy and average alive node number can estimate network lifetime effectively. And figure 5 shows IARTMO, OF-FL and ETXOF of these two statistic metrics in different node density. It is clear to see that these two statistic metrics of IARTMO is much higher than that of OF-FL and ETXOF under different node density. Thus,through using triangle module operator to fuse the membership functions of CNC, EED,NE, HC and ETX, IAR-TMO can effectively extend the network lifetime. Because when selecting preferred parent, IAR-TMO considers CNC, NE, etc. Then, the nodes with low NE and too many CNC will not be selected as preferred parents.

(4) Average hop count

Fig. 3. Average packet loss ratio of different node density.

Fig. 4. Average end-to-end delay of different node density.

Fig. 5. Network lifetime: (a) average remaining energy and (b) average alive node number of different node density.

Figure 6 shows the average hop count of IAR-TMO, OF-FL and ETXOF in different node density. It shows that with low node density, the average hop count of IAR-TMO, OFFL and ETXOF are almost the same. Because,in sparse network the number of neighbors is so few that makes the selection of preferred parents very restricted. But with high node density, without the restricted of neighbors number, the hop count of IAR-TMO is much lower than that of OF-FL and ETXOF. Thus IAR-TMO can reduce the hop count from nodes to root remarkably.

(5) Average parents changed times

Average parents changed times indicates the network topology stability. And figure 7 illustrates this statistic metric of IAR-TMO,OF-FL and ETXOF in different node density.It clear to see that OF-FL has the highest average parents changed times which may makes the network instability although it can improve network performance to some extent. And the average parents changed times of IAR-TMO and ETXOF are almost same. Therefore, IARTMO can effectively improve the network performance and ensure the network topology stability at the same time.

V. CONCLUSIONS

In conclusion, IAR-TMO can simultaneously evaluate CNC, EED, NE, HC and ETX, and fuses their membership functions based on triangle module operator. Then the node selects preferred parent according to the triangle module operator. Moreover, theoretical analysis and simulation results show that IAR-TMO has a great improvement when compared to ETXOF in terms of network lifetime, average hop count, etc of RPL-based AMI networks effectively.

For the future work, we will further our study on membership functions of routing metrics, relevant parameters and triangle module operator. Moreover, we will try to find other technologies to further improve the performances of AMI networks.

ACKNOWLEDGEMENTS

This work is supported by the Beijing Laboratory of Advanced Information Networks.

Fig. 6. Average hop count of different node density.

Fig. 7. Average parents changed times of different node density.

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