Routing and dimensioning of optical networks under traffic growth models: an asymptotic analysis

We consider the problem of routing and dimensioning in a large optical network, assuming the traffic is growing over time. In optical networks, traffic is carried through lightpaths and we model the traffic as follows: lightpaths arrive randomly according to a time-varying Poisson process and hold for a random time with a general distribution. We are interested in dimensioning the links so that the first lightpath request rejection occurs, with high probability, after a specified period of time, T, and thus the network requires no capacity upgrading in that time period. We propose a solution based on the absorption probability - the probability that at least one lightpath request is rejected in the time interval (0, T). Computation of exact absorption probability is possible for a few specific holding time distributions (e.g., exponential) and it requires large computing resources. We propose a method which has low computational complexity to approximate the absorption probability for a general holding time distribution based on an asymptotic analysis and we show that it is quite accurate in the desired range of low absorption probabilities.