Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience
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 i...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/8/715 |
| _version_ | 1811192528858251264 |
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| author | Chesoong Kim Sergey Dudin Alexander Dudin Konstantin Samouylov |
| author_facet | Chesoong Kim Sergey Dudin Alexander Dudin Konstantin Samouylov |
| author_sort | Chesoong Kim |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T23:54:06Z |
| format | Article |
| id | doaj.art-6a95e717ef064dd1992af853382f5a20 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-11T23:54:06Z |
| publishDate | 2019-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-6a95e717ef064dd1992af853382f5a202022-12-22T03:56:24ZengMDPI AGMathematics2227-73902019-08-017871510.3390/math7080715math7080715Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and ImpatienceChesoong Kim0Sergey Dudin1Alexander Dudin2Konstantin Samouylov3Department of Industrial Engineering, Sangji University, Wonju, Kangwon 26339, KoreaDepartment of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, BelarusDepartment of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, BelarusDepartment of Applied Informatics and Probability Theory, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, 117198 Moscow, RussiaWe 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.https://www.mdpi.com/2227-7390/7/8/715queuing networkretrialsstate-dependent marked Markovian arrival processwireless telecommunication networks |
| spellingShingle | Chesoong Kim Sergey Dudin Alexander Dudin Konstantin Samouylov Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience Mathematics queuing network retrials state-dependent marked Markovian arrival process wireless telecommunication networks |
| title | Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience |
| title_full | Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience |
| title_fullStr | Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience |
| title_full_unstemmed | Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience |
| title_short | Analysis of a Semi-Open Queuing Network with a State Dependent Marked Markovian Arrival Process, Customers Retrials and Impatience |
| title_sort | analysis of a semi open queuing network with a state dependent marked markovian arrival process customers retrials and impatience |
| topic | queuing network retrials state-dependent marked Markovian arrival process wireless telecommunication networks |
| url | https://www.mdpi.com/2227-7390/7/8/715 |
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