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 δδ 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 ρρ. We propose an improved multi-hop scheduling algorithm to shorten the duration of scheduling periods. As ρρ is odd, the number of tuning operations on each node is at most ⌈2N/(ρ+1)⌉-1⌈2N/(ρ+1)⌉-1 and the schedule length of our multi-hop scheduling is at most (⌈2Nρ+1⌉-1)ρ(ρ+1)2+δ. As ρρ is even, the tuning time on each node is at most ⌈2N/ρ⌉-1⌈2N/ρ⌉-1 and the schedule length is at most (⌈2N/ρ⌉-1)ρ(ρ-1)2+δ. For general case, when ρ<1+δ+δ2-6δ+52, 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.