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1. (Research Scholar Department of Electronics Engineering, Fr. Conceicao Rodrigues College of Engineering, Agnel Technical Education Complex, Fr. Agnel Ashram, Bandstand, Bandra (West), Mumbai 400050, Maharashtra, India siddharthagoutam@gmail.com )
2. (Principal, Fr. Conceicao Rodrigues College of Engineering, Agnel Technical Education Complex, Fr. Agnel Ashram, Bandstand, Bandra (West), Mumbai 400050, Maharashtra, India srija@frcrce.ac.in)
3. ( Department of Science & Humanities, Fr. Conceicao Rodrigues College of Engineering, Fr. Agnel Ashram, Bandstand, Bandra (West), Mumbai - 400050, Maharashtra, India {prabavarthy, archana}@frcrce.ac.in)

Vertical handover (VHO), Vertical handover decision algorithm (VHDA), Decision matrix, Normalized matrix, Weight matrix, Analytic hierarchy process (AHP), Least cost function, Multi-attribute decision making (MADM)

## 1. Introduction

The telecommunication industry has changed because of the recent developments and growth in the field of wireless communications. These developments have provided high-speed bandwidth to smartphone users, enabling them to use multimedia and real-time services. Various Radio Access Technologies (RATs) are available to smartphone users in Heterogeneous Networks [1]. Fig. 1 shows the presence of Heterogeneous Wireless Networks. 3G and 4G networks have characteristics, such as wide coverage and support mobility. On the other hand, there is the deployment of Wireless Local Area Networks (WLANs), which can provide a high-speed bandwidth [1]. The above radio access technologies overlap each other. There have been significant developments, and new features have been introduced in smartphones, such as the availability of multiple network interfaces and increased memory size. These features help in running multiple applications concurrently in smartphones. The ever-growing demand for uninterrupted, seamless connectivity without degrading the Quality of Service (QoS) has highlighted the need for Vertical Handover (VHO) [2-4].

The organization of the paper is as follows: Section 2 provides a literature review. Section 3 covers the mathematical background. Section 4 gives the system model design and implementation. Section 5 describes the experimental scenario followed by experimental analysis in section 6. Section 7 reports the conclusions and future work.

## 2. Literature Review

A previous study [5] compared algorithms based on the techniques of the network selection. A review paper summarized the prominent mathematical theories used for modelling the VHO [1]. A survey of algorithms for mobility management was reported [6]. Yan et al. [7] published a review paper containing a survey of VHO algorithms. Another review paper outlining vertical handover decision algorithm (VHDA) based on various parameters was presented [8], and another study [9] reported various aspects of handover in 4G networks, with an additional paper focusing on handover management [10]. Obayiuwana and Falowo [11] published a review paper on the analysis of MADM techniques. Khiat et al. [12] reviewed the basics of handover, classification, and analysis of VHDAs.

Khalaf and Badr presented a model for estimating the triggering time for VHO and outage probability [13]. VHDA based on a policy mechanism was reported [4] . The decision for Handover was made using Fuzzy Petri Nets. In [14] the authors presented a VHDA that used On-Boarding Units & navigation system in the car. A VHDA based on a location-aware technique was also proposed [15], and a handover scheme based on an autonomic network architecture was presented [16]. Another study [17] proposed a VHDA that considers the techniques of vehicular networks. Barja et al. [18] evaluated the performance of VHDA based on experiments considering a range of networks, and Ulvan et al. [19] investigated the handovers in a femtocell. A VHDA based on load balancing techniques was reported [20], and Alhabo et al. [21] presented a VHDA between a macro cell and a small cell. The algorithm proposed was based on the throughput and balancing of network load. Barja et al. [22] presented a VHDA that captures network information. The network information was captured using geolocation, map information, and route calculation. An algorithm based on a hybrid scheme of congestion control and alleviation was summarized [23]. Performance analysis of VHDA between 3G & WLAN and performance analysis of VHO between WLAN, WiMax, and 4G were conducted [24,25]; the simulations were done using NS2. A VHDA based on Fuzzy Logic was reported [26]; the main parameters considered were Bit Error Ratio, delay, jitter, and bandwidth. Another study [27] presented an algorithm for the management of the radio resources of small cells. The authors have presented VHDA that minimizes outage probability [28].

