Design of a load balancing Objective Function for RPL

1.Introduction

The emergence of Internet of Things (IoT) has enabled the interaction of heterogeneous devices and technologies to provide a wide range of applications and services [3,40]. The interaction of these power-constrained devices requires accurate design of routing options to maximize network performance and lifetime. Routing plays a vital role in IoT and provides insight of network operation and expected performance. The requirement for developing routing protocols for IoT arises from the fact that the nature of IoT networks does not generally enable full control over the network topology, as sensors may randomly be scattered over the application area. The Routing Protocol for low-power and Lossy networks (RPL) regards as a standard developed by Internet Engineering Task Force (IETF) for Low power devices and Lossy-Networks (LLNs) and constrained objects. RPL is widely used in IoT applications and Wireless Sensor Networks (WSN) [1].

RPL depends on the Objective Function (OF), which relies on one or more metrics. These metrics are used to build the links between disconnected nodes to build the network topology which contains a root node, intermediate and leaf nodes. Data is transmitted through intermediate nodes until reaching the root node, which has been selected by the OF. RPL has two standard OFs: Objective Function Zero (OF0) and Minimum Rank with Hysteresis Objective Function (MRHOF). An OF is distinguished from others according to its quantitative and qualitative metric types. It is easy to switch between different OFs, making RPL a fixable protocol. Furthermore, new OFs can be plugged and work with RPL regardless of its used metrics. Currently, RPL has become an active research area where OFs have been proposed and their performance is compared with standard OFs.

RPL provides great features such as loop prevention, self-healing, energy efficiency and fast topology convergence. Nevertheless, load balancing is considered as an overlooked function in RPL main components. RPL builds up its topology without considering the load distribution between parent nodes. There are a number of sever faults that appear as a consequence of the unbalanced topology, such as, topology congestion and exhaustion of nodes’ energy, resulting in network holes [11,17,43]. In the existing RPL protocol, a node selects its parent regardless of the parent current conditions and ability to accommodate a new child. In other words, in RPL topology construction, a parent node does not have the right to accept or refuse the adoption of a new child. This one-way selection process does not consider the parent node approval which leads to load-unbalanced topologies. Currying out a two-way parent selection process can be implemented by employing a metric calculated at the parent node to inform the child node about the condition of the parent before creating a formal relation.

Based upon the above-mentioned problem, this work proposes a novel OF called Load Balanced Minimum Rank with Hysteresis Objective Function (LB_MRHOF). The main objective is to mitigate the topology congestion and load balancing limitations which exist in the standard OF in RPL. The OF uses the number of children as an indicator of the parent node’s load. The value of this metric is aggregated with a weighted value of the Expected Transmission Count (ETX) of the node to find the Composite ETX and Number of Children (CENOC) metric. A small value of CENOC implies that the node is under-loaded and has higher energy levels, consequently, it is capable of accommodating additional child nodes. In contrast, a node with a high value of CENOC means higher load and lower power, a situation in which it is not preferred to accept additional child nodes for that parent node. When the node attempts to join the topology, it sends a request message to all candidate parents. Each parent checks the number of adopted children at that moment. It also calculates its ETX value then computes CENOC. The node intending to join compares the CENOC values of all candidate parent nodes and selects the most suitable parent (with the minimum CENOC) accordingly. The proposed LB_MRHOF is evaluated and compared to the standard MRHOF, the OF_FUZZY which combines ETX, Latency and remaining power using fuzzy logic, and the OF-EC which combines ETX and energy consumption [19]. The comparison has been carried out in terms of resultant topology, Packet Delivery Ratio (PDR), power consumption and hop-count. In addition, the performance of the proposed OF has been evaluated in random and hierarchical simulation environments. Moreover, the simulation environment uses three network sizes: small, medium and large to investigate the influence of OFs network performance.

The contribution of this work can be summarized as follows:

The rest of the paper is organized as follows Section 2 explains the RPL background, control messages and objective functions. Section 3 surveys related work. Section 4 shows the proposed LB_MRHOF OF. In Section 5, the simulation environment and parameter values are revealed. Section 6 demonstrates the obtained results and discusses them. Finally, Section 7 provides conclusions and suggests future work.

