Polling systems with switch-over times under heavy load: Moments of the delay

Queueing Systems

Volumn 36, Issue 4, 2000, Pages 381-404

  Van Der Mei, R D ^a,b  

^a KPN RESEARCH   (Netherlands)

^b AT AND T LABS RESEARCH   (United States)

Author keywords

Approximations; Delay; Heavy traffic; Moments; Polling systems

Indexed keywords

APPROXIMATIONS; DELAY; HEAVY TRAFFICS; MOMENTS; POLLING SYSTEM;

EID: 0034346383     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: None     Document Type: Article

References (34)

1. K.B. Athreya and P.E. Ney, Branching Processes (Springer, Berlin, 1971).
2. J.P.C. Blanc, Performance analysis and optimization with the power-series algorithm, in: Performance Evaluation of Computer and Communication Systems, eds. L. Donatiello and R. Nelson (Springer, Berlin, 1993) pp. 53-80.
3. J.P.C. Blanc and R.D. van der Mei, Optimization of polling systems with Bernoulli schedules, Performance Evaluation 22 (1995) 139-158.
4. S.C. Borst and O.J. Boxma, Polling models with and without switchover times, Oper. Res. 45 (1997) 536-543.
5. O.J. Boxma and J.W. Cohen, The single-server queue: heavy tails and heavy traffic, in: Self-Similar Network Traffic and Performance Evaluation, eds. K. Park and W. Willinger (Wiley, New York, 2000).
6. G. Choudhury and W. Whitt, Computing transient and steady state distributions in polling models by numerical transform inversion, Performance Evaluation 25 (1996) 267-292.
7. E.G. Coffman, A.A. Puhalskii and M.I. Reiman, Polling systems with zero switch-over times: A heavy-traffic principle, Ann. Appl. Probab. 5 (1995) 681-719.
8. E.G. Coffman, A.A. Puhalskii and M.I. Reiman, Polling systems in heavy-traffic: A Bessel process limit, Math. Oper. Res. 23 (1998) 257-304.
9. R.B. Cooper, S.-C. Niu and M.M. Srinivasan, Setups in polling models: does it make sense to set up if no work is waiting? J. Appl. Probab. 36 (1997) 585-592.
10. M.J. Ferguson, Computation of the variance of the waiting times for token rings, IEEE J. Selected Areas Commun. 4 (1986) 775-782.
11. C. Fricker and M.R. Jaïbi, Monotonicity and stability of periodic polling models, Queueing Systems 15 (1994) 211-238.
12. A.G. Konheim, H. Levy and M.M. Srinivasan, Descendant set: An efficient approach for the analysis of polling systems, IEEE Trans. Commun. 42 (1994) 1245-1253.
13. D.P. Kroese, Heavy traffic analysis for continuous polling models, J. Appl. Probab. 34 (1997) 720-732.
14. S. Kudoh, H. Takagi and O. Hashida, Second moments of the waiting time in symmetric polling systems.
15. C.A. LaPadula and H. Levy, Customer delay in very large multi-queue single-server systems, Performance Evaluation 26 (1996) 201-218.
16. K.K. Leung, Cyclic service systems with probabilistically-limited service, IEEE J. Selected Areas Commun. 9 (1991) 185-193.
17. H. Levy and M. Sidi, Polling models: applications, modeling and optimization, IEEE Trans. Commun. 38 (1991) 1750-1760.
18. D. Markowitz, Dynamic scheduling of single-server queues with setups: A heavy traffic approach, Ph.D. thesis, Operations Research Center (MIT, Cambridge, MA, 1995).
19. M.I. Reiman and L.M. Wein, Dynamic scheduling of a two-class queue with setups, Oper. Res. 46 (1998) 532-547.
20. J.A.C. Resing, Polling systems and multitype branching processes, Queueing Systems 13 (1993) 409-426.
21. D. Sarkar and W.I. Zangwill, Expected waiting time for nonsymetric cyclic queueing systems - Exact results and applications, Mangm. Sci. 35 (1989) 1463-1474.
22. M.M. Srinivasan, H. Levy and A.G. Konheim, The individual station technique for the analysis of cyclic polling models, Naval Res. Logist. 73 (1993) 79-101.
23. M.M. Srinivasan, S.-C. Niu and R.B. Cooper, Relating polling models with zero and nonzero switchover times, Queueing Systems 19 (1995) 149-168.
24. H. Takagi, Analysis of Polling Systems (MIT Press, Cambridge, MA, 1986).
25. H. Takagi, Queueing analysis of polling models: An update, in: Stochastic Analysis of Computer and Communication Systems, ed. H. Takagi (North-Holland, Amsterdam, 1990) pp. 267-318.
26. H. Takagi, Queueing analysis of polling models: progress in 1990-1994, in: Frontiers in Queueing: Models, Methods and Problems, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL, 1997).
27. R.D. van der Mei, Delay in polling systems in heavy traffic, in: Proc. of SPIE Conf. on Performance and Control of Network Systems, eds. W. Lai and R.B. Cooper, Boston, MA, 2-4 November 1998, pp. 168-175.
28. R.D. van der Mei, Polling systems in heavy traffic: higher moments of the delay, Queueing Systems 31 (1999) 265-294.
29. R.D. van der Mei, Delay in polling systems with large switch-over times, J. Appl. Probab. 36 (1999) 232-243.
30. R.D. van der Mei, Waiting-time distributions in polling systems in heavy traffic, in: Teletraffic Engineering in a Competitive World, eds. P. Key and D. Smith (Elsevier, Amsterdam, 1999) pp. 325-334.
31. R.D. van der Mei, Distribution of the delay in polling systems in heavy traffic, Performance Evaluation 38 (1999) 133-148.
32. R.D. van der Mei and H. Levy, Polling systems in heavy traffic: exhaustiveness of the service policies, Queueing Systems 27 (1997) 227-250.
33. R.D. van der Mei and H. Levy, Expected delay in polling systems in heavy traffic, Adv. in Appl. Probab. 30 (1998) 586-602.
34. K.S. Watson, Performance evaluation of cyclic strategies - a survey, in: Proc. of Performance '84, ed. E. Gelenbe (North-Holland, Amsterdam, 1985) pp. 521-533.