A closed form solution for the asymmetric random polling system with correlated levy input process

Mathematics of Operations Research

Volumn 22, Issue 2, 1997, Pages 432-457

  Lee, Thomas ^a  

^a UNIVERSITY OF ILLINOIS AT CHICAGO   (United States)

Author keywords

And 1 limited service policy; Correlated arrival processes; Levy process; Linear quadratic model of uncertainty; Random gated service policy; Random polling systems

Indexed keywords

CORRELATION METHODS; MATHEMATICAL MODELS; OPTIMIZATION; QUEUEING THEORY;

ASYMMETRIC RANDOM POLLING SYSTEMS; CORRELATED LEVY INPUT PROCESS;

RANDOM PROCESSES;

EID: 0031140680     PISSN: 0364765X     EISSN: None     Source Type: Journal    
DOI: 10.1287/moor.22.2.432     Document Type: Article

References (33)

1. Anderson, T. (1984). An Introduction to Multivariate Statistical Analysis, 2nd Ed., John Wiley and Sons, New York.
2. Boxma, O., B. Meister (1987). Waiting time approximations for cyclic-service systems with switch-over times, Performance Evaluation 7 299-308.
3. _, J. Weststrate (1989). Waiting times in polling systems with Markovian server routing, Measurement, Modelling and Performance Evaluation of Computer Systems, Proc. Conference Braunschweig, Springer-Verlag, Berlin, 89-104.
4. Chang, J. (1983). A multibeam packet satellite using random access techniques, IEEE Trans. Comm. 31 1143-1154.
5. Cidon, I., I. Gopal, O. Grover, M. Sidi (1988). Real-time packet switching: A performance analysis, IEEE JSAC 6
6. Cramer, H. (1963). Random Variables and Probability Distributions, 2nd Ed., Cambridge University Press.
7. Denardo, E. V., T. Y. S. Lee (1996). Managing uncertainty in a serial production line, Oper. Res. 44 382-392.
8. _, C. Tang (1992). Linear control of a Markov system, Oper. Res. 40 259-278.
9. Franken, P., D. Konig, U. Arndt, V. Schmidt (1982). Queues and Point Processes, John Wiley and Sons, New York.
10. Fuhrman, S., Y. Wang (1988). Mean waiting time approximations of cyclic service systems with limited service, P. Courtois and G. Latouche, Eds. Performance '87, North Holland, Amsterdam, 253-265.
11. Grillo, D. (1990). Polling mechanism models in communication systems - Some application examples, H. Takagi, Ed., Stochastic Analysis of Computer and Communication Systems, Elsevier, Amsterdam, 659-698.
12. Groenendijk, W. (1989). Waiting-time approximations for cyclic systems with mixed service strategies, M. Bonatti, Ed., Proc. 12th ITC, North Holland, Amsterdam, 1434-1441.
13. Hebuterne, G. (1988). Relation between states observed by arriving and departing customers in bulk systems, Stoc. Proc. Appl. 27 279-289.
14. Holt, C., Modigliani, J. Muth, H. Simon (1969). Planning Production Inventories and Work Force, Prentice Hall, Englewood Cliffs, New Jersey.
15. Horn, R., C. Johnson (1985). Matrix Analysis, Cambridge University Press, New York.
16. Johnson, N., S. Kotz (1969). Discrete Distribution, John Wiley and Sons, New York.
17. Kimura, G. (1989). Approximations for a general token ring system with priority classes of messages, M. Bonatti, Ed., Teletraffic Science for New Cost-Effective Systems, Networks and Services, ITC-12, Elsevier Science Publisher, B. V., 553-559.
18. Kleinrock, L., H. Levy (1988). The analysis of random polling systems, Oper. Res. 36 716-732.
19. Lancaster, P. (1970). Explicit solution of linear matrix equations, SIAM Review 12 544-566.
20. Lee, T. Y. S. (1994). Stability analysis of cyclical schedule and linear lot sizing rule for a production system, Internat. J. System Sci. 25 2361-2376.
21. Leung, K. (1991). Cyclic service systems with probabilistically-limited service, IEEE Trans. Sci. Comm. 9 185-193.
22. Levy, H. (1989). Analysis of cyclic polling systems with binomial-gated service, T. Hasegawa, H. Takagi and Y. Takahashi, Eds., Performance of Distributed and Parallel Systems, Elsevier Science Publishers B. V.
23. _, M. Sidi (1989). Polling systems with correlated arrivals, Proc. INFOCOM '89, 907-913.
24. _, _ (1991). Polling systems with simultaneous arrivals, IEEE Trans. Comm. 39 823-827.
25. _, _, O. Boxma (1990). Dominance relations in polling systems, Queueing Systems 6 155-172.
26. Melamed, B., Whitt, W. (1990). On arrivals that see time averages, Oper. Res. 38 156-172.
27. Mitrani, I., J. Adams, R. Falconer (1986). A modelling study of the Orwell ring protocol, O. Boxma, J. Cohen and H. Tijms, Eds., Teletraffic Analysis and Computer Performance Evaluation, North Holland, Amsterdam, 429-438.
28. Serfozo, R. (1972a). Processes with conditional stationary independent increments, J. Appl. Probab. 9 303-315.
29. _ (1972b). Conditional Poisson process, J. Appl. Probab. 9 288-302.
30. Shiozawa, Y., T. Takine, Y. Takahashi, T. Hasegawa (1990). Analysis of a polling system with correlated input, Computer Networks and ISDN systems 20 297-308.
31. H. Suzuki, H., H. Nagano, T. Takeuchi, S. Iwasaki (1989). Output-buffer switch architecture for asynchronous transfer mode, IEEE Internat. Conf. on Communications 1 99-103.
32. Takagi, H. (1986). Analysis of Polling Systems, MIT Press, Cambridge, Massachusetts.
33. _ (1991). Queueing Analysis: A Foundation of Performance Evaluation, North Holland, New York.