Improvement of multi-hop packet transmission scheduling in WDM optical star networks

This paper addresses the design of multi-hop packet transmissions for the all-to-all broadcast (AAB) problem in a wavelength division multiplexing (WDM) optical star network with N nodes. We assume that each node is equipped with a tunable transmitter and a fixed-tuned receiver (TT-FR), and each tunable transmitter needs a non-negligible tuning latency delta to switch between wavelengths. To reduce the number of O/E/O conversions in the multi-hop scheduling, the maximum hop distance of packet transmissions is limited to rho. We propose an improved multi-hop scheduling algorithm to shorten the duration of scheduling periods. As rho is odd, the number of tuning operations on each node is at most inverted right perpendicular 2N/(p + 1) inverted left perpendicular - 1 and the schedule length of our multi-hop scheduling is at most (inverted right perpendicular 2N/rho+1 inverted left perpendicular - 1) (rho(rho+1)/2 + delta). As 1) is even, the tuning time on each node is at most inverted right perpendicular 2N/pinverted left perpendicular - 1 and the schedule length is at most (inverted right perpendicular 2N/rho+1 inverted left perpendicular - 1) (rho(rho-1)/2 + delta). For general case, when rho < 1+delta+root delta(2)-6 delta+5/2, the schedule length of our multi-hop scheduling algorithm will be less than that of the optimal single-hop scheduling algorithm. This also improves the previous result on the multi-hop schedule length of the AAB problem. (C) 2009 Elsevier B.V. All rights reserved.