Stochastic bandwidth packing process: Stability conditions via Lyapunov function technique

Queueing Systems

Volumn 48, Issue 3-4, 2004, Pages 339-363

  Gamarnik, David ^a  

^a IBM T J WATSON RESEARCH CENTER   (United States)

Author keywords

bin packing; positive recurrence; queueing networks

Indexed keywords

BANDWIDTH; LYAPUNOV FUNCTIONS; QUEUEING NETWORKS; STOCHASTIC SYSTEMS;

ARRIVAL PROCESS; BIN PACKING; COMMUNICATION BANDWIDTH; CONSTRUCTIVE CONDITIONS; EXPECTED QUEUE LENGTHS; POSITIVE RECURRENCE; STABILITY CONDITION; STOCHASTIC BANDWIDTHS;

QUEUEING THEORY;

EID: 8144231440     PISSN: 02570130     EISSN: 15729443     Source Type: Journal    
DOI: 10.1023/B:QUES.0000046581.34849.cf     Document Type: Article

References (19)

1. S. Albers and M. Mitzenmacher, Average-case analysis of first fit and random fit bin packing, Random Struct. Algorithms 16 (2000) 240-259.
2. D. Bertsimas, D. Gamarnik and J. Tsitsiklis, Performance of multiclass Markovian queueing networks via piecewise linear Lyapunov functions, Ann. Appl. Probab. 11(4) (2001) 1384-1428.
3. E.G. Coffman, Jr., C. Courcoubetis, M.R. Garey, D.S. Johnson, L.A. McGeoch, P.W. Shor, R.R. Weber and M. Yannakakis, Fundamental discrepancies between average-case analyses under discrete and continuous distributions: A bin packing case study, in: Proc. of the 23rd Ann. ACM Symposium on the Theory of Computing (STOC) (1991).
4. E.G. Coffman, Jr., S. Halfin, A. Jean-Marie and Ph. Robert, Stochastic analysis of a slotted, FIFO communication channel, IEEE Trans. Inform. Theory 39 (1993) 1555-1566.
5. E.G. Coffman, Jr., P. Robert and A.E. Stolyar. The interval packing process of linear networks, Performance Evaluation Rev. 27(3) (1999).
6. E.G. Coffman, Jr. and A.L. Stolyar, Bandwith packing, Algorithmica 29 (1999) 70-88.
7. J.F. Dantzer, M. Haddani and P. Robert, On the stability of a bandwidth packing algorithm, Probab. Engrg. Inform. Sci. 14(1) (2000) 57-79.
8. J.F. Dantzer and P. Robert, Analysis of a multi-class queueing system, Ann. Appl. Probab. 12(3) (2002) 860-889.
9. G. Fayolle, V.A. Malyshev and M.V. Menshikov, Topics in the Constructive Theory of Countable Markov Chains (Cambridge Univ. Press, Cambridge, 1995).
10. D. Gamarnik, On deciding stability of constrained homogeneous random walks and queueing systems, Math. Oper. Res. 27(2) (2002) 272-293.
11. D.S. Johnson, A. Demers, J.D. Ullman, M.R. Garey and R.L. Graham, Worst case bounds for simple one-dimensional packing algorithms, SIAM J. Comput. 3 (1974) 299-325.
12. C. Kenyon and M. Mitzenmacher, Linear waste of best fit bin packing on skewed distributions, in: Proc. of the 41st Symposium on the Foundations of Computer Science (2000).
13. C. Kenyon, A. Sinclair and Y. Rabani, Biased random walks, Lyapunov functions, and stochastic analysis of best fit bin packing, in: Proc. of the 7th ACM-SIAM Symposium on Discrete Algorithms (1995).
14. C. Kipnis and Ph. Robert, A dynamic storage process, Stochastic Process. Appl. 34 (1990) 155-169.
15. T. Leighton and P.W. Shor, Tight bounds for minimax grid matching with applications to average case analysis of algorithms, Combinatorica 9 (1989) 161-187.
16. S.P. Meyn and R.L. Tweedie, Markov Chains and Stochastic Stability (Springer, Berlin, 1993).
17. S.P. Meyn and R.L. Tweedie, Computable bounds for geometric convergence rates of Markov chains, Ann. Appl. Probab. 4 (1994) 981-1011.
18. A. Rényi, On a one-dimensional random space filling problem, MTA Mat. Kut. Internat. Kzl. 3 (1958) 109-127.
19. P.W. Shor, The average case analysis of some on-line algorithms for binpacking, Combinatorica 6 (1986) 179-200.