2.RPL

RPL is a distance vector routing algorithm, that constructs a Destination Oriented Directed Acyclic Graph (DODAG), which includes many nodes and avoids making loops in the topology [3,5,14,40]. RPL supports communication types such as Point-to-Point (P2P) which is the direct communication between two nodes, Multipoint-to-Point (MP2P) through which messages are sent from nodes to the root, and Point-to-Multipoint (P2MP) where messages are sent from the root to the nodes [17,21,41]. The DODAG construction is a tree structure that starts from a node selected to be the root, as shown in Fig. 1. Other nodes select their parent node based on the value of the Objective Function (OF) of the RPL. One or more metrics are utilized to calculate the value of the OF which increases RPL flexibility making it suitable for any application type. RPL has two standard objective functions: Objective Function Zero (OF0), and Minimum Rank with Hysteresis Objective Function (MRHOF) where each one uses different metrics to calculate its OF. The RPL works together with Internet Control Message Protocol version 6 (ICMPv6) protocol to update the network routes by adding new joining nodes as shown in Fig. 2. Moreover, RPL Protocol cooperates with IPv6 over Low Power Wireless Personal Area Network (6LoWPAN) protocol [35].

Fig. 1.

DODAG topology.

Fig. 2.

ICMPv6 and RPL control messages format.

3.Related work

There are a number of previous studies that proposed using different methods, metrics, and measurements to develop suitable OFs for RPL networks. A clear overview of the RPL protocol and analysis of the most relevant studies was presented in [43]. The paper also explained open research challenges in RPL design as well as pointing out open research issues and future directions. The work in [43] and [23] indicated that RPL does not have an effective mechanism to manage congestion. The random deployment of nodes results in an unbalanced distribution of workload. Lim et al. [23] reviewed numerous studies and have categorized them into three categories: congestion detection, congestion notification and congestion mitigation. In addition, the work has depicted the recent trends of the future researches.

Survey [20] has provided a comprehensive review of RPL background, default OFs (OF0, MRHOF), in addition to link and node metrics and constraints. The survey explained how different approaches combine metrics to implement OFs and classified the approaches into Lexical, Additive and Fuzzy Logic. A statistical analysis of OF related work, RPL limitations and enhancements, and tools (simulations and/or operating systems) used to implement RPL were also explained. Moreover, the survey has presented a beneficial classification of the considered studies and summarized them based upon single and combined metrics. Finally, the survey mentioned the challenges and open issues.

Diniesh et al. [7] has given an overview of RPL, mainly focusing on testing the default OFs (OF0, MRHOF), and how they are used by RPL protocol showing their performance in different scenarios. A number of comparative results were shown.

Considering that RPL control messages are sent periodically, [25] focused on changing of the time interval (by default it is approximately one minute) according to application type. The experiments have been implemented on two existing OF scenarios. Results revealed an increment in PDR and a reduction in the energy consumption induced by increasing RPL time interval. RPL improvements continually moved forward to utilize the node resources in a proper way. The work in [18] proposed D-RPL to improve routing table memory limitations in the nodes at RPL storing mode. It has invented a DAO-NACK message used to stop the spreading of DAO messages all over the network regardless of the memory situation and utilizing the multicast group to reach the root. By reducing the control message overhead the network lifetime and scalability increased.

In [9] the study has focused primarily on DODAG formation techniques. The study has provided a statistical evaluation of the reviewed papers; for instance, nearly 40% of papers utilized single metrics and more than 60% proposed composite metrics. Also, The Contiki OS and Cooja simulator are more popular than other RPL research environments. Moreover, while 18% of researchers use the standard metrics to design OFs, 82% improvised to achieve better results. Qasem et al. [29] has compared the standard OF of MRHOF and OF0 in various network configurations. The results were evaluated in low-density networks, whereas RPL compromises more in high-density networks, finding their work ineffective.

The performance of RPL has been evaluated in [37] for dense and heavily loaded networks. Context-Aware Routing Metric (CARF) utilized both Remaining Power and Queue Utilization of the parent along the path. It shows more load- and power-balanced routes, in addition to lifetime and network stability. A number of studies utilized OF0 and MRHOF objective functions [7,33,34]. Sharma et al. [33] has utilized a single-node static metric with random topology. Four node groups have been subjected to the experiment. The nodes ranged from 40 to 200 node senders with one sink. As parameters, they selected PDR, Overhead, and Power Consumption. Their test results indicated that MRHOF was superior in all instances. Real world experiments were conducted in [34] to determine the best objective function with regard to the power parameter. Results indicated that both OF0 and MRHOF performed equally well, but MRHOF was more energy-efficient. In addition, the number of sink nodes had no effect on power consumption.

