Abstract. To efficiently disseminate data in Wireless Sensor Networks (WSNs), dynamic source routing and angle based source routing algorithms that have been proposed recently. However, such geographic routing protocols cannot fully support large scale WSNs. In this study, this challenging issue is addressed and a novel geographic K-path reliable routing protocol is proposed for WSNs, which can guarantee the data delivery with reduced energy consumption, communication latency and storage with less overhead. To guarantee delivery, K-path routing in WSN, find K paths from the source to any destination by varying the angle dynamically, so as to avoid the void condition and high overhead in low and high density networks. The energy consumption and end-to-end delay to guarantee data delivery is analyzed. The simulation results show the superiority of the proposed scheme in maximizing the network lifetime and minimizing the communication duration by comparing it with the existing scheme, the ADSR.
Keywords: Wireless Sensor Network, Geographic routing, angle-based routing, Energy, Delay, storage.
Introduction
The past decade has witnessed a growing interest in sensor networks. Sensor networks are highly distributed networks containing tiny nodes deployed in numbers, to monitor different types of environments or systems, by using the measurements of physical parameters, such as temperature, light intensity etc. The sensors collect and transmit the respective data to the sink or server. Sensors usually rely on their battery for power, which cannot be recharged or replaced in critical situations. There have been many applications in growing numbers of domains for WSNs. Some of these applications are eminently critical and require a tradeoff between energy and delay. Some of them are military, health, surveillance, monitoring etc. But some of the limited resources like low battery power, relatively low processor capability, small antenna height, etc., are the challenges to be considered while proposing a mechanism for WSNs.
There have been routing protocols designed keeping these challenges in mind, but special emphasis has been paid to reduce the energy consumption. This has led to approaches like sleep/awake schedules and probabilistic forwarding, all of which can prove to be costly, in terms of delay.
But, in contrast to these approaches, geographic routing protocols take decisions locally, based on the location of their neighbors. They are generally robust to topology changes and energy efficient. There are two approaches to geographic routing, namely, the distance-based approach and the direction-based approach. The former selects the next hop as the neighbor closest to the sink, whereas the latter approach selects the node with the minimum deviation angle from the line connecting that node and the sink or the required destination node.
The proposed work is based on the direction based strategy. Generally, protocols using the distance based strategy fail in the presence of voids. The usual recovery procedure is the right hand rule, which is very costly in terms of delay. Hence, a dynamic angle based K-path routing is proposed, to reduce the energy consumption in wireless sensor networks within the shortest possible time, and also store a minimal amount of state in order to make a quick recovery from failures and voids. Previous works focus on static angle based routing, which increases the overhead in highly dense networks and creates a void situation in low density networks. To balance the overhead and void situation, the dynamic angle is proposed with K-path routing. The dynamic angle based K-path routing (DAKR) reduces the energy consumption by reducing the calculation of the next hop selection based on the dynamic angle region. The selection of the next hop node is based on the shortest distance from the destination and an alternative node in case of failures. But once the packet has been forwarded successfully, the source immediately drops its own copy of the packet, and the receiving node is considered as the source; else, it sends the packet down the alternative path. It then starts a neighbor discovery procedure to get another neighbor. Thus the optimal path with the minimum complexity and minimum memory complexity has been determined efficiently. Thus DAKR algorithm increases reliability, by determining the K-path routing of the backup mechanism to reduce energy and delay for alternative path discovery and improve the network’s life time.
The DAKR protocol has the following features:
1) Packet delivery decisions are locally made. No feedback from the sink or any of the global topology is required, and hence the computational complexity of the algorithm is low.
2) The protocol emphasizes explicitly on fast progress.
3) K-path: Recovery from voids and other failures is done through an extremely simple and effective procedure. And hence, delay has been reduced.
4)The amount of state stored is proportional to the k-path in the forwarding region.
5) The network lifetime is maximized by determining the angle dynamically.
The rest of the paper is organized as follows. Section-II presents the related work. In Section-III, DAKR is presented. Section-IV presents the simulation results, wherein the protocol is compared with the ADSR protocol. The paper is concluded in Section-V.
