A Guide to the Stochastic Network Calculus

IEEE Communications Surveys and Tutorials

Volumn 17, Issue 1, 2015, Pages 92-105

  Fidler, Markus ^a   Rizk, Amr ^a  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

end to end performance evaluation; moment generating functions; scheduling; Stochastic network calculus

Indexed keywords

COMPUTER NETWORK PERFORMANCE EVALUATION; SCHEDULING; STOCHASTIC SYSTEMS;

EFFECTIVE BANDWIDTH; END-TO-END ANALYSIS; END-TO-END PERFORMANCE; ENVELOPE FUNCTIONS; MOMENT GENERATING FUNCTION; NETWORK SERVICES; STOCHASTIC NETWORK CALCULUS; TRAFFIC SOURCES;

CALCULATIONS;

EID: 84925863118     PISSN: None     EISSN: 1553877X     Source Type: Journal    
DOI: 10.1109/COMST.2014.2337060     Document Type: Article

References (45)

1. M. Fidler and A. Rizk, "A guide to the stochastic network calculus," presented at the Proc. GI MMBnet, Hamburg, Germany, Sep. 2013, Invited Paper.
2. R. L. Cruz, "A calculus for network delay part I and II: Network elements in isolation and network analysis," IEEE Trans. Inf. Theory, vol. 37, no. 1, pp. 114-141, Jan. 1991.
3. 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.
4. C.-S. Chang, Performance Guarantees in Communication Networks. London, U.K.: Springer-Verlag, 2000.
5. J.-Y. Le Boudec and P. Thiran, Network Calculus A Theory of Deterministic Queuing Systems for the Internet, vol. 2050. Berlin, Germany: Springer-Verlag, 2001, ser. LNCS.
6. 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.
7. F. P. Kelly, Notes on Effective Bandwidths. Oxford, U.K.: Clarendon, 1996, ser. Number 4 in Royal Statistical Society Lecture Notes, pp. 141-168.
8. C.-S. Chang, "Stability, queue length and delay of deterministic and stochastic queueing networks," IEEE Trans. Autom. Control, vol. 39, no. 5, pp. 913-931, May 1994.
9. O. Yaron and M. Sidi, "Performance and stability of communication networks via robust exponential bounds," IEEE/ACM Trans. Netw., vol. 1, no. 3, pp. 372-385, Jun. 1993.
10. R. L. Cruz, "Quality of service management in integrated services networks,"presented at the Proc. Semi-Annual Research Review, Center Wireless Communication, UCSD, San Diego, CA, USA, Jun. 1996.
11. Q. Yin, Y. Jiang, S. Jiang, and P. Y. Kong, "Analysis of generalized stochastically bounded bursty traffic for communication networks," in Proc. IEEE LCN, Nov. 2002, pp. 141-149.
12. F. Ciucu, A. Burchard, and J. Liebeherr, "Scaling properties of statistical end-to-end bounds in the network calculus," IEEE/ACM Trans. Netw., vol. 52, no. 6, pp. 2300-2312, Jun. 2006.
13. A. Burchard, J. Liebeherr, and F. Ciucu, "On superlinear scaling of network delays," IEEE/ACM Trans. Netw., vol. 19, no. 4, pp. 1043-1056, Aug. 2011.
14. M. Fidler, "An end-to-end probabilistic network calculus with moment generating functions," in Proc. IWQoS, Jun. 2006, pp. 261-270.
15. A. Rizk and M. Fidler, "Non-asymptotic end-to-end performance bounds for networks with long range dependent FBM cross traffic," Comput. Netw., vol. 56, no. 1, pp. 127-141, Jan. 2012.
16. J. Liebeherr, A. Burchard, and F. Ciucu, "Delay bounds in communication networks with heavy-tailed and self-similar traffic," IEEE Trans. Inf. Theory, vol. 58, no. 2, pp. 1010-1024, Feb. 2012.
17. Y. Jiang and Y. Liu, Stochastic Network Calculus. London, U.K.: Springer-Verlag, Sep. 2008.
18. S. Mao and S. S. Panwar, "A survey of envelope processes and their applications in quality of service provisioning," IEEE Commun. Surveys Tuts., vol. 8, no. 3, pp. 2-20, Jul. 2006.
19. M. Fidler, "A survey of deterministic and stochastic service curve models in the network calculus," IEEE Commun. Surveys Tuts., vol. 12, no. 1, pp. 59-86, 2010.
20. F. Ciucu and J. Schmitt, "Perspectives on network calculus-No free lunch but still good value," in Proc. ACM SIGCOMM, Aug. 2012, pp. 311-322.
