  The Markovian arrival process (MAP) has proven a versatile model for fitting
dependent and non-exponential interarrival times, with a number of applications
to queueing, teletraffic, reliability or finance. Despite theoretical
properties of MAPs and models involving MAPs are well studied, their estimation
remains less explored. This paper examines maximum likelihood estimation of the
second-order MAP using a recently obtained parameterization of the two-state
MAPs.