VHDA based on the k partite graph, and another Multi-Attribute Decision Making (MADM) techniques and Mahalanobis distance were presented [29,30]. Abid et al. [31] reported a VHDA based on Utility theory. The model was based on the utility function for each parameter. A VHDA based on Markov Model was reported [32]. Another study [33] compared four Multi-Attribute Decision-making techniques, such as Multiplicative Exponential Weighting (MEW), Simple Additive Weighting (SAW), Technique for Order preference by similarity to an Ideal Solution (TOPSIS), and Grey Relational Analysis (GRA). Navarro and Wong [34] reported a VHDA based on the GRA technique. A VHO using MADM techniques, such as SAW and VIKOR, was presented [2]. A previous study [35] outlined a VHDA based on the Score function. The score function was calculated using the bandwidth, cost, and battery status as the input parameters. Yu et al. [36] reported the effects of VHDA mobile weights, network weights, and equal weights. Another VHDA based on the Nash bargaining model was presented [37]. A VHDA based on Modified Multiplicative Exponent Weighting (M2EW) was proposed [38]. Drissi and Oumsis [26] presented aVHDA based on MADM techniques. An analysis of network-centric, user-centric, and mixed schemes for selecting the network was analyzed [3]. A VHDA based on Analytic Hierarchy Process (AHP) and Principal Component Analysis (PCA) was reported [39]. Another study [40] presented a scheme for calculating the weights of the parameters for MADM based on the Bayes approach. A VHDA based on the MADM technique, in which the weights for the parameters are variable [41], a VHDA based on the Utility Function [42], and a VHDA based on MADM techniques [43] were reported. The algorithm considers the parameters in different priorities. A VHDA based on the entropy weights and TOPSIS was presented [44]. Singh and Singh [45] outlined a VHDA-based on MADM techniques, such as SAW, GRA, and TOPSIS. The networks considered are WLAN and WiMax. Mahardhika et al. [46] presented a VHDA using the MADM technique. The main parameters considered were the Received Signal Strength (RSS), traffic class, speed of the mobile user, and occupancy in the network.

Table 1 gives the summary of implementation and observation from key Research papers.

##### Table 1. Summary of Implementation & Observations from Key Research papers.
 Reference Summary of Implementation & Observation [7] It is a review paper in which a comprehensive survey of the VHD algorithms is presented. [8] It is a review paper in which an overview of the VHO techniques and algorithms is presented. [29] VHDA based on K partite graph is presented. The paper gives insight into the use of graph theory for VHDA implementation. [35] VHDA based on score function is presented. Use of Score function to decide the candidate network for handover is introduced. [26] Comparison of SAW, MEW & TOPSIS is presented. Comparison is based on subjective weights only. [17] An algorithm considering details of Vehicular Networks is presented. The algorithm chooses best network using user preferences in vehicular contexts. [14] VHDA is optimized by combining networking information, obtained by the services of the IEEE 802.21 standard, with geolocation, map information, Surround context information and route calculation. The VHDA gives good results in the adopted context. [18] Evaluation of VHO performance is presented. Technology aware VHO mechanism is able to achieve an adequate performance when traffic congestion is low. [54] VHDA based on Fuzzy Logic and Genetic Algorithm is proposed. Proposed algorithm reduces the false handovers.

## 3. Mathematical Background

### 3.1 VHO-phases & Parameters

VHO is divided into three phases. Fig. 2 describes three phases of VHO [47].

The first phase is the information-gathering phase. In this phase, the information and details of all the available candidate networks, along with the parameters, are captured. This is also known as the System Discovery phase. The second phase is very important. In this phase, the decision for the handover is done based on the parameters captured in the first phase. This is also known as the network-selection phase. The third phase refers to the performing of the handover. The handover is performed in this phase. This is also known as the handover implementation phase [8, 48, 47]. Fig. 3 shows the main parameters that need to be considered for an effective VHDA.

$\textit{Handover}=f^{n}\left(\begin{array}{l} RSS,\textit{Bandwidth},\textit{Network}\,\,\textit{Coverage},\\ ~ \textit{Packet}\,Loss,\,\,\textit{Jitter}\,and\,\textit{Latency} \end{array}\right)$.

