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Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers

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  • Baumann, Hendrik
  • Sandmann, Werner

Abstract

We consider multi-server tandem queues where both stations have a finite buffer and all services times are phase-type distributed. Arriving customers enter the first queueing station if buffer space is available or get lost otherwise. After completing service in the first station customers proceed to the second station if buffer space is available, otherwise a server at the first station is blocked until buffer space becomes available at the second station. We provide an exact computational analysis of various steady-state performance measures such as loss and blocking probabilities, expectations and higher moments of numbers of customers in the queues and in the whole system by modeling the tandem queue as a level-dependent quasi-birth-and-death process and applying suitable matrix-analytic methods. Numerical results are presented for selected representative examples.

Suggested Citation

  • Baumann, Hendrik & Sandmann, Werner, 2017. "Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers," European Journal of Operational Research, Elsevier, vol. 256(1), pages 187-195.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:1:p:187-195
    DOI: 10.1016/j.ejor.2016.07.035
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    References listed on IDEAS

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    1. Krishnamoorthy, A. & Babu, S. & Narayanan, Viswanath C., 2009. "The MAP/(PH/PH)/1 queue with self-generation of priorities and non-preemptive service," European Journal of Operational Research, Elsevier, vol. 195(1), pages 174-185, May.
    2. Kim, Chesoong & Dudin, Alexander & Dudina, Olga & Dudin, Sergey, 2014. "Tandem queueing system with infinite and finite intermediate buffers and generalized phase-type service time distribution," European Journal of Operational Research, Elsevier, vol. 235(1), pages 170-179.
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    Cited by:

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    2. Asadabadi, Mehdi Rajabi, 2017. "A customer based supplier selection process that combines quality function deployment, the analytic network process and a Markov chain," European Journal of Operational Research, Elsevier, vol. 263(3), pages 1049-1062.
    3. Chesoong Kim & Sergei Dudin & Olga Dudina, 2019. "Queueing Network with Moving Servers as a Model of Car Sharing Systems," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
    4. Sina Ansari & Seyed M. R. Iravani & Qifeng Shao, 2019. "Optimal control policies in service systems with limited information on the downstream stage," Naval Research Logistics (NRL), John Wiley & Sons, vol. 66(5), pages 367-392, August.
    5. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    6. Chao Fu & Wenjun Chang, 2024. "A Markov Chain-Based Group Consensus Method with Unknown Parameters," Group Decision and Negotiation, Springer, vol. 33(5), pages 1019-1048, October.
    7. Liu, Baoliang & Wen, Yanqing & Qiu, Qingan & Shi, Haiyan & Chen, Jianhui, 2022. "Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    8. Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2020. "Competitive queueing systems with comparative rating dependent arrivals," Operations Research Perspectives, Elsevier, vol. 7(C).
    9. Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2018. "Analysis of queueing model with processor sharing discipline and customers impatience," Operations Research Perspectives, Elsevier, vol. 5(C), pages 245-255.

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