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

Abstract

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