Related Works
All routing protocols of Wireless Sensor Networks mainly fall under the ad-hoc category. Generally, they are classified into Proactive Protocols (table driven), Reactive Protocols (on demand routing) and Hybrid protocols [1]. Proactive protocols like DSDV [2], WRP [3], GSR [4], FSR [5] and CGSR [6] are not suitable for Wireless Sensor Networks, due to the fact that the limited storage and energy supply of the nodes are not suitable for storing tables and routes. Hence, reactive protocols like AODV [7], DSR [8],ORS[21] and CBRP [9] are being preferred for WSNs, though reactive protocols have the disadvantage of high delay, because the route discovery procedure has to be initiated every time there is a demand. Also the flooding mechanism that it involves causes concern for the low energy available for WSN.
When delay is taken as the main criterion, there have been many approaches to reduce delay. [9] uses DSPA, a protocol which achieves a very good energy-delay trade-off. But it requires high storage facility as it maintains a routing table. [10] Proposes DERP, in which any node which is interested in an event constructs a minimum delay tree and uses that for routing. But it uses flooding as part of route maintenance, which is not favorable for energy reduction. In [11], an extension of the AOMDV (a protocol which chooses multiple paths for recovery), called TIDOM is proposed, wherein the nodes delay replying to route requests based on the residual energy capacity. But, it has the overhead of running a path selection algorithm. [12] Proposes dividing the network into three zones based on the estimated distances, and used different forwarding approaches in each zone. It also considers the link quality while selecting the route. However, this protocol, though effective, assumes that no geographical information of the network is available.
QoS factors have been introduced in general routing protocols, by considering delay as part of the cost in routing. [13] Used a Delay Index and Connectivity Index in the OLSR protocol and achieved a lower delay. [14] Proposed DMSR, here for every route, the accumulated delay is calculated for every path and only the nodes having a delay less than a threshold continue the process. Of the multiple paths, a path selection algorithm is used to select one of the paths, and is also useful during route maintenance. Generally, geographic routing protocols [15]-[18] are being considered for WSNs. Recently, a reactive protocol that makes use of the geographical information has been proposed in [16]. In all of these routing protocols, the entire nodes in the forwarding area forwards the received packet and there by increases the energy consumption and implosion.[17] Proposes an approach, wherein the Compass Routing (CR) and Greedy Routing (GR) indices are combined. In Compass Routing source node selects the next hop node such that angle between the source to node and source to destination is minimum and create a concern for low energy consumption. They are not affected by topology changes due to the failure of nodes, as they can simply select some other node as the next hop neighbor. Moreover, they do not require knowledge of the entire topology. In [19] multicast routing is proposed to ensure reliability with increased delay and in the geographical routing [26]-[30] data was delivered with high computational complexity.
In the Distance Routing Effect Algorithm for Mobility (DREAM) [22], the sender of a packet to a destination will forward the packet to all one-hop neighbors that lie in the direction of destination D. That is, if no nodes are present in their respective expected region, then there is no mechanism to forward the routing. Location Aided Routing [23] proposed the use of position information to enhance the route discovery phase of reactive adhoc routing approaches, which use flooding as a means of route discovery.
The ADSR [20] is applicable to Wireless Sensor Networks, but the DSR is only applicable to Ad-hoc networks, even though it is more advantageous than the DSR. In the ADSR, the void problem exists in low density networks due to the fixed angle formation. Further, the link quality in [25], [32] and cluster head selection in [19], [31] were considered for the reduction of energy consumption. By considering previous works, a new routing protocol has been designed to overcome the previous routing algorithms. We focused not only on energy or delay or distance, but we made a tradeoff between energy and delay, and improved the reliability. We designed the expected region based on the dynamic angle to the destination line. We overcame the defect of the ADSR by varying the angle dynamically, according to the nodes in the expected region. If any node has zero energy or a hole in the expected region, a hole avoidance with the rerouting mechanism is invoked. The dynamic angle overcomes all the defects in the above mentioned routing protocols.
Network Environment and Assumptions
In this paper, we assume that the sensing region is a 2D space, sized A X A. The WSN is represented as an undirected graph G(V,E), where V represents a set of sensor nodes and E represents a set of wireless links between the sensors. u,v’V(G) indicates that the distance between the sensor node u and sensor node v is within the communication range Ri (meters). Let ‘S’ denote the source node and Ni ?? denote the set of neighbor nodes of sensor ni. Each sensor is assumed to know its position coordinates via the Global Position System (GPS).
