Queueing Systems

, Volume 53, Issue 3, pp 115–125

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

Authors

    • Department of Electrical Engineering and Computer SciencesUniversity of California
  • V. Anantharam
    • Department of Electrical Engineering and Computer SciencesUniversity of California
Article

DOI: 10.1007/s11134-006-6669-x

Cite this article as:
Sarwate, A.D. & Anantharam, V. Queueing Syst (2006) 53: 115. doi:10.1007/s11134-006-6669-x

Abstract

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, ..., L M 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.

Keywords

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

Copyright information

© Springer Science + Business Media, LLC 2006