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Analysis of Non-Steady Queue-Length Distribution in a Finite-Buffer Model with Group Arrivals and Power Saving Mechanism with Setups

Author

Listed:
  • Wojciech M. Kempa

    (Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 23 Kaszubska Str., 44-100 Gliwice, Poland)

  • Dariusz Kurzyk

    (Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, 5 Bałtycka Str., 44-100 Gliwice, Poland)

Abstract

In the manuscript, a probability distribution of the queue length is studied in a model with group Markov arrivals, arbitrarily distributed service times and finite waiting room. After the period of suspension of service due to lack of packets, each new busy period is preceded by a random setup time. Integral equations for time-dependent queue-length distribution are derived by identifying renewal moments in the operation of the system and by applying total probability law. The representation for the solution of the system is found in terms of Laplace transforms. Computational examples illustrating the impact of system parameters on the queue-length distribution are included.

Suggested Citation

  • Wojciech M. Kempa & Dariusz Kurzyk, 2022. "Analysis of Non-Steady Queue-Length Distribution in a Finite-Buffer Model with Group Arrivals and Power Saving Mechanism with Setups," Energies, MDPI, vol. 15(22), pages 1-15, November.
    • Handle: RePEc:gam:jeners:v:15:y:2022:i:22:p:8471-:d:971215
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    References listed on IDEAS

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    3. Yebai Qi & Dan Wang & Yu Lan & Hongjie Jia & Chengshan Wang & Kaixin Liu & Qing’e Hu & Menghua Fan, 2017. "A Two-Level Optimal Scheduling Strategy for Central Air-Conditioners Based on Metal Model with Comprehensive State-Queueing Control Models," Energies, MDPI, vol. 10(12), pages 1-21, December.
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    5. Peishu Chen & Wenhui Zhou & Yongwu Zhou, 2015. "Equilibrium Customer Strategies in the Queue with Threshold Policy and Setup Times," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, August.
    6. Adrian Kampa & Iwona Paprocka, 2021. "Analysis of Energy Efficient Scheduling of the Manufacturing Line with Finite Buffer Capacity and Machine Setup and Shutdown Times," Energies, MDPI, vol. 14(21), pages 1-25, November.
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