**5. Numerical analysis**

For that, the use of fuzzy logic can be used to deal with imprecise information and combine and evaluate multiple criteria simultaneously. Hence, fuzzy logic concept provides a robust mathematical framework in which handover decision can be formulated as a Fuzzy MADM.

The scale used is represented by the intensities between each other according to the funda‐ mental scale. The fundamental scale is validated according to effectiveness and theoretical justifications according to [18]. The scale consists of nine levels. To make it even easier to judge, one can use a more restricted scale with five levels: 1 is equal importance, 3 is moderate importance, 5 is strong importance, 7 is very strong or demonstrated importance and 9 is extreme importance. Because different application have different requirements, in this paper, we consider two types of application -- VoIP as a real-time application example and Media Content Downloads as a non-real-time application example. Tables 2 and 3 show the pair-wise relative importance of the decision criteria for the real-time and non real-time applications

**Real-time CINR BW Cong. delay**

**Non Real-time CINR BW Cong. delay**

tion and non real-time applications are as shown in equations (17), and (18).

Based on the AHP procedure explained earlier the weighting vector for the real time applica‐

After weighting the decision criteria using the AHP method, the TOPSIS method will be used to rank the alteratives available for the Target Base Station (TBS), and then choose the highest

[0.6186 0.0662 0.3149] *wr* = (17)

[0.6186 0.3149 0.0662] *wnr* = (18)

CINR 1/1 3/1 5/1 BW 1/3 1/1 7/1 Cong. delay 1/5 1/7 1/1

CINR 1/1 5/1 3/1 BW 1/5 1/1 1/7 Cong. delay 1/3 7/1 1/1

**Table 2.** Pair-wise Matrix for real-time application

**Table 3.** Pair-wise Matrix for non real-time application

**4.3. Alternative ranking using TOPSIS**

respectively.

94 Selected Topics in WiMAX

In this section a numerical analysis of the proposed scheme is performed, and then compared with the Weighted Sum Method (WSM) and conventional signal strength based cell selection. The criteria weighting based on user application requirements have been calculated previ‐ ously, as shown in equation (17) and (18) for real-time and non real-time applications respec‐ tively.

Suppose that we have three candidate TBSs as shown in Figure 1. After the information collection stage, the MS will maintain the criteria values in a decision matrix, *Dm*(*A*). The decision matrix consists of three criteria, viz CINR in dB, BW in Kbps and congestion delay in ms for three candidate BSs as shown in (19).

$$\begin{array}{c} \text{CINR BW} \, \text{Cong} \quad \text{Delay} \\ \text{BS1} \begin{bmatrix} 23 & 2048 & 300 \\ 22 & 380 & 100 \\ 24 & 148 & 110 \end{bmatrix} \\ \text{BS3} \begin{bmatrix} 24 & 148 & 110 \end{bmatrix} \end{array} \tag{19}$$

Using the TOPSIS method, *Dm*(*A*) first has to be normalized first using equation (7), because the criteria use different units. The normalized matrix is shown in (20).

$$\begin{array}{c} \text{BS1} \begin{bmatrix} 0.5770 & 0.9807 & 0.8960 \\ 0.5519 & 0.1820 & 0.2987 \\ 0.6021 & 0.0709 & 0.3285 \end{bmatrix} \end{array} \tag{20}$$

After getting the normalized decision matrix, it is weighted using by multiplying it with the weighting factor. Two types of application have been considered, therefore, we have two weighting factors, which will produce two weighted decision matrices.

