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Computation of the steady state distribution for multi-server retrial queues with phase type service process

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  • Che Kim
  • Vilena Mushko
  • Alexander Dudin

Abstract

We consider a multi-server retrial queueing system with the Batch Markovian Arrival Process and phase type service time distribution. Such a general queueing system suits for modeling and decision making in many real life objects including modern wireless communication networks. Behavior of such a system is described by the level dependent multi-dimensional Markov chain. Blocks of the generator of this chain, which is the block structured matrix of infinite size, can have large size if the number of servers is large and distribution of service time is not exponential. Due to this fact, the existing in literature algorithms allow to compute key performance measures of such a system only for a small number of servers. Here we describe the algorithm that allows to compute the stationary distribution of the system for larger number of servers and numerically illustrate its advantage. Importance of taking into account correlation in the arrival process is numerically demonstrated. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Che Kim & Vilena Mushko & Alexander Dudin, 2012. "Computation of the steady state distribution for multi-server retrial queues with phase type service process," Annals of Operations Research, Springer, vol. 201(1), pages 307-323, December.
    • Handle: RePEc:spr:annopr:v:201:y:2012:i:1:p:307-323:10.1007/s10479-012-1254-7
    DOI: 10.1007/s10479-012-1254-7
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    References listed on IDEAS

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    1. Valentina I. Klimenok & Dmitry S. Orlovsky & Alexander N. Dudin, 2007. "Abmap/Ph/Nsystem With Impatient Repeated Calls," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 293-312.
    2. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
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    Cited by:

    1. Sergei A. Dudin & Olga S. Dudina & Olga I. Kostyukova, 2023. "Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    2. Alexander Moiseev & Anatoly Nazarov & Svetlana Paul, 2020. "Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    3. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    4. Alexander N. Dudin & Sergey A. Dudin & Valentina I. Klimenok & Olga S. Dudina, 2024. "Stability of Queueing Systems with Impatience, Balking and Non-Persistence of Customers," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    5. K. R. Rejitha & K. P. Jose, 2018. "A stochastic inventory system with two modes of service and retrial of customers," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 134-149, March.
    6. Qi-Ming He & Attahiru Sule Alfa, 2018. "Space Reduction for a Class of Multidimensional Markov Chains: A Summary and Some Applications," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 1-10, February.
    7. A. N. Dudin & S. A. Dudin & O. S. Dudina, 2023. "Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    8. Wanlu Gu & Neng Fan & Haitao Liao, 2019. "Evaluating readmission rates and discharge planning by analyzing the length-of-stay of patients," Annals of Operations Research, Springer, vol. 276(1), pages 89-108, May.
    9. Alexander Dudin & Chesoong Kim & Olga Dudina & Sergey Dudin, 2016. "Multi-server queueing system with a generalized phase-type service time distribution as a model of call center with a call-back option," Annals of Operations Research, Springer, vol. 239(2), pages 401-428, April.
    10. 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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