Abstract
The operation of intermediate storages is investigated in this paper. The input process is supposed to be a batch process and the output process is assumed to be a continuous one. The operational conditions in the input process are stochastic with respect to time and the amount of material. The goal is the determination of the required size of the buffer to a given reliability. For the solution, an auxiliary function is introduced and an integral equation is set up for it. Its analytical solution is presented in a special case. In general cases we present the approximation of the reliability with the help of a hyperbolic tangent family. We compare the exact and approximate solutions and present the solution of the sizing problem. We investigate the effects of dispersions to present the uncertainties.
Highlights
Intermediate storages are often used in industry, such as chemical, pharmaceutical, food industry, environmental industry, energy production, and so on [1]
In general cases we present the approximation of the reliability with the help of a hyperbolic tangent family
3 Integral equations and solutions In this part we present integral equations which are satisfied by the function m(x,δ) and we provide an analytical solution in a special case
Summary
Intermediate storages are often used in industry, such as chemical, pharmaceutical, food industry, environmental industry, energy production, and so on [1]. Detailed possibilities can be found in [2] They serve as a buffer which is able to balance the differences between the turnout and the usage of the material due to some uncertainties, maintenances, failures and so on. In general sense banks, insurance companies serve as intermediate storages as well. They collect money, while in the industry material is usual. The assumptions concerning the operation correspond distinctive properties of the models. These assumptions demand different toolkits during investigation. The mathematical apparatus can be usually applied only to a certain extent, but it is useful for verifying the tools applied in computer engineering. Determination of the necessary initial amount was investigated earlier in the continuous model in [5], and in the discrete model in [6]
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