Polling systems with simultaneous batch arrivals

Communications in Statistics. Part C: Stochastic Models

Volumn 17, Issue 3, 2001, Pages 271-292

  Van Der Mei, R D ^a,b  

^a KPN RESEARCH   (Netherlands)

^b VU UNIVERSITY AMSTERDAM   (Netherlands)

Author keywords

Batch arrivals; Delay; Heavy traffic; Polling systems; Simultaneous arrivals

Indexed keywords

EID: 0141779803     PISSN: 08820287     EISSN: None     Source Type: Journal    
DOI: 10.1081/stm-100002274     Document Type: Article

References (28)

1. Altman, E., Konstantopoulos, P. and Liu, Z. (1992). Stability, monotonicity and invariant quantities in general polling systems. Queueing Systems 11, 35-57.
2. Altman, E. and Yechiali, U. (1993). Cyclic Bernoulli polling. Z.O.R. Methods and Models in Operations Research 38, 55-76.
3. Boxma, O.J. and Meister, B. (1987). Waiting-time approximations for cyclic-service systems with switch-over times. Perf. Eval. 7, 299-308.
4. Boxma, O.J., Groenendijk, W.P. and Weststrate, J.A. (1990). A pseudo-conservation law for service systems with a polling table. IEEE Trans. Commun. 38, 1865-1870.
5. Chiarawongse, J. and Srinivasan, M.M. (1991). On pseudo-conservation laws for the cyclic server system with compound Poisson arrivals. Oper. Res. Lett. 10, 453-459.
6. Choudhury, G. and Whitt, W. (1996). Computing transient and steady state distributions in polling models by numerical transform inversion. Perf. Eval. 25, 267-292.
7. 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.
8. Coffman, E.G., Puhalskii, A.A. and Reiman, M.I. (1998). Polling systems in heavy-traffic: a Bessel process limit. Math. Oper. Res. 23, 257-304.
9. Cooper, R.B., Niu, S.-C. and Srinivasan, M.M. (1997). Setups in polling models: does it make sense to set up if no work is waiting? J. Appl. Prob. 36, 585-592.
10. Everitt, D. (1986). Simple approximations for token rings. IEEE Trans. Commun. 34, 719-721.
11. Flicker, C. and Jaïbi, M.R. (1994). Monotonicity and stability of periodic polling models. Queueing Systems 15, 211-238.
12. 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), 1434-1441.
13. Konheim, A.G., Levy, H. and Srinivasan, M.M. (1994). Descendant set: an efficient approach for the analysis of polling systems. IEEE Trans. Commun. 42, 1245-1253.
14. Kroese, D.P. (1997). Heavy traffic analyst for continuous polling models. J. Appl. Prob. 34, 720-732.
15. Kudoh, S., Takagi, H. and Hashida, O. (2000). Second moments of the waiting time in symmetric polling systems. J. Oper. Res. Soc. of Japan 43, 306-316.
16. Leland, W., Taqqu, M., Willinger, W. and Wilson, D. (1994). On the self-similar nature of Ethernet traffic. IEEE/ACM Trans. Netw. 2, 1-15.
17. Levy, H. and Sidi, M. (1991). Polling models: applications, modeling and optimization. IEEE Trans. Commun. 38, 1750-1760.
18. Levy, H. and Sidi, M. (1991). Polling systems with simultaneous arrivals. IEEE Trans. Commun. 39, 823-827.
19. Markowitz, D. (1995). Dynamic Scheduling of Single-Server Queues with Setups: A Heavy Traffic Approach. Ph.D. Thesis, Operations Research Center, MIT, Cambridge, MA.
20. Paxson, V. and Floyd, S. (1995). Wide area traffic: the failure of Poisson modeling. IEEE/ACM Trans. Netw. 3, 226-244.
21. Reiman, M.I. and Wein, L.M. (1998). Dynamic scheduling of a two-class queue with setups. Oper. Res. 46, 532-547.
22. Takagi, H. (1990). Queueing analysis of polling models: an update. In: Stochastic Analysis of Computer and Communication Systems, ed. H. Takagi (North-Holland, Amsterdam), 267-318.
23. Takagi, H. (1997). Queueing analysis of polling models: progress in 1990-1994. In: Frontiers in Queueing: Models and Applications in Science and Technology, ed. J.H. Dshalalow (CRC Press, Boca Raton, FL), 119-146.
24. Van der Mei, R.D. and Levy, H. (1998). Expected delay in polling systems in heavy traffic. Adv. Appl. Prob. 30, 586-602.
25. Van der Mei, R.D. (1999). Polling systems in heavy traffic: higher moments of the delay. Queueing Systems 31, 365-394.
26. Van der Mei, R.D. (2000). Polling systems with switch-over times in heavy traffic: moments of the delay. Queueing Systems 36, 381-404.
27. Van der Mei, R.D. (1999). Distribution of the delay in polling systems in heavy traffic. Perf. Eval. 38, 133-148.
28. Van der Mei, R.D. (2000). Polling systems with correlated batch arrivals. In: Proc. 1st Polish-German Symposium on Teletraffic (Dresden, September 25-26), 161-168.