The studies in [36] and [44] have focused on utilizing IoT to combat fires around different environments. Using the Cooja simulator with different transmission ranges (50 m and 80 m) of the sensor nodes, the network was analyzed based on measurements including power consumption and duty cycle. Results have shown better energy consumption than the normal energy consumption indicators [36].

Zaatouri et al. [44] have assessed the performance of RPL based on three essential parameters: network density, throughput, and sink localization. It employed the Expected Transmission Count (ETX), Hop-Count (HC) and the energy metric. The results indicated that regardless of the scenarios, the number of nodes influenced the parameters. In terms of PDR and the energy metric, the ETX metric performed well in all scenarios.

Respectively, previous work related to the design of OFs for RPL into single-metric routing, multi-metric routing and load balancing routing are classified.

4.Proposed load balancing Objective Function

This work proposes an OF that attempts to fix the RPL limitations mentioned in [11,17,43], in particular unbalanced topology and congestion. The proposed Load Balancing Minimum Rank with Hysteresis Objective Function (LB_MRHOF) uses a multi-metric method that is designed by combining the load balanced metrics (a counter of the node’s number of children), the ETX value of parent nodes, and uses the node rank as a constraint. The method combines the load balanced metric and ETX using a weight parameter producing the Composite ETX and Number of Children CENOC metric. The ETX value is generated at the root node, then it is passed down the topology for child nodes to calculate their respective ETX and so on. In contrast, the load value is collected by nodes having the highest ranks (leaf nodes) and passed one level up the topology towards the root. The RPL DAO control message of the ICMPv6 protocol is utilized to collect the load by attaining the flag of the message. The parent node receives DAO messages from child nodes and counts the number of children. The DAO and DAO-ACK message flags are able to inform the parent node about child nodes that have selected them as parent, or have left them and selected a different parent to balance the load. Therefore, a given node calculates the number of children from messages received from lower-level nodes and determines the ETX value from messages passed down from higher-level nodes. This is shown in Fig. 3.

Fig. 3.

LB_MRHOF metrics combination.

The load indicator CENOC of a node is calculated from the ETX value by applying a flexible weighted parameter (w) in addition to the node’s number of children as illustrated in Equation (3). This equation is calculated for each candidate parent.

The proposed OF uses the minimum aggregation function that prefers lower values of CENOC. A new node that attempts to join the DODAG will decide to connect to a parent node with the minimum CENOC and acceptable network metrics, resulting in the final topology being well-balanced.

This work proposes a Stability Ratio parameter (StabRatio), shown in Equation (4), to manipulate the threshold value which controls switching between two parents. At the beginning of the DODAG formation, the parameter StabRatio is set at a large value. This reduces the value of min_diff consequently increasing the sensitivity of parent selection. In other words, the small threshold will result in less stability in the topology and consequently a trivial advancement of a candidate parent’s CENOC will lead to a topology change. As simulation time progresses, more stability is required, and the final topology formation approaches. The value of StabRatio is gradually decreased during simulation time to increase the topology stability. When the value of min_diff approaches 1, the threshold mechanism becomes similar to the standard MRHOF. Note that in the case of a parent loss, the problem is solved by the self-healing feature provided by RPL where a set of candidate parents are selected and one of these nodes is chosen as the new parent.

Algorithm 1 shows the best parent selection algorithm of LB_MRHOF. the dag refers to the DODAG that contains the two parents. ETX1 and ETX2 are the network metric of parent 1 and parent 2 respectively. rankP1 and rankP2 are the ranks of parent 1 and parent 2 respectively. The algorithm uses Equation (4) at first. The value of StabRatio gradually decreases until it reaches 1, when LB_MRHOF continues to behave similarly to the standard MRHOF.

The Objective Function of LB_MRHOF is a minimization equation and is indicated in Equation (5):

Algorithm 1:

LB_MRHOF – best parent selection

5.Simulation environment and evaluation criteria

This work conducts extensive experiments on RPL considering the trade-off between a balanced topology and improved performance. For benchmarking the proposed LB_MRHOF, the standard MRHOF employing the ETX metric is considered.

