Routing and dimensioning in optical networks under traffic growth models: an asymptotic approach

We consider the problem of routing and dimensioning in a large optical network where traffic is growing over time. A model of traffic in optical network lightpaths is presented. Lightpaths arrive randomly according to a time-varying Poisson process and hold for a random time with a general distribution. We propose a wavelength division multiplexing network that requires no capacity upgrading in a given time period T while allowing the operator to accommodate all the lightpath requests. We obtain an exact solution of the routing and dimensioning problem under an asymptotic regime where both the capacities and the arrival rates are large. For moderate link capacities, we propose a method to dimension the links so that the first lightpath request rejection occurs, with high probability, after the specified time T. This involves the computation of capacity-exhaustion probability $the probability that at least one lightpath request is rejected in the time period (0, T) due to lack of bandwidth/capacity on some link. Computation of the exact capacity-exhaustion probability is possible for a few specific holding time distributions (e.g., exponential). Since this requires large computing resources, it is feasible only for small networks. We propose a method to estimate the capacity-exhaustion probabilities for a large optical network with general holding time distribution based on the results of an asymptotic analysis. We show that this method has a low computational complexity and is quite accurate in the desired range of low capacity-exhaustion probabilities.