We consider sensor nodes as mobile and the sink node as stationary with an unlimited power source. Each node has a unique ID and shares its own information with its neighbors. We assume that the network is connected and highly dense. That is, given an arbitrary pair of nodes, data can be sent from one to another in a multi-hop manner.
Table 1. Notations and their Descriptions
Notation
Description
Dx, Dy Coordinates assigned to the destination node
Sx,Sy Coordinates assigned to the source node
nix ,niy Coordinates assigned to the neighbor node
Ni Set of neighbor nodes
S Source
D Destination
Ei , Et, En Initial energy, Energy threshold and Energy of node n
??i ,??d Initial angle and increased angle by ??
np Number of packet transfers from node in unit time.
pt Transmission power of the node to send a packet.
PR ,DAKR Packet rate, energy-delay parameter
?? Energy efficiency
r delivery rate
t Number of transmissions
R Coverage area of a sensor node
Each node contains an internal battery to support its sensing and communication activities. The initial energy of node ni is assumed to be Ei (Joules). When an event occurs, the surrounding nodes first exchange the information about the event, the remaining energy, unique ID, and location, and select one of them to be the source node. When different events occur in different regions within the coverage area, data from the different source nodes are not aggregated along the path to the sink node.
Definition 1(K-path): The path is defined as a route which consists of N nodes from the source node to the destination node. The primary path and an alternative path established for a node ni with the given set of neighbor node Ni is known as K-path, such that K’ Ni.
The alternative path replaces the primary path, if there is no node in the restricted region, with the remaining battery energy and with good quality links from the current node in the primary path. At the same time, the second alternative path is selected and replaces the existing alternative path only if the primary path fails, and the process is repeated until the packet reached the destination.
Definition 2(Dynamic angle): The initial angle is decided as ??i ; then the angle is dynamically increased to cover the region that contains the sensor nodes with sufficient resource, within the communication range of node ni.
Given ??i, S and D, the dynamic angle ??d is to cover at least a sensor with sufficient resource, by increasing the angle ?? from ??i. Let Ni denote the set of neighbor nodes of node ni in the angle region ??i, where Ni = {ni…,nn}; Let Nj denotes the ‘K’ best active sensor nodes based on the remaining energy and shortest distance from the destination in the restricted region of angle ??i, such that Nj Ni. If Nj = {??}, then the angle is increased from ??i to ??d ,so as to cover the minimum active sensor node.
DAKR Algorithm
The energy efficient Dynamic Angle K-based Routing is proposed in three phases. Phase 1 deal with dynamic angle formation, where, information about all the nodes and sink node is considered. The Angle dynamically varies, according to the mobility of the nodes to improve efficiency. Phase 2 deals with the next hop selection, where the node’s remaining energy and distance is considered. Here, the rank table is calculated for each node by calculating the optimal value between energy and the distance of the neighboring node. Phase 3 deals with K-path routing, where the network contains holes or link failures. K-path routing contains the primary and backup path to ensure reliability.
At first, the DAKR routing protocol considers the battery energy of the node as the main parameter, because the total network lifetime is based on the remaining battery energy; Second parameter is the delay parameter, which can be formulated from the number of packets transmitted in unit time, and the transmission power of the node to send to other nodes. The third parameter is the PR, the packet rate, which is formulated by the remaining battery energy of the node and the delay parameter. The fourth parameter, DAKR, is formulated as the product of PR and the distance value.
4.1 Phase1-Dynamic angle formation
In geographic based routing, each node calculates its forwarding region, in accordance with the sink position, and transmission is based on the neighbor nodes within that forwarding region. As shown in Fig. 1(a), the angle is calculated, with respect to the line passing from the source to the destination; due to that, we have almost overcome the computational cost, but our routing protocol works more efficiently, if the source node has dense nodes in the range. The angle can be varied dynamically in order to overcome the void and mobility problem. Due to its mobility, the network topology and nodes positions change. So, static angle based routing suffers from the void condition. To overcome this problem, dynamic angle based routing, implements the dynamic angle region calculation, if no nodes present within the angle region R. Furthermore, the static angle needs an optimal angle value. If the maximum angle is considered to avoid the void problem, there may be a problem of more nodes competing for the next hop selection, in the case of a highly dense network. If the minimum angle is considered to improve efficiency, there may be a problem of void condition. The routing of source node is cancelled.
