Scheduling Packet Transmissions on Logical Topologies in WDM Optical Star Networks

In this paper, we address 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. The tunable transmitter on each node needs a nonnegligible tuning latency δ to switch between wavelengths. To decrease the affection of the packet delay in multi-hop scheduling, the maximum of hop distance of each packet transmission is limited to a constant ρ. We propose an improved multi-hop scheduling algorithm to shorten the duration of scheduling periods. The number of tuning operations on each node is at most d 2N ρ+1e − 1 and the schedule length of our multi-hop scheduling is at most (d 2N ρ+1e − 1)( 2 + δ) if ρ is odd. Otherwise, the tuning time on each node is at most d 2N ρ e − 1 and the schedule length is at most (d 2N ρ e−1)(ρ(ρ−1) 2 +δ). For general case, when ρ < 1+δ+ √ δ2−6δ+5 2 , the schedule length of our multihop scheduling algorithm is shorter than that of the optimal single-hop scheduling algorithm. This also improves the previous results on the multi-hop scheduling length of the AAB problem.