Emulation of an Optical Flexible Delay Line by Parallel Variable Optical Delay Lines

In this letter, we consider the discrete-time setting and propose a construction of an optical flexible delay line by parallel variable optical delay lines (VODLs) under a very simple packet routing scheme. We show that to exactly emulate an optical flexible delay line with maximum delay d (time slots), where d is a positive integer, it is necessary and sufficient to have at least [(2d+1)/3] VODLs with maximum delay d (time slots) in our proposed architecture. We also show that under a uniform traffic model, the average number of busy VODLs is approximately d+1-(2d+1)(d/(d+1))^d, which is quite close to our simulation result. Through simulations, we further show that if we can tolerate a loss probability of, say 10^-3, then we only need at most 1.7 times of the average number of busy VODLs, which is much smaller than the worst-case bound [(2d+1)/3].