Criteria Evaluation

The choice of selecting a candidate site for computation offloading is more straight- forward when considering only one factor, such as decreasing execution time. However, other Quality of Service (QoS)-based criteria such as current bandwidth between Host Mobile Device and the site and the computation power of the sites as well as availability, security, and the monetary costs of the sites need to be considered when making offloading decisions. Five offloading impact factors are presented to show the construction and operation of the offloading model. This model can be easily extended to incorporate new factors to make offloading decision making more comprehensive.

Bandwidth depends on the quality of the wireless connection between the mobile device and the offloading sites. It is shown in previous work in the literature [77] that offloading is not beneficial when the wireless connection is poor due to high wastage of energy of the mobile devices. Speed is an important criterion that compares the speed of the offloading site with that of the mobile device. Failures may occur due to the mobility of mobile devices and unstable connectivity of wireless communication; Thus, availability also affects the offloading outcome. Security and privacy are important concerns for mobile users, especially if the credibility of the offloading site is unknown. Security and privacy are two crucial concepts that need to be maintained during the offloading process. The financial cost is another factor that needs to be considered when comparing different offers from multiple service providers. The operations of computation offloading and data transfer between cloud resources incur additional costs on end-users. Therefore, economic factors should be taken into consideration while making offloading decisions.

4.5 Multi-criteria Solver 71

Fig. 4.1 Standard AHP Comparison Scale

4.5.1.1 AHP Pairwise Comparison

In this work, a popular MCDM approach called Analytic Hierarchy Process (AHP) [116] is used for determining the relative importance of a set of alternatives in a multi-criteria decision problem. It converts the evaluations to numerical values that can be processed and compared and derives a numerical weight or priority for each element of the hierarchy. The criteria will be compared as to how important they are to the decision makers, with respect to the goal. This multi-criteria technique incorporates the intangible aspects associated with the human factor through the use of pairwise comparisons. The results of the pairwise comparison on n criteria can be expressed in an evaluation matrix A illustrated below:

A = (aij)n×n =         a11 a12 · · · a1N a21 a22 · · · a2n ... ... ... ... an1 an2 · · · ann         , aii = 1, aji = 1/aij (4.17)

Offloading decisions involve different qualitative and quantitative parameters [11]. As described earlier, the five chosen decision criteria for selecting offloading sites are bandwidth, speed, availability, security, and price denoted as C1, C2, C3,

C4, C5 respectively. The priory of importance depends on what we care about

most in the selection of an offloading site. Bandwidth is considered the most significant since it decides the extra communication cost between mobile devices and the sites [12]. Speed also has high importance because it saves execution time which leads to better user experience and less local energy consumption. We assume the priory of importance is ranked as: bandwidth > speed > availability > security > price. However, the priority of these five criteria can be varied in other situations as described in Subsection 4.5.2. The relative performance of each

Table 4.4 Pairwise comparison matrix (A) for offloading criteria

Bandwidth Speed Availability Security Price

Bandwidth 1 1 5 7 9

Speed 1 1 5 6 8

Availability 1 / 5 1 / 5 1 3 3

Security 1 / 7 1 / 6 1 / 3 1 2

Price 1 / 9 1 / 8 1 / 3 1 / 2 1

criterion against another can be evaluated in a pair-wise manner according to the rubric in Figure 4.1 with 1 being equal and 9 being much better. As a result, the pairwise comparison matrix is generated as shown in Table 4.4.

Using Row Geometric Mean prioritization Method (RGMM) [34], the final weighting results for each criteria w = (w1, w2, ..., wn) are: Bandwidth (C1):

0.4072, Speed (C2): 0.3885, Availability (C3): 0.1083, Security (C4): 0.0572, Price (C5): 0.0384.

4.5.1.2 Consistency Check

The purpose of the consistency check is to test the coordination of the importance degree between each criterion. This is used to avoid the contradiction situation, i.e. for a user, A is more important than B, B is more important than C, and C is more important than A. For example, it is inconsistent in the case where a Decision Maker (DM) thinks availability is strongly more important than security, and security is more important than price, however, the price is more significant than availability in the same context.

A consistency index to measure individual matrix consistency, namely the Geometric Consistency Index (GCI) is developed by [3]. Let A = aij be a

judgement matrix, and let w = (w1, w2, ..., wn) be the priority vector derived from

A using the RGMM. The Geometric Consistency Index (GCI) is given below:

GCI(A) = 2

(n − 1) (n − 2)

X

i<j

(log (aij) − log (wi) + log (wj))2 (4.18)

If GCI(Ak) = 0, we have a fully consistent matrix. GCI is also provided by

[3] for GCI: GCI = 0.31 for n = 3; GCI = 0.35 for n = 4; GCI = 0.37 for n > 4. When GCI (A) < GCI the matrix A is of acceptable individual consistency. Using Eq. (4.18), the calculated GCI (A) for the pairwise matrix is 0.099 which is much less than 0.37 for n = 5.

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