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Investigation of G-network with bypasses of queueing systems by positive customers at a non-stationary regime

Naumenko Victor, Kopats Dmitry, Matalytski Mikhail, Pankov Andrey

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 3

85--97

EN

An open queuing network (QN) with single-line queuing systems (QS) is considered. QS are characterized by the presence of bypasses and the possibility of coming of negative customers. The network receives two independent elementary streams. The first stream is formed from the ordinary (positive) customers, while the second is composed of negative customers. Arriving of each negative customer to the system destroys exactly one positive customer in the queue, if those are contained. Negative customers do not require maintenance as the service of positive customers in the network systems is carried out in accordance with the FIFO discipline. Positive customers with a probability depending on the state of the node when they are sent to it are added to the queue, and with an additional probability, they immediately bypass it and behave in the future as served. The service in the systems is exponential, the routing of positive customers in the network is Markov, taking into account the possibility of turning the customer into a negative one after sending it to another system.

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Modeling the process of purchase payment as a constituent of information security in e-commerce

Skitsko V., Ignatova I.

Operations Research and Decisions

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2016

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Vol. 26, No. 3

83--99

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.

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Multi-criteria approach to comparison of inspection allocation for multi-product manufacturing systems in make-to-order sector

Korytkowski P., Wiśniewski T., Zaikin O.

Control and Cybernetics

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2010

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Vol. 39, no 1

97-116

EN

This paper studies multi-product production manufacturing systems with in-line quality control. Quality control is carried at inspection stations located within a production line. Quality control has an impact on performance of the system: throughput decreases and resource utilization increases. Production lines are modeled as a multi-product Open Jackson Network, where stochastic character of routing is a result of quality control operations. Quality inspection can result in feedback to a work station of the manufacturing system. The approach developed allows for comparing different inspection allocations using three principal indices: overall cost, lead-time and equipment utilization.