Stability of the multiserver queue with addressed retrials
- 135 Downloads
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.
KeywordsRetrial queue Addressed retrial Ergodicity
I thank the referees for their remarks and comments, which helped me to improve the clarity of the article.
- Falin, G. I., & Templeton, J. G. C. (1997). Retrial queues. London: Chapman and Hall. Google Scholar
- 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
- Malyshev, V. A., & Menshikov, M. V. (1979). Ergodicity, continuity and analyticity of countable Markov chains. Proceedings of the Moscow Mathematical Society, 39. Google Scholar
- 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
- 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
- Riordan, J. (1962). Stochastic service systems. New York: Wiley. Google Scholar