In recent years, fog computing has become an important environment for dealing with the Internet of Things. Fog computing was developed to handle large-scale big data by scheduling tasks via cloud computing. Task scheduling is crucial for efficiently handling IoT user requests, thereby improving system performance, cost, and energy consumption across nodes in cloud computing. With the large amount of data and user requests, achieving the optimal solution to the task scheduling problem is challenging, particularly in terms of cost and energy efficiency. In this paper, we develop novel strategies to save energy consumption across nodes in fog computing when users execute tasks through the least-cost paths. Task scheduling is developed using modified artificial ecosystem optimization (AEO), combined with negative swarm operators, Salp Swarm Algorithm (SSA), in order to competitively optimize their capabilities during the exploitation phase of the optimal search process. In addition, the proposed strategy, Enhancement Artificial Ecosystem Optimization Salp Swarm Algorithm (EAEOSSA), attempts to find the most suitable solution. The optimization that combines cost and energy for multi-objective task scheduling optimization problems. The backpack problem is also added to improve both cost and energy in the iFogSim implementation as well. A comparison was made between the proposed strategy and other strategies in terms of time, cost, energy, and productivity. Experimental results showed that the proposed strategy improved energy consumption, cost, and time over other algorithms. Simulation results demonstrate that the proposed algorithm increases the average cost, average energy consumption, and mean service time in most scenarios, with average reductions of up to 21.15% in cost and 25.8% in energy consumption.

This paper proposes a flexible probability mass function for modeling count data, particularly over-dispersed and asymmetric observations. A novel two-parameter discrete distribution, the discrete power inverted Topp–Leone distribution, is presented using a survival discretization technique. The following statistical characteristics are examined: factorial moments, probability-generating function, quantiles, mean, variance, mean residual life, and entropy measures. The best estimators of the unknown parameters were obtained using various techniques, such as maximum likelihood, moments, least squares, Anderson–Darling, and Cramér-von Mises. A simulation study showed that the accuracy of the estimates improves with larger samples, although higher parameter values may affect precision. The findings indicate that the efficiency of these estimation methods varies under different conditions. Applications to liver lesions, chromatid aberrations, and criminal sociology datasets confirm the model's usefulness for discrete count data in fields such as social sciences, pharmacology, and environmental health. Finally, for modeling count data, the new probabilistic model can be employed as a competitive alternative to other existing distributions.