Stability of polling systems with exhaustive service policies and state-dependent routing

Annals of Applied Probability

Volumn 6, Issue 1, 1996, Pages 116-137

  Foss, Serguei ^a   Last, Günter ^b  

^a NOVOSIBIRSK STATE UNIVERSITY   (Russian Federation)

^b TECHNICAL UNIVERSITY OF BRAUNSCHWEIG   (Germany)

Author keywords

Ergodicity of Markov chains; Greedy server; Polling system; Stability

Indexed keywords

EID: 0030547903     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968068     Document Type: Article

References (22)

1. ALTMAN, E. and LEVY, H. (1994). Queueing in space. Adv. in Appl. Probab. 26 1095-1116.
2. BACCELLI, F. and FOSS, S. (1995). On the saturation rule for the stability of queues. J. Appl. Probab. 32 494-507.
3. BOROVKOV, A. A. (1994). Ergodicity and Stability of Stochastic Processes. TVP Publishers, Moscow. To appear.
4. BOROVKOV, A. A. and SCHASSBERGER, R. (1994). Ergodicity of a polling network. Stochastic Process. Appl. 50 253-262.
5. COFFMAN, E. G., JR. and GILBERT, E. N. (1987). Polling and greedy servers on a line. Queueing Systems Theory Appl. 2 115-145.
6. DAI, J. G. (1995). On positive Harris recurrence for multiclass queueing networks: A unified approach via fluid limit models. Ann. Appl. Probab. 5 49-77.
7. FAYOLLE, G. and LASGOUTTES, J. (1994). A state-dependent polling model with Markovian routing. INRIA Report 2279.
8. FAYOLLE, G., MALYSHEV, V. A. and MENSHIKOV, M. V. (1995). Topics in the Constructive Theory of Countable Markov Chains. Cambridge Univ. Press.
9. FOSS, S. and CHERNOVA, N. (1996). Ergodic properties of polling systems. Problems Inform. Transmission. To appear.
10. FOSS, S. and LAST, G. (1995). On the stability of greedy polling systems with general service policies. Preprint.
11. FRICKER, C. and JAIBI, M. R. (1994). Monotonicity and stability of periodic polling systems. Queueing Systems Theory Appl. 15 211-238.
12. GEORGIADIS, L. and SZPANKOWSKI, W. (1992). Stability of token passing rings. Queueing Systems Theory Appl. 11 7-34.
13. KROESE, D. P. and SCHMIDT, V. (1992). A continuous polling system with general service times. Ann. Appl. Probab. 2 906-927.
14. KROESE, D. P. and SCHMIDT, V. (1994). Single-server queues with spatially distributed arrivals. Queueing Systems Theory Appl. 17 317-345.
15. LAST, G. and BRANDT, A. (1995). Marked Point Processes on the Real Line: The Dynamic Approach. Springer, New York.
16. LEVY, H., SIDI, M. and BOXMA, O. J. (1990). Dominance relations in polling systems. Queueing Systems Theory Appl. 6 155-171.
17. MALYSHEV, V. A. and MENSHIKOV, M. V. (1982). Ergodicity, continuity and analyticity of countable Markov chains. Trans. Moscow Math. Soc. 1 1-48.
18. MASSOULIÉ, L. (1995). Stability of non-Markovian polling systems. Queueing Systems Theory Appl. 21 67-95.
19. MEYN, S. P. and TWEEDIE, R. L. (1993). Markov Chains and Stochastic Stability. Springer, London.
20. MEYN, S. P. and TWEEDIE, R. L. (1994). State-dependent criteria for convergence of Markov chains. Ann. Appl. Probab. 4 149-168.
21. SCHASSBERGER, R. (1993). Stability of polling networks with state-dependent server routing. Technical Report 12/93, Technical Univ. Braunschweig.
22. TAGAKI, H. (1990). Queueing analysis of polling systems. In Stochastic Analysis of Computer and Communication Systems (H. Takagi, ed.) 267-318. North-Holland, Amsterdam.