(PDF) MD-MARS: Maintainability Framework Based on Data Flow Prediction Using Multivariate Adaptive Regression Splines Algorithm

Received 11 January 2023, accepted 25 January 2023, date of publication 30 January 2023, date of current version 3 February 2023. Digital Object Identifier 10.1109/ACCESS.2023.3240504 MD-MARS: Maintainability Framework Based on Data Flow Prediction Using Multivariate Adaptive Regression Splines Algorithm in Wireless Sensor Network MEENA PUNDIR1 , JASMINDER KAUR SANDHU2 , DEEPALI GUPTA1 , PUNIT GUPTA 3, SAPNA JUNEJA 4 , ALI NAUMAN 5 , AND AMENA MAHMOUD 6 1 Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab 140401, India 2 Department of Computer Science and Engineering, Chandigarh University, Gharuan, Mohali 140413, India 3 School of Computer Science, University College Dublin, Dublin 4, D04 V1W8 Ireland 4 International Islamic University, Kuala Lumpur 53100, Malaysia 5 Department of Information and Communication Engineering, Yeungnam University, Gyeongsan-si, Gyeongsangbuk-do 38541, South Korea 6 Faculty of Computers and Information, Kafrelsheikh University, Kafr El-Shaikh 33516, Egypt Corresponding author: Punit Gupta (

) ABSTRACT The demand for Wireless Sensor Networks is increasing day by day because of their diverse nature. Due to the limited energy, it is a complex task to retract the sensor node after deployment. So, there is a requirement for network maintainability before the deployment phase for its smooth working. It is achieved in three phases: hardware of the sensor node, communication and external environmental phase. This paper focuses on network maintainability in the communication phase. A novel framework MD-MARS is presented to enhance the network maintainability. This framework is classified into three phases namely analysis of performance parameters, data flow optimization and maintainability evaluation. In the initial phase, the performance parameter is analyzed using NS2 simulator. The next phase deals with data flow optimization using a machine learning algorithm. It reduces congestion and enhances network performance. The proposed algorithm is finely tuned to different degrees using the Grid Search approach to achieve the highest accuracy. The best model is selected based on accuracy and minimizes the prediction error. This algorithm predicts with the highest accuracy of 99.83%, lowest being 21.17%. Maintainability is achieved in the last phase using the total time taken to optimize the data flow. Several observations of repair time are determined for the best-tune model during the prediction of optimized data flow. These observations are used to calculate the mean time to repair, standard deviation, probability density function, maintainability and repair rate. The maximum maintainability achieved in this paper is 97.67% at a repair time of 26.07 milliseconds. INDEX TERMS Data flow prediction, maintainability, multivariate adaptive regression splines (MARS), Quality of Service, repair time, wireless sensor network. I. INTRODUCTION environmental monitoring, prediction of natural disasters, The rapid growth of smart sensors has enabled Wireless military surveillance, Internet of Things (IoT), flora and Sensor Networks (WSNs) usage in diverse applications such fauna [1], [2], [3], [4]. Maintainability is a significant param- as health care, industrial monitoring, urban monitoring, eter of Quality of Service (QoS) which is mandatory in a real-time environment [5], [6]. It is defined as ‘‘the ability The associate editor coordinating the review of this manuscript and of system under given conditions of use, to be retained in, approving it for publication was Guangjie Han . or restored to, a state in which it can perform a required This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ 10604 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction probability density function (PDF) and repair rate is con- sidered time-based parameters of maintainability. Economic based parameters deal with user-specific layers. It comprises direct maintenance cost/hour and direct maintenance man- hours/hour [18]. These issues have attracted researchers to work on maintainability parameter in WSN. In this paper, maintainability is estimated at the designing phase of the net- work which improves the maintainability in the operational phase. In this paper, it is evaluated based on performance attributes in terms of time-based parameters such as Mean Time to Repair (MTTR) and repair rate. The maintainability depends on various factors demon- strated in FIGURE 2. It is divided into three phases as follows [19]: Hardware of Sensor Nodes: This phase deals with the designing of hardware sensor nodes. The energy of the sensor FIGURE 1. The Anatomy of Maintainability [8]. nodes is limited and depleted during working operation. The maintainability of the network is directly affected by power failure. Generally, simple nodes are designed for WSN due function, when maintenance is performed under given con- to hardware cost. There is a maximum chance of simple node ditions and using stated procedures and resources’’ [7]. failure in an adverse environment. FIGURE 1 represents an anatomy of maintainability along Communication: The various factors affect communica- with its threats, attributes and definitions [8]. Threats are tion such as data flow, topology, packet loss and transmission unlawful activities that main aim is to breach information. delay. When multiple nodes transmit information simultane- It can be accidental or intentional which leads to network ously in a limited bandwidth, then a collision will occur which failure. Maintainability is not a single measure, it is evaluated increases the data loss rate and leads to poor maintainabil- based on several attributes such as performance, fault tol- ity. Due to the self-organizing characteristic of WSN stable