6.LB_MRHOF performance evaluation

The motivation behind LB_MRHOF is to optimally distribute child nodes among the parents taking into account other evaluation criteria, such as Packet Delivery Ratio (PDR), energy consumption, and hop-count. In order to evaluate the performance of the proposed LB_MRHOF, a sensor network topology is set in a 100 m x 50 m area having Zolertia Z1 devices with one sink node. The Cooja simulator is run to deliver messages originating at network nodes to be forwarded to the sink node. The simulation was executed by applying various sets of input values on each OF. The values of outputs have been calculated by finding the average of several runs of each experiment. In order to evaluate the impact of network topology on the performance of the proposed OF, random and hierarchical topologies have been assumed. Moreover, the simulation has been executed with networks having 20, 40 and 60 nodes. The performance of the proposed OF has been compared with the standard MRHOF, OF_FUUZY and OF-EC. The topology has been created and compared under each OF, and results have been obtained for PDR, power consumption and hop-count. The following subsection demonstrates these results.

6.1.Random topology

In a random network environment, nodes are scattered randomly in the application area with no clear rank. The selection of parent nodes does not consider the rank of the nodes. The formation of network topology under this type is considered less complicated. The network topologies created by both the proposed LB_MRHOF and the standard MRHOF are shown in Fig. 5 (a) and Fig. 5 (b), respectively. By observing and comparing the two topologies in Fig. 5 (a) and Fig. 5 (b), the OFs try to construct the topology from reachable neighbor nodes base upon their metrics. The load balancing extra factor in LB_MRHOF arranges and distributes the topology in contrast to the standard MRHOF. In Fig. 5 (b) a number of central hub points appear in the topology, which may lead to network holes over time. The LB_MRHOF OF results in fewer nodes that have no children compared to the standard MRHOF. Figure 6 shows the number of child nodes for each parent under 20, 40 and 60 nodes.

Fig. 5.

Random network topology created by both OFs under 60 nodes.

Fig. 6.

The number of child nodes per parent under random topology.

Fig. 7.

Random topology PDR.

Fig. 8.

Average PDR of the random topology.

6.1.1.Packet Delivery Ratio (PDR)

In terms of the PDR, LB_MRHOF shows unexpected behavior during the first minutes of the experiments. Low PDR has been observed, and then it has gradually improved, as shown in Fig. 7. This behavior is due to the efforts of the LB_MRHOF to arrange nodes in the topology under low stability conditions. As experiment time progresses, the stability increases resulting in improving PDR. The results have shown that the overall PDR of the network is better under the proposed OF compared to the standard MRHOF, especially under large-scale networks as Fig. 8 and Table 3 prove. The improvement in the PDR in the different node groups is 2.2% and 1.5% for medium and large-scale groups respectively. PDR is less than 1% lower compared to the standard OF in the small-scale group.

6.1.2.Power consumption

The initial simulation time has witnessed notable exchange of messages under the LB_MRHOF, which is due to the topology instability explained in Equation (4). Low stability implies more switching between parents in order to achieve load balancing. This process leads to increased instantaneous power consumption at the beginning of the simulation (first 10 minutes) as can be seen in Fig. 9. Nevertheless, load balancing saves power during the rest of the simulation, which balances the overall power consumption. These savings are expected to increase for longer simulation times, since the momentary power increase occurs only once at the start of the simulation. Load balancing considers the trade-off between reducing power consumption due to fewer children and additional power consumed due to the deeper topology. Power consumed by both OFs is comparable, with marginal savings of 1.7% in power consumption under medium and large-scale networks and negligible increase of 0.46% in small-scale networks. This increase is caused by the additional messages exchange at the start of the experiment. The average power consumption of both OFs is shown in Fig. 10 and Table 4.

Table 3

Random – PDR average for each node group

Node groups	LB_MRHOF	MRHOF
20	99	100
40	95	95
60	97	93
AVG	97	96

Fig. 9.

Random topology power consumption.

Fig. 10.

Random topology average power consumption.

6.1.3.Number of hops

The Hop-count is mainly controlled by the OF configuration. Load balancing arranges the traffic entering nodes and divides it between parents, which has lead to a small increment in the hop-count of the proposed OF as shown in Fig. 11. The OF selects a parent with a lower rank, fewer children and better ETX, resulting in a network topology with more depth. The average hop-count has increased in the proposed OF. The hop count of both the MRHOF and LB_MRHOF are (1.75 and 1.80) for the small-scale network, (3.15 and 3.10) for the medium-scale network, and (3.0 to 2.13) for the large-scale network, respectively.

