Joint arrival process of multiple independent batch Markovian arrival processes

The joint arrival process of multiple independent batch Markovian arrival processes (BMAP) is analyzed. First, the parameter matrices of the joint arrival process are constructed, and their relations with the parameter matrices of the component BMAPs are also obtained. Second, it is proved that the parameter matrices of the joint arrival process have the same properties as the BMAP; and based on these properties, in analyzing the queueing models, some relations for the joint arrival process either can inherit from the existing literature on the BMAP and the multiple-BMAP, or can be derived with the same complexity as the case for the BMAP.