A LIFO queue in heavy traffic

Annals of Applied Probability

Volumn 11, Issue 2, 2001, Pages 301-331

  Limic, Vlada ^a  

^a Department of Obstetrics Gynecology   (United States)

Author keywords

Branching; Heavy traffic; LIFO queue; Measure valued process

Indexed keywords

EID: 0035538465     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1015345294     Document Type: Article

References (37)

1. ABATE, J. and WHITT, W. (1997). Limits and approximations for the M/G/1 LIFO waiting-time distribution. Oper. Res. Lett. 20 199-206.
2. ALDOUS, D. J. (1993). The continuum random tree III. Ann. Probab. 21 248-289.
3. ATHREYA, K. B. and NEY, P. E. (1972). Branching Processes. Springer, New York.
4. BASKETT, F., CHANDY, K. M., MUNTZ, R. R. and PALACIOS, F. G. (1975). Open, closed and mixed networks of queues with different classes of customers. J. ACM 22 248-260.
5. BERTOIN, J. (1996). Lévy Processes. Cambridge Univ. Press.
6. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
7. BRAMSON, M. (1998). State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems: Theory Appl. 30 89-148.
8. BREIMAN, L. (1968). Probability. Addison-Wesley, Reading, MA.
9. COFFMAN, E. G. and MITRANI, I. (1988). Storage of the single-server queue. In Queueing theory and Its Applications. 193-205. North-Holland, Amsterdam.
10. DAWSON, D. (1993). Measure-Valued Markov Processes. École d'Été de Probabilités de Saint-Flour XXI. Lecture Notes in Math. 1541. Springer, Berlin.
11. DURRETT, R. (1991). Probability. Theory and Examples. Wadsworth and Brooks/Cole, Pacific Grove, CA.
12. DYNKIN, E. B. (1994). An Introduction to Branching Measure-Valued Processes. Amer. Math. Soc., Providence, RI.
13. ETHIER, S. N. and KURTZ, T. G. (1986). Markov Processes: Characterization and Convergence. Wiley, New York.
14. LE GALL, J. F. and LE JAN, Y. (1998). Branching processes in Lévy processes: Laplace functionals of snakes and superprocesses. Ann. Probab. 26 1407-1432.
15. LE GALL, J. F. and LE JAN, Y. (1998). Branching processes in Lévy processes: the exploration process. Ann. Probab. 26 213-252.
16. GEIGER, J. and KERSTING, G. (1997). Depth-first search of random trees, and Poisson point processes. IMA Vol. Math. Appl. 84 111-126.
17. GRIMVALL, A. (1974). On the convergence of sequences of branching processes. Ann. Probab. 2 1027-1045.
18. HARRIS, T. E. (1974). First passage and recurrence distributions. Trans. Amer. Math. Soc. 73 471-486.
19. HARRISON, J. M. (1978). The diffusion approximation for tandem queues in heavy traffic. Adv. in Appl. Probab. 10 886-905.
20. HEATH, D., RESNICK, S. and SAMORODNITSKY, G. (1998). Heavy tails and long range dependence in on/off processes and associated fluid models. Math. Oper. Res. 23 145-165.
21. IGLEHART, D. L. and WHITT, W. (1970). Multiple channel queues in heavy traffic I. Adv. in Appl. Probab. 2 150-177.
22. IGLEHART, D. L. and WHITT, W. (1970). Multiple channel queues in heavy traffic II. Adv. in Appl. Probab. 2 355-364.
23. JACOD, J. and SHIRYAEV, A. N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin.
24. JAGERMAN, D. L., MELAMED, B. and WILLINGER, W. (1997). Stochastic modeling of traffic processes. In Frontiers in Queueing. 271-320. CRC Press, Boca Raton, FL.
25. KELLY, F. P. (1975). Networks of queues with customers of different types. J. Appl. Probab. 12 542-554.
26. KENDALL, D. G. (1951). Some problems in the theory of queues. J. Roy. Statist. Soc. B 13 151-185.
27. KINGMAN, J. F. C. (1961). The single server queue in heavy traffic. Proc. Cambridge Philos. Soc. 57 902-904.
28. KOLCHIN, V. F. (1986). Random Mappings. Optimization Software, New York. [Trans. of Russian original.]
29. LIMIC, V. (2000). On the behavior of LIFO preemptive resume queues in heavy traffic. Electron. Comm. Probab. 5 13-27.
30. LINDVALL, T. (1974). Limit theorems for some functionals of certain Galton-Watson branching processes. Adv. in Appl. Probab. 6 309-321.
31. REIMAN, M. I. (1984). Open queueing networks in heavy traffic. Math. Oper. Res. 9 441-458.
32. SHALMON, M. (1988). Analysis of the GI/GI/1 queue and its variations via the LCFS preemptive resume discipline and its random walk interpretation. Probab. Engng. Inform. Sci. 2 215-230.
33. SHANTHIKUMAR, J. G. and SUMITA, U. (1986). On G/G/1 queues with LIFO-P service discipline. J. Oper. Res. Soc. Japan 29 220-231.
34. SIGMAN, K. (1996). Queues under preemptive LIFO and ladder height distributions for risk processes: a duality. Comm. Statist. Stochastic Models 12 725-735.
35. WHITT, W. (1971). Weak convergence theorems for priority queues: preemptive-resume discipline. J. Appl. Probab. 8 74-94.
36. WILLIAMS, R. J. (1996). On the approximation of queueing networks in heavy traffic. In Stochastic Networks: Theory and Applications (S. Zachary, F. P. Kelly and I. Ziedins, eds.) 35-56. Clarendon Press, Oxford.
37. WILLIAMS, R. J. (1998). Diffusion approximations for open multiclass queueing networks: sufficient conditions involving state space collapse. Queueing Systems Theory Appl. 30 27-88.