Publication: On the identifiability of the two-state BMAP
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2012-05
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Abstract
The capability of modeling non-exponentially distributed and dependent inter-arrival times as
well as correlated batches makes the Batch Markovian Arrival Processes (BMAP) suitable in
different real-life settings as teletraffic, queueing theory or actuarial contexts. An issue to be
taken into account for estimation purposes is the identifiability of the process. This is an open
problem concerning BMAP-related processes. This paper explores the identifiability issue of the
two-state BMAP noted BMAP2(k), where k is the maximum batch arrival size. It is proven
that for k = 2 the process cannot be identified, under the assumptions that both the interarrival
times and batches sizes are observed. Additionally, a method to obtain an equivalent BMAP2(2)
to a given one is provided.
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Batch Markovian Arrival Process (BMAP), Identifiability problems, Hidden Markov models, Redundant representations