A Calculus for Network Delay, Part I: Network Elements in Isolation

IEEE Transactions on Information Theory

Volumn 37, Issue 1, 1991, Pages 114-131

  Cruz, Rene L ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

burstiness; flow control; high speed networks; packet; Queueing networks; switching

Indexed keywords

DATA TRANSMISSION--PACKET SWITCHING;

BUFFERING REQUIREMENTS; BURSTINESS CONSTRAINTS; NETWORK DELAY;

TELECOMMUNICATION SYSTEMS;

EID: 0026000660     PISSN: 00189448     EISSN: 15579654     Source Type: Journal    
DOI: 10.1109/18.61109     Document Type: Article

References (25)

1. R. Cruz, “A calculus for network delay and a note on topologies of interconnection networks.” Technical Report UILU-ENG-87-2246, Coordinated Science Laboratory, Univ. of Illinois at Urbana-Champaign, 1987.
2. D. Bertsekas and R. Gallager, Data Networks. Englewood Cliffs, NJ: Prentice Hall, 1987.
3. A. E. Eckberg, “Approximations for bursty (and smoothed) arrival queueing delays based on generalized peakedness,” in Proc. 11th Int. Teletraffic Congress, Kyoto, 1985.
4. K. W. Fendick and W. Whitt, “Measurements and approximations to describe the offered traffic and predict the average workload in a single server queue,” Proc. IEEE, vol. 77, no. 1, pp. 171–194, Jan. 1989.
5. W. Whitt, “The queueing network analyzer,” Bell Syst. Tech. J., vol. 62, no. 9, part 1, pp. 2779–2816, Nov. 1983.
6. D. Mitra and R. Cieslak, “Randomized parallel communications on an extension of the Omega network,” J. ACM, vol. 34, no. 4, pp. 802–824, Oct. 1987.
7. S. L. Hakimi, “Analysis and design of communication networks with memory,” J. Franklin Inst., vol. 287, no. 1, pp. 1–17, Jan. 1969.
8. E. Hahne, “Round robin scheduling for fair flow control in data communication networks,” Technical Report LIDS-TH- 1631, Laboratory for Information Decision Systems, Massachusetts Inst, of Technol., Dec. 1986.
9. I. Cidon, I. Gopal, G. Grover, and M. Sidi, “Real time packet switching: A performance analysis,” IEEE J. Selected Areas in Commun., vol. 6, no. 9, pp. 1576–1586, Dec. 1988.
10. G. Sasaki, “Input buffer requirements for round robin polling systems,” Proc. 27th Ann. Allerton Conf. Commun., Contr., and Computing, Monticello, IL, Sept. 27–29, 1989.
11. J. R. Perkins and P. R. Kumar, “Stable, distributed, real-time scheduling of flexible manufacturing/assembly/disassembly systems,” IEEE Trans. Automatic Contr., vol. 34, no. 2, pp. 139–148, Feb. 1989.
12. P. R. Kumar and T. I. Seidman, “Dynamic instabilities and stabilization methods in distributed real-time scheduling of manufacturing systems,” IEEE Trans. Automatic Contr., vol. 35, no. 3, pp. 289–298 Mar. 1990.
13. C. H. Lu and P. R. Kumar, “Distributed scheduling based on due dates and buffer prioritization,” Technical Report, Coordinated Science Laboratory, Univ. of Illinois at Urbana- Champaign, 1990. •
14. S. Stidham, Jr., “A Last Word on L = λW,” Oper. Res., vol. 22, 417–421, 1974.
15. W. Whitt, “Comparing counting processes and queues,” Adv. Appl. Probability, vol. 13, pp. 207–220, 1981.
16. G. F. Newell, Applications of Queueing Theory, Second ed. London: Chapman and Hall, 1982.
17. P. Kermani and L. Kleinrock, “Virtual cut-through: A new computer communications switching technique,” Comput. Net-works, vol. 3, pp. 267–286, 1979.
18. J. Turner, “New directions in communications (or which way to the information age?),” IEEE Commun. Mag., vol. 24, no. 10, pp. 8–15, Oct. 1986.
19. M. Sidi, W. Z. Liu, I. Cidon, and I. Gopal, “Congestion control through input rate regulation,” in Proc. IEEE Globecom ’89, pp. 1764–1768, 1989.
20. M. W. Beckner, S. E. Minzer, and T. T. Lee, “A protocol and prototype for broadband subscriber access to ISDN’s,” Proc. IEEE Int. Switching Symp., pp. 462–469, 1987.
21. A. E. Eckberg, D. T. Luan, and D. M. Lucantoni, “An approach to controlling congestion in ATM networks,” Int. J. Digital Analog Commun. Syst., vol. 3, pp. 199–209, 1990.
22. L. Kleinrock, Queueing Systems Volume 2: Computer Applications. New York: John Wiley, 1976.
23. E. Reich, “On the integrodifferential equation of Takacs. I,” Ann. Math. Statist., vol. 29, pp. 563–570, 1958.
24. D. G. Luenberger, Optimization by Vector Space Methods. New York: John Wiley, 1969.
25. R. L. Cruz, “A calculus for network delay, Part II: Network analysis,” IEEE Trans. Inform. Theory, vol. 37, no. 1, pp. 132–141, Jan. 1991.