  In this paper, we propose the first exact Markov model for connection
blocking analysis in elastic optical networks, based on the occupancy status of
spectrum slices on all links due to arrivals and departures of various classes
of connections in a network. Since the complexity of the exact Markov model
grows exponentially with the link capacity, number of links, routes, and
classes of demands, we further advance the state-of-the-art in computing
approximate blocking probability in elastic optical networks and propose two
novel approximations, i.e., load-independent and load-dependent. These
approximations are used to compute state-dependent per-class connection setup
rates in multi-class elastic optical networks with or without spectrum
converters by taking into account the spectrum fragmentation factor in each
state. We validate approximation analysis by exact and/or simulation results,
and show that load-independent and load-dependent approximations can be more
accurately used than previously proposed approximations, under a random-fit
(RF) and a first-fit (FF) spectrum allocation policies. The approximate results
match closely with the exact model, for smaller networks, and with the
simulations under a variety of network scenarios.

Networking and Internet Architecture