Planning Fog networks for time-critical IoT requests

The massive growth of the Internet of Things (IoT) applications and the challenges of Cloud computing have increased the importance of Fog networks for timely processing the requests from delay-sensitive applications. A Fog network provides local aggregation, analysis, and processing of IoT requests that may or may not be time-critical. One of the major issues of Fog is its capacity planning considering the traffic load of time-critical requests. The response time can be huge if a time-critical request is processed on Cloud. The response time of a time-critical request can be big on the Fog layer if it is not prioritized. Hence, there is a need to handle the time-critical traffic on a priority basis at the Fog layer. In this paper, a priority queuing model with preemption has been proposed considering the mixed types of requests at the Fog layer. The proposed approach determines the required number of Fog nodes in order to satisfy the desired Quality of Service (QoS) requirements of IoT requests. The proposed mechanism is evaluated through simulations using the iFogSim simulator. The work can be used in the capacity planning of Fog networks

Some Hermite-Hadamard type integral inequalities whose n-times differentiable functions are s-logarithmically convex functions

In this paper, the authors have tried to prove some new resultsof Hermite-Hadamard type integral inequality for n-times differentiable s-logarithmically convex functions and as a consequences the authors haveconcluded some well-known inequalities for such type of the functions

Hermite-Hadamard-Fejér Type Inequalities with Generalized K-Fractional Conformable Integrals and Their Applications

In this work, we introduce new definitions of left and right-sides generalized conformable K-fractional derivatives and integrals. We also prove new identities associated with the left and right-sides of the Hermite-Hadamard-Fejér type inequality for ϕ-preinvex functions. Moreover, we use these new identities to prove some bounds for the Hermite-Hadamard-Fejér type inequality for generalized conformable K-fractional integrals regarding ϕ-preinvex functions. Finally, we also present some applications of the generalized definitions for higher moments of continuous random variables, special means, and solutions of the homogeneous linear Cauchy-Euler and homogeneous linear K-fractional differential equations to show our new approach

q1q2-Ostrowski-Type Integral Inequalities Involving Property of Generalized Higher-Order Strongly n-Polynomial Preinvexity

Quantum calculus has numerous applications in mathematics. This novel class of functions may be used to produce a variety of conclusions in convex analysis, special functions, quantum mechanics, related optimization theory, and mathematical inequalities. It can drive additional research in a variety of pure and applied fields. This article’s main objective is to introduce and study a new class of preinvex functions, which is called higher-order generalized strongly n-polynomial preinvex function. We derive a new q1q2-integral identity for mixed partial q1q2-differentiable functions. Because of the nature of generalized convexity theory, there is a strong link between preinvexity and symmetry. Utilizing this as an auxiliary result, we derive some estimates of upper bound for functions whose mixed partial q1q2-differentiable functions are higher-order generalized strongly n-polynomial preinvex functions on co-ordinates. Our results are the generalizations of the results in earlier papers. Quantum inequalities of this type and the techniques used to solve them have applications in a wide range of fields where symmetry is important

<i>q</i>₁<i>q</i>₂-Ostrowski-Type Integral Inequalities Involving Property of Generalized Higher-Order Strongly <i>n</i>-Polynomial Preinvexity

Quantum calculus has numerous applications in mathematics. This novel class of functions may be used to produce a variety of conclusions in convex analysis, special functions, quantum mechanics, related optimization theory, and mathematical inequalities. It can drive additional research in a variety of pure and applied fields. This article’s main objective is to introduce and study a new class of preinvex functions, which is called higher-order generalized strongly n-polynomial preinvex function. We derive a new q1q2-integral identity for mixed partial q1q2-differentiable functions. Because of the nature of generalized convexity theory, there is a strong link between preinvexity and symmetry. Utilizing this as an auxiliary result, we derive some estimates of upper bound for functions whose mixed partial q1q2-differentiable functions are higher-order generalized strongly n-polynomial preinvex functions on co-ordinates. Our results are the generalizations of the results in earlier papers. Quantum inequalities of this type and the techniques used to solve them have applications in a wide range of fields where symmetry is important

Hermite-Hadamard Type Integral Inequalities for Functions Whose Mixed PartialDerivatives Are Co-ordinated Preinvex

The main objective of this article is to establish integral iden-tity relating the left side of Hermite- Hadamard type inequality. By usingthis identity, we establish some new Hermite-Hadamard type integral in-equalities for functions whose mixed partial derivatives are co-ordinatedpreinvex. These consequences generalize numerous outcomes establishedin previous studies for these classes of functions

Some New Quantum Hermite–Hadamard-Type Estimates Within a Class of Generalized (s,m)-Preinvex Functions

In this work, we discover a new version of Hermite&ndash;Hadamard quantum integrals inequality via m-preinvex functions. Moreover, the authors present a quantum integrals identity and drive some new quantum integrals of Hermite&ndash;Hadamard-type inequalities involving generalized ( s , m ) -preinvex functions

Hermite–Hadamard-Type Inequalities Involving Harmonically Convex Function via the Atangana–Baleanu Fractional Integral Operator

Fractional integrals and inequalities have recently become quite popular and have been the prime consideration for many studies. The results of many different types of inequalities have been studied by launching innovative analytical techniques and applications. These Hermite–Hadamard inequalities are discovered in this study using Atangana–Baleanu integral operators, which provide both practical and powerful results. In this paper, a symmetric study of integral inequalities of Hermite–Hadamard type is provided based on an identity proved for Atangana–Baleanu integral operators and using functions whose absolute value of the second derivative is harmonic convex. The proven Hermite–Hadamard-type inequalities have been observed to be valid for a choice of any harmonic convex function with the help of examples. Moreover, fractional inequalities and their solutions are applied in many symmetrical domains

q-Hermite-Hadamard Inequalities for Generalized Exponentially (s, m; eta)-Preinvex Functions

In this article, we introduce a new extension of classical convexity which is called generalized exponentially (s, m; eta)-preinvex functions. Also, it is seen that the new definition of generalized exponentially (s, m; eta)-preinvex functions describes different new classes as special cases. To prove our main results, we derive a new (m kappa 2)q-integral identity for the twice (m kappa 2)q-differentiable function. By using this identity, we show essential new results for Hermite-Hadamard-type inequalities for the (m kappa 2)q-integral by utilizing differentiable exponentially (s, m; eta)-preinvex functions. The results presented in this article are unification and generalization of the comparable results in the literature.Zhejiang Normal University [321004]This research was supported by Zhejiang Normal University, Jinhua, 321004, China.WOS:0006649684000022-s2.0-8510538340

Quantum Inequalities of Hermite-Hadamard Type for r-Convex Functions

In this present study, we first establish Hermite-Hadamard type inequalities for r-convex functions via (q)(k2)-definite integrals. Then, we prove some quantum inequalities of Hermite-Hadamard type for product of two r-convex functions. Finally, by using these established inequalities and the results given by (Brahim et al. 2015), we prove several quantum Hermite-Hadamard type inequalities for coordinated r-convex functions and for the product of two coordinated r-convex functions.Philosophy and Social Sciences of Educational Commission of Hubei Province of China [20Y109]; Key Projects of Educational Commission of Hubei Province of China [D20192501]; Special Soft Science Project of Technological Innovation in Hubei Province [2019ADC146]This research was supported by Philosophy and Social Sciences of Educational Commission of Hubei Province of China (20Y109), Key Projects of Educational Commission of Hubei Province of China (D20192501), and Special Soft Science Project of Technological Innovation in Hubei Province (2019ADC146).WOS:0006271368000042-s2.0-8510231058