erance, availability, reliability, safety and security. Network topology should be considered [20]. Adjusting the data flow performance deals with the quality of the network [9]. Fault mechanism reduces packet collision and packet loss. tolerance is the capability of the network to work smoothly External Environment: WSN works in harsh environ- in the presence of faults and is correlated to reliability ments such as outer space, wild forests, oceans and volcano [10], [11]. Availability is ‘‘the ability of a network to be in regions where external factors affect the normal working of a state to perform a required function at a given instant of the network such as geographical factors, weather factors and time within a given time interval; assuming that the external electromagnetic interference. resources if required, are provided’’. Reliability is defined as The system workflow is shown in FIGURE 3. In the initial ‘‘a measure of the continuity of correct service’’ [12]. Safety phase, sensor nodes are deployed based on Relative Identifi- deals with the harmless state of the network. Security is ‘‘a cation and Direction-Based Sensor Routing (RIDSR) topol- process to design an activity to protect the network from ogy. This topology is reliable and energy-efficient [21], [22]. unauthorized users’’. It provides integrity, confidentiality and The primary data is generated using NS-2.35 simulator based authenticity [13]. Integrity belongs to the consistency of on eleven performance parameters [12]. These parameters are information; confidentiality deals with sensitive information analyzed at the network layer. In the next step, the reliability and authenticity is the process of user vetting through their of network is examined. If the working of the network is credentials. It provides several essential and non-essential smooth then there is no need for data flow optimization. But services based on applications. These services are performed if performance is hampered then the prediction of optimized across the network such as fault resistance, fault recognition data flow is performed using Multivariate Adaptive Regres- and fault recovery. It is a challenging task to maintain the sion Splines (MARS) algorithm. It includes the basic MARS good functioning of WSNs due to the stochastic behavior model and the hyperparameters based MARS model. Hyper- of these networks [14], [15], [16]. The unreliable nodes can parameter models are selected based on the Grid Search cause network failure and affect the network maintainabil- approach. Hyperparameters are tuned at different degrees ity. Here, QoS needs serious efforts to make the network such as degree 1, degree 2 and degree 3. The best-tune model reliable and efficient with optimal packet delivery time with is selected based on the highest accuracy to achieve optimized the minimum possible failure rate. Maintainability can be data flow. The total time taken for optimal DF is known as achieved from two perspectives: Time based parameters and time to repair or restore time. Time to repair observations Economic based parameters [17]. Time based parameters deal are collected for the best-tuned model. These observations with network-specific layers. It is evaluated using optimal estimate the MTTR value. MTTR further evaluates the stan- data flow. Mean time to repair (MTTR), standard deviation, dard deviation. MTTR and standard deviation are used to VOLUME 11, 2023 10605 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction FIGURE 2. Factors Affecting the Maintainability [20]. FIGURE 3. System Workflow. determine the probability density function (PDF). It is used to • Primary dataset is generated using NS-2.35 simulator. calculate the maintainability across the WSN. Maintainability It includes several parameters such as Sent Packets (SP), and PDF are used to estimate the repair rate. Packet Delivery Ratio (PDR), Received Packets (RP), Routing Overhead (RO), Routing Agent (RA), Packet Forfeit (PF), Average Path Length (APL), Data Flow A. CONTRIBUTION (DF), Number of Nodes (NN), Throughput (TH) and This research work emphasizes data flow parameter (DF) Protocol Name (PN). DF is act as the target param- that improves the network performance in terms of maintain- eter and the other ten parameters are used as input ability. This DF optimization minimizing the count of fault parameters. and regulates the flow of data [23]. It maintains the good • MARS model is used to optimize the DF parame- functioning of a network where sensor is deployed in specific ter and collects the samples of repair time during DF topology. ML algorithm provide generalized solution for data optimization. optimization using accuracy. • The repair time determines the maintainability using The acronyms are listed in TABLE 1 for the readability of normal distribution method. the researchers. The contribution of the paper is summarized as: B. ORGANIZATION • MD-MARS framework is presented to improve network The paper is organized as: Section I presents the intro- maintainability.in quantitative manner. duction to network maintainability and also describes the 10606 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction TABLE 1. Acronym. MD-MARS for maintainability analysis. It includes the for- mulation of maintainability, dataset and MARS ML algo- rithm. The performance evaluation and detailed discussion have been described in Section III. Section IV presents findings of the research work and Section V concludes the article with future research directions. II. RELATED WORK Several prediction models are used by researchers to esti- mate maintainability. It can be determined in various aspects such as software maintainability as well as network maintainability. Software maintainability is crucial for the success of soft- ware. It is predicted using distinct ML approaches [23]. It includes fault correction inclusion of new code