Fig. 1. (a)Forwarding and Restricted region (b)K-path implementation
Consider the right angled triangle between the source node and the neighbor node, to find the angle which neighbor node lies within the region of the source node. The equation of the line passing from the source to destination is
(x-Sx)/(Dx’Sx)=(y-Sy)/(Dy ‘ Sy) (1)
The perpendicular distance from a neighbor node to the line passing from the source to the destination is determined from equations (2) and (3). Dv gives the distance from the neighbor node to the source node. The perpendicular distance, ?? gives the opposite side of the right angled triangle.
??=((Dx’Sx)*(Sy’ny)'(Sx’nx)*(Dy’Sy)) (2)
Dv= (3)
?? = ?? / Dv (4)
.
The distance between the source and the neighbor node, is calculated in Di, to find the adjacent side in the right angled triangle consideration. The angle ?? between the source node-neighbor node to the source node-destination node is calculated and the equation is given below.
Di = (5)
?? = ?? / Di) (6)
Further, the angle region is divided into three sectors. Nodes within sector 1 are closer to the source node, and nodes within sector 2 are between the source and the sink node. Sector 3 contains the farthest node from the source. To avoid the blacklisting problem and to reduce the energy, the nodes within sector 2 compete for the next hop selection.
Algorithm 1. Dynamic angle formation
Input: S, D,R
Output: ??d, Fa, Ra
Let ‘R’ be the range of the sensor node
if ||D-S|| ‘ R then
Source node S forwards the packet directly to the destination D
else
Compute Forwarding region
Let ‘r’ be the radius between the source and sink node
Fa ‘ Draw the circle with radius r and center as source
Compute the restricted region
?? ‘ 0.20 * R
Restricted region area Ra ‘ ??
Compute initial angle ??i
for each node of the neighbor set Ni in the initial region ??i
Construct rank table for K node based on energy and the transmission power
end for
if all the nodes in Ni have low energy and weak links then
??d = ??i + ??
end if
end if
end procedure
In Fig. 1(a), for source node S (SRC), the forwarding area with radius ‘r’ is calculated by the distance between the source S and the destination D (DEST). The angle region for the source node S is formed based on the slope between S and D. Only, nodes B, C, D, E and G are considered for the next hop selection. Nodes E and G are avoided due to the blacklisting problem. Node B is discarded, because it is closer to the source node S. So, only C and D compete for the next hop selection.
4.2 Phase2 – Next hop selection
To transmit data to the next hop in WSNs, different routing protocols follow different approaches to achieve efficiency. Some of the protocols consider energy as the main parameter, some delay, some the distance, and some follow the cluster approach, focusing mainly on decreasing the energy and computational cost. But our protocol considers energy, and distance as the parameters to formulate a formula, to select the next hop node in an efficient way. This selection is better than the previous routing protocols, hence, in our routing protocol, the next hop selection is based on both energy and distance.
Table 2. Neighbor-table
Node-ID x-Coordinate y-Coordinate Timestamp Time received
According to the greedy approach, the packet is forwarded to the neighbor node that is nearer to the destination. However, this approach is not efficient in lossy wireless networks, where the node in the network exhibits ‘poor links’ or "unreliable links". The energy efficiency E, can be computed directly from the packet delivery rate ‘r’ and the total transmissions ‘t’, which is given as
E (7)
Algorithm 2: Neighbor Set Formation
Input- none
Output- Each node knows its neighbors and maintains a Neighbour set Ni
for all nodes that belongs to angle region ??i do
each node ni broadcasts HELLO packet
all nodes that hear the broadcast message update the node ni in their Neighbour set
node nj that is neighbor of the node ni sends HELLO packet to ni
end for
end procedure
Hence to maximize the energy efficiency ??, the forwarding strategy must forward the packet to the neighbor that has good quality links in the restricted region. The restricted region is calculated based on the transmission range ‘R’. For example if the transmission range of a node is considered to be 100m and the blacklisting of weak links threshold is 20%, then the farthest 20% of the transmission range, i.e., 20m is blacklisted, and the neighbor that is closest to the destination is selected among those neighbors in the restricted region(80m).