Received Signal Strength (RSS) is the most critical parameter to be continuously monitored to ensure good connectivity. Quality of Service (QoS) depends on Latency (L), Jitter (J), Packet Loss (PL). Good Network Coverage can reduce frequent handover overheads [49-51] %.

Table 2 captures the details of the parameters for VHDA [7, 48, 49, 52-55]

##### Table 2. Details of parameters for VHDA.
 S. No Parameter Details of parameter 1 Received Signal Strength (RSS) RSS is the most prominent and widely used parameter in the algorithm for VHO. RSS changes with the distance of the mobile user from the base station or access point. This is measured in dBm. 2 Bandwidth (B) Bandwidth determines the ability of the access network to hold a number of simultaneous transmissions of voice calls or data sessions. This is measured in Mbps. 3 Latency (L) Latency can be described as the mean time used by the data packet for reaching the destination. This is measured in msec. 4 Jitter (J) Jitter can measure the relative inconsistency in delivering data packets between the two endpoints of the access network. This is measured in msec. 5 Packet Loss (PL) Packet Loss can be described as the loss of packets during transmission in the access network. This is measured in %. 6 Network Coverage (NC) Network coverage is the geographical area that is covered by a base station or access point. It is measured in meters.

### 3.2 Analytic Hierarchy Process (AHP)

The process for AHP is as follows:

1.Construct pairwise comparison and build a pairwise matrix to make a decision.

The pairwise comparison is as follows -

##### (1)
$X=\left[\begin{array}{lll} x_{11} & x_{12} & \ldots \ldots x_{1n}\\ x_{21} & x_{22} & \ldots \ldots x_{2n}\\ x_{n1} & x_{n2} & \ldots \ldots x_{nn} \end{array}\right].$

where n denotes the number of attributes compared

##### (2)
$x_{ji}=\left\{\begin{array}{l} 1if\,\,i=j\\ \frac{1}{x_{ij}}if\,\,i\neq j \end{array}\right.$

$x_{ij}~$are obtained based on Saaty’s scale for the pairwise comparison mentioned in Table 3.

2.Construct Normalized decision Matrix, applying the sum normalization technique to matrix X. The normalized matrix A

$A=\left[\begin{array}{lll} a_{11} & a_{12} & \ldots \ldots a_{1n}\\ a_{21} & a_{22} & \ldots \ldots a_{2n}\\ a_{n1} & a_{n2} & \ldots \ldots a_{nn} \end{array}\right]$

where a$_{\mathrm{ij}}$ is given by

##### (3)
$a_{ij}=\frac{x_{ij}}{\sum _{i=1}^{n}x_{ij}}$

3.Determine the weight of each criteria using the formula

##### (4)
$W_{i}=\frac{\sum _{j=1}^{n}a_{ij}}{n}$

Such that $\sum _{i=1}^{n}W_{i}$ = 1

4.Verify the consistency of the pairwise comparison using Consistency Ratio (CR) given by the formula [26,29]

$CR=\frac{CI}{RI}$

where CI denotes the consistency index and is obtained as

##### (5)
$CI=\frac{\lambda _{max}-n}{n-1}$
##### (6)
$\lambda _{max}=\frac{\sum _{i=1}^{n}b_{i}}{n}$
##### (7)
$b_{i}=\frac{\sum _{j=1}^{n}W_{j}\mathrm{*}a_{ij}}{W_{i}}$

where RI is the Random Index

For n = 6, RI = 1.24 [56]

CR denotes the degree of consistency in the pairwise comparison of attributes. The smaller the value of CR, the better the pairwise comparison of the attributes. The maximum allowable limit for CR is 10% [2]

Condition of acceptance: If CR < 0.1, the pairwise comparison is accepted.

