Expected delay analysis of polling systems in heavy traffic

Advances in Applied Probability

Volumn 30, Issue 2, 1998, Pages 586-602

  Van Der Mei, R D ^a   Levy, H ^b  

^a AT AND T LABS RESEARCH   (United States)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Expected delay; Heavy traffic; Optimization; Polling systems

Indexed keywords

EID: 0000985595     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0001867800047443     Document Type: Article

References (25)

1. ATHREYA, K. B AND NEY, P. E. (1971). Branching Processes. Springer, Berlin.
2. BLANC, J. P. C. (1992). Performance evaluation of polling systems by means of the power-series algorithm. Ann. Operat. Res. 35, 155-186.
3. BLANC, J. P. C. AND VAN DER MEI, R. D. (1995). Optimization of polling systems with Bernoulli schedules. Perf. Eval. 22, 139-158.
4. BOXMA, O. J. AND GROENENDIJK, W. P. (1987). Pseudo-conservation laws in cyclic service systems. J. Appl. Prob. 24, 949-964.
5. CHOUDHURY, G. AND WHITT, W. (1994). Computing transient and steady state distributions in polling models by numerical transform inversion. Perf. Eval. 25, 267-292.
6. COFFMAN, E. G., PUHALSKII, A. A. AND REIMAN, M. I. (1995). Polling systems with zero switch-over times: a heavy-traffic principle. Ann. Appl. Prob. 5, 681-719.
7. COFFMAN, E. G., PUHALSKII, A. A. AND REIMAN, M. I. (1995). Polling systems in heavy-traffic: a Bessel process limit. To appear in Math. Oper. Res.
8. GROENENDIJK, W. P. (1988). Waiting-time approximations for cyclic-service systems with mixed service strategies. In Teletraffic Science for New Cost-Effective Systems, ed. M. Bonatti. North-Holland, Amsterdam, pp. 1434-1441.
9. FRICKER, C. AND JAÏBI, M. R. (1994). Monotonicity and stability of periodic polling models. Queueing Systems 15, 211-238.
10. KARLIN, S. (1966). A First Course in Stochastic Processes. Academic Press, New York.
11. KATO, T. (1966). Perturbation Theory for Linear Operators. Springer, New York.
12. KONHEIM, A. G., LEVY, H. AND SRINIVASAN, M. M. (1994). Descendant set: an efficient approach for the analysis of polling systems. IEEE Trans. Comm. 42, 1245-1253.
13. LEUNG, K. K. (1991). Cyclic service systems with probabilistically-limited service. IEEE J. Sel. Areas Commun. 9, 185-193.
14. LEVY, H. AND SIDI, M. (1991). Polling models: applications, modeling and optimization. IEEE Trans. Commun. 38, 1750-1760.
15. LEVY, H., SIDI, M. AND BOXMA, O. J. (1990). Dominance relations in polling systems. Queueing systems 6, 155-171.
16. MARKOWITZ, D. (1995). Dynamic Scheduling of Single-Server Queues with Setups: A Heavy Traffic Approach. Ph.D. Thesis, Operations research Center, MIT, Cambridge, MA.
17. REIMAN, M. I. AND WEIN, L. M. (1998). Dynamic scheduling of a two-class queue with setups. To appear in Math. Oper. Res.
18. RESING, J. A. C. (1993). Polling systems and multitype branching processes. Queueing Systems 13, 409-426.
19. SRINIVASAN, M. M., LEVY, H. AND KONHEIM, A. G. (1996). The individual station technique for the analysis of cyclic polling systems. Naval Research Logistics 73, 79-101.
20. TAKAGI, H. (1986). Analysis of Polling Systems. The MIT Press, Cambridge, MA.
21. TAKAGI, H. (1990). Queueing analysis of polling models: an update. In Stochastic Analysis of Computer and Communication Systems, ed. Fi Takagi. North-Holland. Amsterdam, pp. 267-318.
22. TAKAGI, H. (1994). Queueing analysis of polling models: progress in 1990-1993. In Frontiers in Queueing: Models, Methods and Problems, ed. J. H. Dshalalow. CRC Press.
23. VAN DER MEI, R. D. AND LEVY, H. (1996). Expected delay analysis of polling systems in heavy traffic. Technical Report RRR 17-96, RUTCOR, Rutgers University.
24. VAN DER MEI, R. D. AND LEVY, H. (1997). Polling systems in heavy traffic: exhaustiveness of the service policies. Queueing Systems and their applications 27, 227-250.
25. VAN DER MEI, R. D. (1997). Polling systems in heavy traffic: higher moments of the delay. In Teletraffic Contributions for the Information Age, eds. V. Ramaswamy and P. E. Wirth. Elsevier, Amsterdam, pp. 275-284.