Annals of Operations Research

, Volume 196, Issue 1, pp 241–246 | Cite as

Stability of the multiserver queue with addressed retrials

  • G. FalinEmail author


In the recent paper (Mushko et al. in Ann. Oper. Res. 141:283—301, 2006) Mushko, Jacob, et al. considered an M/M/c type queueing system with retrials. Given that returning customers have access to any server they obtained a sufficient condition for the stability of the system. We suggest an alternative approach to the problem and get the necessary and sufficient condition for the stability in more general situation, when some servers are reserved for processing of primary requests and do not serve returning customers.


Retrial queue Addressed retrial Ergodicity 



I thank the referees for their remarks and comments, which helped me to improve the clarity of the article.


  1. Falin, G. I., & Templeton, J. G. C. (1997). Retrial queues. London: Chapman and Hall. Google Scholar
  2. Klimenok, V. I., & Dudin, A. N. (2006). Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory. Queueing Systems, 54, 245–259. CrossRefGoogle Scholar
  3. Malyshev, V. A. (1972). Homogeneous random walks on the product of a finite set and a half-line. In Probabilistic Methods of Research. Moscow: Moscow State University (in Russian). Google Scholar
  4. Malyshev, V. A., & Menshikov, M. V. (1979). Ergodicity, continuity and analyticity of countable Markov chains. Proceedings of the Moscow Mathematical Society, 39. Google Scholar
  5. Mushko, V. V. (2006). M/M/c system with address retrial strategy and back-up servers. Automatic Control and Computer Sciences, 40, 58–65. Google Scholar
  6. Mushko, V. V., Jacob, M. J., Ramakrishnan, K. O., Krishnamoorthy, A., & Dudin, A. N. (2006). Multiserver queue with addressed retrials. Annals of Operations Research, 141, 283–301. CrossRefGoogle Scholar
  7. Neuts, M. F. (1978). Markov chains with applications in queueing theory, which have a matrix geometric invariant probability vector. Advances in Applied Probability, 10(1). Google Scholar
  8. Riordan, J. (1962). Stochastic service systems. New York: Wiley. Google Scholar
  9. Tweedie, R. L. (1975). Sufficient conditions for regularity, recurrence and ergodicity of Markov processes. Mathematical Proceedings of the Cambridge Philosophical Society, 78, 125–136. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Probability Theory, Mechanics and Mathematics FacultyMoscow State UniversityMoscowRussian Federation

Personalised recommendations