Performance bounds and pathwise stability for generalized vacation and polling systems

Operations Research

Volumn 46, Issue 1, 1998, Pages 137-148

  Altman, Eitan ^a   Foss, Serguei ^b   Riehl, Eric ^c   Stidham Jr , Shaler ^c  

^a INRIA   (France)

^b SOBOLEV INSTITUTE OF MATHEMATICS   (Russian Federation)

^c UNIVERSITY OF NORTH CAROLINA   (United States)

Author keywords

Communications: token ring local area networks; Queues: polling and vacation systems, pathwise analysis, performance bounds

Indexed keywords

ITERATIVE METHODS; MATHEMATICAL MODELS; POLYNOMIALS; PROBABILITY; PROCESS CONTROL; QUEUEING THEORY;

POLLING SYSTEMS; POLYNOMIALLY BOUNDED TAIL PROBABILITY; UP MODE PROCESSES;

OPERATIONS RESEARCH;

EID: 0031701711     PISSN: 0030364X     EISSN: None     Source Type: Journal    
DOI: 10.1287/opre.46.1.137     Document Type: Article

References (26)

1. ALTMAN, E. AND S. G. FOSS. 1997. Polling on a Space With General Arrival and Service Time Distribution. O. R. Letts. 20, 187-194.
2. ALTMAN, E., S. G. FOSS, E. R. RIEHL, AND S. STIDHAM. 1994. Sample Path Analysis of Token Rings. The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks. In Proceedings of the 14th International Teletraffic Congress. Antibes Juan-les-Pins, France, 811-820.
3. ALTMAN, E. AND D. KOFMAN. 1994. Bounds for Performance Measures of Token Rings. IEEE/ACM Transactions on Networking, 292-299.
4. ALTMAN, E., P. KONSTANTOPOULOS, AND Z. LIU. 1992. Stability, Monotonicity, and Invariant Quantities in General Polling Systems. Queueing Systems: Theory and Applications, 11, 35-58.
5. ALTMAN, E. AND H. LEVY. 1994. Queueing in Space. Adv. in Appl. Probab. 26, 1095-1116.
6. ALTMAN, E. AND Z. LIU. 1994. Improving the Stability Characteristics of Asynchronous Traffic in FDDI Token Rings. In High Speed Networks and Their Performance, H. G. Perros and Y. Viniotis (eds.) 441-460. North-Holland, Amsterdam.
7. ALTMAN, E. AND F. SPIEKSMA. 1996. Ergodicity, Moment Stability and Central Limit Theorems of Station Times in Polling Systems. Comm. Statist. Stochastic Models 12, 307-328.
8. ASMUSSEN, S. 1987. Applied Probability Processes and Queues. J. Wiley, New York.
9. BOROVKOV, A. A. 1984. Asymptotic Methods in Queueing Theory. J. Wiley, New York.
10. BOROVKOV, A. A. AND R. SCHASSBERGER. 1994. Ergodicity of a Polling System. Stochastic Process, and Appl. 50, 253-262.
11. CHANG, C.-S. 1994. Stability, Queue Length, and Delay in Deterministic and Stochastic Queueing Networks. IEEE Trans. on Automat. Control. 39, 913-931.
12. CRUZ, R. L. 1991. A Calculus for Network Delay, Part I: Network Elements in Isolation. IEEE Trans. Inform. Theory, 37, 114-131.
13. CRUZ, R. L. 1992. A Calculus for Network Delay, Part II: Network Analysis. IEEE Trans. Inform. Theory. 37, 132-141.
14. EL-TAHA, M. AND S. STIDHAM JR. 1993. Sample-Path Analysis of Stochastic Discrete-Event Systems. Discrete Event Dynamic Systems: Theory and Applications, 3, 325-346.
15. FOSS, S. AND A. RYBKO. 1996. Stability of Multiclass Jackson - Type Networks. Markov Process. Related Fields 2, 461-486.
16. FRICKER, C. AND M. R. JAIBI. 1994. Monotonicity and Stability of Periodic Polling Models. Queueing Systems, 15, 211-238.
17. GEORGIADIS, L. AND W. SZPANKOWSKI. 1992. Stability of Token-Passing Rings. Queueing Systems: Theory and Applications, 11, 7-33.
18. GEORGIADIS, L., W. SZPANKOWSKI, AND L. TASSIULAS. 1993. Stability of Ring Networks With Spatial Re-use. In Proceedings of the Conference on Applied Probability in Engineering, Computer and Communication Sciences. INRIA/ ORSA/TIMS/SMAI, June 16-18, Paris.
19. KINGMAN, J. F. C. 1970. Inequalities in the Theory of Queues. J. Royal Stat. Soc., Series B, 32, 102-110.
20. KROESE, D. P. AND V. SCHMIDT. 1992. A Continuous Polling System With General Service Times. Anns. Appl. Prob. 2, 906-927.
21. KROESE, D. P. AND V. SCHMIDT. 1994. Single-server Queues With Spatially Distributed Arrivals. QUESTA, 17, 317-345.
22. MASSOULIÉ, L. 1993. On the Construction of Stationary Point Processes in Polling Systems. In Proceedings of the Conference on Applied Probability in Engineering, Computer and Communication Sciences. INRIA/ORSA/TIMS/ SMAI, June 16-18, Paris.
23. RESING, J. A. C. 1993. Polling Systems and Multitype Branching Processes. Queueing Systems, 13, 409-426.
24. STIDHAM, S., JR. AND M. EL-TAHA. 1993. A Note on Sample-Path Stability Conditions for Input-Output Processes. O. R. Letts. 14, 1-7.
25. YARON, O. AND M. SIDI. 1994. Performance and Stability of Communication Networks via Robust Exponential Bounds. IEEE/ACM Trans. Networking, 1, 372-385.
26. ZHDANOV, V. S. AND E. A. SAKSONOV. 1979. Conditions of Existence of Steady-state Modes in Cyclic Queueing Systems. Automat. Remote Control, 40, 176-184.