##### Table 3. Table for Saaty’s scale.
 Scale Relative Importance 1 Equally Important 3 Moderately Important 5 Strongly Important 7 Very Strong Important 9 Extremely Important 2,4,6,8 Intermediate Values

### 3.3 Digraph Model

The digraph model is a graphical representation of the available networks and their inter-connections. The model consists of nodes and edges, where a node represents an available network, and an edge defines the cost of the connection. Fig. 4 shows the Digraph Model that was used for the selection of networks across the user path [29]

### 3.4 Calculation of Cost Function

The calculation of the cost function is as follows -

$C\left(e_{ij}\right)=~ \left\{\begin{array}{l} C_{1}when\,\,e_{ij}\,is\,link\,\textit{between}\,User\,and\,\textit{Access}\,\textit{Point}\\ C_{2}when\,e_{ij}\,is\,the\,link\,\textit{between}\,two\,\textit{Access}\,\textit{Points} \end{array}\right. \\$
##### (8)
$C_{1}\left(e_{ij}\right)=W_{1}L+~ W_{2}J+W_{3}PL+W_{4}NC+W_{5}B+W_{6}RSS$
##### (1)
$C_{2}\left(e_{ij}\right)=~ W_{1}L_{m}+W_{2}J_{m}+W_{3}PL_{m}+W_{4}NC_{m}+W_{5}B_{m}+W_{6}RSS_{m}$

where L$_{\mathrm{m}}$, J$_{\mathrm{m}}$, PL$_{\mathrm{m}}$, NC$_{\mathrm{m}}$, B$_{\mathrm{m}}$, and RSS$_{\mathrm{m}}$ represent the average of parameters between the two access networks installed on edges e$_{\mathrm{ij}}$ [29]

## 4. System Model Design & Implementation

### 4.1 Proposed Algorithm for VHO

The proposed algorithm for VHO is based on the cost function, which was calculated using Eqs. (8) and (9). Other studies used AHP to calculate the MADM techniques, SAW, MEW, M2EW, TOPSIS, and GRA. The weights of the parameters using AHP and decision for handover was calculated based on the least value of the cost function.

Figs. 5 and 6 gives the flowchart and algorithm for AHP. Figs. 7 and 8 show the flowchart and algorithm, respectively, for VHO based on the Least Cost function.

## 5. Experimental Scenario

The simulation has been done for practical values. Considering the scenario of a mobile user traveling across the road. The mobile user comes across two networks 4G and WLAN (Public WLAN with APs deployed across the road). Fig. 9 shows the associated cost of the two available networks.

The following are the notations used in the graph.

V$_{1}$ - Mobile User

V$_{2}$ - 4G

V$_{3}$ -WLAN

V$_{4}$-WLAN

V$_{5}$- 4G

The screenshots of the measured values of parameters are captured in the following figures.

## 6. Experimental Analysis

The following analysis has been done based on the above scenario. Table 4 lists the Decision Matrix X.

##### Table 4. Decision matrix.
 Parameter Latency Jitter Packet Loss Network Coverage Bandwidth RSS Latency 1 1 1/3 1/5 1/7 1/9 Jitter 1 1 1/3 1/4 1/7 1/9 Packet Loss 3 3 1 1/4 1/5 1/9 Network Coverage 5 4 4 1 1/7 1/5 Bandwidth 7 7 5 7 1 1/3 RSS 9 9 9 5 3 1

RSS is more important than Network coverage. Therefore, number 5 is captured for the RSS row against the network coverage column.

Although RSS and bandwidth are important, RSS plays a larger role than bandwidth for VHO. Hence, number 3 is placed in the RSS row for the bandwidth column.

Table 5 Normalized Matrix.

##### Table 5. Normalized Matrix.
 Parameter Latency Jitter Packet Loss Network Coverage Bandwidth RSS Latency 1/26 1/25 1/59 2/137 5/162 5/84 Jitter 1/26 1/25 1/59 5/274 5/162 5/84 Packet Loss 3/26 3/25 3/59 5/274 5/162 5/84 Network Coverage 5/26 4/25 12/59 10/137 5/162 3/28 Bandwidth 7/26 7/25 15/59 70/137 35/162 5/28 RSS 9/26 9/25 27/59 50/137 35/54 15/28

Table 6 Weight Matrix

##### Table 6. Weight Matrix.
 Parameter Weights Latency 0.033 Jitter 0.034 Packet Loss 0.068 Network Coverage 0.128 Bandwidth 0.285 RSS 0.452 Total 1.00

Table 6 shows that RSS has the highest weight, followed by the bandwidth.

