A multiclass closed queueing network with unconventional heavy traffic behavior

Annals of Applied Probability

Volumn 6, Issue 1, 1996, Pages 1-47

  Harrison, J M ^a,b   Williams, R J ^a,c  

^a STANFORD UNIVERSITY   (United States)

^b STANFORD UNIVERSITY   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Brownian motion; Closed multiclass queueing networks; Heavy traffic theory; M1 convergence; Reflecting barrier

Indexed keywords

EID: 0030546578     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034968064     Document Type: Article

References (23)

1. BILLINGSLEY, P. (1968). Convergence of Probability Measures. Wiley, New York.
2. BRÉMAUD P. (1981) Point Processes and Queues. Springer, New York.
3. CHEN, H. and MANDELBAUM, A. (1991). Leontief systems, RBV's and RBM's. In Applied Stochastic Analysis (M. H. A. Davis and R. J. Elliott, eds.) 1-43. Gordon and Breach, New York.
4. CHEN, H. and MANDELBAUM, A. (1991). Stochastic discrete flow networks: diffusion approximations and bottlenecks. Ann. Probab. 19 1463-1519.
5. CHUNG, K. L. and WILLIAMS, R. J. (1990). Introduction to Stochastic Integration, 2nd ed. Birkhäuser, Boston.
6. DAI, J. G. and WEISS, G. (1996). Stability and instability of fluid models for certain re-entrant lines. Math. Oper. Res. To appear.
7. DAI, J. G. and WILLIAMS, R. J. (1995). Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Teor. Veroyatnost. i Primenen. 40 3-53 (in Russian); Theor. Probab. Appl. 21. To appear.
8. DAI, J. G. and WILLIAMS, R. J. (1995). Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Teor. Veroyatnost. i Primenen. 40 3-53 (in Russian); Theor. Probab. Appl. 21. To appear.
9. ETHIER S. N. and KURTZ, T. G. (1986). Markov Processes. Wiley, New York.
10. HARRISON, J. M. (1985). Brownian Motion and Stochastic Flow Systems. Wiley, New York.
11. HARRISON, J. M. and NGUYEN, V. (1993). Brownian models of multiclass queueing networks: current status and open problems. Queueing Systems Theory Appl. 13 5-40.
12. HARRISON, J. M. and NGUYEN, V. (1995). Some badly behaved closed queueing networks. In Stochastic Networks (F. P. Kelly and R. J. Williams, eds.) Springer, New York.
13. HARRISON, J. M., WILLIAMS, R. J. and CHEN, H. (1990). Brownian models of closed queueing networks with homogenous customer populations. Stochastics Stochastics Reports 29 37-74.
14. KURTZ, T. G. (1991). Random time changes and convergence in distribution under the Meyer-Zheng conditions. Ann. Probab. 19 1010-1034.
15. KURTZ, T. G. and PROTTER, P. (1991). Weak limit theorems for stochastic integrals and stochastic differential equations. Ann. Probab. 19 1035-1070.
16. LU, S. H. and KUMAR, P. R. (1991). Distributed scheduling based on due dates and buffer priorities. IEEE Trans. Automat. Control 36 1406-1416.
17. POMAREDE J. L. (1976). A unified approach via graphs to Skorohod's topologies on the function space D. Ph.D. dissertation, Dept. Statistics, Yale Univ.
18. PROTTER, P. (1990). Stochastic Integration and Differential Equations. Springer, New York.
19. RYBKO, A. N. and STOLYAR, A. L. (1991). Ergodicity of stochastic processes describing the operation of an open queueing networks. Problemy Peredachi Informatsii 28 2-26.
20. SHARPE, M. (1988). General Theory of Markov Processes. Academic Press, San Diego.
21. SKOROKHOD, A. V. (1956). Limit theorems for stochastic processes. Theory Probab. Appl. 1 261-290.
22. WHITT, W. (1980). Some useful functions for functional limit theorems. Math. Oper. Res. 3 67-85.
23. WILLIAMS, R. J. (1995). Semimartingale reflecting Brownian motions in the orthant. In Stochastic Networks (F. P. Kelly and R. J. Williams, eds.) Springer, New York.