6.2.Hierarchical topology

In a hierarchical network environment, nodes are easily arranged with respect to rank, and the parent nodes’ selection process considers the rank. Consequently, it is undesired to connect a child to a parent with a higher rank, and connections between nodes of the same rank should be minimized to reduce hop-count. Figure 12 (a) and Fig. 12 (b) demonstrate the hierarchical network topologies that have been created by both the proposed LB_MRHOF and the standard MRHOF, respectively. Observing the two topologies in Fig. 12 (a) and Fig. 12 (b), comparisons can be made. With respect to connections between nodes at the same rank (horizontal connection), in Fig. 12 (b) two horizontal connections have been formed. On other hand, in Fig. 12 (a) no vertical connections are formed, which ensures hop-count minimization. Also, it is clear that the proposed OF has exceeded the standard OF in terms of fair node distribution. Under the standard MRHOF, parent nodes have 1, 2 or 3 child nodes, whereas the proposed LB_MRHOF has resulted in parents having only 1 or 2 children (with the exception of the root).

Table 4

Random – power consumption average under each node group

Node groups	LB_MRHOF	MRHOF
20	0.89	0.90
40	0.94	0.93
60	1.08	1.06
AVG	0.97	0.96

Fig. 11.

The frequency of hop-count per node in the random topology.

Fig. 12.

The hierarchical network topology created by both OFs under 20 nodes.

The Load Balancing OF has decreased the number of child nodes per parent, and this increases the depth of the topology. Figure 13 displays the distribution of child nodes among parents for groups of (a) 20 nodes, (b) 40 nodes and (c) 60 nodes for both standard and proposed OFs.

Fig. 13.

The number of child nodes per parent at the hierarchical topology.

6.2.1.Packet Delivery Ratio (PDR)

The proposed LB_MRHOF outperforms the standard MRHOF in terms of PDR. Figure 14 indicates that LB_MRHOF has achieved better PDR compared to MRHOF under all three topology sizes. Improvements in PDR achieved by the proposed OF are 1.8% under 20 nodes, 1.2% under 40 nodes, and 7% in a group of 60 nodes. It is obvious that LB_MRHOF achieves more improvement in PDR in large-scale groups. Figure 15 and Table 5 show the difference between the two OFs for different network sizes.

Fig. 14.

Hierarchical topology PDR.

Fig. 15.

Average PDR under hierarchical topology.

Table 5

Hierarchical – PDR average for each node group

Node groups	LB_MRHOF	MRHOF
20	98	96
40	97	97
60	87	80
AVG	94	91

6.2.2.Power consumption

Similar to the random topology, under a hierarchical topology, the power consumption at the start of the simulation is high due to message exchange during topology instability. The proposed OF has successfully balanced load amongst topology nodes without compromising power consumption. Figure 16 shows the power consumption of a hierarchical topology for group sizes of 20, 40 and 60 nodes. Figure 17 and Table 6 show the average power consumption under (a) 20, (b) 40 and (c) 60 nodes. The maximum difference in average power consumption between the two OFs is 2.5%.

Fig. 16.

Hierarchical topology power consumption.

Fig. 17.

Hierarchical topology average power consumption.

Table 6

Hierarchical – power consumption average under each node group

Node groups	LB_MRHOF	MRHOF
20	0.88	0.87
40	0.94	0.96
60	1.18	1.18
AVG	1.00	1.00

6.2.3.Number of hops

The hop-count relates directly to the depth of the constructed topology. Even though load balancing focuses on well-optimizing the number of children per node, apparently this fact does not negatively impact the resultant hop-count. Figure 18 shows the number of hops under (a) 20, (b) 40 and (c) 60 nodes. Figure 18 demonstrates that the proposed LB_MRHOF works well on the large-scale topology, providing a smaller maximum hop-count (9) compared to the standard MRHOF (11). This can be explained by the same-rank connections made by the standard MRHOF as shown in Fig. 12 (b). Under MRHOF, in some situations the node chooses its left or right neighbor as a parent, instead of choosing from the set of upper-level nodes which are on the path towards the root, resulting in increasing the hop-count. The average hop-count of MRHOF and LB_MRHOF is (2.80 and 2.65) in the small-scale network, (2.68 and 2.68) in the medium-scale network, and (5.63 and 4.34) in the large-scale network, respectively.