Algorithm 3: Next hop selection
Input: S, D, Ni, ??i
Output: ??d
for each Ni ??i
if (En > Et) then
Construct the Rank table
Select two node of highest rank based on DAKR value
Send data to the first highest rank node
if (hole|| void||lost_ack) then
Select a node of next highest rank from the rank table
Send data to the second highest rank node
Update rank table with a new highest rank node
end if
else
??d = ??i + ??
end if
end for
end procedure
To further maximize the energy efficiency, the neighbor node in the restricted region is selected, based on the quality links as well as the distance. Hence, to maximize the energy efficiency ??, the parameter DAKR needs to be maximized. Using the DAKR parameter, the source node maintains a rank table, which sorts the neighbor node,
d = np / pt (8)
PR = En / d (9)
DAKR = PR * Distance (10)
based on the energy and DAKR value. This procedure is repeated until the data reaches the destination by maximizing the network’s lifetime. In Fig.1(b), the source node S (SRC) has rank table with nodes D and E. Node S selects the next hop node, based on the rank table information. The node which has highest rank is selected for the next hop.
In the case of a highly dense network, the calculation for the next hop node within that restricted region creates a high overhead and computation cost, which reduces the energy of the source node because the nodes in the range are more in number. Hence, to reduce the computation cost in the geographic based routing ,angle based routing is performed, which reduces the computation cost by considering only the nodes within the restricted region and within the angle region ??.
4.3 Phase3-Multipath routing
The routing protocol with K-path is implemented. Routing is considered on one main path known as primary path and the other path known as alternative path for the backup mechanism; i.e., K=2, because of the packet loss and some other environmental factors, such as path break up, in many cases, the traffic on the path is taken into consideration. Hence, to avoid such difficulties, we followed a mechanism called K-path, which is initially assumed to be 2, and later increased by factor 1, if there is a failure path.
First, in the routing protocol, each node maintains a rank table to maximize the network’s lifetime. The next hop node with the highest rank is chosen; i.e., the node in the range of the source node having more value on the routing parameter. The rank table is based on the remaining energy and distance between the neighbors and sinks.
In case the primary path fails ,due to path break up, packet loss, holes, congestion and other factors, then the second highest rank node is chosen as the next hop node and the routing continues until there is a void condition. Whenever the primary path fails , the alternative path in the rank table replaces the existing primary path and at the same time, a new alternative path is selected and updated in the place of existing alternative path. Thus the transmission is mainly done on a single route, but each node maintains a back up to overcome failure, and that improves reliability. In our routing protocol, the hole avoidance is carried out, with the rerouting mechanism by K-path implementation.
Performance Evaluation
The performance evaluation of the proposed scheme is achieved through simulations, using the OMNET++ discrete event simulator.
5.1 Scenarios
The simulation scenario consists of 42 mobile nodes, and a fixed sink node. The distance between each node is considered as 100m and the communication range of each node is 200m by default. Mobile nodes move with an acceleration of 1mps in the linear velocity mode.
5.2 Simulation parameters and settings
The proposed DAKR algorithm is compared with the ADSR algorithm, which has the same goal as that of our proposed approach. The simulation parameters are shown in Table 2. The following metrics were considered for the performance evaluation.
Table 2. Simulation parameters
Parameters Values
No of nodes 42
No of Sink 1
Playground Size 1000m
Distance between Nodes 100m
Node Coverage 200m
Node Mobility Type Linear and Circular
Node Speed 1mps
Node Acceleration 0mps
Sink Mobility Static
Implosion. It is the duplicate data that has been sent to the same node.
Energy efficiency. It is the measure of the total energy spent by the sensor nodes for end-to end transmission.
Memory efficient. The total number of routes saved in the routing table of each node.
Delay. It is the time cost that is measured for end-to-end transmission.
Reliability. This metric indicates the quality of the routing mechanism.
Complexity. It is the measure of the computational cost of the routing protocol at each intermediate node.
5.3 Simulation Results
The energy consumption of a node is calculated based on the transmission of data and processing of received data. The computation cost for the next hop selection is reduced by considering nodes within the dynamic angle region. Nodes within the angle region receive RTS from source node when an event occurs. Nodes that receive RTS send their remaining energy along with the current position and velocity information through the CTS packet. The current node that receives CTS computes the rank table, based on both the energy and transmission power. DAKR chooses the best value between energy and transmission power to overcome the energy depletion of nodes and the link reliability problem. To evaluate the performance of DAKR with different node densities, nodes are deployed in a 1000m square grid. In Fig.2 , the hop count for every node to reach the destination is depicted. The DAKR protocol has the lowest hop count compared with the ADSR, which selects the next hop in a static angle within the available nodes in the angle region The hop count decreases with the node density due to the estimation of the reduced angle formation with more number of nodes. The DAKR excels the ADSR, irrespective of high or low node density.
