Analysis of a phase transition phenomenon in packet networks

Advances in Applied Probability

Volumn 33, Issue 1, 2001, Pages 260-280

  Mandjes, Michel ^a   Kim, Jeong Han ^b  

^a CWI   (Netherlands)

^b NONE   (United States)

Author keywords

ATM multiplexers; Buffer overflow; IP routers; Large deviations asymptotics; Packet and burst scale; Phase transition; Queueing theory

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; MULTIPLEXING; PROBABILITY; QUEUEING THEORY;

BIT RATE TRAFFIC STREAMS; BUFFER OVERFLOW; BURST SCALE MODEL;

PACKET NETWORKS;

EID: 0035271984     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/999187907     Document Type: Article

References (27)

1. ANICK, D., MITRA, D. AND SONDHI, M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell Syst. Tech. J. 61, 1871-1894.
2. BOTVICH, D. AND DUFFIELD, N. (1995). Large deviations, the shape of the loss curve, and economies of scale in large multiplexers. Queueing Systems 20, 293-320.
3. COURCOUBETIS, C., SIRIS, V. AND WEBER, R. (1997). Investigation of cell scale and burst scale effects on the cell loss probability using large deviations. In Proc. 13th UK Workshop Perf. Eng. of Comput. and Telecommunication Systems, Ilkley, UK.
4. COURCOUBETIS, C. AND WEBER, R. (1996). Buffer overflow asymptotic for a buffer handling many traffic sources. J. Appl. Prob. 33, 886-903.
5. DEMBO, A. AND ZEITOUNI, O. (1993). Large Deviations Techniques and Applications. Jones and Bartlett, Boston.
6. DRON, L., RAMAMURTHY, G. AND SENGUPTA, B. (1991). Delay analysis of continuous bit rate traffic over an ATM network. IEEE J. Sel. Areas Commun. 9, 402-407.
7. DUFFTELD, N. (1998). Conditioned asymptotics for tail probabilities in large multiplexers. Performance Evaluation 31, 281-300.
8. ECKBERGO, A. (1979). The single-server queue with periodic arrival process and deterministic service time. IEEE Trans. Commun. 27, 556-562.
9. GIBBENS, R. AND KELLY, F. (1999). Distributed connection acceptance control for a connectionless network. In Proceedings ITC 16: Teletraffic Engineering in a Competitive World, eds P. Key and D. Smith. Elsevier, Amsterdam, pp. 941-952.
10. HEFFES, H. AND LUCANTONI, D. (1986). A Markov modulated characterization of packetized voice and data traffic and related statistical multiplexer performance. IEEE J. Sel. Areas Commun. 4, 856-868.
11. HUI, J. (1988). Resource allocation for broadband networks. IEEEJ. Sel. Areas Commun. 6, 1598-1608.
12. KELLY, F. (1996). Notes on effective bandwidths. In Stochastic Networks: Theory and Applications, eds F. Kelly, S. Zachary. and I. Ziedins. Oxford University Press, pp. 141-168.
13. KELLY, F. (2000). Models for a self-managed Internet. Phil. Trans. R. Soc. A 358, 2335-2348.
14. LIKHANOV, N. AND MAZUMDAR, R. (1999). Cell loss asymptotics in buffers fed with a large number of independent stationary sources. J. Appl. Prob. 36, 86-96.
15. MANDJES, M. AND BOOTS, N.-K. (2000). The shape of the loss curve, and the impact of long-range dependence on network performance. Submitted.
16. MANDJES, M. AND BORST, S. (2000). Overflow behavior in queues with many long-tailed inputs. Adv. Appl. Prob. 32, 1150-1167.
17. MANDJES, M. AND KIM, J.-H. (1999). Large deviations for small buffers: an insensitivity result. To appear in Queueing Systems.
18. MANDJES, M. AND RIDDER, A. (1999). Optimal trajectory to overflow in a queue fed by a large number of sources. Queueing Systems 31, 137-170.
19. NORROS, I., ROBERTS, J., SIMONIAN, A. AND VIRTAMO, J. (1991). The superposition of variable bit rate sources in an ATM multiplexer. IEEE J. Sel. Areas Commun. 9, 378-387.
20. ROBERTS, J. (ed.) (1992). Performance Evaluation and Design of Multiservice Networks: Final Report (Euraton Publications EUR 14152). Commission of the European Communities, Luxembourg.
21. SCHOUTE, F. (1988). Simple decision rules for acceptance of mixed traffic streams. In Teletraffic Science for New Cost-Effective Systems, Networks and Services (Proc. 12th Int. Teletraffic Congress, Turin), ed. M. Bonatti. North-Holland, Amsterdam, pp. 1-7.
22. SCHWARTZ, M. (1996). Broadband Integrated Networks. Prentice Hall, Upper Saddle River, NJ.
23. SHWARTZ, A. AND WEISS, A. (1995). Large deviations for performance analysis, queues, communication, and computing. Chapman and Hall. New York.
24. SIMONIAN, A. AND GUIBERT, J. (1995). Large deviations approximation for fluid queues fed by a large number of on/off sources. IEEE J. Sel. Areas Commun. 13, 1017-1027.
25. SRIRAM, K. AND WHITT, W. (1986). Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Sel. Areas Commun. 4, 833-846.
26. WEISS, A. (1986). A new technique of analyzing large traffic systems. Adv. Appl. Prob. 18, 506-532.
27. WISCHIK, D. (1999). Sample path large deviations for queues with many inputs. To appear in Ann. Appl. Prob.