Fluid limit of an asynchronous optical packet switch with shared per link full range wavelength conversion

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 Ploss(N) as N tends to infinity (while the load and conversion ratio σ = C/N remains fixed). More specifically, for σ ≤ λ2 the loss probability tends to (λ2 − σ)/λ(1+λ), while for σ > λ2 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...

• Type: Journal
• Year: 2012
• Where: SIGMETRICS
• Authors: Benny Van Houdt, Luca Bortolussi
• Keywords: Hardware, SIGMETRICS 2012, Smooth Dynamical Systems, Wavelength Conversion, Wavelength Converters