INTRODUCTION
A mobile ad hoc network (MANET) is a multihop wireless network formed
by a group of mobile nodes that have wireless capabilities and are near to each
other (Boppana and Mathur, 2005). The process of moving
information packets and messages across a network from a source node to a destination
node is called the routing process. Due to the dynamic movement of nodes in
such a network, a link that is created by a pair of nodes can be destroyed in
an unpredictable way. Considering that, an efficient routing protocol should
be designed to solve the problem. Abolhasan et al.
(2004) reviewed some protocols that have been designed which can be categorised
as proactive and reactive protocols, in which they differ in terms of how to
disseminate routing information through the intermediate nodes.
The overall performance of any routing protocol in MANET would be affected
by several factors. Its performance can be improved by optimising those factors.
A number of previous works have been done to study on the performance of MANET
routing protocols through simulationbased (Broch et al.,
1998; Das et al., 2000; Boukerche,
2004). They evaluated and quantified the effects of factors that may influence
the measure of a single performance by adopting onefactoratone time approach.
The Taguchi experimental design is a structured application of design and analysis
of experiments for the purpose of designing and improving product or process
quality (Ross, 1996; Roy, 2001).
It utilizes a set of orthogonal arrays to study the effects of factors on particular
performance measures in order to decide the optimum factor combination. Manna
and Bhattacharyya (2004), Das and Sahoo (2010)
and Ballal et al. (2012) have applied Taguchi
orthogonal array in the optimization of the manufacturing process. It is not
only applied in the field of production engineering, but also in the field of
communication and information technology. AlDarrab et
al. (2009) applied the Taguchi Method for optimising the parameters,
in order to maximise text message sending task performance of the mobile phone.
The original Taguchi technique is mostly applied in the optimisation of a single
performance measure. However, the routine problem which exists in product or
process design is in determining the optimal factor levels when there are multiple
responses that should be considered simultaneously. While dealing with multiple
performance measures, it is very incredible to find a setting for the control
factors which could optimise all the performance measures simultaneously. Thus,
several adjustments have been suggested to the original Taguchi technique in
dealing with multiple performance measures.
This study proposes an optimisation approach using the orthogonal array and
Grey Relational Analysis (GRA) in order to optimise the multiple performance
measures simultaneously. Grey analysis is one of the multiple performance measures
integration technique that has been widely applied to various fields in dealing
with poor, incomplete and uncertain information (Kuo et
al., 2008). The grey analysis is a part of the grey system theory proposed
by Deng (1989) which is suitable in figuring out a variety
of multiple attribute decision making problems. It has been successfully applied
in many areas, such as in solving the problem of plant layout design (Yang
and Hung, 2007) and in the manufacturing process (Moshat
et al., 2010; Esme, 2010; Balasubramanian
and Ganapathy, 2011). The grey analysis is capable of representing the grade
of relationship between two sequences, so, that the distance of two factors
can be measured separately, even with less data and many factors (Caydas
and Hascalik, 2008).
MATERIALS AND METHODS
Taguchi’s experimental design
is used in measuring the network performance metrics and in analysing the effect
of each of the parameters on multiple responses. The parameters which are considered
in this research are terrain size (A), network size (B), transmission rates
(C), number of sources (D), node speed (E) and pause time (F). The different
levels of these factors are shown in Table 1.
The orthogonal array L_{8}, Table 2 is used because
it requires only eight runs for the combination of six parameters, varied at
two levels. The Network Simulator 2 is used to run the simulations. Each combination
of factor levels is run for three times (for a total of 24 experiments) and
the throughput, the routing overhead and packet drops are recorded. All simulations
are performed on the Intel Pentium IV processor at 2.00 GHz, 2046 MB of RAM
running Linux Fedora Core 4. Each simulation is executed for 500 sec.
In the grey relational analysis, data preprocessing is normally required,
since the range and unit in one data sequence may differ from others or when
the sequence scatter range is too large (Balasubramanian
and Ganapathy, 2011). In this study, the data preprocessing for throughput
is the higherthebetter as in Eq. 1. However, the routing
overhead and packet drop is the lowerthebetter as in Eq. 2:
where, x_{i} (k) is the value of the normalized data, min y_{i}
(k) is the smallest value of y_{i} (k) and max y_{i} (k) is
the largest value of y_{i }(k) for each performance metric.
The definition of the grey relational grade (GRG) in the grey relational analysis
is to show the relational degree between the eight sequences (Table
2). To calculate the GRG, the grey relational coefficient γ_{i}
(k) should be calculated first.
where, Δ_{i} (k) is the absolute value of the difference between
the reference sequence, x_{o} (k) and the comparability sequence, x_{i
}(k), i.e., Δ_{i} (k) = x_{o} (k)x _{ i}(k),
Δ_{min}= min {Δ_{i }(k), i = 1, 2, ..., 8; k = 1,2,3},
Δ_{max} = max {Δ_{i} (k), i = 1, 2,..., 8; k = 1,
2, 3}, ζ is the distinguished coefficient with the values in the range
of 0 and 1 and 0.5 is used in this work.
Table 1: 
Factors and level values used in the experiment 

