# Indetermsoft-Set-Based D* Extra Lie Framework for Resource Provisioning in Cloud Computing
## 4 Proposed Work
### Indetermsoft Set Task Manager (ISSTM)
\[E\bigg{(}\frac{PC(D^{*}\ extra\ late)}{D^{*}(\ TSP)},\ FT\bigg{)}= \int_{x}^{y}\frac{\sum_{a\in\pi}PC(D^{*}\ extra\ late)(a)}{|D^{*}(\ TSP)|}\] \[E\bigg{(}\frac{PC(D^{*}\ extra\ late)}{D^{*}(\ TSP)},\ FT \bigg{)}=\sum\limits_{d\in D}d\int_{x}^{y}\frac{\sum_{a\in\pi}PC(D^{*}\ extra\ late)(a)}{|D^{*}(\ TSP)|}\] \[\qquad E\bigg{(}\frac{PC(D^{*}\ extra\ late)}{D^{*}(\ TSP)},\ FT \bigg{)}=\frac{E\Big{(}1*\pi*\sum_{i=1}^{i=n}PC(RCI_{i})\bigg{)}}{P(D^{*}( \ TSP))}\] \[=\sum\limits_{d\in D}d\int_{q}^{Q}\big{[}\ PC\big{(}vm_{i}^{max} \big{)}-PC\big{(}vm_{i}^{min}\big{)}\big{]}*R\mathrm{U}(vm_{i})+PC\Big{(}vm_{ i}^{idle}\Big{)}\big{]}\] \[=\int_{q}^{Q}Q*dP\frac{\big{[}\ PC\big{(}vm_{i}^{max}\big{)}-PC \big{(}vm_{i}^{min}\big{)}\big{]}*R\mathrm{U}(vm_{i})+PC\Big{(}vm_{i}^{idle} \Big{)}\big{]}}{D^{*}(\ TSP)}\] \[\qquad\mathrm{PC}(\mathrm{D*}\ extra\ late):\ E\bigg{(}\frac{PC(D ^{*}\ extra\ late)}{D^{*}(\ TSP)},\ FT\bigg{)}\approx\mathit{Low}\] \[\qquad\mathrm{PC}(\mathrm{EW1}):\ E\bigg{(}\frac{PC(EW1)}{D^{*}( \ TSP)},\ FT\bigg{)}\approx\mathit{Medium}\] \[\qquad\mathrm{PC}(\mathrm{EW2}):\ E\bigg{(}\frac{PC(EW2)}{D^{*}( \ TSP)},\ FT\bigg{)}\approx\mathit{High}\] \[\qquad\mathrm{PC}(\mathrm{EW3}):\ E\bigg{(}\frac{PC(EW3)}{D^{*}( \ TSP)},\ FT\bigg{)}\approx\mathit{High}\]

PO2: Resource Utilization (RU(D' late)): The resource utilization of D* extra life is mainly influenced by the over-utilization of resources of resource center instance \(RCI_{i}^{outer}\) and under-utilization of resources of resource center instance \(RCI_{i}^{under}\). The RU(D' late) is high as it combines an incremental search and a heuristic search strategy for task mapping. The resource utilization of EW1 is low due to improper formulation of the workflow model which leads to more resource wastage. The resource utilization of EW2 is moderate as the model is not capable of dealing with a large-state-space environment and takes alonger time to converge to Nash equilibrium. The RU(EW3) is low due to convergence to suboptimal solutions and poor task-routing capability. PO3: Total Execution Time (TET(D* lite)): The total execution time of D* extra lite is mainly influenced by the total execution time of the Indetermsoft set function of user tasks ISF(\(UT_{i}\)), Indetermsoft set function of resource instances \(ISF(\textit{RCI}_{i})\), and D* policy \(D^{*}(\textit{Tsp}_{i})\). The TET(D* lite) is low as it is capable of handling dynamic obstacles in cloud scenarios using an incremental search strategy. The TET(EW1) is moderate due to inappropriate mapping of resources. The TET(EW2) is very high because of poor workflow classification and softmax parametrization taking an infinite period of time for convergence. The TET(EW3) is low due to bad local search capability and a poor convergence rate. \[ \begin{split} E\bigg{(}\frac{\textit{TET}(D^{*}\ \textit{extra lite})}{D^{*}(\text{TSP})},\ \textit{FT}\bigg{)}=\int_{x}^{y}\frac{\sum_{\textit{e}\pi T}\textit{TET}(D^{*} \ \textit{extra lite})(a)}{|D^{*}(\text{TSP})|}\\ E\bigg{(}\frac{\textit{TET}(D^{*}\ \textit{extra lite})}{D^{*}( \text{TSP})},\ \textit{FT}\bigg{)}=\sum\limits_{d\in\mathcal{D}}d\int_{x}^{y} \frac{\sum_{\textit{e}\pi T}\textit{TET}(D^{*}\ \textit{extra lite})(a)}{|D^{*}(\text{TSP})|}\\ =\frac{E\Big{(}1*\pi*\sum_{i=1}^{i=m}\textit{TET}(ISF(UT_{i}))+ \sum_{i=1}^{i=m}\textit{TET}(ISF(\textit{RCI}_{i}))+\sum_{i=1}^{i=m}\textit{ TET}(D^{*}(\textit{Tsp}_{i}))\Big{)}}{P(D^{*}(\text{TSP}))}\\ =\int_{d}^{Q}Q\textit{tp}\frac{\sum_{i=1}^{i=m}\textit{TET}(ISF(UT _{i}))+\sum_{i=1}^{i=m}\textit{TET}(ISF(\textit{RCI}_{i}))+\sum_{i=1}^{i=m} \textit{TET}(D^{*}(\textit{Tsp}_{i}))}{D^{*}(\text{TSP})}\\ \text{TET}(\text{D* extra lite}):\ E\bigg{(}\frac{\textit{TET}(D^{*} \ \textit{extra lite})}{D^{*}(\text{TSP})},\ \textit{FT}\bigg{)}\approx\textit{Low}\\ \text{TET}(\text{EW1}):\ E\bigg{(}\frac{\textit{TET}(EW1)}{D^{*}( \text{TSP})},\ \textit{FT}\bigg{)}\approx\textit{Medium}\\ \text{TET}(\text{EW3}):\ E\bigg{(}\frac{\textit{TET}(EW3)}{D^{*}( \text{TSP})},\ \textit{FT}\bigg{)}\approx\textit{Low}\\ \end{split}