# Indetermsoft-Set-Based D* Extra Lie Framework for Resource Provisioning in Cloud Computing
## 4 Proposed Work
### Indetermsoft Set Task Manager (ISSTM)
8:Function SOLUTION FOND(0)
9:Return TOP OPEN = \(S_{start}\) or Visited (\(S_{start}\)) AND NOT OPEN (\(S_{start}\))
10:Function INITIALZE(0)
11:\(K_{m}=0\), Visited (\(S_{start}\)) = True, Parent \(\left(S_{goal}\right)=\) NULL, g (\(S_{goal}\)) = 0
12:PUSH OPEN (\(S_{goal}\), CALCULATE KEY (\(S_{goal}\))
13:Function SEARCH STEP 0
14:\(s\) = TOP OPEN 0
15:POP OPEN (0)
16:\(k_{add}=k(s)/(s)\)
17:\(k_{new}=\) CALCULATE KEY (\(S_{goal}\))
18:\(k_{add}<k_{new}\)then
19:PUSH OPEN(s, CALCULATE KEY(s))
20:else
21:for all \(s^{\prime}\in Pred(s)\) do
22:if NOT VISIFT (\(s^{\prime}\)) OR \(g(s^{\prime})>cost(s^{\prime},s)+g(s)\)then
23:\(S_{start}=S_{start}\)
24:for all \(s\in S\) ends do
25:if \(visited(s)\) AND NOT OPEN(\(S\)) THEN
26:\(s\) = 0
27:Function GENITIALZE (0
28:if any edge cost changed then
29:CUT BRANCHES
30:if \(is\
eq i\) then
31:\(K_{m}=K_{m}+H(S_{start},S_{start})\)
32:\(S_{init}=S_{start}\)
33:for all \(s\in S\) ends do
34:if \(visited(s)\) AND NOT OPEN(\(S\)) THEN
35:PUSH OPEN (s, CALCULATE KEY(s))
36:\(s\) = 0
37:Function CUT BRANCHES (0)
38:Reopen_start = false
39:For all directed edges (u, v) with changed cost do
40:if visited (u) AND visited (v) then
41:cold = cost (u, v)
42:Update edge cost (u, v)
43:if cold \(<\) cost (u, v) then
44:if \(g(start)>g(v)+cost(u,v)+h(S_{start},u)\) then
45:reopen_start = true
46:seeds = seeds \(\cup\) p
47:else if cold \(<\) cost (u, v) then
48:if \(parent(u)=v\) then
49:CUT BRANCHES (u)
50:if \(rep_{start}=true\ AND\ visited(S_{start})\)then
51:seeds = seeds \(\cup\) S_start_
52:End for
53:Function CUT BRANCHES(s)
54:Visited(s) = false
55:Parent(s) = NULL
56:REMOVE OPEN(s)
57:for all \(s^{\prime}\in Succ(s)\) do
58:if visited (\(s^{\prime}\)) AND NOT parent (\(s^{\prime}\)) = s then
59:seeds = seeds \(\cup\) s^{\prime}
60:End for all \(s^{\prime}\in Pred(s)\) do
61:if visited (\(s^{\prime}\)) AND parent (\(s^{\prime}\)) = s then
62:if visited (\(s^{\prime}\)) AND parent (\(s^{\prime}\)) = s then
63:cut CUT BRANCHES (\(s^{\prime}\))
64:End for
65:Output \(D^{\prime}(RPP)=\{D^{\prime}(RPP_{1}),D^{\prime}(RPP_{2}),\ldots,D^{\prime}( RPP_{n})\}\)
```

**Algorithm 3**Working of D*EL

## 5 Mathematical Modeling

This section presents the mathematical structures, equations, and algorithms that are central to this resource-provisioning study, providing a rigorous basis for our theoretical and empirical investigations. The performance of the D* extra life framework is analyzed through mathematical modeling. For modeling purposes, a limited cloud setup that is composed of a predefined set of user tasks and resource center instances is considered. The performance objectives considered for evaluation purposes are power consumption (PC(D' extra life)), resource utilization (RU(D' extra life)), total execution time (TET(D' extra life)), and learning rate (LR(D' extra life)). The expected value analysis is performed to determine the performance metrics for the future time FT. Finally, the performance of the proposed D* extra life framework is compared with three existing works: EW1-TP [13], EW2-AC [14], and EW3-GC [16]. PO1: Power Consumption (PC(D' extra life)): The power consumption of D* extra life is mainly influenced by the power consumed by the virtual machines during the maximum power consumption state \(PC\big{(}vm_{i}^{max}\big{)}\) and minimum power consumption state \(PC\big{(}vm_{i}^{min}\big{)}\). The PC(D* extra life) is low as D* extra life performs smooth matching of tasks and resource instances by finding safer paths, whereas the power consumption of EW1 is comparatively higher as it performs static classification of tasks as computation-intensive, memory-intensive, and storage-intensive by considering the present traffic scenario and ignoring the history. The power consumption of EW2 and EW3 is higher than that of EW1 due to loose function approximation, poor scalability, and inappropriate selection of resources.