and removal of obsolete code [24]. An imbalanced dataset generates low maintainability due to biased predictions. The safe-level- SMOTE approach is used to preprocess the unbalanced dataset before software maintainability prediction [25]. Code smell issue is addressed in an article [26]. It is a confusing, complex and unstructured code of the software. This code is identified by a fuzzy genetic based automatic refactoring approach. Naïve ayes classifier corrects the software compo- nent and reduces the fault rate [27]. Dependency Injection mechanism is used to improve maintainability [28]. Network maintainability is performed by Fault Management Frame- work (FMF). It includes fault identification, tolerance and recovery mechanism [29]. These faults can cause failure to occur in the network. Different type of fault is identified by distinct mechanisms that achieve network reliability [30]. Reliability is correlated with maintainability and availabil- ity [31], [32]. Network maintainability depends on several factors such as communication and external factors [33]. Net- work maintainability is determined from two perspectives: economic and time-based parameters. Economic parameters- based maintainability is evaluated using a Bayesian net- work [15]. Time based maintainability is achieved in terms of repair rate. The data discretization mechanism predicts the optimal data flow [34]. An optimized data rate pro- vides a congestion-free environment to improve communica- tion [35]. It maintains network reliability. The above articles have a specific framework or model based on their problem formulation. Our proposed framework provides a generalized efficient framework to enhance maintainability using data flow optimization. The previous literature is summarized in tabular form as TABLE 2. III. PROPOSED FRAMEWORK FOR MAINTAINABILITY Reliable network performance is mandatory for the good functioning of the network [46], [47]. The presence of fault occurrence is more prone in WSNs as compared to traditional wireless networks. This fault generates an error that leads to network failure and depletes network performance [48]. Maintainability is a parameter which is affected by an acci- acronyms in tabular format. Section I-A elaborates on related dental failure. Here, MD-MARS framework is proposed to work in detail. Section II presents an efficient framework enhance the network performance shown in FIGURE 4. The VOLUME 11, 2023 10607 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction TABLE 2. Literature survey on maintainability. 10608 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction TABLE 2. (Continued.) Literature survey on maintainability. proposed framework is divided into three phases: network the base station. In each sector, the manager node is present. parameters analysis using simulation, data flow optimization Each sensor node is represented with its hop ID. If the man- using MARS algorithm and maintainability achieved using ager node and sensor node are present in the same sector with time to repair. communication range, then hop ID 1 is assigned to the sensor node. It determines the shortest distance for routing with less A. ANALYSIS OF NETWORK PARAMETERS complexity. This network configuration is performed using This is the initial phase of the network where sensors are NS-2.35 simulator. The simulation parameters are shown randomly deployed based on RIDSR topology to provide reli- in TABLE 3. The channel type used for communication is able and energy-efficient routing in a static environment [22]. wireless. Two-Ray Ground is used as a radio-propagation In RIDSR, the sensing area is divided into sectors. A base model for routing from source to destination node. Omni- station provides a unique sector ID to every sector based on directional is selected as the antenna model. DropTail and the quadrant name and provides an estimated distance from CMUPriQueue are used in Interface Queue. As the name VOLUME 11, 2023 10609 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction FIGURE 4. MD-MARS Framework. TABLE 3. NS-2.35 simulation parameters. TABLE 4. Dataset description. Based on these simulation parameters dataset is con- suggests, DropTail drops packets when the interface queue structed [12]. It comprises 10,000 records with eleven per- is full. CMUPriQueue is used to prioritize the packets. The formance parameters. The description of these parameters is maximum packets interface queue is set to 150. The number shown in TABLE 4. The values of SP, RP, RA, RO, APL, of nodes considered in the network design is between 5 to 50. PDR, PF and TH are measured using simulation. These values 1000 m × 1000 m area is selected for simulation. Dynamic are evaluated using trace files generated during simulation. Source Routing (DSR) and Ad-hoc On-Demand Distance These files are analyzed by awk scripts which are used for Vector (AODV) protocols are used for routing. AODV and generating reports. The values of PN, NN and DF are user- DSR are reactive and demand-driven routing protocols that specific. The dataset sample is represented in TABLE 5. This initiate the discovery of a route on demand [49]. The reactive dataset is free from missing and redundant values. protocols outperform as compared to proactive protocols. The performance parameters are used to optimize DF to It generates less routing overhead and consumes minimum achieve maintainability. Ten parameters are used as an input resources. The data flow range lies between 0.1 to 10Mbps variable and DF behaves as the target variable. These param- and the simulation time is set to 20 milliseconds. eters are correlated with each other and their diagrammatic 10610 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction TABLE 5. Dataset sample. representation of correlation is shown in FIGURE 5. The cor- an inverse relationship between parameters. The