21. A. Rizk and M. Fidler, "On multiplexing models for independent traffic flows in single- and multi-node networks," IEEE Trans. Netw. Serv. Manage., vol. 10, no. 1, pp. 15-28, Mar. 2013.
22. C.-S. Chang, R. L. Cruz, J.-Y. Le Boudec, and P. Thiran, "A min, + system theory for constrained traffic regulation and dynamic service guarantees,"IEEE/ACM Trans. Netw., vol. 10, no. 6, pp. 805-817, Dec. 2002.
23. J. Liebeherr, M. Fidler, and S. Valaee, "A system theoretic approach to bandwidth estimation," IEEE/ACM Trans. Netw., vol. 18, no. 4, pp. 1040-1053, Aug. 2010.
24. D. Starobinski and M. Sidi, "Stochastically bounded burstiness for communication networks," IEEE Trans. Inf. Theory, vol. 46, no. 1, pp. 206-212, Jan. 2000.
25. R. Lübben, M. Fidler, and J. Liebeherr, "A foundation for stochastic bandwidth estimation of networks with random service," in Proc. IEEE INFOCOM, Apr. 2011, pp. 1817-1825.
26. D. O. Wu and R. Negi, "Effective capacity: A wireless link model for support of quality of service," IEEE Trans. Wireless Commun., vol. 2, no. 4, pp. 630-643, Jul. 2003.
27. K. Lee, "Performance bounds in communication networks with variablerate links," in Proc. ACM SIGCOMM, Aug. 1995, pp. 126-136.
28. F. Ciucu, J. Schmitt, and H. Wang, "On expressing networks with flow transformations in convolution-form," in Proc. IEEE INFOCOM, 2011, pp. 1979-1987.
29. th ed. Upper Saddle River, NJ, USA: Prentice-Hall, 2002.
30. H. Al-Zubaidy, J. Liebeherr, and A. Burchard, "A (min,x)-network calculus for multi-hop fading channels," in Proc. IEEE INFOCOM, Apr. 2013, pp. 1833-1841.
31. rd ed. London, U.K.: Oxford Univ. Press, 2001.
32. nd ed. Hoboken, NJ, USA: Wiley, 2006.
33. F. Ciucu, "Exponential supermartingales for evaluating end-to-end backlog bounds," in Proc. MAMA Workshop ACM SIGMETRICS, Jun. 2007, pp. 21-23.
34. M. Fidler, "A network calculus approach to probabilistic quality of service analysis of fading channels," in Proc. IEEE GLOBECOM, Nov. 2006, pp. 1-6.
35. G. Mayor and J. Silvester, "Time scale analysis of an ATM queueing system with long-range dependent traffic," in Proc. IEEE INFOCOM, Apr. 1997, pp. 205-212.
36. N. Fonseca, G. Mayor, and C. Neto, "On the equivalent bandwidth of self-similar sources," ACM Trans. Model. Comput. Simul., vol. 10, no. 2, pp. 104-124, Apr. 2000.
37. C. Melo and N. Fonseca, "Envelope process and computation of the equivalent bandwidth of multifractal flows," Comput. Netw., vol. 48, no. 3, pp. 351-375, Jun. 2005.
38. N. G. Duffield and N. O'Connell, "Large deviations and overflow probabilities for the general single-server queue, with applications," Math. Proc. Camb. Phil. Soc., vol. 118, no. 2, pp. 363-375, Sep. 1995.
39. I. Norros, "On the use of fractional Brownian motion in the theory of connectionless networks," IEEE J. Sel. Areas Commun., vol. 13, no. 6, pp. 953-962, Aug. 1995.
40. K. Mahmood, A. Rizk, and Y. Jiang, "On the flow-level delay of a spatial multiplexing MIMO wireless channel," in Proc. IEEE ICC, Jun. 2011, pp. 1-6.
41. R. Lübben and M. Fidler, "On the delay performance of block codes for discrete memoryless channels with feedback," in Proc. IEEE Sarnoff Symp., May 2012, pp. 1-6.
42. R. Agrawal, R. L. Cruz, C. M. Okino, and R. Rajan, "Performance bounds for flow control protocols," IEEE/ACM Trans. Netw., vol. 7, no. 3, pp. 310-323, Jun. 1999.
43. S. Akin and M. C. Gursoy, "Effective capacity analysis of cognitive radio channels for quality of service provisioning," IEEE Trans. Wireless Commun., vol. 9, no. 11, pp. 3354-3364, Nov. 2010.
44. F. Ciucu, "On the scaling of non-asymptotic capacity in multiaccess networks with bursty traffic," in Proc. IEEE ISIT, Aug. 2011, pp. 2547-2551.
45. M. Bredel and M. Fidler, "Understanding fairness and its impact on quality of service in IEEE 802.11," in Proc. IEEE INFOCOM, Apr. 2009, pp. 1098-1106.