Dimensioning optical networks under traffic growth models

In this paper, we consider the problem of dimensioning a large optical wavelength-division multiplexing (WDM) network assuming the traffic is growing over time. Traffic between pairs of nodes is carried through lightpaths which are high-bandwidth end-to-end circuits, occupying a wavelength on each link of the path between two nodes. We are interested in dimensioning the WDM links so that the first lightpath request rejection will occur, with high probability, after a specified period of time T. Here we introduce the concept of capacity exhaustion probability - the probability that at least one lightpath request will be rejected in the time period (0,T) due to lack of bandwidth/capacity on some link. We propose a network dimensioning method based on a traffic growth model which eventually results in a nonlinear optimization problem with cost minimization as the objective and route capacity exhaustion probabilities as the constraints. Computation of exact capacity exhaustion probabilities requires large computing resources and is thus feasible only for small networks. We consider a reduced load approximation for estimating capacity exhaustion probabilities of a wavelength routed network with arbitrary topology and traffic patterns. We show that the estimates are quite accurate and converge to the correct values under a limiting regime in the desired range of low-capacity exhaustion probabilities.