strength relation is used to determine the linear relationship between depends on the value of r. If the value of r lies between two variables or features of a dataset. It is calculated as: 0.7 to 1, then it belongs to a strong relationship. A value PNI less than 0.3 shows weak relationship. If the value of r i=1 (xi −x̄)(yi − ȳ) is 0 then it means there is no linear relationship between r = qP (1) NI 2 PNI (x i=1 i − x̄) (y i=1 i − ȳ) 2 parameters. DF is strongly associated with the PF variable. When DF is optimized then it will minimize PF across the where r is correlation coefficient, x represents actual value, x̄ network [12]. depicts the mean of actual values, y indicates predicted value, ȳ depicts the mean of predicted values and NI represents the count of instances. B. DATA FLOW OPTIMIZATION Here, a matrix is created based on Pearson Correlation Data Flow optimization is the second phase of the pro- that determines the relationship between pair of parame- posed framework. The complete methodology is shown in ters [50], [51], [52]. Pearson Correlation Matrix (PCM) of FIGURE 7. SP, RP. PF, RA, RO, PDR, APL, NN, PN and the dataset is represented in FIGURE 6. It measures the TH are input variables. MARS model is applied to the dataset relationship between variables of the dataset. It comprises which is partitioned into 70:30 ratio. 70 percent of data is two properties strength and direction. Strength deal with utilized for training and 30 percent is used for validating the the linear relationship and direction deals with the direct data. The basic MARS model (without tuning) and tuned or inverse relationship among variables. The range of r lies MARS models are applied to achieve optimal DF. Hyper- between +1 to −1. The + sign represents a positive or parameters are the explicit parameters used in the learning direct relationship between parameters and the – sign denotes process of the model. It strengthens the training process. The VOLUME 11, 2023 10611 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction FIGURE 5. Diagrammatic Representation for correlation of dataset features. FIGURE 6. Correlation Matrix. maximum degree of interaction and count of retained terms DF. The total time taken during DF optimization is used in are the hyperparameters of the MARS Model. These param- phase 3. eters are tuned at different degrees to achieve an optimal result. Tuning is performed using a Grid Search Algorithm 1) MULTIVARIATE ADAPTIVE REGRESSION SPLINES that builds every combination of hyperparameters and esti- ALGORITHM (MARS) mates each model. At last, it provides the best combination MARS algorithm is a flexible regression model that of hyperparameters to reduce prediction error. The differ- resolves the complex problem of high dimensionality on ent degrees of interaction such as degree 1, degree 2 and a large scale. This model uses lesser variables to main- degree 3 are applied to MARS training that provides a distinct tain a relationship between dependent and independent vari- trained model. The best-tune model is the best-fit model that ables [53], [54], [55]. It utilizes recursive auto-regressive and is selected based on accuracy for the prediction of optimal projection tracking methods. MARS comprise multiple spline 10612 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction FIGURE 7. Methodology to predict optimized data flow. functions which are known as basis function (BF ). Algorithm 1 : Multivariate Adaptive Regression Splines Algorithm u = u1 , u2 , u3 . . . . . . . . . . . . . . . ..um (2) Input SP. RP. PF, RA. RO. PDR. APL, TH, PN, NN z = (f1 (u), f2 (u), f3 (u) . . . . . . . . . . . . fh (u)) + e (3) Output DF 1 Initialize intercept term. where z is the output variable dependent on the u parameter. 2 Construct Bp. Here, e represents an error vector (1 X h). 3 Call Forward Pass Algorithm. The main aim of MARS algorithm is to perform regression 4 Delete redundant Bp. analysis on a dataset using BF . It fits the best model for a 5 Call Backward Pass Algorithm. non-linear relationship among the parameters. It splits the 6 Select best model based on accuracy. dataset into smaller regions and each region behaves as a linear function. BF is applied at each region for best fit. MARS model is represented using basis function BF . Each spline function. BF comprises hinge functions and each hinge function is ( represented as a knot. (u − tN )+ u > tN [S N (uv(N ) − tN )]+ = (6) XK 0 otherwise ẑ = fˆK (u) = α0 + αk Bk (U ) (4) ( k=1 (tN − u)+ u < tN [S N (uv(N ) − tN )]+ = (7) where 0 otherwise YN Eqautions (9) and (10) show that there is a knot present Bk (U ) = [SN uv(N )− tN ) + . (5) due to the presence of two linear models. When the linear n model increases then the knot will be increased. But there is In MARS formula, ẑ is the predicted value of the DF param- a requirement for an optimal knot which gives the best results. eter. αk represents as a coefficient of a kth spline function, Algorithm 1 illustrates the MARS Algorithm. DF is an Bk (U) acts as a spline function and N depicts the count of output variable and the other 10 parameters are used as nodes. The value of SN is either a positive one (+1) or a an input variable. MARS algorithm includes three steps to negative one (−1). A positive one represents the function in achieve the output namely Forward Pass, Backward Pass and the right direction and a negative one shows function in the Model Selection. A forward mechanism is used to construct left direction. v(N) is the independent variable’s identifier. tN the BF that is required for optimum results. It splits the dataset is the node’s position. Here Bk (U) can be a single or multiple and applies the spline function to each region for best fit and VOLUME 11, 2023 10613 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction determine new BF . Due to the large count of BF in a Forward Algorithm 2 : Forward Pass Algorithm Pass generates an overfitted model. This issue is resolved by Input Intercept, Hinge function using a Backward Pass mechanism. It eliminates duplicates Output BF (term) BF and provides the best fit model with accuracy. Finally, 1 Construct Bp (term). the best model is selected from many models based on the 2 while there is no paired BF do accuracy parameter. 