Revisiting stochastic loss networks: Structures and algorithms

SIGMETRICS'08: Proceedings of the 2008 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems

Volumn 36, Issue 1 SPECIAL ISSUE, 2008, Pages 407-418

  Jung, Kyomin ^a   Lu, Yingdong ^b   Shah, Devavrat ^a   Sharma, Mayank ^b   Squillante, Mark S ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

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

Author keywords

Erlang loss formula and fixed point approximation; Loss networks; Multidimensional stochastic processes; Stochastic approximations

Indexed keywords

APPROXIMATION THEORY; BOOLEAN FUNCTIONS; COMPUTER SYSTEMS; PAPER; POLYNOMIAL APPROXIMATION; PROBABILITY; PROBABILITY DISTRIBUTIONS;

ALGORITHMIC PROBLEMS; ERLANG LOSS FORMULA AND FIXED-POINT APPROXIMATION; EXACT RESULTS; LOSS NETWORKS; LOSS PROBABILITIES; MULTIDIMENSIONAL STOCHASTIC PROCESSES; NOVEL ALGORITHMS; NUMERICAL EXPERIMENTS; POOR PERFORMANCES; STATIONARY DISTRIBUTIONS; STOCHASTIC APPROXIMATIONS;

COMPUTER NETWORKS;

EID: 57449120683     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1375457.1375503     Document Type: Conference Paper

References (27)

1. S. Berezner, A. Krzesinski, P. Taylor. On the inverse of Erlang's formula. J. Appl. Prob., 35:246-252, 1998.
2. S. Bhadra, Y. Lu, M. Squillante. Optimal capacity planning in stochastic loss networks with time-varying workloads. In Proc. ACM SIGMETRICS, 227-238, 2007.
3. T. Bonald. The Erlang model with non-Poisson call arrivals. In Proc. SIGMETRICS-Performance, 276-286, 2006.
4. D. Burman, J. Lehoczky, Y. Lim. Insensitivity of blocking probabilities in a circuit-switching network. J. Appl. Prob, 21:850-859, 1984.
5. A. Erlang. Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges. In E. Brockmeyer, H. Halstrom, A. Jensen, eds., The Life and Works of A.K. Erlang, Denmark, 1948.
6. P. Hunt, F. Kelly. On critically loaded loss networks. Adv. Appl. Prob., 21:831-841, 1989.
7. P. Jelenkovic, P. Momcilovic, M. Squillante. Scalability of wireless networks. IEEE/ACM Trans. Networking, 15:295-308, 2007.
8. K. Jung, Y. Lu, D. Shah, M. Sharma, M. Squillante. Revisiting stochastic loss networks: Structures and algorithms. Research Report, IBM Research, Nov. 2007.
9. F. Kelly. Reversibility and Stochastic Networks. John Wiley & Sons, New York, 1979.
10. F. Kelly. Stochastic models of computer communication systems. J. Royal Stat. Soc., B, 47:379-395, 1985.
11. F. Kelly. Blocking probabilities in large circuit-switched networks. Adv. Appl. Prob., 18:473-505, 1986.
12. F. Kelly. Routing in circuit-switched networks: Optimization, shadow prices and decentralization. Adv. Appl. Prob., 20:112-144, 1988.
13. F. Kelly. Loss networks. Ann. Appl. Prob., 1:319-378, 1991.
14. J. Lasserre. Global optimization with polynomials and the problems of moments. SIAM J. Opt., 11:796-817, 2001.
15. J. Little. A proof of the queuing formula L = λW. Open Res., 9:383-387, 1961.
16. G. Louth, M. Mitzenmacher, F. Kelly. Computational complexity of loss networks. Theor. Comp. Sci, 125:45-59, 1994.
17. Y. Lu, A. Radovanović, M. Squillante. Optimal capacity planning in stochastic loss networks. Perf. Eval. Rev., 35, 2007.
18. Z. Luo, P. Tseng. On the linear convergence of descent methods for convex essentially smooth minimization. SIAM J. Cont. Opt., 30:408-425, 1992.
19. D. Mitra, J. Morrison, K. Ramakrishnan. ATM network design and optimization: A multirate loss network framework. IEEE/ACM Trans. Networking, 4:531-543, 1996.
20. D. Mitra, P. Weinberger. Probabilistic models of database locking: Solutions, computational algorithms and asymptotics. J. ACM, 31:855-878, 1984.
21. K. Ross. Multiservice Loss Models for Broadband Telecommunication Networks. Springer-Verlag, 1995.
22. A. Saleh, J. Simmons. Evolution toward next-generation core optical network. J. Lightwave Tech., 24:3303-3321, 2006.
23. B. Sevastyanov. An ergodic theorem for Markov processes and its application to telephone systems with refusals. Theor. Prob. Appl, 2:104-112, 1957.
24. L. Valiant. The complexity of computing the permanent. Theor. Comp. Sci, 8:189-201, 1979.
25. W. Whitt. Blocking when sendee is required from several facilities simultaneously. AT&T Bell Lab. Tech. J., 64:1807-1856, 1985.
26. S. Xu, J. Song, B. Liu. Order fulfillment performance measures in an assemble-to-order system with stochastic leadtime. Oper. Res., 47:131-149, 1999.
27. I. Ziedins, F. Kelly. Limit theorems for loss networks with diverse routing. Adv. Appl. Prob, 21:804-830, 1989.