Strong stability in retrial queues
Authors:
Louisa Berdjoudj and Djamil Aissani
Journal:
Theor. Probability and Math. Statist. 68 (2004), 11-17
MSC (2000):
Primary 60J25, 60K25
DOI:
https://doi.org/10.1090/S0094-9000-04-00595-2
Published electronically:
May 24, 2004
MathSciNet review:
2000390
Full-text PDF Free Access
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Additional Information
Abstract:
In this paper we study the strong stability in retrial queues after perturbation of the retrial’s parameter.
Our objective is to obtain the necessary and sufficient conditions to approximate the stationary characteristics of the $M/G/1/1$ retrial queue by the classical $M/G/1$ correspondent ones. After clarifying the approximation conditions, we obtain the stability inequalities with an exact computation of the constants.
References
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- ---, Strong stability of an imbedded Markov chain in an M/G/1 system, Theor. Probability and Math. Statist. 29 (1984), 1–5. MR 85d:60167
- D. Aissani, Application of the operator methods to obtain inequalities of stability in an M2/G2/1 system with a relative priority, Annales Maghrébines de l’Ingénieur, Numéro Hors série 2 (1991), 790–795.
- A. M. Alexandrov, A queueing system with repeated orders, Engineering Cybernetics Review 12 (1974), no. 3, 1–4. MR 52:6905
- E. Altman and A. A. Borovkov, On the stability of retrial queues, Queueing systems 26 (1997), 343–363. MR 2000b:60213
- Q. H. Choo and B. Conolly, New results in the theory of repeated orders queueing systems, Journal of Applied Probability 16 (1979), 631–640. MR 80j:60118
- G. I. Falin, A survey of retrial queues, Queueing Systems 7 (1990), 127–168. MR 91m:60166
- ---, Ergodicity and stability of systems with repeated calls, Ukr. Math. J. 41 (1989), no. 5. MR 91c:60125
- V. V. Kalashnikov and G. S. Tsitsiashvili, On the stability of queueing systems with respect to disturbances of their distribution functions, Queueing Theory and Reliability (1971), 211–217. MR 49:8133
- N. V. Kartashov, Strong stability of Markov chains, Proceedings of the All-Union Seminar VNISSI (Stability Problems for Stochastic Models), vol. 30, 1981, pp. 54–59. MR 84b:60089
- ---, Strong stable Markov chains, VSP/TBiMC, Utrecht/Kiev, 1996. MR 99e:60150
- J. Keilson, V. A. Cozzolino, and H. Young, A service system with unfilled requests repeated, Operations Research 16 (1968), 1126–1137.
- V. M. Zolotarev, On the continuity of stochastic sequences generated by recurrent processes, Theory of Probability and its Applications 20 (1975), 819–832. MR 53:4199
References
- D. Aissani and N. V. Kartashov, Ergodicity and stability of Markov chains with respect to operator topology in the space of transition kernels, Dokl. Akad. Nauk Ukr. SSR (ser. A) 11 (1983), 3–5. MR 85c:60110
- ---, Strong stability of an imbedded Markov chain in an M/G/1 system, Theor. Probability and Math. Statist. 29 (1984), 1–5. MR 85d:60167
- D. Aissani, Application of the operator methods to obtain inequalities of stability in an M2/G2/1 system with a relative priority, Annales Maghrébines de l’Ingénieur, Numéro Hors série 2 (1991), 790–795.
- A. M. Alexandrov, A queueing system with repeated orders, Engineering Cybernetics Review 12 (1974), no. 3, 1–4. MR 52:6905
- E. Altman and A. A. Borovkov, On the stability of retrial queues, Queueing systems 26 (1997), 343–363. MR 2000b:60213
- Q. H. Choo and B. Conolly, New results in the theory of repeated orders queueing systems, Journal of Applied Probability 16 (1979), 631–640. MR 80j:60118
- G. I. Falin, A survey of retrial queues, Queueing Systems 7 (1990), 127–168. MR 91m:60166
- ---, Ergodicity and stability of systems with repeated calls, Ukr. Math. J. 41 (1989), no. 5. MR 91c:60125
- V. V. Kalashnikov and G. S. Tsitsiashvili, On the stability of queueing systems with respect to disturbances of their distribution functions, Queueing Theory and Reliability (1971), 211–217. MR 49:8133
- N. V. Kartashov, Strong stability of Markov chains, Proceedings of the All-Union Seminar VNISSI (Stability Problems for Stochastic Models), vol. 30, 1981, pp. 54–59. MR 84b:60089
- ---, Strong stable Markov chains, VSP/TBiMC, Utrecht/Kiev, 1996. MR 99e:60150
- J. Keilson, V. A. Cozzolino, and H. Young, A service system with unfilled requests repeated, Operations Research 16 (1968), 1126–1137.
- V. M. Zolotarev, On the continuity of stochastic sequences generated by recurrent processes, Theory of Probability and its Applications 20 (1975), 819–832. MR 53:4199
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Additional Information
Louisa Berdjoudj
Affiliation:
L.A.M.O.S., Laboratory of Modelisation and Optimization of Systems, Faculty of Sciences and Engineer Sciences, University of Béjaia, 06000, Algeria
Djamil Aissani
Affiliation:
L.A.M.O.S., Laboratory of Modelisation and Optimization of Systems, Faculty of Sciences and Engineer Sciences, University of Béjaia, 06000, Algeria
Email:
lamos_bejaia@hotmail.com
Keywords:
Retrial queues,
perturbation,
strong stability,
approximation
Received by editor(s):
June 1, 2001
Published electronically:
May 24, 2004
Article copyright:
© Copyright 2004
American Mathematical Society