Table 2: 
Experimental layout using an L_{8} orthogonal array 

The value of ζ can be adjusted according to the actual requirements.
Changing its value will only change the value of the magnitude of the relative
value; it will not affect the ranking of the grey relational grade (Lee,
2012).
The grey relational grade can be obtained using Eq. 4:
where, w_{j} represents the weighting value of the kth performance
metric and . In this work, the corresponding weighting values are obtained based
on the correlation matrix as was obtained in Mohamed et
al. (2011). The grey relational grade, Φ_{i}, represents
the correlation between the reference sequence and the comparability sequence.
Higher grey relational grade means that the corresponding factor combination
is closer to the optimum performance.
This study has used a level average analysis in determining the best factors
combination, while the analysis of variance (ANOVA) has been used in quantifying
the significant factors that contribute to the performance of the routing performance
in the MANETs.
RESULTS AND DISCUSSION
A level average analysis is adopted to interpret the results. This analysis
is based on the combination of the data associated with each level for each
factor. The difference in the average results for the highest and lowest average
response is the measure of the effect of that factor. The greatest value of
this difference is related to the largest effects of that particular factor.
The preprocessing data of each performance metric according to Eq.
1 and 2 are given in Table 3.
The Grey Relational Coefficients (GRC) and Grey Relational Grade (GRG) for
each performance metric according to Eq. 3 and 4
are given in Table 4. In this work, the importance of all
the performance metrics is determined using the correlation matrix method, without
the experience and judgement of the experts. The weight for each performance
metric is 0.319, 0.332 and 0.349 for throughput, routing overhead and packet
drop, respectively.
According to the Taguchi method, statistic delta is used to determine the most
influential factor.
Table 3: 
Data preprocessing of experimental results for each performance
metric 

Table 4: 
Grey relational coefficient of each performance metric and
their grey relational grade 

Table 5: 
Response table for the grey relational grade 


Fig. 1: 
Grey relational grade response graph 
Statistic delta is defined as the difference between the highest and the lowest
effects of each factor. The higher the grey relational grade, the closer it
is to the optimal condition. The mean of the grey relational grade for each
level of the different factors is summarized in Table 5. A
response graph of the grey relational analysis is shown in Fig.
1. Table 5 and Fig. 1 indicate that
the optimal factor sets are A_{2}, B_{2}, C_{2}, D_{2},
E_{2} and F_{1}, that is a terrain of 1000 m χ 1000 m,
network size of 100 nodes, transmission rates of 8 packets sec^{1},
source number of 24 nodes, node speed of 10 m sec and pause time of 20 sec.
Based on the results presented in Table 5, number of sources
has the largest effect on the multiple performance metrics.
Table 6: 
ANOVA on grey relational grade 

This finding is consistent with the findings of the study by Perkins
et al. (2002) which studies the effects of various factors on the
overall performance of adhoc networks but focuses only on one performance
response at a time and also the different level values. The sequence of the
effects is as follows; terrain is second and is followed by transmission rates,
pause time, speed and network size.
The Analysis of Variance (ANOVA) is used to investigate the factors that significantly
affect the routing performance. The ANOVA module of the QUALITEK software is
used in finding out the effects of the factors on the grey relational grade.
The results of ANOVA in Table 6 indicate that those three
input factors contribute towards the multiple performance metrics (Fratio of
the factor A, C and D is greater than F_{0.05,1} = 161.5). The ANOVA
has also produced results in the same order of importance as the network parameters,
which is in the order of: D, A, C, F, E and B.
After the optimal level of the different factors is selected, the final step
is to predict and verify the adequacy of the model in determining the multiple
performance metrics. The estimated mean of the grey relational grade is calculated
using the following additive law model.
where,
is the estimated mean of the grey relational grade,
is the total mean of the grey relational grade,
is the mean of the grey relational grade at the optimum level and s is the number
of factors that significantly affect the multiple performance metrics. The expected
mean of the grey relational grade at optimal setting is found to be 0.961.
A 95% confidence interval (CI) for the predicted mean of the grey relational
grade on a confirmation test is estimated using Eq. 6:
where, F_{α;1;fe} is the Fratio required for 100 (1α)%
CI, fe is the degree of freedom for error, V_{e} is the error of variance,
r is the number of replications of the confirmation experiment, n_{eff}
is the effective number of replications:
where, N is the number of experiments in the orthogonal array and v is the
total number of degrees of freedom of significant parameters. Therefore, 95%
confidence interval of the predicted grey relational grade at optimum condition
is between 0.834 and 1.088.
If the predicted and observed grey relational grade values of the multiple
performance metrics are close to each other, the effectiveness of the optimal
condition can then be ensured. In order to test the predicted results, confirmation
experiments were conducted 5 times at the optimum conditions. The relational
grade for the experiment is 0.853 which is in the range of the 95% confidence
interval. Hence, the results of the confirmatory experiment tests show that
the use of the additive law model is justified in the optimisation of the multiple
performance metrics.
CONCLUSION
This study looks at the use of the Taguchigrey relational analysis in determining
the optimum parameter with multiple performance metrics in mobile adhoc.
In this study, the effects of six factors (terrain, network size, speed, pause
time, number of sources and transmission rate) have been evaluated and quantified
simultaneously using the combination of Taguchi experimental design and Grey
Relational Analysis (GRA) with regards to three performance metrics (throughput,
routing overhead and the number of packet drop). The optimisation of the complicated
multiple performance metrics can be converted into the optimisation of a single
grey relational grade. As a result, complicated processess can be greatly simplified
through this approach. However, all the findings in this study are based on
the factor levels considered in the design and may vary if different factor
levels are used. Future work will look into the different approach in finding
weight factors for GRA so that the best approach can be identified.