Waiting-time distributions in polling systems with simultaneous batch arrivals

Annals of Operations Research

Volumn 113, Issue 1-4, 2002, Pages 155-173

  Van der Mei, R D ^a,b  

^a KPN RESEARCH   (Netherlands)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Batch processes; Heavy traffic; Polling; Simultaneous arrivals; Waiting time distribution

Indexed keywords

EID: 0036431419     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1023/A:1020918230560     Document Type: Conference Paper

References (22)

1. 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) pp. 143-169.
2. O.J. Boxma, Q. Deng and J.A.C. Resing, Polling systems with regularly varying service and/or switch-over times, Adv. Performance Anal. 3 (2000) 71-107.
3. O.J. Boxma and W.P. Groenendijk, Waiting times in discrete-time cyclic-service systems, IEEE Trans. Commun. 36 (1988) 64-70.
4. G. Choudhury and W. Whitt, Computing transient and steady state distributions in polling models by numerical transform inversion, Performance Evaluation 25 (1996) 267-292.
5. K.L. Chung, A Course in Probability, 2nd. ed. (Academic Press, 1974).
6. 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.
7. 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.
8. J.H. Foster, Branching processes involving immigration, Ph.D. Thesis, University of Wisconsin (1969). (A copy is available from the author upon request.)
9. 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.
10. D.P. Kroese, Heavy traffic analysis for continuous polling models, J. Appl. Probab. 34 (1997) 720-732.
11. S. Kudoh, H. Takagi and O. Hashida, Second moments of the waiting time in symmetric polling systems, J. Oper. Res. Soc. Japan 43 (2000) 306-316.
12. C. Langaris, A polling model with retrial customers, J. Oper. Res. Soc. Japan 40 (1997) 489-508.
13. C. Langaris, Gated polling models with customers in orbit, Math. Comput. Modelling 30 (1999) 171-187.
14. C. Langaris, Markovian polling systems with mixed service disciplines and retrial customers, Top 7 (1999) 305-323.
15. H. Levy and M. Sidi, Polling systems with simultaneous arrivals, IEEE Trans. Commun. 39 (1991) 823-827.
16. J.A.C. Resing, Polling systems and multitype branching processes, Queueing Systems Theory Appl. 13 (1993) 409-426.
17. H. Takagi, Analysis of Polling Systems (MIT Press, Cambridge, MA, 1986).
18. 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.
19. R.D. van der Mei, Distribution of the delay in polling systems in heavy trafiic, Performance Evaluation 31 (1999) 163-182.
20. R.D. van der Mei, Polling systems in heavy traffic: higher moments of the delay, Queueing Systems Theory Appl. 31 (1999) 265-294.
21. R.D. van der Mei, Polling systems with switch-over times under heavy load: moments of the delay, Queueing Systems Theory Appl. 36 (2000) 381-404.
22. R.D. van der Mei, Polling systems with simultaneous batch arrivals, Stochastic Model. 17 (2001) 271-292.