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Some Conditions for Ergodicity and Recurrence of Markov Chains

Author

Listed:
  • A. G. Pakes

    (Monash University, Victoria, Australia)

Abstract

This paper finds sufficient conditions for the ergodicity and recurrence of irreducible and aperiodic Markov chains. They extend some of the ones commonly used. The paper also indicates their use in discussing a certain class of queuing problem with state dependent service times.

Suggested Citation

  • A. G. Pakes, 1969. "Some Conditions for Ergodicity and Recurrence of Markov Chains," Operations Research, INFORMS, vol. 17(6), pages 1058-1061, December.
    • Handle: RePEc:inm:oropre:v:17:y:1969:i:6:p:1058-1061
    DOI: 10.1287/opre.17.6.1058
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    Cited by:

    1. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    2. Shweta Upadhyaya, 2020. "Investigating a general service retrial queue with damaging and licensed units: an application in local area networks," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 716-745, September.
    3. Falin, G.I., 2010. "A single-server batch arrival queue with returning customers," European Journal of Operational Research, Elsevier, vol. 201(3), pages 786-790, March.
    4. Sunggon Kim & Jongwoo Kim & Eui Lee, 2006. "Stationary distribution of queue length in G / M / 1 queue with two-stage service policy," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 64(3), pages 467-480, December.
    5. V. Jailaxmi & R. Arumuganathan & M. Senthil Kumar, 2017. "Performance analysis of an M/G/1 retrial queue with general retrial time, modified M-vacations and collision," Operational Research, Springer, vol. 17(2), pages 649-667, July.
    6. Kahraman, Aykut & Gosavi, Abhijit, 2011. "On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form," European Journal of Operational Research, Elsevier, vol. 212(2), pages 352-360, July.
    7. Baumann, Hendrik & Sandmann, Werner, 2014. "On finite long run costs and rewards in infinite Markov chains," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 41-46.
    8. Ioannis Dimitriou, 2013. "A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 542-571, October.
    9. T. Deepak, 2015. "On a retrial queueing model with single/batch service and search of customers from the orbit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 493-520, July.
    10. I. Atencia & G. Bouza & P. Moreno, 2008. "An M [X] /G/1 retrial queue with server breakdowns and constant rate of repeated attempts," Annals of Operations Research, Springer, vol. 157(1), pages 225-243, January.
    11. P. Rajadurai & V. M. Chandrasekaran & M. C. Saravanarajan, 2016. "Analysis of an M[X]/G/1 unreliable retrial G-queue with orbital search and feedback under Bernoulli vacation schedule," OPSEARCH, Springer;Operational Research Society of India, vol. 53(1), pages 197-223, March.

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