Limit theorems for polling models with increasing setups

Probability in the Engineering and Informational Sciences

Volumn 15, Issue 1, 2001, Pages 35-55

  Olsen, Tava Lennon ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ENGINEERING; INDUSTRIAL ENGINEERING;

DISCRETE RANDOM VARIABLES; EXHAUSTIVE SERVICE; HEAVY TRAFFICS; LIMIT THEOREM; POLLING MODEL; SINGLE SERVER; UNIFORM DISTRIBUTION; UNIFORM RANDOM VARIABLES;

RANDOM VARIABLES;

EID: 0035628939     PISSN: 02699648     EISSN: None     Source Type: Journal    
DOI: 10.1017/S026996480115103X     Document Type: Article

References (28)

1. Baccelli, F. & Brémaud, P. (1991). Elements of queueing theory. Berlin: Springer-Verlag.
2. Bertsimas, D. & Mourtzinou, G. (1999). Decomposition results for general polling systems and their applications. Queueing Systems Theory and Applications 31: 295-316.
3. Boxma, O., Groenendijk, W., & Weststrate, J. (1990). A pseudoconservation law for service systems with a polling table. IEEE Transactions on Communications COM-38(10): 1865-1870.
4. Boxma, O., Levy, H., & Weststrate, J. (1991). Efficient visit frequencies for polling tables: Minimization of waiting cost. Queueing Systems Theory and Applications 9(1-2): 133-162.
5. Choudhury, G.L. & Whitt, W. (1996). Computing transient and steady-state distributions in polling models by numerical transform inversion. Performance Evaluation 25: 267-292.
6. Coffman, E., Jr., Puhalskii, A., & Reiman, M. (1998). Polling systems in heavy-traffic: A Bessel process limit. Mathematics of Operations Research 23(2): 257-304.
7. Cooper, R.B., Niu, S., & Srinivasan, M.M. (1997). Setups in polling models: Does it make sense to set up if no work is waiting? Working paper.
8. Duenyas, I. (1994). The limitations of sub-optimal policies. Interfaces 24(5): 77-84.
9. Everitt, D. (1986). Simple approximations for token rings. IEEE Transactions on Communications COM-34(7): 719-721.
10. Federgruen, A. & Katalan, Z. (1994). Approximating queue size and waiting time distributions in general polling systems. Queueing Systems Theory and Applications 18: 353-386.
11. Federgruen, A. & Katalan, Z. (1996). The impact of setup times on the performance of multi-class service and production systems. Operations Research 44(6): 989-1001.
12. Federgruen, A. & Katalan, Z. (1996). The stochastic economic lot scheduling problem: Cyclical base stock policies with idle times. Management Science 42(6): 783-796.
13. Fuhrmann, S.W. & Cooper, R.B. (1985). Stochastic decompositions in the M/G/1 queue with generalized vacations. Operations Research 33(5): 1117-1129.
14. Gupta, D. & Srinivasan, M.M. (1996). The variance paradox and its implications for Japanese production theory. Interfaces 26: 69-77.
15. Harrison, J.M. (1985). Brownian motion and stochastic flow systems. New York: Wiley.
16. Lennon, T.M. (1994). Response-time approximations for multi-server polling models, with manufacturing applications. Unpublished Ph.D. thesis, Stanford University.
17. Levy, H. & Sidi, M. (1990). Polling systems: Applications, modeling, and optimization. IEEE Transactions on Communications COM-38(10): 1750-1760.
18. Olsen, T.L. (1998). Approximations for the waiting time distribution in polling models with and without state-dependent setups. Operations Research Letters (to appear).
19. Olsen, T.L. (1999). A practical scheduling method for multi-class production systems with setups. Management Science 45(1): 116-130.
20. Resing, J.A.C. (1993). Polling systems and multitype branching processes. Queueing Systems Theory and Applications 13: 409-426.
21. Sarkar, D. & Zangwill, W. (1991). Variance effects in cyclic production systems. Management Science 37(4): 443-453.
22. Takagi, H. (1986). Analysis of polling systems. Cambridge, MA: The MIT Press.
23. Takagi, H. (1990). Queueing analysis of polling models: An update. In H. Takagi (ed.), Stochastic analysis of computer and communication systems. Amsterdam: Elsevier Science/North-Holland, pp. 267-318.
24. Takagi, H. (1997). Queueing analysis of polling models: Progress in 1990-1994. In J.H. Dshalalow (ed.), Frontiers in queueing. Boca Raton, FL: CRC Press, pp. 119-146.
25. van der Mei, R.D. (1999). Polling systems in heavy traffic: Higher moments of the delay. Queueing Systems Theory and Applications 31: 265-294.
26. van der Mei, R.D. (1999). Polling systems with periodic server routing in heavy traffic. Stochastic Models 15: 273-297.
27. van der Mei, R.D. & Levy, H. (1997). Polling systems in heavy traffic: Exhaustiveness of service policies. Queueing Systems Theory and Applications 27: 227-250.
28. Whitt, W. (1982). Refining diffusion approximations for queues. Operations Research Letters 1(5): 165-169.