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Article

Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience

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Department of Industrial Engineering, Sangji University, Wonju, Kangwon 26339, Korea
2
Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
3
Department of Applied Informatics and Probability Theory, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, Russia
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(8), 715; https://doi.org/10.3390/math7080715
Received: 10 July 2019 / Revised: 3 August 2019 / Accepted: 5 August 2019 / Published: 7 August 2019
(This article belongs to the Special Issue Stochastic Processes: Theory and Applications)
We consider a queuing network with single-server nodes and heterogeneous customers. The number of customers, which can obtain service simultaneously, is restricted. Customers that cannot be admitted to the network upon arrival make repeated attempts to obtain service. The service time at the nodes is exponentially distributed. After service completion at a node, the serviced customer can transit to another node or leave the network forever. The main features of the model are the mutual dependence of processes of customer arrivals and retrials and the impatience and non-persistence of customers. Dynamics of the network are described by a multidimensional Markov chain with infinite state space, state inhomogeneous behavior and special structure of the infinitesimal generator. The explicit form of the generator is derived. An effective algorithm for computing the stationary distribution of this chain is recommended. The expressions for computation of the key performance measures of the network are given. Numerical results illustrating the importance of the account of the mentioned features of the model are presented. The model can be useful for capacity planning, performance evaluation and optimization of various wireless telecommunication networks, transportation and manufacturing systems. View Full-Text
Keywords: queuing network; retrials; state-dependent marked Markovian arrival process; wireless telecommunication networks queuing network; retrials; state-dependent marked Markovian arrival process; wireless telecommunication networks
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MDPI and ACS Style

Kim, C.; Dudin, S.; Dudin, A.; Samouylov, K. Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience. Mathematics 2019, 7, 715. https://doi.org/10.3390/math7080715

AMA Style

Kim C, Dudin S, Dudin A, Samouylov K. Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience. Mathematics. 2019; 7(8):715. https://doi.org/10.3390/math7080715

Chicago/Turabian Style

Kim, Chesoong, Sergey Dudin, Alexander Dudin, and Konstantin Samouylov. 2019. "Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience" Mathematics 7, no. 8: 715. https://doi.org/10.3390/math7080715

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