Distributed Computing

, Volume 5, Issue 1, pp 1–6 | Cite as

Bounds on evacuation time for deflection routing

  • B. Hajek


Upper bounds are given on the timeT needed to evacuatek packets from a synchronous packet network using deflection routing, whereby all packets that arrive at a node during one time slot leave the node during the next slot. For example,T≤n+2(k−1) for a binaryn-cube network when priority is given to packets closer to their destination, and for a single destination networkT is less than or equal to the network diameter plusk−1 times the network deflection index. Deflection routing for one pass through an omega network is also considered.

Key words

Adattive routing Hot potato routing Deflection routing Misrouting Hypercube network 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Baran P: On distributed communication networks. IEEE Trans Commun Syst 12:1–9 (1964)Google Scholar
  2. 2.
    Borodin A, Hopcroft JE: Routing, merging and sorting on parallel models of computation. J Comput Syst Sci 30:130–145 (1985)MathSciNetGoogle Scholar
  3. 3.
    Greenberg AG, Goodman J: Sharp approximate models of adaptive routing in mesh networks. In: Boxma OJ, Cohen JW, Tijms JC (eds) Teletraffic analysis and computer performance evaluation. Amsterdam: Elsevier 1986, pp 255–270Google Scholar
  4. 4.
    Greenberg AG, Hajek B: Average case performance of deflection routing in a hypercube. Preprint 1989Google Scholar
  5. 5.
    Hillis D: The connection machine. Boston: MIT Press 1985Google Scholar
  6. 6.
    Lawrie D: Access and alignment of data on an array processor. IEEE Trans Comput 24:1145–1155 (1975)MATHMathSciNetGoogle Scholar
  7. 7.
    Lawrie DH, Padua DA: Analysis of message switching with single-exchanges in multiprocessors. Proc IEEE Workshop on Interconnection Networks for Parallel and Distributed Computing 1980, pp 116–127. Also in: Wu, Feng (eds) Interconnection networks. Silverspring: IEEE Comput Soc PressGoogle Scholar
  8. 8.
    Ngai JY, Seitz CL: A framework for adaptive routing in multicomputer networks. Proc ACM Sympon Parallel Algorithms and Architecture, Santa Fe, New Mexico 1989, pp 1–9Google Scholar
  9. 9.
    Smith B: Architecture and applications of the HEP multiprocessor computer system. In: Tao TF (ed) Real-time signal processing IV—Proc SPIE 298. Soc Photo-Optical Eng 1981, pp 241–248Google Scholar

Copyright information

© Springer-Verlag 1991

Authors and Affiliations

  • B. Hajek
    • 1
    • 2
  1. 1.Department of Electrical and Computer EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  2. 2.Coordinated Science LaboratoryUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations