A multi-dimensional martingale for Markov additive processes and its applications

Advances in Applied Probability

Volumn 32, Issue 2, 2000, Pages 376-393

  Asmussen, Søren ^a   Kella, Offer ^b  

^a LUND UNIVERSITY   (Sweden)

^b HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

EOQ model; Fluid queues; L vy process; Markov modulation; Multivariate martingale; Reflected Brownian motion; Storage process

Indexed keywords

BROWNIAN MOVEMENT; EIGENVALUES AND EIGENFUNCTIONS; INTEGRATION; MARKOV PROCESSES; MATHEMATICAL MODELS; THEOREM PROVING;

EOQ MODEL; FLUID QUEUES; LEVY PROCESS; MARKOV ADDITIVE PROCESSES; MARKOV MODULATION; MULTIVARIATE MARTINGALE; STORAGE PROCESS;

PROBABILITY;

EID: 0034206151     PISSN: 00018678     EISSN: None     Source Type: Journal    
DOI: 10.1239/aap/1013540169     Document Type: Article

References (24)

1. Anick, D., Mitra, D. and SONDHI, M. M. (1982). Stochastic theory of a data-handling system with multiple sources. Bell System Tech. J. 61,1871-1894.
2. Asmussen, S. (1989). Risk theory in a Markovian environment. Scand.Act. J. 1989,69-100.
3. Asmussen, S. (1991). Ladder heights and the Markov-modulated M/ G/1 queue. Stoch. Proc. Appl. 37,313-326.
4. Asmussen, S. (1994). Busy period analysis, rare events and transient behavior in fluid flow models. J. Appl. Math. Stoch. Anal. 7, 269-299.
5. Asmussen, S. (1995). Stationary distributions for fluid flow models with or without Brownian noise. Stoch. Models 11, 21-49.
6. Asmussen, S. (1995). Stationary distributions via first passage times. In Advances in Queueing: Models, Methods & Problems, ed. J. Dshalalow. CRC Press, Boca Raton, FL, pp. 79-102.
7. ASMUSSEN, S. (1998). Extreme value theory for queues via cycle maxima. Extremes 1,137-168.
8. ASMUSSEN, S and Perry, D. (1992). On cycle maxima, first passage problems and extreme value theory for queues. Stock. Models 8, 421-458.
9. ASMUSSEN, S and Perry, D. (1997). Operational calculus for matrix-exponential distributions, with applications to Brownian (q, Q) models. Matk. Operat. Res. 23, 166-176.
10. BACCELLI, F. and MAKOWSKI, A. M.(1991). Exponentialmartingalesfor queuesinarandomenvironment: the M/ G/1 case. Stock. Proc. Appl 38, 99-133.
11. BERMAN, A. and Plemmons, R. J. (1979). Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York.
12. CINLAR, E. (1971). Markov additive processes I-II. Z. Wakrsckeinlickkeitstk. 24, 85-121.
13. Borovkov, A. A. (1976). Stockastic Processes in Queueing Theory. Springer, New York.
14. HARRISON, J. M. (1985). Brownian Motion and Stockastic Flow Systems. Wiley, New York.
15. HEATH, D., Resnick, S. and Samorodnitsky, G. (1998). Heavy tails and long range dependence in On/Off processes and associated fluid models. Matk. Operat. Res. 23,145-165.
16. KASPI, H. (1984). Storage processes with Markov additive input and output. Matk. Operat Res. 9, 424-440.
17. KELLA, O. and WHITT, W. (1992). Useful martingales for stochastic storage processes with Levy input. J. Appl. Prob. 29, 396-403.
18. KELLA, O. and WHITT, W. (1996). Stability and structural properties of stochastic storage networks. J. Appl. Prob. 33,1169-1180.
19. NAHMIAS, S. (1989). ProductionandOperationsAnalysis. Irwin, Homewood, IL.
20. Neuts, M. F. (1979). A versatile Markovian point process. J. Appl. Prob. 16,764-779.
21. NEVEU, J. (1961). Une generalisation des processus a accroissementespositifsindependantes.Abk. Matk. Sem. Hamburg 23,36-61.
22. PROTTER, P. (1990). Stockastic Integration and Differential Equations. Springer, New York.
23. REGTERSCHOT, G. J. K. and DE SMIT, J. H. A. (1986). The queue M/ G/1 with Markov-modulated arrivals and services. Matk. Operat. Res. 11, 465-483.
24. ROGERS, L. C. G. (1994). Fluid models in queueing theory and Wiener-Hopf factorization of Markov chains. Ann. Appl Prob. 4 390-413.