For the real-time application, the weighted decision matrix is as shown in equation (21).

$$\begin{array}{c} \text{BS1} \begin{bmatrix} 0.3569 & 0.0649 & 0.2822 \\ 0.3414 & 0.0120 & 0.0941 \\ \end{bmatrix} \\ \text{BS3} \begin{bmatrix} 0.3724 & 0.0047 & 0.1035 \end{bmatrix} \end{array} \tag{21}$$

For the non real-time application, the weighted decision matrix is as shown in equation (22).

$$\begin{array}{c} \text{BS1} \begin{bmatrix} 0.3569 & 0.3088 & 0.0593 \\ 0.3414 & 0.0573 & 0.0198 \\ \text{BS3} \begin{bmatrix} 0.3724 & 0.0223 & 0.0217 \end{bmatrix} \end{array} \tag{22}$$

For real-time applications, WSM ranks B3 as the best, and TOPSIS ranks B2 as the best. Both two results are reasonable, because all of them have good CINR and small delay. However, TOPSIS ranks B2 as the best, because it provides the lowest delay. So the TOPSIS looks like more sensitive to the criteria weighting. The conventional signal strength scheme ranks B3 as

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For the non real-time application, both WSM and TOPSIS ranks B1 as the best, because it has the highest BW while the conventional signal strength scheme ranks B3 as the best; although it has the best CINR, It provides the worst BW, which is an important criteria in the Media

From table 4, we can see that application requirement or the weighting factor has an influence on the ranking order. As mentioned before, both WSM and TOPSIS have different ranking orders for VoIP as a real-time applicatipn. This is further exemplified by the sensitivity analysis

When the congention delay criteria weighting is changed, and other parameters are kept constant we found that the ranking result is more sensitive when TOPSIS method is used. For example, in Figure 6 using WSM method the BS2 score changes form 0.6 to 0.95 when the congestion delay creiteria weighting is changed, so the range of the score change is 0.35. Whereas in Figure 7 using TOPSIS method when the congention delay criteria weighing is changed, the BS2 score changes from 0.18 to 0.92, so the range of the score change is 0.74, and

form this it is clear that TOPSIS method is more sensitive to the weighting factor.

the best, because it provides the best CINR.

**Figure 4.** The WSM and TOPSIS scores for real-time applications

on the weighting factor in Figure 6 and Figure 7 respectively.

Content Download application.

To calculate the distance from the positive ideal solution (PIS) and the farthest from the negative ideal solution (NIS), equations (8) - (11) are used. CINR and BW are considered as benefit criteria and congestion delay is considered as a cost criteria. The ranking of the alternative TBSs for real-time and non real-time application are shown in equation (23) and (24) for real time and non real time application respectively.

$$\begin{array}{cccc} & BS1 & BS2 & BS3\\ R\_r = [0.2479 & 0.7543 & 0.7484] \end{array} \tag{23}$$

123 [0.8710 0.1724 0.1454 ] *nr BS BS BS <sup>R</sup>* <sup>=</sup> (24)

Table 4 shows the summary of the ranking of the available alternative TBSs using TOPSIS compared with WSM and also illustrated in Figures 4 and 5 respectively.


**Table 4.** Ranking of the available alternatives using WSM and TOPSIS

Using other wayS of viewing the cell selection results, Table 5 compare between TOPSIS, WSM and conventional signal strength-based cell selection.


**Table 5.** Selected cell using TOPSIS, WSM and the conventional signal strength schemes

For real-time applications, WSM ranks B3 as the best, and TOPSIS ranks B2 as the best. Both two results are reasonable, because all of them have good CINR and small delay. However, TOPSIS ranks B2 as the best, because it provides the lowest delay. So the TOPSIS looks like more sensitive to the criteria weighting. The conventional signal strength scheme ranks B3 as the best, because it provides the best CINR.

For the non real-time application, both WSM and TOPSIS ranks B1 as the best, because it has the highest BW while the conventional signal strength scheme ranks B3 as the best; although it has the best CINR, It provides the worst BW, which is an important criteria in the Media Content Download application.

**Figure 4.** The WSM and TOPSIS scores for real-time applications

For the non real-time application, the weighted decision matrix is as shown in equation (22).

( ') 2 0.3414 0.0573 0.0198

*nr*

*Dm A BS*

96 Selected Topics in WiMAX

(24) for real time and non real time application respectively.