3 for all new pair of BF do 4 if pair of Bp give reduction in sum of square error, 2) FORWARD PASS ALGORITHM then In basis iteration (BI) zero, the first pair of BF is constant in 5 add pair of Bp. the MARS algorithm i.e. BF0 = 1 and every base iteration 6 else generates two BF when BI is greater than one (BI>1). 7 check next pair of Bp 8 end if B2BI −1 (u) = Bp (u)c(uv |R) (8) 9 end for B2BI (u) = Bp (u)c(uv |R̄) (9) 10 Each BF is multiplied with hinge function. R = (s, t)R̄ = (−s, t) (10) 11 end while where Bp (u) shows the previous iteration BF and uv behaves as an input variable. Here, t is the spline base’s node. At every Algorithm 3 : Backward Pass Algorithm iteration, the constructed model accuracy is affected by the Input BF node’s position. The total estimated time of the MARS model Output GRSq, Number of Remaining Term (nprunc) depends on the count of nodes. It is not feasible to calculate 1 Delete BF . each input data that can cause a very small distance to be 2 while there is large set of Bf do created between adjacent nodes. This issue can be avoided 3 for all Bf do by considering minimum step size D for every input variable. 4 if GCV value is large Its formula is defined as: 5 delete BF . 1 6 else D (b) = −log2 [− BIn(1 − b)]/2.5 (11) RN 7 best fit Bf . The range of b lies between 0.01 to 0.05 (0.05>b>0.01). 8 endif Model accuracy will not be affected after defining the min- 9 end for imum step size. It will become fast as well as minimize 10 end while calculation time to build a model. This model takes care of interaction among distinct functions and improves the model’s accuracy. During the building model, BF is contin- K is denoted as a count of BF , B represents a matrix of K −1 uous increases till the maximum value (Kmax ). X L, trace (B(BT B) BT )+1 is used as a count of effective coefficient in the model and a depicts as a coefficient of Kmax = 2XK ∗ (12) penalty.The optimal MARS model is selected based on the Algorithm 2 represents the forward pass algorithm. The value of GCV. The model which has a minimum GCV value, important point about this algorithm is that it produces a large that model is selected as the optimal MARS model. At last, count of BF that will generate results as overfitting. the formula of MARS model is achieved as: K X YN fˆK (u) = α0 + αk [SN uv(N )− tN ) + . 3) BACKWARD PASS ALGORITHM (15) n The Forward Iteration Pass constructs a large count of BF that k=1 produces overfit results and increases the model’s complexity. Algorithm 3 represents Backward Pass Algorithm. It pro- It doesn’t provide a generalized solution. This problem is vides a generalized solution to predict the output with solved by using Backward Pass Algorithm. It is a pruning accuracy. process that deletes BF which are generated during a forward pass based on Generalized Cross-Validation (GCV) criterion. 4) MODEL SELECTION It is used to penalized model complexity. It is defined as the process to determine the best-fit model for 1 lk=1 (zi − ẑi )2 P the predictive modelling problem. It can be selected based on GCV (K ) = (13) performance evaluation metrics such as correlation, coeffi- l l(1 − P(K ) l)2 cient of determination, root mean square error and accuracy. where P(K) represents a penalty function. 1) Correlation (r): It determines the relationship among all features of a dataset. The formula of correlation is −1 T P(K ) = trace(B(BT B) B ) + 1 + aK (14) represented as equation (1). 10614 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction 2) Coefficient of Determination ( R2 ): The primary result TABLE 6. Sample of repair time. of MARS is evaluated as a coefficient of determination. The range of R2 is between 0 to 1 (1> R2 >0). If the value of R2 is towards zero then it defines the failure of the MARS model. But if its value is near 1 then it shows the best fit to the MARS model. Mathematically, it is represented as the square of correlation. It is estimated as: R2 = r ∗ r (16) (iii) Root Mean Square Error (RMSE): RMSE represents the total amount of error that occurs between the predicted and actual output. The formula of RMSE is defined as: s PNI 2 i=1 (yi − xi ) RMSE = (17) NI TABLE 7. Performance evaluation. where y is the predicted output variable, x is the actual output variable and NI is the total count of instances. (iv) Accuracy: Accuracy determines the closeness between the actual and predicted value. The best model is selected for a specific problem based on accuracy [36]. It is estimated as: 100 XNI Accuracy = gi (NI i=1 1 if abs (yi − xi ) ≤ er gi = (18) TABLE 8. Comparative analysis for data flow optimization. 0 otherwise where yi is the predicted target output, xi is actual output, NI indicates the count of instances and er depicts an accept- able error. The selected MARS model provides samples of the restora- tion or repair time of the network. The total time taken to opti- mize the DF parameter is known as repair time or restore time. This parameter is used in phase 3 to evaluate maintainability. C. MAINTAINABILITY EVALUATION The observations of repair time are collected during optimiza- tion shown in TABLE 6. These values determine the MTTR, standard deviation, probability density function (PDF), maintainability and repair rate. The mathematical formulation of each parameter is dis- cussed below: Here, g(t) indicates the probability density function (PDF) or 1) MATHEMATICAL FORMULATION OF MAINTAINABILITY repair density function. It is defined as ‘‘the probability of ‘‘Maintainability is the probability that a failed system or faulty system or component is repaired to normal condition component will be restored or repaired to a specified con- in δt’’ [56]. It is calculated as: dition within a specified period of time when maintenance is ((MT ct i )−(MT ct ))2 " # − performed in accordance with prescribed procedures’’ [56]. 