Queueing Systems

, Volume 53, Issue 3, pp 115–125 | Cite as

Exact emulation of a priority queue with a switch and delay lines



All-optical packet switched networking is hampered by the problem of realizing viable queues for optical packets. Packets can be buffered in delay lines, but delay lines do not functionally emulate queues from an input-output point of view. In this paper we consider the problem of exact emulation of a priority queue of size K using a switching system comprised of a switch of size (M + 1) × (M + 1), which has one distinguished input for external arrivals, one distinguished output for external departures, and fixed-length delay lines of lengths L1, L2, ..., LM connecting the other inputs and outputs in pairs. We measure the complexity of such an emulation by M + 1. We prove that \(M \ge \lceil \log (K -1) \rceil\) and present a construction which works with \(M = O(\sqrt{K})\); further, in our construction \(\sum_{m=1}^M L_m = K + O(\sqrt{K})\). We also sketch an idea for an all-optical packet switched communication network architecture based on approximate emulation of priority queues of finite size using switches and delay lines, with erasure control coding at the packet level.


Erasure control coding Error control coding Networking Optical networking Priority queues Queueing Switching 


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  1. 1.
    A. Albanese, J. Blorner, J. Edmonds, M. Luby and M. Sudan, ‘Priority encoded transmission’. In: Proceedings of the 35th Annual ACM Symposium on the Foundations of Computer Science (1994).Google Scholar
  2. 2.
    N. Alon and M. Luby, ‘A linear time erasure-resilient code with nearly optimal recovery’. IEEE Transactions on Information Theory 42(6) (1996), 1732–1736.CrossRefGoogle Scholar
  3. 3.
    V. Anantharam and T. Konstantopoulos, ‘A methodology for the design of optimal traffic shapers in ATM networks’. IEEE Transactions on Automatic Control 44(3) (1999), 583–586.CrossRefGoogle Scholar
  4. 4.
    R.E. Blahut, Algebraic Codes for Data Transmission. Cambridge, UK: Cambridge University Press (2003).Google Scholar
  5. 5.
    J.W. Byers, M. Luby and M. Mitzenmacher, ‘A digital fountain approach to asynchronous reliable multicast’. IEEE Journal on Selected Areas in Communications 20(8) (2002), 1528–1540.CrossRefGoogle Scholar
  6. 6.
    C. Chang, D. Lee and C. Tu, ‘Recursive construction of FIFO optical multiplexers with switched delay lines’. submitted to IEEE Transactions of Information Theory (2002).Google Scholar
  7. 7.
    C.-S. Chang, D.-S. Lee and C.-K. Tu, ‘Using switched delay lines for exact emulation of FIFO multiplexers with variable length bursts’. In: Proceedings of IEEE INFOCOM (2003).Google Scholar
  8. 8.
    R.L. Cruz, ‘A calculus for network delay I: network elements in isolation’. IEEE Transactions on Information Theory 37(1) (1991a), 114–131.CrossRefGoogle Scholar
  9. 9.
    R.L. Cruz, ‘A calculus for network delay II: network analysis’. IEEE Transactions on Information Theory 37(1) (1991b), 132–141.CrossRefGoogle Scholar
  10. 10.
    D. Hunter, M. Chia and I. Androvic, ‘Buffering in Optical Packet Switches’. IEEE Journal of Lightwave Technology 16(12) (1998), 2081–2094.CrossRefGoogle Scholar
  11. 11.
    T. Konstantopoulos and V. Anantharam, ‘Optimal flow control schemes that regulate the burstiness of traffic’. IEEE/ACM Transactions on Networking 3(4) (1995), 423–432.Google Scholar
  12. 12.
    M. Luby, M. Mitzenmacher, M.A. Shokrollahi and D.A. Spielman, ‘Efficient erasure correction codes’. IEEE Transactions on Information Theory 47(2) (2001), 569–584.CrossRefGoogle Scholar
  13. 13.
    R. Medina, 2002, ‘Photons vs. electrons [all optical network]’. Potentials 21, 9–11.CrossRefGoogle Scholar
  14. 14.
    R. Ramaswami and K. Sivarajan, Optical Networks: a practical perspective. San Francisco: Morgan Kaufmann (2002).Google Scholar
  15. 15.
    E.J. Tyler, P. Kourtessis, M. Webster, E. Rochart, T. Quinlan, S.E.M. Dudley, S.D. Walker, R.V. Petty and I.H. White, ‘Towards Terabit-per-second Capacities over Multimode fiber links using SCM/WDM Techniques’. Journal of Lightwave Technology 21 (2003), 3237–3243.CrossRefGoogle Scholar

Copyright information

© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Electrical Engineering and Computer SciencesUniversity of CaliforniaBerkeley

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