We consider an asynchronous all optical packet switch (OPS) where each link consists of N wavelength channels and a pool of C ≤ N full range tunable wavelength converters. Under the assumption of Poisson arrivals with rate λ (per wavelength channel) and exponential packet lengths, we determine a simple closed-form expression for the limit of the loss probabilities P loss (N) as N tends to infinity (while the load and conversion ratio σ=C/N remains fixed). More specifically, for σ ≤ λ 2  the loss probability tends to (λ 2 -σ)/λ(1+λ), while for σ > λ 2  the loss tends to zero. We also prove an insensitivity result when the exponential packet lengths are replaced by certain classes of phase-type distributions. A key feature of the dynamical system (i.e., set of ODEs) that describes the limit behavior of this OPS switch, is that its right-hand side is discontinuous. To prove the convergence, we therefore had to generalize some existing result to the setting of piece-wise smooth dynamical systems.
['Benny Van Houdt', 'Luca Bortolussi']
Fluid limit of an asynchronous optical packet switch with shared per link full range wavelength conversion