  The possibility of flexibly assigning spectrum resources with channels of
different sizes greatly improves the spectral efficiency of optical networks,
but can also lead to unwanted spectrum fragmentation.We study this problem in a
scenario where traffic demands are categorised in two types (low or high
bit-rate) by assessing the performance of three allocation policies. Our first
contribution consists of exact Markov chain models for these allocation
policies, which allow us to numerically compute the relevant performance
measures. However, these exact models do not scale to large systems, in the
sense that the computations required to determine the blocking
probabilities---which measure the performance of the allocation
policies---become intractable. In order to address this, we first extend an
approximate reduced-state Markov chain model that is available in the
literature to the three considered allocation policies. These reduced-state
Markov chain models allow us to tractably compute approximations of the
blocking probabilities, but the accuracy of these approximations cannot be
easily verified. Our main contribution then is the introduction of
reduced-state imprecise Markov chain models that allow us to derive guaranteed
lower and upper bounds on blocking probabilities, for the three allocation
policies separately or for all possible allocation policies simultaneously.
