Ergodicity of the BMAP/PH/s/s + K retrial queue with PH-retrial times

Queueing Systems

Volumn 35, Issue 1-4, 2000, Pages 323-347

  He, Qi Ming ^a   Li, Hui ^b   Zhao, Yiqiang Q ^c  

^a DALHOUSIE UNIVERSITY   (Canada)

^b MOUNT SAINT VINCENT UNIVERSITY   (Canada)

^c UNIVERSITY OF WINNIPEG   (Canada)

Author keywords

Batch Markov arrival process (BMAP); Ergodicity; Impatient customer; Lyapunov function; Matrix analytic methods; Mean drift method; PH distribution; Retrial queue; Sample path method

Indexed keywords

LYAPUNOV FUNCTIONS;

ERGODICITY; IMPATIENT CUSTOMERS; MARKOV ARRIVAL PROCESS; MATRIX ANALYTIC METHODS; MEAN-DRIFT METHOD; PH DISTRIBUTION; RETRIAL QUEUE; SAMPLE-PATH METHOD;

QUEUEING THEORY;

EID: 0034342004     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/a:1019110631467     Document Type: Article

References (23)

1. J.R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Modelling 30 (1999) 1-6.
2. S. Asmussen, Applied Probability and Queues (Wiley, Chichester/New York, 1987).
3. B.D. Choi, K.K. Park and C.E.M. Pearce, An M/M/1 retrial queue with control policy and general retrial times, Queueing Systems 14 (1993) 275-292.
4. J.W. Cohen, The Single Server Queues (North-Holland, Amsterdam, 1982).
5. J. Diamond, Matrix analytic methods for retrial queues, Ph.D. thesis, Department of Mechanical and Industrial Engineering, University of Manitoba (1995).
6. J. Diamond and A.S. Alfa, Matrix analytic methods for M/PH/1 retrial queues, Stochastic Models 11 (1995) 447-470.
7. J. Diamond and A.S. Alfa, The MAP/PH/1 retrial queue, Stochastic Models 14 (1998) 1151-1178.
8. J.E. Diamond and A.S. Alfa, Matrix analytical methods for retrial queues with finite buffers, submitted to Queueing Systems.
9. J.E. Diamond and A.S. Alfa, Matrix analytical method for multiserver retrial queues with finite buffers, accepted Workshop on Retrial Queues (WRQ'98), Madrid (September 1998).
10. G.I. Falin, On sufficient conditions for ergodicity of multi-channel queueing systems with repeated calls, Adv. in Appl. Probab. 16 (1984) 447-448.
11. G.I. Falin, A survey of retrial queues, Queueing Systems 7 (1990) 127-167.
12. G.I. Falin and J.G.C. Templeton, Retrial Queues (Chapman & Hall, London, 1997).
13. F.R. Gantmacher, The Theory of Matrices (New York, Chelsea, 1959).
14. V.G. Kulkarni and H.M. Liang, Retrial queues revisited, in: Frontiers in Queueing: Models and Applications in Science and Engineering, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL, 1997) pp. 19-34.
15. H. Li and T. Yang, The steady-state distribution of the PH/M/1 retrial queue, in: Advances in Matrix Analytic Methods for Stochastic Models, eds. A.S. Alfa and S.R. Chakravarthy (Notable Publications, 1998) pp. 135-150.
16. H.M. Liang and V.G. Kulkarni, Stability condition for a single server retrial queue, Adv. in Appl. Probab. 25 (1993) 690-701.
17. D.M. Lucantoni, New results on the single server queue with a batch Markovian arrival process, Stochastic Models 7 (1991) 1-46.
18. M.F. Neuts, A versatile Markovian point process, J. Appl. Probab. 16 (1979) 764-779.
19. M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach (Johns Hopkins Univ. Press, Baltimore, MD, 1981).
20. M.F. Neuts, Structured Stochastic Matrices of M/G/1 Type and Their Applications (Marcel Dekker, New York, 1989).
21. M.F. Neuts and B.M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems 7 (1990) 169-189.
22. T. Yang, M.J.M. Posner, J.G.C. Templeton and H. Li, An approximation method for the M/G/1 retrial queue with general retrial times, European J. Oper. Res. 76 (1994) 552-562.
23. T. Yang and J.G.C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987) 201-233.