In Mobile ad hoc Networks (MANETs), the packet scheduling process is considered the major challenge because of errorprone connectivity among mobile nodes that introduces intolerable delay and insufficient throughput with high packet loss. In this paper, a Modified Firefly Optimization Algorithm improved Fuzzy Schedulerbased Packet Scheduling (MFPAFSPS) Mechanism is proposed for sustaining Quality of Service (QoS) in the network. This MFPAFSPS mechanism included a Fuzzybased priority scheduler by inheriting the merits of the Sugeno Fuzzy inference system that potentially and adaptively estimated packets’ priority for guaranteeing optimal network performance. It further used the modified Firefly Optimization Algorithm to optimize the rules utilized by the fuzzy inference engine to achieve the potential packet scheduling process. This adoption of a fuzzy inference engine used dynamic optimization that guaranteed excellent scheduling of the necessitated packets at an appropriate time with minimized waiting time. The statistical validation of the proposed MFPAFSPS conducted using a oneway Analysis of Variance (ANOVA) test confirmed its predominance over the benchmarked schemes used for investigation.
In Mobile ad hoc Networks (MANETs), a temporary network is constructed with a collection of randomly distributed wireless mobile nodes without depending on a centralized administration or an existing network infrastructure [
Initially, a fuzzybased priority scheduler was proposed by Gomathy et al. [
This proposed MFPAFSPS Mechanism completely focuses on the utilization of the fuzzy logic concept to estimate the priority index of the packets. The proposed scheduler utilizes three parameters that include data rate, SignaltoNoise Ratio (SNR) and queue length as input and the fuzzy logic integrates these parameters to determine the priority of the packet. The complete workflow of the proposed MFPAFSPS Mechanism is presented in
The proposed MFPAFSPS Scheme uses fuzzy logic as it is the potential to implement the preferences and experiences through membership rules and membership functions. This mathematical model adopts the merits of the Takagi–Sugeno–Kang (TSK) inference system that utilizes a complete rule base that envelops the entire rule base of the packet scheduling process. It utilizes the datadriven rulebased generation strategy that aids in supporting the characteristics of the TSK inference system. However, this TSK inference system lacks inheriting selflearning capabilities from the developed knowledgebased design for the packet scheduling process. Thus, Modified Firefly Optimization Algorithm (MFOA) is included to improve the selflearning capabilities of the TSK inference system.
In this proposed scheduler, trapezoidal and triangular membership functions are utilized due to their low computational complexity and simplicity. The linguistic variables considered with the input variables of data rate, SNR and queue length are low (L), medium (M) and high (H). The membership function associated with input data rate, SNR and queue length is presented in
The 27 conditional rules, formulated with three input parameters (data rate, SNR and queue size), utilized for this proposed fuzzy MFPAFSPS scheduler are presented in
This proposed MFPAFSPS scheduler utilizes the Takaki Sugenobased Fuzzy inference engine for constructing the fuzzy index (priority index), which is useful for estimating the packet priority during the scheduling process with the added advantage of handling the uncertain data as depicted in
Suppose a fuzzy rule based on the Takaki SugenoKang (TSK) inference engine consists of n rules and each has k antecedents.
where
This TSK inference engine facilitates the inference process through the following process.
where
where,
where
From
Finally, the output of the TSK fuzzy inference engine needs to be optimized before the process of defuzzification. In this proposed fuzzy scheduler, the process of optimization is achieved based on Modified Firefly Algorithm (MFOA)based optimization as explained in the subsequent section.
Once the raw rule base is constructed, it needs to be potentially optimized for successful finetuning of the membership functions using a significant metaheuristic optimization algorithm. At this juncture, Modified Firefly Optimization Algorithm (MFOA) is utilized in this proposed scheduler for attaining rule base optimization. In particular, the Tidal forceimproved firefly algorithm [
where
where,
When a firefly moves towards another firefly based on the degree of attraction attributed to its brightness factor, the movement of the fireflies is modelled based on
In this proposed scheduler, the FOA algorithm is improved based on the inclusion of the Tidal force formula to handle the basic algorithms’ shortcomings. The tidal force represents the force quantified in a scenario in which an object (Tidal water) completely depends on the impact of the gravitational impact of another twoobject mass (Earth and Moon). The tidal force is inversely proportional to the square of the distance between two objects, while the gravitational attractive force is inversely proportional to the square of the distance from the objects. Thus, the tidal force (
where,
In this proposed fuzzy scheduler, tidal force is included in the primitive firefly algorithm for obtaining the global minimum value with minimized generations. If the population is
In this context, the lower and upper threshold of the distance between any fireflies (fuzzy rules comparison) in each ‘
Then the tidal force in each ‘
The tidal force and firefly algorithms are utilized mutually for sustaining the balance between exploitation and exploration.
In this proposed scheduler, the centre of gravity (COG) is utilized for the process of Defuzzification Process. The TSK fuzzy consists of five points of output corresponding to output (very low (VL), low (L), medium (M), high (H) and very high (VH)), which is considered to be a constant. It is also identified that the output of the fuzzy inference process is a constant, on par with the fuzzy set considered during the evaluation of rules.
As a result, the proposed MFPAFSPS Mechanism achieved the optimal process of packet scheduling through the parameters of data rate, SNR, and queue length as input. It adopted the concept of fuzzy logic and integrated them for estimating the priority of the packet depending on the Takaki Sugenobased Fuzzy inference system. This adopted inference system played an anchor role in calculating the firing strength associated with each rule of inference, estimating the sub output attained for each possible formulated rule and determining the complete set of all suboutputs from the defined collection of rules. However, the defined rules are optimized in the inference engine based on the merits of the modified firefly optimization algorithm. Finally, the optimized rules aided in determining the output of the TSK fuzzy inference engine through the aggregation of the fuzzy sets and the defuzzification process that was applied.
The proposed MFPAFSPS mechanism, and the benchmarked schemes, are evaluated through OPNET modeller and verified using MATLAB fuzzy toolbox with different network loads of constant bit rate (CBR) and variable bit rate (VBR) data traffic. The simulation environment is modelled using Optimized Network Engineering Tools (OPNET) simulator with a network of 200 mobile nodes that are randomly distributed within a terrain area of 1000 × 1000 square meters. A channel capacity of 2 Mpbs is selected with each mobile node’s radio propagation range set to 250 m. The simulation experiments are conducted with multiple runs consisting of different seed values corresponding to each scenario and the data is collected and averaged over the simulation runs. In this simulation, each source mobile node is made to transmit data packets with CBR and VBR data traffic at a minimum rate of 20 packets/second to 60 packets/second.
The output membership functions for TSK are presented as follows: The randomization parameter of the firefly algorithm, fixed light absorption and attractiveness coefficient is set to 0.2, 1 and 1, respectively at the initial iteration. The two parameters are such that a tolerance of 104 and a maximum number of iterations of 3000 are used for halting the functions depending on the dimensions considered for evaluations. The complete experiments are run 50 times to prevent the influence of the initially set parameters during the evaluation process. In specific, the output membership functions for TSK refer to Type1.
The proposed MFPAFSPS and the benchmarked DPSVAM, SVMPS and DPSF schemes are compared based on packet delivery ratio, throughput, endtoend delay, and energy consumption with different CBR data traffic rates.
In the second part of the investigation, the proposed MFPAFSPS, and the benchmarked DPSVAM, SVMPS and DPSF schemes are compared using packet delivery ratio, throughput, endtoend delay and energy consumption with different VBR data traffic rates.
The packet delivery rate of the proposed MFPAFSPS scheme with optimization under CBR data traffic was visualized to be increased by 21.38%, while an improvement of 15.68% only was identified without optimization. Further, the throughput of the proposed MFPAFSPS algorithm with optimization under CBR data traffic was estimated to be improved by 18.27%, as opposed to 12.48% without optimization. Endtoend delay facilitated by the proposed MFPAFSPS technique with CBR data traffic is reduced by 24.72%, while a reduction of 17.26% was determined without optimization. Moreover, the energy consumption enabled by the proposed MFPAFSPS technique with CBR data traffic is considerably minimized by 19.38%, while a reduction of 13.26% was confirmed without optimization. In addition, the packet loss provisioned by the proposed MFPAFSPS technique with CBR data traffic is also drastically minimized by 20.64%, while a reduction of 16.36% is observed without optimization. The packet delivery rate of the proposed MFPAFSPS scheme with optimization under VBR data traffic was confirmed to have been increased by 15.64%, while an improvement of 11.21% only was observed without optimization. Throughput of the proposed MFPAFSPS algorithm with optimization under VBR data traffic was identified to have been enhanced by 10.16%, while an improvement of 8.42% was determined without optimization. Furthermore, endtoend delays facilitated by the proposed MFPAFSPS technique with VBR data traffic were reduced by 19.43%, while a reduction of 15.12% was determined without optimization. The energy consumption enabled by the proposed MFPAFSPS technique with VBR data traffic was considerably minimized by 16.34%, while a reduction of 10.64% was confirmed without optimization. In addition, the packet loss provisioned by the proposed MFPAFSPS technique with VBR data traffic is also potentially minimized by 17.16%, while a reduction of 11.34% is visualized without optimization. As seen, there is a marked improvement both under CBR and VBR data traffic when the proposed MFPAFSPS scheme with optimization is used.
The accuracy of the proposed MFPAFSPS scheme with Sugeno fuzzy inference engine under CBR data traffic was identified to have improved by 11.21%, while Mamdani fuzzy inference engine if used, showed only an improvement of 7.32%. The precision of the proposed MFPAFSPS approach with Sugeno fuzzy inference engine under CBR data traffic was identified to have improved by 13.65%, while Mamdani fuzzy inference engine if used, exhibited only an improvement of 9.42%. In addition, the recall of the proposed MFPAFSPS approach with Sugeno fuzzy inference engine under CBR data traffic was confirmed to get enhanced by 12.68%, while Mamdani fuzzy inference, if used, exhibited only an improvement of 8.39%. This enhancement in performing the proposed MFPAFSPS scheme with Sugeno fuzzy inference engine is mainly because of its potential ability in handling CBR data traffic packets and reduced computational complexity compared to the Mamdani fuzzy inference engine.
The accuracy of the proposed MFPAFSPS scheme with Sugeno fuzzy inference engine under VBR data traffic was enhanced by 10.32%, while Mamdani fuzzy inference engine if used, showed only an improvement of 6.54%. The precision of the proposed MFPAFSPS approach with Sugeno fuzzy inference engine under VBR data traffic was improved by 11.28%, while Mamdani fuzzy inference engine if used, exhibited only an improvement of 8.54%. In addition, the recall of the proposed MFPAFSPS approach with Sugeno fuzzy inference engine under VBR data traffic was confirmed to be enhanced by 11.42%, while Mamdani fuzzy inference, if used, exhibited only an improvement of 7.28%. This improvement by the proposed MFPAFSPS scheme with Sugeno fuzzy inference engine is mainly because of its adaptability in handling VBR data traffic packets.
In this section of the investigation,
Pause time (s)  Mean PDR  

MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  0.982  0.964  0.952  0.946 
150  0.981  0.956  0.942  0.948 
300  0.976  0.948  0.940  0.932 
600  0.972  0.937  0.934  0.912 
800  0.968  0.934  0.928  0.911 
1000  0.964  0.931  0.922  0.906 
Pause time (s)  Mean throughput (packets/s)  
MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  1.98  1.62  1.57  1.52 
150  2.16  1.74  1.68  1.62 
300  2.34  1.89  1.74  1.68 
600  2.79  2.34  2.26  2.13 
800  2.88  2.24  2.18  2.11 
1000  2.96  2.48  2.29  2.24 
Pause time (s)  Mean endtoend delay (s)  
MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  2.24  3.42  3.56  3.78 
150  2.12  3.24  3.48  3.76 
300  2.18  3.64  3.54  3.68 
600  2.21  3.22  3.44  3.72 
800  2.16  3.42  3.39  3.84 
1000  2.19  3.38  3.36  3.82 
Pause time (s)  Mean energy consumption (joules)  
MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  3.98  5.54  6.89  7.46 
150  4.86  6.78  7.24  8.58 
300  5.68  7.96  8.54  9.59 
600  6.34  8.32  9.78  10.42 
800  7.24  9.24  10.24  11.82 
1000  8.68  11.46  11.68  12.76 
Pause time (s)  Mean PDR  

MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  0.968  0.944  0.932  0.921 
150  0.964  0.946  0.930  0.918 
300  0.961  0.938  0.928  0.912 
600  0.958  0.927  0.926  0.906 
800  0.951  0.914  0.921  0.904 
1000  0.948  0.901  0.918  0.902 
Pause time (s)  Mean throughput (packets/s)  
MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  1.82  1.54  1.42  1.34 
150  2.04  1.65  1.54  1.42 
300  2.12  1.76  1.64  1.56 
600  2.54  1.88  1.82  1.78 
800  2.65  2.12  1.97  1.84 
1000  2.82  2.28  2.04  1.96 
Pause time (s)  Mean endtoend delay (s)  
MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  2.12  2.86  3.12  3.24 
150  2.04  2.84  3.16  3.22 
300  2.02  2.79  3.18  3.21 
600  2.06  2.85  3.15  3.25 
800  2.11  2.83  3.13  3.23 
1000  2.10  2.89  3.17  3.26 
Pause time (s)  Mean energy consumption (joules)  
MFPAFSPS  DPSVAM  SVMPS  DPSF  
50  4.78  6.54  7.89  8.98 
150  5.86  7.78  8.98  9.76 
300  6.68  8.96  9.98  10.21 
600  7.34  9.32  10.78  11.86 
800  8.24  10.24  11.24  12.82 
1000  9.68  10.46  12.64  13.45 
The packet delivery ratio of the proposed MFPAFSPS scheme is identified to be improved by an average of 8.21% and 7.46% for the CBR and VBR data traffic. The throughput of the proposed MFPAFSPS scheme gets enhanced, on average, by 7.42% and 6.21%, and the endtoend delay in the proposed MFPAFSPS scheme is systematically reduced, on average by 9.36% and 8.39%. In addition, the energy consumption of the proposed MFPAFSPS scheme is inferred to be significantly minimized, on average by 8.42% and 7.38%. This superior performance of the proposed MFPAFSPS scheme with different pause times is mainly achieved because of the diminished complexity of the Sugeno fuzzy inference engine used for the prioritybased packet scheduling process. In addition,
Number of packets  Mean PDR  

