On the identifiability of the two-state BMAP

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.