Polling on a space with general arrival and service time distribution

Operations Research Letters

Volumn 20, Issue 4, 1997, Pages 187-194

  Altman, Eitan ^a   Foss, Serguei ^a  

^a INRIA   (France)

Author keywords

General arrival; Polling systems; Service and walking times; Stability condition

Indexed keywords

EID: 0042765318     PISSN: 01676377     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-6377(97)00002-3     Document Type: Article

References (27)

1. E. Altman and S. Foss, "Polling on a graph with general arrival and service time", INRIA Report No. 1992.
2. E. Altman, S. Foss, E.R. Riehl and S. Stidham, "Performance Bounds and Pathwise Stability for Generalized Vacation and Polling Systems", Research Report UNC/OR TR93-8, Univ. of North Carolina, Chapel Hill, USA, 1993; to appear in: Oper. Res.
3. E. Altman and D. Kofman, "Bounds for Performance Measures of Token Rings", IEEE/ACM Trans. Networking 292-299 (1996).
4. E. Altman, P. Konstantopoulos and Z. Liu, "Stability, monotonicity and invariant quantities in general polling systems", Queuing Systems (Special Issue on Polling Models) H. Takagi and O. Boxma (eds.), 1992, pp. 35-57.
5. E. Altman and H. Levy, "Queueing in space", Adv. Appl. Probab. 26, 1095-1116 (1994).
6. E. Altman and Z. Liu, "Improving the stability characteristics of asynchronous traffic in FDDI token rings", in: H. Perros and Y. Viniotis (eds.), High Speed Networks and their Performance, North-Holland, Amsterdam, 1994, pp. 441-460.
7. E. Altman and F. Spieksma, "Polling systems: moment stability of station times and central limit theorems", Stochastic Models 12, 307-328 (1996).
8. S. Asmussen, Applied Probability and Queues, Wiley, New York, 1987.
9. A.A. Borovkov, Ergodicity and Stability of Stochastic Processes, to appear.
10. A.A. Borovkov, "Limit theorems for queueing networks", Theory Prob. Appl. 31, 413-427 (1986).
11. A.A. Borovkov and R. Schassberger, "Ergodicity of a polling system", Stochastic Processes Appl. 50, 253-262 (1994).
12. L. Greorgiadis and W. Szpankowski, "Stability of token passing rings", QUESTA (Special Issue on Polling Models). H. Takagi and O. Boxma (eds.), 1992, pp. 7-33.
13. S. Foss and A. Rybko, "Stability of multiclass Jackson-type networks", submitted to: Markov Processes Related Fields.
14. C. Fricker and M.R. Jaibi, "Monotonicity and stability of periodic polling models", QUESTA 15, 211-238 (1994).
15. S. Karlin and H.M. Taylor, A First Course in Stochastic Processes, Academic Press, New York, 1975.
16. D.P. Kroese and V. Schmidt, "A continuous polling system with general service times", Ann. Appl. Probab. 2, 906-927, (1992).
17. D.P. Kroese and V. Schmidt, "Single-server queues with spatially distributed arrivals", submitted.
18. H. Levy, M. Sidi and O.J. Boxma, "Dominance relations in polling systems", QUESTA 6, 155-172 (1990).
19. T. Lindvall, Lecture on the Coupling Method, Wiley, New York, 1992.
20. S.P. Meyn and R.L. Tweedie, "Stability of Markovian processes I: criteria for discrete time chains", Adv. Appl. Probab. 24, 542-574 (1992).
21. J.A.C. Resing, "Polling systems and multi-type branching processes", QUESTA 13, 409-426 (1993).
22. V. Sharma, "Stability and continuity of polling systems", QUESTA 16, 115-137 (1994).
23. H. Takagi, Analysis of Polling Systems, The MIT Press, Cambridge, MA, 1986.
24. H. Takagi, "Queuing analysis of polling models: an update", in: Takagi (ed.), Stock. Anal. Computer and Communications Systems, Elsevier, Amsterdam, 1990, pp. 267-318.
25. R.L. Tweedie, "Criteria for classifying general Markov chains", Adv. Appl. Probab. 8, 737-771 (1976).
26. R.L. Tweedie, "Criteria for rates of convergence of Markov chains, with application to queuing and storage theory", in: J.F.C. Kingman and G.E.H. Renter (eds.), Probability, Statistics and Analysis, London Math Soc. Lecture Notes, Vol. 79, Cambridge Univ. Press, Cambridge, 1983, pp. 260-276.
27. V.S. Zhdanov and E.A. Saksonov, "Conditions of existence of steady-state modes in cyclic queuing systems", Automation Remote Control 40, 176-184 (1979).