A Markovian growth-collapse model

Advances in Applied Probability

Volumn 38, Issue 1, 2006, Pages 221-243

  Boxma, Onno ^a,b   Perry, David ^c   Stadje, Wolfgang ^d   Zacks, Shelemyahu ^e  

^a EURANDOM   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c UNIVERSITY OF HAIFA   (Israel)

^d UNIVERSITY OF OSNABRÜCK   (Germany)

^e BINGHAMTON UNIVERSITY   (United States)

Author keywords

Duality; Growth collapse process; Hitting time; Markov modulation; Piecewise deterministic Markov process; Stationary distribution; Uniform cut off

Indexed keywords

DIFFERENTIAL EQUATIONS; LAPLACE TRANSFORMS; MATHEMATICAL MODELS; POISSON DISTRIBUTION; PROBABILITY DENSITY FUNCTION;

GROWTH-COLLAPSE PROCESS; HITTING TIME; MARKOV MODULATION; PIECEWISE-DETERMINISTIC MARKOV PROCESS; STATIONARY DISTRIBUTION; UNIFORM CUT-OFF;

MARKOV PROCESSES;

EID: 33646094947     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1143936148     Document Type: Article

References (23)

1. Albrecher, H. and Boxma, O. J. (2004). A ruin model with dependence between claim sizes and claim intervals. Insurance Math. Econom. 35, 245-254.
2. Albrecher, H. and Boxma, O. J. (2005). On the discounted penalty function in a Markov-dependent risk model. Insurance Math. Econom. 37, 650-672.
3. Altman, E., Avrachenkov, K., Barakat, C. And Núñez-Queija, R. (2001). State-dependent M/G/1 type queueing analysis for congestion control in data networks. In Proc. IEEE INFOCOM 2001 (Anchorage, AK, April 2001), IEEE, Piscataway, NJ, pp. 1350-1359.
4. Altman, E., Avrachenkov, K., Kherani, A. A. and Prabhu, B. J. (2005). Performance analysis and stochastic stability of congestion control protocols. In Proc. IEEE INFOCOM 2005 (Miami, FL, Match 2005), eds K. Makki and E. Knightly, IEEE, Piscataway, NJ.
5. Asmussen, S. (2000). Ruin Probabilities (Adv. Ser. Statist. Sci. Appl. Prob. 2). World Scientific, Singapore.
6. Asmussen, S. (2003). Applied Probability and Queues, 2nd edn. Springer, New York.
7. Bak, P. (1996). How Nature Works: The Science of Self-Organized Criticality. Copernicus, New York.
8. Bekker, R., Borst, S. C., Boxma, O. J. And Kella, O. (2003). Queues with workload-dependent arrival and service rates. Queueing Systems 46, 537-556.
9. Boxma, O. J. and Perry, D. (2001). A queueing model with dependence between service and interarrival times. Europ. J. Operat. Res. 128, 611-624.
10. Boxma, O. J., Kella, O. and Perry, D. (2001). An intermittent fluid system with exponential on-times and semi-Markov input rates. Prob. Eng. Inf. Sci. 15, 189-198.
11. Boxma, O. J., Kaspi, H., Kella, O. and Perry, D. (2005). On/off storage systems with state-dependent input, output and switching rates. Prob. Eng. Inf. Sci. 19, 1-14.
12. Budhiraja, A., Hernandez-campos, F., Kulkarni, V. G. and Smith, F. D. (2004). Stochastic differential equation for TCP window size: analysis and experimental validation. Prob. Eng. Inf Sci. 18, 111-140.
13. Cohen, J. W. (1982). The Single Server Queue. North-Holland, Amsterdam.
14. Davis, M. H. A. (1984). Piecewise-deterministic Markov processes: a general class of non-diffusion stochastic models. J. R. Statist. Soc. B 46, 353-388.
15. Davis, M. H. A. (1993). Markov Models and Optimization. Chapman and Hall, London.
16. Eliazar, I. and Klafter, J. (2004). A growth-collapse model: Lévy inflow, geometric crashes, and generalized Ornstein-Uhlenbeck dynamics. Physica A 334, 1-21.
17. Keilson, J. and Mermin, N. D. (1959). The second-order distribution of integrated shot noise. IRE Trans. Inf. Theory 5, 75-77.
18. Kella, O. and Stadje, W. (2001). On hitting times for compound Poisson dams with exponential jumps and linear release. J. Appl. Prob. 38, 781-786.
19. Kherani, A. A. and Kumar, A. (2002). Stochastic models for throughput analysis of randomly arriving elastic flows in the Internet. In Proc. IEEE INFOCOM 2002 (New York, June 2002), IEEE, Piscataway, NJ.
20. Perry, D. and Stadje, W. (2003). Duality of dams via mountain processes. Operat. Res. Lett. 31, 451-458.
21. Polyanin, A. D. and Zaitsev, V. F. (1995). Handbook of Exact Solutions for Ordinary Differential Equations. CRC, Boca Raton, FL.
22. Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. (1999). Stochastic Processes for Insurance and Finance. John Wiley, New York.
23. Scheinhardt, W., Van Foreest, N. and Mandjes, M. (2005). Continuous feedback fluid queues. Operat. Res. Lett. 33, 551-559.