# Indetermsoft-Set-Based D* Extra Lie Framework for Resource Provisioning in Cloud Computing
## 3 System Model  
This section provides the details of the structure, components, and interactions among the components of the proposed cloud resource-provisioning system. A detailed representation of its operational dynamics and a discussion of its theoretical foundations are also presented. The Indetermsoft-set-based D* extra like framework for edge computing systems is composed of three functional modules: Indetermsoft set task manager, Indetermsoft set resource manager, and D* extra like. The user submits a set of tasks (UTs) to the system accessibility layer, i.e., \(UT_{1}=\{ut_{1},ut_{2},ut_{3},\ldots,ut_{m}\}\), \(UT_{2}=\{ut_{1},ut_{2},ut_{3},\ldots,ut_{m}\}\), \(\ldots,UT_{m}=\{ut_{1},ut_{2},ut_{3},\ldots,ut_{m}\}\). The system accessibility layer places these user tasks into the task queue of the task manager. The Indetermsoft set task manager applies the Indetermsoft set function (ISF) to the user tasks. That is,  
\[ISF(UT_{1}) =\big{\{}isf(ut_{1}),isf(ut_{2}),isf(ut_{3}),\ldots,isf(ut_{m}) \big{\}},\] \[ISF(UT_{2}) =\big{\{}isf(ut_{1}),isf(ut_{2}),isf(ut_{3}),\ldots,isf(ut_{m}) \big{\}},\] \[ISF(UT_{m}) =\big{\{}isf(ut_{1}),isf(ut_{2}),isf(ut_{3}),\ldots,isf(ut_{m}) \big{\}} \tag{1}\]  
Similarly, the resource center is composed of several resource instances, each instance consists of a set of hosts, and a set of virtual machines are mounted on each host. \[RCI_{1}=\{H_{1}(vm_{1},\ vm_{2},\ldots,vm_{n}),\ldots,H_{n}(vm_{1},\ vm_{2}, \ldots,vm_{n})\ \},\]  
\[RCI_{2}=\{H_{1}(vm_{1},\ vm_{2},\ldots,vm_{n}),\ldots,H_{n}(vm_{1},\ vm_{2}, \ldots,vm_{n})\ \},\]  
\[RCI_{n}=\{H_{1}(vm_{1},\ vm_{2},\ldots,vm_{n}),\ldots,H_{n}(vm_{1},\ vm_{2}, \ldots,vm_{n})\ \} \tag{2}\]  
The Indetermsoft set resource manager applies the Indetermsoft set function to the resource instances. \[ISF(RCI_{1})=\{isf(H_{1}(vm_{1},\ vm_{2},\ldots,vm_{n}))\ldots isf(H_{n}(vm_{1}, \ vm_{2},\ldots,vm_{n}))\},\]  
\[ISF(RCI_{2})=\{isf(H_{1}(vm_{1},\ vm_{2},\ldots,vm_{n}))...isf(H_{n}(vm_{1},\ Vm_{2}, \ldots,vm_{n}))\},\]  
\[ISF(RCI_{n})=\{isf(H_{1}(vm_{1},\ vm_{2},\ldots,vm_{n}))...isf(H_{n}(vm_{1},\ vm_{2}, \ldots,vm_{n}))\ \} \tag{3}\]  
The D* extra like functional module combines the Indetermsoft set function of user tasks and the resource. It is an incremental heuristic search algorithm which is a dynamic form of the A* algorithm that generates D* extra like task resource-provisioning policies:  
\[D^{*}(RPP)=\{\ D^{*}(RPP_{1}),\ D^{*}(RPP_{2}),\ldots,D^{*}(RPP_{n})\ \} \tag{4}\]  
The following performance objectives (POs) are set for the D* extra like framework. PO1: Power Consumption (PC(D' extra like)): The power consumption of the D* extra like framework is the summation of the power consumption of the resource instances \(PC(RCI_{i})\). \[ISF(UT_{2}) =\big{\{}isf(ut_{1}),isf(ut_{2}),isf(ut_{3}),\ldots,isf(ut_{m}) \big{\}},\]0  
where \(PC(RCI_{i})\) is determined by the summation of the power consumption of the host \(PC(H_{i})\), i.e., \(PC(RCI_{i})=\sum_{i=1}^{i=n}PC(H_{i})\). Here, \(PC(H_{i})\) is determined by considering the maximum power consumption state \(PC(vm_{i}^{max})\), minimum power consumption state \(PC(vm_{i}^{min})\), and idle state power consumption \(PC(vm_{i}^{idle})\) of the virtual machine:  
\[ISF(UT_{2}) =\big{\{}isf(ut_{1}),isf(ut_{2}),isf(ut_{3}),\ldots,isf(ut_{m}) \big{\}},\]1PO2: Resource Utilization (RU(D\({}^{*}\) extra lite)): The resource utilization of the D* extra lite framework is computed by the summation of the resources utilized by the resource instances \(RU(RCI_{i})\). \[ISF(UT_{2}) =\big{\{}isf(ut_{1}),isf(ut_{2}),isf(ut_{3}),\ldots,isf(ut_{m}) \big{\}},\]2  
where \(RU(RCI_{i})\) is determined by the summation of the resources consumed by the host \(RU(H_{i})\), i.e., \(RU(RCI_{i})=\sum_{i=1}^{i=n}RU(H_{i})\). Here, \(RU(H_{i})\) is the measure of the utilities of the virtual machines that are used by the user tasks.