1 2(Std MT ct )2 It is estimated using the normal distribution method. This g (t = MT ct ) = √ e (20) method is used for the analysis of maintainability for straight- Std MT ct 2π forward repair actions. Straightforward action deals with MTcti is the individual maintenance action (repair time). The simple removal and replacement tasks. The formula of main- average maintenance of n observation is known as Mean Time tainability is expressed as [8]: To Repair (MTTR) and is calculated as: Z t P MT ct i MT (t) = g(t)dt (19) MT ct = (21) 0 n VOLUME 11, 2023 10615 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction FIGURE 8. Fitting of MARS Model. The median time to repair is equal to MTTR due to the specific percentage. It is expressed as: symmetry of normal distribution and is expressed as: P ^ MTMaxct = MTct + φStdMTct (24) MTcti ] MT ct = (22) φ is the value of the normal distribution function for the n percentage of maintainability function. It evaluates the main- The standard deviation of n observations during maintenance tainability. action is: s ^ MT Maxct − (MT ct ) P MT ct i − (MT ct ) 2 φ = z(t1−α ) = (25) Std MT ct = (23) Std MT ct n−1 The repair rate is defined as ‘‘it is the conditional proba- The maximum time to repair is defined as it the maximum bility that the component or system is repaired to specified time required to complete all maintenance actions for a function in (t, t+ δt) when the component or system fails at 10616 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction TABLE 9. Maintainability. time t’’ [57]. It is expressed as: 10-fold Cross-Validation generates optimal target output using tuning of hyperparameters. There are two significant g(t) hyperparameters namely the count of retained terms and the µ(t) = (26) degree of interaction. These hyperparameters are tuned to 1 − MT (t) three degrees based on the Grid Search algorithm. In our IV. RESULT AND DISCUSSION results, the cross-validated RMSE of three degrees is repre- MD-MARS framework evaluates network maintainability. sented in FIGURE 9. The predicted RMSE value at degree=1 Here, the dataset is generated using NS2 simulator [12]. is 0.26, degree=2 is 0.13 and degree=3 is 3.3. This shows that Simulation parameters are discussed along with dataset fea- degree=2 gives the best results in terms of RMSE. tures in Section II. MARS algorithm with different tun- TABLE 7 shows the comparison of performance in terms ing parameters is applied using R Studio for optimal data of RMSE, correlation, R2 and accuracy. The correlation of flow. FIGURE 8 represents the fitting of MARS model. MARS without tuning is 0.99, R2 is 0.99, RMSE value is In model selection, the x-axis represents the count of retained 0.26 and accuracy is 96%. At degree=1, the performance terms, the y-axis(right) indicates the count of used pre- parameter value is the same without tuning performance dictors and the y-axis (left) shows GRSq and RSq. GRSq parameter. At degree 2, the correlation is 1, R is 1, RMSE is a GCV R2 which is represented as a solid black line. is 0.13 and accuracy is 99.83. At degree 3, the correlation is It is the actual value of the data flow parameter. RSq 0.03, R is 0, RMSE is 3.3 and accuracy is 21.17. is a predicted value of the data flow parameter and is The final model is selected based on the accuracy of the represented as a red dotted line. FIGURE 8(a) shows a predicted model. Here, degree 2 shows the maximum accu- model selection based on MARS without tuning parame- racy of 99.83 as compared to other tuning degrees 1 and 3. ters. FIGURE 8(b), 8(c) and 8(d) represent model selection The MARS model with tuning (degree=2) is selected as the based on tuning parameters. FIGURE 8(a) and 8(b) comprise final model in the proposed framework. The final MARS 12 non-intercept terms. Additional retained term improves model includes four predictors of the dataset such as PF, the GCV R2 . Similarly, FIGURE 8(c) consists of 16 non- RA, RP and TH. These predictors show their importance intercept terms and FIGURE 8(d) shows 18 non-intercept as compared to other predictors. It is selected based on the terms. impact on GCV and Residual Sum of Squares (RSS) values. VOLUME 11, 2023 10617 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction TABLE 10. Comparative analysis for maintainability. probability density function (PDF), normal distributed func- tion z(t), maintainability MT(t) and repair rate µ(t) shown in FIGURE 9. RMSE. TABLE 9. The graphical representation of the probability density function, cumulative density function or maintainability and repair rate with respect to repair time is shown in FIGURE 12, 13 and 14. FIGURE 12 represents a plot of the normal distribution pdf of the repair time to optimize the data flow. FIGURE 13 represents a graphical representation of maintainability with respect to repair time. When maintainability is compared with the existing approaches then it performs well shown in TABLE 10. The proposed framework achieved maximum maintainabil- ity of 97.67% at a repair time of 26.07 milliseconds. FIGURE 14 represents the repair rate is directly proportional FIGURE 10. Importance of Predictors. to the repair time. It is increasing with increasing repair time. GCV is used for the trade-off between model complexity and best fit. RSS is a technique used to determine the level V. FINDING DISCOURSE of variance that occurs in the error term. The value of RSS The proposed framework evaluates network maintainability defines the level of model fitness. For high value, it is a poor