${\lambda}$$_{\mathrm{max}}$= 0.9988

RI = 1.24 [56]

CI = -1.0002

CR = -0.8066 < 0.1

Since CR < 0.1, the comparison is accepted.

The values of the parameters are normalized on the scale of 0 to 1. Table 7 lists the normalized values for 4G & WLAN.

##### Table 7. Normalized values for 4G & WLAN.
 Parameter Normalized Values for 4G (A) Normalized Values for WLAN (B) Mean Values (A+B)/2 Latency 0.6 0.5 0.55 Jitter 0.6 0.5 0.55 Packet Loss 0.6 0.5 0.55 Network Coverage 0.6 0.1 0.35 Bandwidth 0.1 0.7 0.4 RSS 0.9 0.9 0.9

The calculation of the cost function is shown in Table 8.

##### Table 8. Calculation of Cost Function for 4G and WLAN.
 Parameter Weights (Wi) Values for 4G Values for WLAN Mean Values Latency 0.033 0.020 0.017 0.018 Jitter 0.034 0.020 0.017 0.019 Packet Loss 0.068 0.041 0.034 0.037 Network Coverage 0.128 0.077 0.013 0.045 Bandwidth 0.285 0.028 0.199 0.114 RSS 0.452 0.407 0.407 0.407 Cost Function Value 0.593 0.687 0.640

Fig. 14 shows the Graph Model.

##### Fig. 14. Graph Model.

Table 9 provides details of the path-wise cost. Fig. 15 shows the path-wise details of the cost function.

##### Table 9. Path-wise details of the cost function.
 Path Node Value of Cost Function P1 V1 – V2 – V4 1.23 P2 V1 – V2 – V5 1.19 P3 V1 – V3 – V4 1.37 P4 V1 – V3 – V5 1.33

Observation from Table 9 - The least-cost path has been selected as

V1 (MU) ---- V2(4G) ----V5 (4G) because the path gives the least cost value.

In this scenario, with the parameters under consideration, the preferred network was 4G over WLAN, due mainly to the better QoS offered by 4G, as evident from the measurement figures.

## 7. Conclusion & Future Work

This study designed and implemented VHDA based on the least cost function. A real-life scenario with measured parameter values was considered. The weights of the parameters were evaluated using Analytic Hierarchy Process. These weights were used to calculate the path costs for selecting the best network for handover along the route. Future studies will extend the scope of the algorithm by increasing the input parameters to VHDA, based on the network set-up, and implement the same where multiple candidate networks are available. In addition, a network fitness function will be derived for each network to make the algorithm more robust.

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## Author

##### Siddharth Goutam

Siddharth Goutam Obtained his bachelor degree in Electronics & Telecommunication Engineering and Masters in Engineering in Electronics & Telecommunication Engineering with specialization in Communication Systems Engineering. He is currently a student member of the IEEE.

##### Srija Unnikrishnan

Srija Unnikrishnan is Principal at Fr. Conceicao Rodrigues College of Engineering, affiliated with the University of Mumbai, India. She has over 35 years of teaching experience at the UG and PG level. She received her Bachelor's Degree in Engineering from the University of Kerala, a Master’s Degree from Osmania University, and Ph.D. from the University of Mumbai. Her broad areas of interest are Mobile Communication and Signal Processing.

##### Sundary S. Prabavathy

Sundary S. Prabavathy pursued a Master of Science, Master of Philosophy (Mathematics), B.Ed (Mathematics). Worked under UGC Research Project as UGC JRF for three years. Field of Specialization: Epidemic Models (Stochastic Proce-sses). She possesses 30 years of teaching experience. Currently, she is working as Associate Professor in Mathematics in Fr. Conceicao Rodrigues College of Engineering., Fr. Agnel Ashram, Band-Stand, Bandra (West). Mumbai, India.

##### Archana Karandikar

Archana Karandikar is an Assistant Professor (Mathematics) in the Department of Science & Humanities at Fr. Conceicao Rodrigues College of Engineering, affiliated with the University of Mumbai, India. She has received her Bachelor's Degree in Science (Mathematics) from the University of Mumbai, Master’s Degree in Science (Mathematics) from the University of Mumbai. She is SET Qualified. Her area of interest includes Discrete Mathematics.