TCP and iso-stationary transformations

Queueing Systems

Volumn 63, Issue 1, 2009, Pages 459-475

  van Leeuwaarden, J S H ^a   Lopker A H ^a   Ott, T J ^b  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b Ott Associates   (United States)

Author keywords

Piecewise deterministic Markov process; Space time change; Stationary distribution; TCP; Time transformation

Indexed keywords

MARKOV CHAINS; STOCHASTIC CONTROL SYSTEMS;

DISCRETE TIME MARKOV CHAINS; PIECEWISE DETERMINISTIC MARKOV PROCESS; POISSON PROCESS; SCALING LIMITS; SPACE TIME; SPACE-TIME TRANSFORMATIONS; STATIONARY DISTRIBUTION; TIME TRANSFORMATION;

TRANSMISSION CONTROL PROTOCOL;

EID: 72249097506     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1007/s11134-009-9145-6     Document Type: Article

References (24)

1. Altman, A., Avrachenkov, K., Kherani, A. A., Prabhu, B. J.: Performance analysis and stochastic stability of congestion control protocols. In: Proceedings of IEEE Infocom 2005 (2005).
2. Asmussen, S.: Applied Probability and Queues, 2nd edn. Springer, New York (2003).
3. Baccelli, F., Kim, K. B., McDonald, D.: Equilibria of a class of transport equations arising in congestion control. Queueing Syst. 55, 1-8 (2007).
4. Borovkov, K., Vere-Jones, D.: Explicit formulae for stationary distributions of stress release processes. J. Appl. Probab. 37, 315-321 (2000).
5. Borovkov, K., Novikov, A.: On a piece-wise deterministic Markov process model. Stat. Probab. Lett. 53, 421-428 (2001).
6. Boxma, O., Perry, D., Stadje, W., Zacks, S.: A Markovian growth-collapse model. Adv. Appl. Probab. 38, 221-243 (2006).
7. Davis, M. H. A.: Markov Models and Optimization. Chapman & Hall, London (1993).
8. Dumas, V., Guillemin, F., Robert, Ph.: A Markovian analysis of Additive-Increase Multiplicative-Decrease (AIMD) algorithms. Adv. Appl. Probab. 34, 85-111 (2002).
9. Dynkin, E. B.: Markov Processes I. Springer, New York (1965).
10. Ethier, S. N., Kurtz, T. G.: Markov Processes. Characterization and Convergence. Wiley, New York (1986).
11. Guillemin, F., Robert, Ph., Zwart, B.: AIMD algorithms and exponential functionals. Ann. Appl. Probab. 14, 90-117 (2004).
12. Last, G.: Ergodicity properties of stress release, repairable system and workload models. Adv. Appl. Probab. 36, 471-498 (2004).
13. Last, G., Szekli, R.: Time and Palm stationarity of repairable systems. Stoch. Process. Their Appl. 79, 17-43 (1999).
14. Löpker, A. H., van Leeuwaarden, J. S. H.: Transient moments of the TCP window size process. J. Appl. Probab. 45, 163-175 (2008).
15. Maulik, K., Zwart, B.: An extension of the square root law of TCP. Ann. Oper. Res. 170(1), 217-232 (2009).
16. Ogata, J., Vere-Jones, D.: Inference for earthquake models: a self-correcting model. Stoch. Process. Their Appl. 17, 337-347 (1984).
17. Ott, T. J.: Transport protocols in the TCP paradigm and their performance. Telecommun. Syst. 30, 351-385 (2005).
18. Ott, T. J.: Rate of convergence for the square root formula in the Internet transmission control protocol. Adv. Appl. Probab. 38, 1132-1154 (2006).
19. Ott, T. J., Kemperman, J. H. B.: The transient behavior of processes in the TCP paradigm. Probab. Eng. Inf. Sci. 22, 431-471 (2008).
20. Ott, T. J., Swanson, J.: Asymptotic behavior of a generalized TCP congestion avoidance algorithm. J. Appl. Probab. 44, 618-635 (2007).
21. Ott, T. J., Kemperman, J. H. B., Mathis, M.: The stationary behavior of ideal TCP congestion avoidance. Unpublished manuscript (1996). Available at http://www.teunisott.com/Papers/TCP_Paradigm.
22. Vere-Jones, D.: Earthquake prediction: a statistician's view. J. Phys. Earth 26, 129-146 (1978).
23. Vere-Jones, D.: On the variance properties of stress release models. Aust. J. Stat. 30, 123-135 (1988).
24. Zheng, X.: Ergodic theorems for stress release processes. Stoch. Process. Their Appl. 37, 239-258 (1991).