quantitively using the normal distribution method. NS2 sim- fit and for low value, it is a better fit. But if the value of RSS is ulation scenario is created for a dataset. RIDSR topology zero, it defines the model as a perfect fit. FIGURE 10 shows is used for deployment which enables energy-efficient data that all four predictors have little change when the count of delivery from sensor nodes to a base station and also enhances terms is increased. the network lifetime. Eleven performance parameters are When accuracy is compared with existing techniques such analyzed using a trace file with awk scripts. DF is the core as random forest, weka lazy model, conditional inference parameter of the network that affects the network’s maintain- tree, ensemble model with equal weight [12], KNN [58], ability. It is used as a target variable. DF parameter range Bayesian [59], Ensemble Classifier [60] and enhanced deep lies between 0.1 MB to 10 MB. The high value of the DF reinforcement learning [61], it will show that the proposed parameter increases the congestion in the network due to the framework outperforms well shown in TABLE 8. FIGURE 11 limited bandwidth. The packet loss ratio is increased and shows the scatter plot relation between the actual and pre- leads to network failure. Similarly, the lower value of the dicted MARS model with and without tuning parameters. DF takes more time to reach the destination. The optimized FIGURE 11(a) and 11(b) show variations between the actual DF maintains the smooth functioning of the network. It is and predicted output. FIGURE 11(c) represents the best-fit optimized using the MARS algorithm. The variation of the relation between the predicted and actual model where the MARS model is used to optimize the DF parameter such tuning parameter is degree 2. FIGURE 11(d) shows the model as the basic model and the hyperparameter-tuned model at is poorly fit at degree 3. different degrees. Model selection with degree 2 shows the The total time duration to achieve optimized data flow is best results based on accuracy. It shows that there is very termed repair or restore time. The sample of repair time is less error between actual and predicted DF. It provides good collected during optimization at degree 2. It is expressed in results as compared to existing literature. The best tuned terms of milliseconds. This repair time is used to evaluate the MARS model provides distinct observations of repair time. 10618 VOLUME 11, 2023 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction FIGURE 11. Scatter Plot showing the relation between Actual and Predicted MARS Model based on Tuning Parameters. FIGURE 12. Plot of Normal Distribution pdf of Repair Time. FIGURE 13. Plot of Normal Distribution pdf of Repair Time. • Maintainability is evaluated through DF optimization Repair time is the core metric of maintainability. It uses the using the MARS algorithm. normal distribution method to achieve maximum maintain- • Normal distribution method is used to estimate the main- ability. The main novelty of this research work is: tainability in a quantified manner. VOLUME 11, 2023 10619 M. Pundir et al.: MD-MARS: Maintainability Framework Based on Data Flow Prediction approach shows better results in the comparison of existing approaches such as maintainability achieved using virtuality reality, analytic network process and super position degree using Bayesian, AHP and fuzzy. The proposed work has some limitations. It is limited to a small scale and provides the best results for a single parameter. The future direction of this research work is: • The more network parameters can be evaluated using the proposed framework such as availability and security. • This work emphasizes a small scale which can be extended to a large scale using new protocols. ACKNOWLEDGMENT (Meena Pundir and Ali Nauman contributed equally to this FIGURE 14. Plot of Repair Rate with respect to Repair Time. work.) REFERENCES VI. CONCLUSION AND FUTURE DIRECTION [1] D. Kandris, C. Nakas, D. Vomvas, and G. Koulouras, ‘‘Applications of Quality assurance is a popular and mandatory buzzword for wireless sensor networks: An up-to-date survey,’’ Appl. Syst. Innov., vol. 3, no. 1, pp. 14–37, Feb. 2022. real-time applications. It is a challenging task to configure the [2] S. M. Chowdhury and A. Hossain, ‘‘Different energy saving schemes in network that enhances QoS metrics and improves the network wireless sensor networks: A survey,’’ Wireless Pers. Commun., vol. 114, performance. It depends on various metrics such as through- no. 3, pp. 2043–2062, Oct. 2020. put, maintainability, reliability, latency, PDR and availability. [3] D. P. Kumar, A. Tarachand, and C. S. R. Annavarapu, ‘‘Machine learning algorithms for wireless sensor networks: A survey,’’ Inf. 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Chen, ‘‘A hybrid study of plasma sources and fabrication of micro- or nanostructured surfaces. method for evaluation of maintainability towards a design process Her awards and honors include the Frew Fellowship (Australian Academy of using virtual reality,’’ Comput. Ind. Eng., vol. 140, pp. 106227–106252, Science), the I. I. Rabi Prize (APS), the European Frequency and Time Forum Feb. 2020. Award, the Carl Zeiss Research Award, the William F. Meggers Award, and [63] Z. Li, Y. Li, L. Meng, and D. Meng, ‘‘Multisource data fusion analysis of the Adolph Lomb Medal (OSA). maintainability for overlapping degree high performance computing,’’ Sci. Program., vol. 2022, pp. 5643898–5643906, Jun. 2022. MEENA PUNDIR received the B.Tech. degree in IT from Kurukshetra University, Haryana, and the M.Tech. degree in CSE from Punjabi Uni- PUNIT GUPTA received the B.Tech. degree in versity, Punjab. She is currently pursuing the computer science and engineering from Rajiv Ph.D. degree in computer science and engineer- Gandhi Proudyogiki Vishwavidyalaya, Madhya