Large deviation bounds for single class queueing networks and their calculation

Queueing Systems

Volumn 48, Issue 1-2, 2004, Pages 103-134

  Majewski, Kurt ^a  

^a SIEMENS AG   (Germany)

Author keywords

complementarity problem; minimizing path; set valued upper semicontinuity; variational problem

Indexed keywords

PIECEWISE LINEAR TECHNIQUES; QUEUEING THEORY; VARIATIONAL TECHNIQUES;

COMPLEMENTARITY PROBLEMS; FIXED POINT EQUATION; LARGE DEVIATION PRINCIPLE; MINIMIZATION PROBLEMS; MINIMIZING PATH; UPPER SEMI-CONTINUITY; UPPER SEMICONTINUOUS; VARIATIONAL PROBLEMS;

QUEUEING NETWORKS;

EID: 4444289687     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/B:QUES.0000039890.04317.5a     Document Type: Article

References (19)

1. R. Atar and P. Dupuis, Large deviations and queueing networks: Methods for rate function identification, Stochastic Process. Appl. 84 (1999) 255-296.
2. D. Bertsimas, I.C. Paschalidis and J.N. Tsitsiklis, On the large deviations behaviour of acyclic networks of G/G/1 queues, Ann. Appl. Probab. 8(4) (1998) 1027-1069.
3. C.-S. Chang, Sample path large deviations and intree networks, Queueing Systems 20 (1995) 7-36.
4. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications (Jones and Bartlett, London, 1993).
5. P. Dupuis and R.S. Ellis. Large deviation analysis of queueing systems, in: Stochastic Networks, eds. F. Kelly and R. Williams (Springer, New York, 1995) pp. 347-366.
6. P. Dupuis and R.S. Ellis, The large deviation principle for a general class of queueing systems I, Trans. Amer. Math. Soc. 347(8) (1995) 2689-2751.
7. P. Dupuis and K. Ramanan, A multiclass feedback queueing network with a regular Skorohod problem, Queueing Systems 36(4) (2000) 327-349.
8. A. Ganesh and N. O'Connell, A large deviation principle with queueing applications, Stochastics Stochastics Rep. 73(1/2) (2002) 25-35.
9. I. Ignatiouk-Robert, Large deviations of Jackson networks, Ann. Appl. Prob. 10(3) (2000) 962-1001.
10. I. Ignatyuk, V. Malyshev and V. Scherbakov, Boundary effects in large deviation problems, Russian Math. Surveys 49(2) (1994) 41-99. Translation from Uspekhi Mat. Nauk 49(2) (1994) 43-102.
11. I. Ignatyuk, V. Malyshev and V. Scherbakov, Boundary effects in large deviation problems, Russian Math. Surveys 49(2) (1994) 41-99. Translation from Uspekhi Mat. Nauk 49(2) (1994) 43-102.
12. J.R. Jackson, Networks of waiting lines, Oper. Res. 5 (1957) 518-521.
13. Z.-Q. Luo, J.-S. Pang and D. Ralph, Piecewise sequential quadratic programming for mathematical programs with nonlinear complementarity constraints, in: Multilevel Optimization: Algorithms and Applications, ed. A. Migdalas (Kluwer Academic Publishers, Boston, 1998) pp. 209-229.
14. K. Majewski, Large deviations of the steady-state distribution of reflected processes with applications to queueing systems, Queueing Systems 29(2-4) (1998) 351-381.
15. K. Majewski, Single class queueing networks with discrete and fluid customers on the time interval ℝ, Queueing Systems 36(4) (2000) 405-435.
16. K. Majewski, Set-valued upper semicontinuity of the behavior of single class queueing networks, Working paper (2002).
17. K. Majewski, Large deviations for multi-dimensional reflected fractional Brownian motion, Stochastics Stochastics Rep. 75(4) (2003) 233-257.
18. M. Mandjes and A. Ridder, Optimal trajectory to overflow in a queue fed by a large number of sources, Queueing Systems 31 (1999) 137-170.
19. A.L. Stolyar, Control of end-to-end delay tails in a multiclass network: LWDF discipline optimality, Ann. Appl. Probab. 13(3) (2003) 1151-1206.