The functional and mathematical models of call center working in case of overload are constructed and analyzed. In the model the following features are considered: the possibility of serving of coming request by IVR (Interactive Voice Response); the option of waiting the beginning of service in case of blocking and the opportunity of request repetition in case of occupation of all waiting positions or unsuccessful finishing of waiting time. Markov process that describes model functioning is defined. Main performance measures of requests coming and serving are given with help of values of stationary probabilities of model's states. The values of performance measures are found after solving the system of state equations by Gauss-Zeidel iterative approach. Expressions that relates the model's main performance measures in form of local and global conservation laws are found. The obtained results can be used for indirect measurement of intensity of primary requests and the probability of call repetition. It is shown how to use the model and the derived results for reducing the negative effects of overload by filtering the input flows of primary and repeated attempts. The usage of the model for calculation of the numbers of operators and waiting places required to serve the incoming traffic flows with given value of probability of call losses and mean value of waiting the beginning of service is considered. Numerical results that illustrate the implementation of the derived expressions and algorithms are given.
This paper is dedicated to a study of aluminum influence on the improvement of surface adhesion strength. The main purpose of this work is to investigate the strength of adhesion to the substrate by mixing flame spray powder with aluminum, which not only possesses high corrosion resistance and conductivity, but also provides additional strength, as it combines and reacts with other components of the powder.
Research results of sandblasting dependence on surface roughness parameter Ra are demonstrated.
The paper describes authors’ original device for a measuring instrument “Profilometer”, which was also used for measuring roughness parameter in order to obtain comparative results.
Authors present results of adhesion measurements given obtained values of surface roughness by mixing nominal chemical composition of PR-30X13 powder, used as a testing material, with aluminum, which reacts with oxides on the surface of steel substrates, imparts strength to the bonding between the coating and the substrate, protects the base metal due to a combination of chemical components of the powder and creates a layer of dense surface coating. These dependencies are analyzed and parameters, exerting the greatest influence on their values, are identified.
Taking into account the results obtained through numerical modeling, authors propose a mathematical model of a dependency between adhesion strength and certain values of surface roughness for different chemical compositions of flame spray powder. These studies will help in the development of certain material types for spraying and hardening of steel parts and products in order to improve their durability.
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