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EN
A mathematical model of the process of payment for purchases in an online store has been pre-sented. The model belongs to the class of semi-open queueing networks with four phases of exponential servers and Poisson arrivals. The authors describe in detail the derivation of the equations describing the system. Analytic expressions are derived on the basis of the proposed model for the average number of online store customers who have already paid for goods. Practical implementation of the model allows us to determine the number of clients who have added goods to their cart, but have not yet passed through the payment verification system, and thus determine the stream of real customers of the online store.
EN
Cloud technologies are a very considerable area that influence IT infrastructure, network services and applications. Research has highlighted difficulties in the functioning of cloud infrastructure. For instance, if a server is subjected to malicious attacks or a force majeure causes a failure in the cloud’s service, it is required to determine the time that it takes the system to return to being fully functional after the crash. This will determine the technological and financial risks faced by the owner and end users of cloud services. Therefore, to solve the problem of determining the expected time before service is resumed after a failure, we propose to apply Markovian queuing systems, specifically a model of a multi-channel queuing system with Poisson input flow and denial-of-service (breakdown).
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