Fig. 18.

The frequency of hop-count per node in the hierarchical topology.

Fig. 19.

Average PDR of the four OFs.

6.3.Comparison with previously proposed methods

To fully evaluate the performance of the proposed OF, the attained results of LB_MRHOF have been compared with MRHOF, OF_FUZZY, and OF-EC. OF_FUZZY and OF-EC both use fuzzy logic to combine their metrics. The OF_FUZZY is an objective function which combines ETX, latency and remaining power, while the OF-EC is an objective function which combines ETX and energy consumption [19]. The PDR of the four OFs has been compared and shown in Fig. 19 and Table 7. PDR results show that the proposed LB_MRHOF has achieved the highest PDR among evaluated OFs with an improvement of 2%, 10%, and 17% under MRHOF, OF_FUZZY and OF-EC, respectively. Also, the power consumption comparison results are shown in Fig. 20 and Table 8. MRHOF has consumed similar power compared to LB_MRHOF and (33.3% and 47.3%) less power compared to OF_FUZZY and OF-EC, respectively. Comparison results have proven the improvement of the proposed OF over existing OFs.

Table 7

Average PDR for all OFs

No	Objective function	PDR
1	MRHOF	94
2	OF_FUZZY	80
3	OF-EC	79
4	LB_MRHOF	96

Fig. 20.

Average power consumption of the four OFs.

The average PDR and power consumption have been calculated for the four OFs and shown in Table 7 and Table 8, respectively.

Table 8

Average power consumption for all OFs

No	Objective function	Power consumption AVG
1	MRHOF	0.98
2	OF_FUZZY	1.47
3	OF-EC	1.86
4	LB_MRHOF	0.98

It is worth mentioning that the investigation carried out in this work demonstrates results for the most significant metrics that directly influence network performance. There is a number of other metrics that also could be evaluated for further analysis of the proposed OF. These metrics include throughput, packet loss and delay. Nevertheless, it is possible to estimate the expected impact of the proposed OF on some of these metrics. For instance, network delay is strongly related to the number of hops and congestion at intermediate nodes. Attained results have shown that the proposed LB_MRHOF has reduced hop count under random and hierarchical topologies. In addition, the fair distribution of load amongst parent nodes ensures minimum congestion at intermediate nodes. As a result, it is apparent that the proposed OF is expected to reduce the average and overall network delay compared to the standard MRHOF. Furthermore, packet loss can be estimated from PDR, since PDR signifies successful packet delivery. Accordingly, and since LB_MRHOF has been able to increase PDR under random and hierarchical topology (except random low scale networks), it is safe to predict that the proposed OF is likely to result in less packet loss compared to the standard MRHOF.

Evaluation results have proven that the proposed LB_MRHOF outperforms existing OFs in major performance evaluation parameters. Nevertheless, the proposed OF suffers from increased computational overhead at the start of simulation due to frequent parent switching to ensure load balancing. This initial topology instability implies higher power consumption. Reducing the number of candidate parents can consequently improve the stability of the topology which regulates computational overhead. However, this compromises load balancing, which negatively impacts other parameters and LB_MRHOF will behave similar to MRHOF.

7.Conclusions and future work

This work has proposed a load balancing OF to overcome RPL main limitations including the unbalanced topology and congestion around nodes closest to the root. The proposed LB_MRHOF constructs the RPL topology considering the distribution of nodes among their parents. The selection process of the best parent is based on the load-based Composite ETX and Number of Children (CENOC) metric which is calculated at parent nodes. The evaluation has considered random and hierarchical network topologies and has investigated the influence of the number of nodes. The proposed OF has been evaluated using a number of parameters including PDR, power consumption and hop count. Attained results have proven that the proposed OF was able to reduce the number of children per node and average hop count, compared to the standard MRHOF. The proposed OF has significantly outperformed OF_FUZZY and OF-EC in PDR and power consumption. The load balancing process has resulted in additional message exchange at the start of the simulation. This improves the overall performance of the OF with no compromise on overall power consumption. Results have also revealed that the proposed OF constructs a well-balanced topology and performs better under large-scale networks. Future work intends to evaluate the LB_MRHOF considering performance metrics which have not been tested including delay, throughput and packet loss. It also plans to investigate the influence of the weight parameter (w) of the CENOC metric on performance evaluation.

Conflict of interest

The authors have no conflict of interest to report.