A sufficient condition for the positive recurrence of a semimartingale reflecting Brownian motion in an orthant

Annals of Applied Probability

Volumn 6, Issue 3, 1996, Pages 758-765

  Chen, Hong ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Fluid network; Linear Lyapunov function; Positive recurrence; Semimartingale reflecting Brownian motion on an orthant; Stationary distribution

Indexed keywords

EID: 85041120433     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968226     Document Type: Article

References (17)

1. BERMAN, A. and PLEMMONS, R. J. (1979). Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York.
2. n. Stochastics Stochastics Rep. 34 149-167.
3. CHEN, H. (1995). Fluid approximations and stability of multiclass queueing networks: work-conserving disciplines. Ann. Appl. Probab. 5 637-665.
4. CHEN, H. and ZHANG, H. (1995). Diffusion approximations for re-entrant lines with a first-buffer-first-served priority discipline. Unpublished manuscript.
5. COTTLE, R. W., HABETLER, G. J. and LEMKE, C. E. (1970). On classes of copositive matrices. Linear Algebra Appl. 3 295-310.
6. COTTLE, R. W., PANG, J. S. and STONE, R. E. (1992). The Linear Complementarity Problem. Academic Press, New York.
7. DAI, G. J. and WEISS, G. (1996). Stability and instability of fluid models for certain re-entrant lines. Math. Oper. Res. To appear.
8. DAI, J. G., YEH, D. H. and ZHOU, C. (1994). The QNET method for re-entrant queueing networks with priority disciplines. Oper. Res. To appear.
9. DOWN, D. and MEYN, S. (1994). Piecewise linear test functions for stability of queueing networks. In Proceedings of the 33rd Conference on Decision and Control 2069-2074.
10. DUPUIS, P. and WILLIAMS, R. J. (1994). Lyapunov functions for semimartingale reflecting Brownian motions. Ann. Probab. 22 680-702.
11. HARRISON, J. M. and WILLIAMS, R. J. (1992). Brownian models of feedforward queueing networks: quasireversibility and product form solutions. Ann. Appl. Probab. 2 263-293.
12. HOBSON, D. G. and ROGERS, L. C. G. (1994). Recurrence and transience of reflecting Brownian motion in the quadrant. Math. Proc. Cambridge Philos. Soc. 113 387-399.
13. MANDELBAUM, A. and VAN DER HEYDEN, L. (1987). Complementarity and reflection. Unpublished manuscript.
14. PETERSON, W. P. (1991). A heavy traffic limit theorem for network of queues with multiple customer types. Math. Oper. Res. 16 90-118.
15. REIMAN, M. I. and WILLIAMS, R. J. (1988). A boundary property of semimartingale reflecting Brownian motions. Probab. Theory Related Fields 77 87-97.
16. TAYLOR, L. M. and WILLIAMS, R. J. (1993). Existence and uniqueness of semimartingale reflecting Brownian motions in an orthant. Probab. Theory Related Fields 96 283-317.
17. WILLIAMS, R. J. (1985). Recurrence classification and invariant measure for reflected Brownian motion in a wedge. Ann. Probab. 13 758-778.