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A Stochastic Performance Model and Mobility Analysis in the Integrated Cloud-Fog-Edge Computing System

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Abstract

In line with digital transformation and the rapid progress on the Internet, technology has led to new hierarchical infrastructures for seamless connectivity. The integrated cloud-fog-edge computing system is a hierarchical infrastructure that provides better operational connectivity for users at all network ends. Lack of mobility management, the requirement for high-speed internet connectivity, limited bandwidth, and security issues are some of the issues that result in poor Quality of Service (QoS) in such environments. Mobility or seamless connectivity of users is one of the main challenging factors in the performance evaluation of an integrated cloud-fog-edge computing system. Hence, to obtain better QoS and support seamless connectivity, new and efficient modelling approaches are necessary. Thus, a stochastic performance model is considered in this paper for QoS analysis. The performance analysis is done to determine the operational space of the proposed model. This gives an idea of how to design and develop more efficient architectures for such systems. The mean queue length, throughput, and mean response time results are examined for performance evaluation. A discrete event simulation is also presented to validate the proposed analytical model.

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  1. Electrical and Electronics Engineering Department, Faculty of Engineering, European University of Lefke, Lefke, TR-10 Mersin, North Cyprus

    Yönal Kırsal

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Appendix A

Appendix A

$$\begin{aligned} \displaystyle \sum \limits _{n=C}^{\infty } \frac{r^{n}}{C^{n-C}C!}= & {} \dfrac{r^C}{C!} \displaystyle \sum \limits _{n=C}^{\infty } \left( \frac{r}{C}\right) ^{n-C} \nonumber \\= & {} \dfrac{r^C}{C!} \displaystyle \sum \limits _{m=0}^{\infty } \left( \frac{r}{C}\right) ^{m}\nonumber \\ {}= & {} \dfrac{r^C}{C!} \dfrac{1}{1-\dfrac{r}{C}} \end{aligned}$$
(A1)
$$\begin{aligned} Q_C= & {} \displaystyle \sum \limits _{n=C+1}^{\infty }(n-C)P_n = \displaystyle \sum \limits _{n=C+1}^{\infty }(n-C) \frac{r^{n}}{C^{n-C}C!}P_0 \nonumber \\= & {} \frac{r^{C}P_0}{C!} \displaystyle \sum \limits _{n=C+1}^{\infty }(n-C) \rho ^{n-C} \nonumber = \frac{r^{C}P_0}{C!} \displaystyle \sum \limits _{m=1}^{\infty }m\rho ^{m} \nonumber \\= & {} \frac{r^{C}\rho P_0}{C!} \displaystyle \sum \limits _{m=1}^{\infty }m\rho ^{m-1} \nonumber = \frac{r^{C}\rho P_0}{C!}\dfrac{d}{d\rho } \displaystyle \sum \limits _{m=1}^{\infty }\rho ^{m} \nonumber \\= & {} \frac{r^{C}\rho P_0}{C!}\dfrac{d}{d\rho } \left( \dfrac{1}{1-\rho }-1\right) = \frac{r^{C}\rho P_0}{C!(1-\rho )^2} \nonumber \\= & {} \frac{r^{n}\rho }{C!(1-\rho )^2} P_0 \end{aligned}$$
(A2)

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Kırsal, Y. A Stochastic Performance Model and Mobility Analysis in the Integrated Cloud-Fog-Edge Computing System. Mobile Netw Appl (2023). https://doi.org/10.1007/s11036-023-02202-x

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