On superlinear scaling of network delays

IEEE/ACM Transactions on Networking

Volumn 19, Issue 4, 2011, Pages 1043-1056

  Burchard, Almut ^a   Liebeherr, Jörg ^a   Ciucu, Florin ^b  

^a UNIVERSITY OF TORONTO   (Canada)

^b DEUTSCHE TELEKOM LABORATORIES   (Germany)

Author keywords

Delay analysis; network calculus; scaling properties

Indexed keywords

CROSS-TRAFFIC; DELAY ANALYSIS; DELAY BOUND; END TO END DELAY; INDEPENDENCE ASSUMPTION; NETWORK CALCULUS; NETWORK DELAYS; NETWORK NODE; NETWORK PATHS; PROBABILISTIC ANALYSIS; SCALING BEHAVIOR; SCALING PROPERTIES; SUPERLINEAR; TRAFFIC FLOW; WORST-CASE ANALYSIS;

EID: 80051789960     PISSN: 10636692     EISSN: None     Source Type: Journal    
DOI: 10.1109/TNET.2010.2095505     Document Type: Article

References (30)

1. R. Agrawal, R. L. Cruz, C. Okino, and R. Rajan, "Performance bounds for flow control protocols," IEEE/ACM Trans. Netw., vol. 7, no. 3, pp. 310-323, Jun. 1999.
2. S. Ayyorgun and R. Cruz, "A service-curve model with loss and a multiplexing problem," in Proc. 24th IEEE ICDCS, Mar. 2004, pp. 756-765.
3. F. Baskett, K. M. Chandy, R. R. Muntz, and F. G. Palacios, "Open, closed and mixed networks of queues with different classes of customers," J. ACM, vol. 22, no. 2, pp. 248-260, Apr. 1975.
4. R. Boorstyn, A. Burchard, J. Liebeherr, and C. Oottamakorn, "Statistical service assurances for traffic scheduling algorithms," IEEE J. Sel. Areas Commun., vol. 18, no. 12, pp. 2651-2664, Dec. 2000. (Pubitemid 32252004)
5. J. Y. Le Boudec and P. Thiran, Network Calculus. New York: Springer-verlag, 2001, vol. LNCS 2050, Lecture Notes in Computer Science.
6. O. Boxma, "On a tandem queueing model with identical service times at both counters," Adv. Appl. Probab., vol. 11, no. 3, pt. 1, 2, pp. 616-659, 1979.
7. A. Burchard, J. Liebeherr, and F. Ciucu, "On 1+Nvscaling of network delays," in Proc. IEEE INFOCOM,May 2007, pp. 1866-1874.
8. A. Burchard, J. Liebeherr, and S. D. Patek, "A min-plus calculus for end-to-end statistical service guarantees," IEEE Trans. Inf. Theory, vol. 52, no. 9, pp. 4105-4114, Sep. 2006. (Pubitemid 44363836)
9. S. B. Calo, "Delay properties of message channels," in Proc. IEEE ICC, Boston, MA, 1979, pp. 43.5.1-43.5.4.
10. C.-S. Chang, Performance Guarantees in Communication Networks. New York: Springer-verlag, 2000.
11. F. Ciucu, A. Burchard, and J. Liebeherr, "Scaling properties of statistical end-to-end bounds in the network calculus," IEEE Trans. Inf. Theory, vol. 52, no. 6, pp. 2300-2312, Jun. 2006. (Pubitemid 43898893)
12. J. W. Cohen, The Single Server Queue. Amsterdam, The Netherlands: North Holland, 1969.
13. R. L. Cruz, "Quality of service guarantees in virtual circuit switched networks," IEEE J. Sel. Areas Commun., vol. 13, no. 6, pp. 1048-1056, Aug. 1995.
14. M. Fidler, "An end-to-end probabilistic network calculus with moment generating functions," in Proc. 14th IEEE IWQoS, Jun. 2006, pp. 261-270. (Pubitemid 46938153)
15. P. Le Gall, "The overall sojourn time in tandem queues with identical successive service times and renewal input," Stoch. Process. Appl., vol. 52, no. 1, pp. 165-178, Aug. 1994.
16. P. W. Glynn and W. Whitt, "Departures from many queues in series," Ann. Appl. Probab., vol. 1, pp. 546-572, 1991.
17. G. Grimmett and D. Stirzaker, Probability and Random Processes. Oxford, U.K.: Oxford Univ. Press, 2001.
18. Y. Jiang, "A basic stochastic network calculus," in Proc. ACM SIGCOMM, Sep. 2006, pp. 123-134. (Pubitemid 44623721)
19. Y. Jiang and Y. Liu, Stochastic Network Calculus. New York: Springer, 2008.
20. F. I. Karpelevitch and A. Ya. Kreinin, "Asymptotic analysis of queuing systems with identical service," J. Appl. Probab., vol. 33, no. 1, pp. 267-281, 1996.
21. F. P. Kelly, "Networks of queues with customers of different types," J. Appl. Probab., vol. 3, no. 12, pp. 542-554, Sep. 1975.
22. F. P. Kelly, , F. P. Kelly, S. Zachary, and I. B. Ziedins, Eds., "Notes on effective bandwidths," in Stochastic Networks: Theory and Applications, ser. Roy. Stat. Soc. Lec. Notes. Oxford, U.K.: Oxford Univ. Press, 1996, vol. 4, pp. 141-168.
23. K. Lee, "Performance bounds in communication networks with variable-rate links," in Proc. ACM SIGCOMM, 1995, pp. 126-136.
24. C. Li, A. Burchard, and J. Liebeherr, "A network calculus with effective bandwidth," IEEE/ACM Trans. Netw., vol. 15, no. 6, pp. 1442-1453, Dec. 2007.
25. S. McCreary and K. Claffy, "Trends in wide area IP traffic patterns," in Proc. 13th ITC Special. Sem. Internet Traffic Meas. Model., Sep. 2000, pp. 1-11.
26. P. I. Richards, "Shock waves on the highway," Oper. Res., vol. 4, no. 1, pp. 42-51, Feb. 1956.
27. O. P. vinogradov, "A multiphase system with identical service," Sov. J. Comput. Syst. Sci., vol. 24, no. 2, pp. 28-31, Mar. 1986.
28. O. P. vinogradov, "A multiphase system with many servers and identical service times," (in Russian) Stoch. Process. Appl., vol. 24, pp. 42-45, 1989.
29. O. P. vinogradov, "On certain asymptotic properties of waiting time in a multiserver queueing system with identical times," SIAM Theory Probab. Appl., vol. 39, no. 4, pp. 714-718, 1994. (Pubitemid 126043861)
30. O. Yaron and M. Sidi, "Performance and stability of communication networks via robust exponential bounds," IEEE/ACMTrans. Netw., vol. 1, no. 3, pp. 372-385, Jun. 1993.