This paper deals with FINITE CAPACITY single server queuing system with vacations. Vacation starts at rate u if the system is empty. Also, the server takes another vacation if upon his arrival to the system, finds the system empty. Customers arrive in the system in Poisson fashion at rate λ0 during vacation, faster rate λf during active service and slower rate λs³0 during the breakdown. Customers are served exponentially with the rate m. Server breakdowns at rate b and it immediately repaired exponentially with the rate r. We derive the explicit formulas for queue length distribution, average queue length, average number of customers in the system and average waiting time for a customer in queue and in the system. Numerical illustrations have been cited to show the model proposed is practically sound.

The granular pile anchor (GPA) is a relatively new and uncomplicated ground improvement technique that can support tensile loads effectively. In this study, the uplift CAPACITY of GPAs embedded in clay was assessed using FINITE element limit analysis (FELA) with an adaptive mesh. The analysis considered a broad range of parameters, including the GPA’s diameter and length, the undrained shear strength of the surrounding clay, and the friction angle and unit weight of the GPA material. Results showed that the dimensionless uplift CAPACITY generally increased with a higher length-to-diameter ratio. However, the nature of this increase varied for certain cases due to shifts in the failure mechanism of the GPA. Multiple linear regression was applied to establish a practical correlation,, resulting in a predictive equation for dimensionless variables. The model's goodness-of-fit was evaluated using statistical measures such as the ztest, demonstrating its reliability. This study's findings provide valuable insights for designing GPAs in clayey soils and contribute to more effective engineering applications.

We address the batch arrival m[x]/G/1 systems with FINITE CAPACITY under partial batch acceptance strategy where service times or rates oscillate between two forms according to the evolution of the number of customers in the system. Applying the theory of Markov regenerative processes and resorting to Markov chain embedding, we present a new algorithm for computing limit distributions of the number customers in the system. The numerical results are given in the paper for a clearer expression of the proposed computational methodologies

The ultimate bearing CAPACITY of ring footings for different conditions such as internal to external diameter ratio, base roughness and thickness of sand layer were determined in the laboratory. The deformed shape of the soil under footing at failure was investigated, and accordingly a semi-empirical relation for determining the bearing CAPACITY of ring footings was developed. The bearing CAPACITY of ring footings was also determined using FINITE element method. The results of experiments, a semi-empirical relation and numerical methods were compared, and reasonable agreements were observed.

In this paper, finding Dynamic Load Carrying CAPACITY (DLCC) of flexible link manipulators in point to-point motion was formulated as an optimal control problem. The FINITE element method was employed for modelling and deriving the dynamic equations of the system. The study employed indirect solution of optimal control for system motion planning. Due to offline nature of the method, many difficulties such system nonlinearities and all types of constraints can be catered for and implemented easily. The application of Pontryagin’s minimum principle to this problem was resulted in a standard two-point boundary value problem (TPBVP), solved numerically. Then, the formulation was developed to find the maximum payload and corresponding optimal path. The main advantage of the proposed method is that the various optimal trajectories can be obtained with different characteristics and different maximum payloads. Therefore, the designer can select a suitable path among the numerous optimal paths. In order to verify the effectiveness of the method, a simulation study considering a two-link flexible manipulator was presented in details.