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...

In this paper we consider the problem of identifiability of the two-state Markovian Arrival process (MAP2). In particular, we show that the MAP2 is not identifiable and conditions are given under which two different sets of parameters, induce identical stationary laws for the observable process.

Two types of transitions can be found in the Markovian Arrival process or MAP: with and without arrivals. In transient transitions the chain jumps from one state to another with no arrival; in effective transitions, a single arrival occurs. We assume that in practice, only arrival times are...

In this paper, we study how the lack of a unique representation for the two-state Markovian arrival process (MAP <Subscript>2</Subscript>) can influence statistical estimation for the MAP <Subscript>2</Subscript>/G/1 queueing system. In particular, given two equivalent representations of the same MAP <Subscript>2</Subscript>, we find that the steady-state...</subscript></subscript></subscript>