ing with the Chitkara University Institute of Engi- Pradesh, in 2010, and the M.Tech. degree in com- neering and Technology, Punjab. She is having puter science and engineering (trust management approximately eight years of teaching experience. in cloud computing) from the Jaypee Institute Her research interests include wireless sensor of Information Technology (Deemed University), networks, machine learning, Quality of Service, in 2012. He is currently a Postdoctoral Researcher underwater wireless sensor networks, and network security. with the University College Dublin, Ireland. SAPNA JUNEJA received the master’s and Ph.D. JASMINDER KAUR SANDHU received the degrees in computer science and engineering from M.Tech. degree (Hons.) in CSE from Punjabi Uni- M. D. University, Rohtak, in 2010 and 2018, versity, Patiala. She is currently pursuing the Ph.D. respectively. She is currently a Professor with the degree in computer science and engineering with Department of Computer Science, KIET Ghazi- the Thapar Institute of Engineering and Technol- abad, India. She has more than 18 years of teaching ogy, Patiala. She is currently working as an Asso- experience. Her broad area of research is software ciate Professor and the Ph.D. Coordinator with the reliability of embedded systems. Her areas of inter- Department of Computer Science and Engineer- ests include software engineering, computer net- ing, Chandigarh University, Gharuan, Mohali. She works, operating systems, database management is having approximately 12 years of research and systems, and artificial intelligence. She has guided several research Thesis teaching experience. Her research interests include machine learning, ensem- of UG and PG students in computer science and engineering. She is editing ble modeling artificial intelligence, soft computing, dependability evalua- book on recent technological developments. She is having several papers tion, Quality of Service, wireless sensor networks, and ad-hoc networks. in various international journals of repute and various patents as well. Her She is an Active Reviewer of many reputed journals such as IEEE ACCESS current area of research is block chain technology, machine learning, and and International Journal of Machine Learning and Cybernetics (Springer). artificial intelligence. She has more than 50 publications in reputed SCI-Indexed Journals and International Conferences 2008 and the IEEE Electromagnetic Compatibility ALI NAUMAN received the M.Sc. degree in wire- Society Best Symposium Paper Award, in 2011. less communications from the Institute of Space Technology, Islamabad Pakistan, in 2016, and the Ph.D. degree in information and communication DEEPALI GUPTA is currently working as a engineering from Yeungnam University, Repub- Professor of research with the Chitkara Univer- lic of Korea, in 2022. He is currently working sity Research and Innovation Network (CURIN), as an Assistant Professor with the Department of Chitkara University, Punjab, India. She special- Information and Communication (ICE), Yeung- izes in software engineering, cloud computing, nam University, Republic of Korea. He has con- the IoT, and genetic algorithms. She has worked tributed to five patents and authored/coauthored with undergraduate and postgraduate students and three book chapters and more than 20 technical articles in leading jour- research scholars throughout her career and plans nals and peer-reviewed conferences. His research interests include artificial to continue to involve students in her research and intelligence-enabled wireless networks for tactile healthcare, multimedia, eager to participate in projects and guide indepen- and industry 5.0. His research interests also include resource allocation dent student’s research. She has published more than 120 research papers in for 5G and beyond-5G (B5G) networks, device-to-device communication national and international journals and conferences. Based on these areas, (D2D), the Internet of Everything (IoE), URLLC, tactile internet (TI), and she has guided many Ph.D. and M.E. scholars. She has worked at various artificial intelligence (AI). administrative positions such as the principal, the head (CSE), the dean academics, an IBM (Spoc), a remote centre coordinator (IITB), a coordinator for IITB spoken tutorial, an executive committee member at the Computer AMENA MAHMOUD received the master’s Science Division of Haryana State Centre (IEI), President Sangam Kala degree in virtual reality specification from the Group(Kurukshetra, Mohali and Chandigarh Chapter), Member of Anti- Computer Science Department, Helwan Univer- Ragging Committee, Academic Council, Faculty of Engineering and Tech- sity, Egypt, and the Ph.D. degree in bioinfor- nology, Board of Management, Chairperson SC/ST Cell of MMU, Sadopur, matics from the Computer Science Department, and the principal (MMGI, Sadopur). Mansoura University, Egypt. She is currently an She is an Active Member of various professional bodies such as IEI Assistant Professor with the Department of Com- (India), IETE, and ISTE. Apart from being an Editor-in-Chief of MMU puter Science beside being the Vice Director of journal, she is an editorial board member and a reviewer of various jour- the Quality Assurance Center, Kafrelsheikh Uni- nals. Recently, she received certificate of appreciation from The Institution versity, Egypt. She is currently a Researcher in of Engineers (India), Haryana State Centre acknowledging her valuable computer science and interested in bioinformatics, machine learning, and technical contribution rendered to the nation as a Tech Samaritan, during other topics such as pattern recognition, image processing, and natural COVID-19 Pandemic and reaffirming the credence of the profession of engi- language processing. neering on the occasion of 54th Engineers’ Day Celebration. Fundamental 10622 VOLUME 11, 2023