MFPAFSPS  FBRPS [ 
ABOMLMDSS [ 
APA [ 

200  0.991  0.978  0.956  0.932 
400  0.986  0.956  0.943  0.921 
600  0..981  0.942  0.932  0.912 
800  0.976  0.937  0.923  0.904 
1000  0.954  0.924  0.912  0.896 
Number of packets  Mean throughput (packets/s)  
MFPAFSPS  FBRPS [ 
ABOMLMDSS [ 
APA [ 

200  1.56  1.44  1.39  1.32 
400  1.53  1.41  1.36  1.28 
600  1.49  1.38  1.33  1.23 
800  1.46  1.34  1.28  1.21 
1000  1.42  1.32  1.23  1.17 
Number of packets  Mean endtoend delay (s)  
MFPAFSPS  FBRPS [ 
ABOMLMDSS [ 
APA [ 

200  1.76  1.98  1.84  1.94 
400  1.62  1.86  1.74  1.86 
600  1.54  1.76  1.65  1.78 
800  1.42  1.65  1.56  1.74 
1000  1.38  1.52  1.49  1.62 
Number of packets  Mean energy consumption (joules)  
MFPAFSPS  FBRPS [ 
ABOMLMDSS [ 
APA [ 

200  3.98  4.59  5.12  5.26 
400  4.06  4.68  5.24  5.34 
600  4.21  4.74  5.38  5.49 
800  4.32  4.87  5.49  5.57 
1000  4.37  4.98  5.57  5.64 
The endtoend delay of the proposed MFPAFSPS scheme is minimized by 9.12%, 10.76% and 11.98%, this is a vast improvement over the benchmarked FBRPS, ABOMLMDSS and APA schemes. In addition, the mean energy consumption of the proposed MFPAFSPS scheme is improved by 8.26%, 9.42% and 11.42%. In addition, the performance validation of the proposed MFPAFSPS scheme, and the benchmarked FBRPS, ABOMLMDSS and APA approaches are conducted using a oneway ANOVA test concerning a confidence interval of 95%. In this process of validation, the samples related to the mean energy consumption were identified for the proposed MFPAFSPS scheme and the benchmarked FBRPS, ABOMLMDSS and APAbased packet scheduling algorithms were considered for investigation. It is identified from the descriptive investigation that the proposed MFPAFSPS scheme is capable enough of achieving the highest mean score of 1.748.
The pvalue of significance based on the ANOVA test is 0.000, which is less than 0.05 (0.000 < 0.005). Hence, the null hypothesis (which states that the mean value of energy consumption related to the proposed MFPAFSPS scheme, and the baseline algorithms are equal) is rejected. Thus, the alternative hypothesis proved that the proposed MFPAFSPS scheme is significantly on par with the benchmarked packet scheduling algorithms used for investigation.
In this paper, MFPAFSPS was contributed as an optimized fuzzybased packet scheduling technique with the merits of Sugeno fuzzy inference engine possibly being finetuned by the MFOA optimization algorithm. The simulation results of the proposed MFPAFSPS confirmed an improvement in packet delivery rate by 23.84%, throughput by 18.94%, reducing endenddelay by 20.74% and energy consumption by 19.62%, compared to the benchmarked schemes with respect to CBR data traffic. The proposed MFPAFSPS is also determined to enhance the packet delivery rate by 13.28%, throughput by 12.39%, reducing endenddelay by 13.84% and energy consumption by 12.62%, compared to the benchmarked schemes with respect to VBR data traffic. The results also portrayed that the MFPAFSPS approach with Sugeno fuzzy inference engine improved the accuracy by 6.32%, precision by 5.48% and recall by 7.38%, compared to the utilization of the Mamdani inference engine. The proposed MFPAFSPS approach to optimization using MFOA confirmed an excellent performance on par with the proposed scheme without the inclusion of the optimization process.
The authors received no specific funding for this study.
The authors declare that they have no conflicts of interest to report regarding the present study.