*BS*

*BS*

1 0.3569 0.3088 0.0593

é ù ê ú <sup>=</sup>

3 0.3724 0.0223 0.0217

To calculate the distance from the positive ideal solution (PIS) and the farthest from the negative ideal solution (NIS), equations (8) - (11) are used. CINR and BW are considered as benefit criteria and congestion delay is considered as a cost criteria. The ranking of the alternative TBSs for real-time and non real-time application are shown in equation (23) and

> 1 23 [0.2479 0.7543 0.7484] *<sup>r</sup> BS BS BS*

> > 123

Table 4 shows the summary of the ranking of the available alternative TBSs using TOPSIS

**MCDM methods WSM TOPSIS**

VoIP(real-time) [0.7640, 0.8942, 0.9097] [0.2479, 0.7543, 0.7484] Media Content Download (non real-time) [0.9298, 0.6917, 0.7015] [0.8710, 0.1724, 0.1454]

Using other wayS of viewing the cell selection results, Table 5 compare between TOPSIS, WSM

VoIP BS3 BS3 BS2 Media Content Download BS3 BS1 BS1

**Table 5.** Selected cell using TOPSIS, WSM and the conventional signal strength schemes

**Signal strength WSM TOPSIS**

[0.8710 0.1724 0.1454 ] *nr BS BS BS*

compared with WSM and also illustrated in Figures 4 and 5 respectively.

**Table 4.** Ranking of the available alternatives using WSM and TOPSIS

and conventional signal strength-based cell selection.

*<sup>R</sup>* <sup>=</sup> (23)

*<sup>R</sup>* <sup>=</sup> (24)

BS1 BS2 BS3 BS1 BS2 BS3

ë û

(22)

From table 4, we can see that application requirement or the weighting factor has an influence on the ranking order. As mentioned before, both WSM and TOPSIS have different ranking orders for VoIP as a real-time applicatipn. This is further exemplified by the sensitivity analysis on the weighting factor in Figure 6 and Figure 7 respectively.

When the congention delay criteria weighting is changed, and other parameters are kept constant we found that the ranking result is more sensitive when TOPSIS method is used. For example, in Figure 6 using WSM method the BS2 score changes form 0.6 to 0.95 when the congestion delay creiteria weighting is changed, so the range of the score change is 0.35. Whereas in Figure 7 using TOPSIS method when the congention delay criteria weighing is changed, the BS2 score changes from 0.18 to 0.92, so the range of the score change is 0.74, and form this it is clear that TOPSIS method is more sensitive to the weighting factor.

**Figure 7.** Sensitivity of congestion delay weighting using TOPSIS

Mobile WiMAX is one of the 3G/4G broadband wireless technology network that is capable of delivering triple play (voice, data, and video) services. The variety of user application needs different network requirements. So, handover mechanism and the cell selection scheme have to be efficient to meet the application need during and after the handover process. This paper described a smart way of TBS selection. It is based on multi-criteria based selection to meet the user requirements during handover. We proposed the AHP method for criteria weighting and TOPSIS for alternative BSs ranking as a multi-criteria decision-making selection scheme to meet the MS application requirements. The proposed, Hybrid AHP and TOPSIS-based Cell Selection (HATSC) scheme is based on multi-criteria such as CINR, bandwidth (BW) and congestion delay to select the TBS. Numerical analysis shows that TOPSIS is more sensitive to criteria weighting factor, and WSM gives a relative conservative ranking result, and both of

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them results in better performance than the conventional signal strength scheme.

Mohammed A. Ben-Mubarak, Borhanuddin Mohd. Ali, Nor Kamariah Noordin,

Department of Computer and Communication Systems Engineering, Faculty of Engineer‐

**6. Conclusion**

**Author details**

Alyani Ismail and Chee Kyun Ng

ing, Universiti Putra Malaysia, Selangor, Malaysia

**Figure 5.** The WSM and TOPSIS scores for the non- real-time application

**Figure 6.** Sensitivity of congestion delay weighting using WSM

**Figure 7.** Sensitivity of congestion delay weighting using TOPSIS
