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Resource Retrial Queue with Two Orbits and Negative Customers

Author

Listed:
  • Ekaterina Lisovskaya

    (Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 634050 Tomsk, Russia)

  • Ekaterina Fedorova

    (Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 634050 Tomsk, Russia)

  • Radmir Salimzyanov

    (Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 634050 Tomsk, Russia)

  • Svetlana Moiseeva

    (Institute of Applied Mathematics and Computer Science, National Research Tomsk State University, 634050 Tomsk, Russia)

Abstract

In this paper, a multi-server retrial queue with two orbits is considered. There are two arrival processes of positive customers (with two types of customers) and one process of negative customers. Every positive customer requires some amount of resource whose total capacity is limited in the system. The service time does not depend on the customer’s resource requirement and is exponentially distributed with parameters depending on the customer’s type. If there is not enough amount of resource for the arriving customer, the customer goes to one of the two orbits, according to his type. The duration of the customer delay in the orbit is exponentially distributed. A negative customer removes all the customers that are served during his arrival and leaves the system. The objects of the study are the number of customers in each orbit and the number of customers of each type being served in the stationary regime. The method of asymptotic analysis under the long delay of the customers in the orbits is applied for the study. Numerical analysis of the obtained results is performed to show the influence of the system parameters on its performance measures.

Suggested Citation

  • Ekaterina Lisovskaya & Ekaterina Fedorova & Radmir Salimzyanov & Svetlana Moiseeva, 2022. "Resource Retrial Queue with Two Orbits and Negative Customers," Mathematics, MDPI, vol. 10(3), pages 1-19, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:321-:d:729510
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    Cited by:

    1. Wei Xu & Liwei Liu & Linhong Li & Zhen Wang & Sabine Wittevrongel, 2023. "Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors," Mathematics, MDPI, vol. 11(16), pages 1-23, August.

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