In Fig.3, the RTS count is compared between the DAKR and ADSR. There is a huge improvement in the RTS count. The energy efficiency can be compared by considering the number of RTS count sent, and the CTS count that are received. The RTS has been sent to the single neighbor node in the angle region, which has been chosen based on its remaining energy level and transmission power. It avoids the blacklisting problem due to long links between the source node and the next hop node.
Fig. 2. DAKR Performance at different node density level. a)Hop count
Fig.3. DAKR Performance at different node density level. b) RTS count
In DAKR, the K-path routing technique is used. To reduce the K-path overhead, only single primary path is used at a time for routing, and the backup path is used, only if the primary path fails, this increases the network’s lifetime. The backup path is chosen by considering the rank table data. If highest rank node fails to route the data, the second highest rank node is selected for transmission. Thus the reliability of data transmission to reach the destination is increased with the minimum computation.
The dynamic angle based DAKR is compared with the static angle based ADSR algorithm by energy and delay in Fig 4 and Fig 5. The DAKR has the highest remaining energy in comparison with the ADSR due to the minimal computation at each node for the next hop selection. In a highly dense network, more nodes lie within the static angle, and the ADSR algorithm sends more RTS request for transmission. DAKR improves the remaining energy of the node by sending RTS to nodes within the angle region. Delay in transmission between the source and the destination is compared for the ADSR and DAKR algorithm . The Delay for each node in the network to route the data to the
Fig. 4. Performance of the proposed DAKR compared with ADSR. c) Delay
Fig. 5. Performance of the proposed DAKR compared with ADSR. d)Energy efficiency
the data to the sink node is calculated and plotted against the ADSR. The ADSR algorithm selects the next hop node within a fixed static angle region. If no nodes are
present within the angle region, the algorithm fails to select the next hop for routing and it creates the void situation. DAKR overcomes the void problem, by dynamically varying the angle region, and improves the delay performance through k-path routing with the help of the rank table. The high delay in the middle nodes compared with the other nodes was due to high transmission in the middle nodes. This can be improved by increasing the speed of the node mobility.
5.4 Advantages of DAKR
No Implosion- Even though the DAKR is a K-path algorithm, implosion never occurs, because unlike other multipath algorithms, we did not send duplicate copies of the same data, unless the first chosen path fails or becomes void or is unavailable. Hence, the duplication of data to the same node is avoided.
Delay Efficient- At each step we are geographically one step closer to the destination, and the failure does not reinitialise the process of route finding; because of the K-path, it is more delay efficient in emergency applications.
Memory Efficient- It is highly memory efficient, because there is no need to store entire routes or many copies of the packet.
Less Complexity- Both the routing and recovery are extremely simple. For every destination, we need to compute the Euclidean distances for all neighbours only once. Extensive computations are not necessary.
Energy Efficiency-The number of RTS counts sent and CTS counts received is restricted only to the angle region nodes. The total energy spent for end-to-end transmission is reduced.
Reliability-The K-path routing improves reliability, in the case of void and node failure.
Conclusion
DAKR, a new routing protocol that improves the delay and energy performance, has been proposed in this paper. The protocol has less memory requirements, which is very desirable for Wireless Sensor Networks in general. The protocol also minimizes flooding of packets, and the number of copies of the packets held by the sensor networks is also minimum. This is highly desirable for the energy constrained Wireless Sensor Networks. The simulation results show the lesser delay and memory required by DAKR over a standard geographic protocol like the ADSR. The energy and delay efficiency is achieved by three steps, such as initialization, route discovery, and data transmission. The initialization step performs the formation of the angle region along with restricted area and rank table formation. The route discovery step selects the next hop node, based on the calculation of energy and distance within the angle region. The data transmission step transmits the data to the sink. The tradeoff between energy and delay in a wireless sensor is reduced, by employing dynamic k-route discovery with low strength bits. Comparative analysis depicted the efficiency and effectiveness of the approach.
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